Research ArticleHierarchical Precoding in a Realistic Ultradense HeterogeneousEnvironment Exceeding the Degrees of Freedom

Mohamed Shehata1 Martin Kurras2 Khaled Hassan3 and Lars Thiele2

1 Information Engineering and Technology German University in Cairo Cairo Egypt2Fraunhofer Heinrich Hertz Institute Berlin Germany3Fraunhofer Institute for Integrated Circuits (IIS) Erlangen Germany

Correspondence should be addressed to Martin Kurras martinkurrashhifraunhoferde

Received 19 February 2016 Revised 14 July 2016 Accepted 21 July 2016

Academic Editor Giuseppe Castaldi

Copyright copy 2016 Mohamed Shehata et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Cell densification is a widely used approach to increase the spectral efficiency per area of cellular networks Such UltradenseNetworks (UDNs) consisting of small cells are often coordinated by macro base stations (BSs) With universal frequency reuseinterference from themacroBS limits the system spectral efficiency In thisworkwe exploit the degrees of freedomat themacroBS toapply interference coordinationWe propose a hierarchical precoding strategy in the spatial domain in order to project interferencefrom the macro BS into the subspace of small cell users enabling linear cancellation The macro BS interference towards small cellusers is aligned within the joint null space of users served by the macro BS Compared to classical interference alignment ourscheme does not require coordination between macrocells and small cells We present three algorithms in the first the interferenceis minimized by iterative alignment in the second the uncoordinated interference from the small cells is considered and in thethird iterativeMinimumMean Square Error (MMSE) technique is usedWe provide numerical evaluation complexity analysis androbustness analysis of these algorithms based on a realistic channel model showing the benefit of hierarchical precoding comparedto the uncoordinated case

1 Introduction

Throughout the last decades wireless communication tech-nologies witnessed a large number of challenges such as thegreat evolution in data traffic and the massive increase in theamount of mobile User Equipment (UE) Thus one of themain objectives for future wireless technologies is supplyingthe UEs with high data rates in order to support real timeapplications Another objective is extending the coverage andsupporting more UEs while taking into account the scarcityof the current licensed spectrum resources

This continuous increase in the data traffic and number ofUEs can be satisfied by using a combination ofmore spectrumresources enhancing spectrum efficiency [1] and cell densi-fication One approach to achieve this combination is Ultra-dense Network (UDN) deployment Such dense deploymentsare often in the form of a heterogeneous network (HetNet)[2ndash4] where many small cells are deployed having less

capabilities that is less transmit power than the macro basestations (BSs) see Figure 1 In a universal frequency reusethis power imbalance results in interference limitation atusers served by these small cells This interference limitationis caused by the macro BS transmitting to users which arenot in the coverage of a small cell Therefore the focus inthis paper is on increasing the system spectral efficiency byspatial interference coordination from the macro BS to smallcell users in a HetNet The idea is to utilize the degreesof freedom at the macro BSs from the ldquolargerdquo number ofantennas Compared to massive Multiple-Input Multiple-Output (MIMO) [5 6] originated in [7] where the numberof antennas is assumed to be infinity we focus on 4 and 8antennas already provided in the standard [8]The degrees offreedom are used to project interference from the macro BStowards small cell connected UEs such that it can be canceledwith linear receivers Simultaneously themacro BS still servesUEs which are not in the coverage of a small cell

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 4796474 11 pageshttpdxdoiorg10115520164796474

2 International Journal of Antennas and Propagation

Hence we propose a two-stage hierarchical precod-ingbeamforming approach to protect the small cell con-nected UEs from the macrointerference while serving themacro UEs simultaneously This is achieved by combiningthe idea of interference alignment (IA) [9 10] by iterativeminimization [11] with operating in the null space of macroUEs served by Block Diagonalization (BD) [12] in a two-stage or hierarchical precoding approach This is achievedby modifying an iterative IA algorithm introduced in [1113 14] to operate in the joint null space of the macro UEsobtained using BD Thus we ensure interference decouplingof macro and small cell connected UEs In [15] we presentedtwo extensions of the algorithm presented in [14] In thefirst algorithm called ldquoBlock Diagonalization-InterferenceAlignment (BDIA) uncoordinatedrdquo uncoordinated interfer-ence from small cells or surroundingmacroBSs is consideredIn the second algorithm the iterative IA objective is changedto Minimum Mean Square Error (MMSE) called ldquoBDIAMMSE Joint Transmit and Receive (JTR) structurerdquo

These algorithms require that Channel State Information(CSI) at the transmitter (CSIT) from the macro and smallcell connected UEs is available As a baseline we assumehaving perfect knowledge of the CSI and then we extendour work to include the imperfect CSI scenario We alsoextend our work in [15] by evaluating the spatial hierarchicalprecoding schemes in a more realistic ultradense HetNetThus we exceed the macro BS degrees of freedom withup to 10 small cells in the coverage area of a macro BSMoreover we consider the out-of-cell interference fromothermacro BSs tiers in the hierarchical precoding frameworkThis can be achieved by utilizing the advantage of addingthe MMSE pre- and postcoder to the proposed hierarchicalframework Finally we provide a comprehensive study on thecontradicting effects of the proposed hierarchical algorithmson both the signal and interference received power as wellas spectral efficiency separately for macro and small cellattached UEs

The novel contributions in this work are summarized asfollows

(1) A complexity analysis and comparison of the algo-rithms are presented In this analysis we separatethe required steps of the algorithms and provide thecomplexity required in each of the steps

(2) Furthermore we investigated the trade-off on thesystem spectral efficiency exceeding the degrees offreedom available at the macro BS In an UDN thenumber of small cells can easily exceed the numberof antennas at the macro BS

(3) Finally we analyze the ldquorobustnessrdquo of our proposedalgorithms In [11 13ndash16] perfect channel knowledgeis considered which is why we introduce a channeluncertainty and investigate in this work its impact onthe system spectral efficiency Additionally we alsotake into account the impact frommultiplemacro BSsand show the advantage of our proposed algorithmsincreasing the number of antennas and thereforedegrees of freedom at the macro BS

19 hexagonal macrocell network deployments with with three-sector sites

MacrouserPicouser

Sector of interestPicocell

Coordinated cluster

Figure 1 Deployment and transmissionmode of the heterogeneousnetwork

Remark 1 Throughout our work all the processing for thehierarchical precoding scheme is handled at the macro BSwhich enables independent transmission at the small cellsThis implies that no user data or feedback exchange isrequired between transmit nodes

For notational convenience throughout the whole papera scalar is denoted as119909 a vector as x and amatrix asXMatrixconjugate transpose is denoted as (sdot)119867 The most dominanteigenvector of a matrix (sdot) is expressed as 120585max(sdot) which isthe eigenvector corresponding to the largest eigenvalue whilethe least dominant one is expressed as 120585min(sdot) The Frobeniusnorm is represented as (sdot)2

119865 The matrix I

119873denotes 119873 times 119873

identity matrix Esdot stands for the expectation operator

2 System Model

In this work we consider the HetNet deployment shown inFigure 1 and investigate the downlink scenario within coher-ent channel bandwidthThe system considered is a Multiuser(MU-) MIMO Orthogonal Frequency Division Multiplexing(OFDM) system with constant CSI per Resource Block (RB)The deployment is a central macro BS serving a specifiedset of UEs within its transmission range and surroundedby multiple tiers of macrosites Each macrosite is dividedinto three 120∘ sectors and within each sector small cellsare deployed Each macrosector and each small cell has anindependent cell identity (ID) such that we have a total set ofcells M with cardinality 119872 = |M| We can split the set Minto the disjoint subsetsM

119903subM andM

119901subM representing

macrocells and small cells within the system respectivelysuch thatM

119903cupM119901=M andM

119903capM119901= 0

Further we assume that a macrosector together with theunderlying small cells forms a cluster given byM

119888subM with

cardinality119872119888= |M

119888| for example Figure 1 Coordination

between the macrocell and small cells is only done within thesame cluster Since we are assuming full spectral frequencyreuse within M other macrosectors (and small cells) cause

International Journal of Antennas and Propagation 3

residual uncoordinated interference henceforth referred toas intercluster interference (ICI)

The setK represents all UEs located within the coveragearea of a cluster (connected to a cell within the cluster)and K

119898sub K a subset of UEs connected to 119898th BS

Consequently the subsetK119903subK represents UEs connected

to a macrocell and K119901sub K are the users attached to

the small cells Furthermore we denote with K119888sub K the

UEs selected (scheduled) for simultaneously spatial downlinktransmission on the same time-frequency resource in clusterM119888 The number of antennas at macrocells small cells and

UEs is set to 119873119898119905 119873119901119905 and119873

119903 respectively

With these assumptions the received signal of user 119896 isinK connected to cell 119898 on a time-frequency resource (RB) isdefined as follows

y119896= H119898119896

b119898119896radic

119901119898119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

L119896

x119896+ sum

119895isinK119898119896

H119898119896

s119898119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

S119896

+ sum

119899isinM119888119898

sum

119895isinK119899

H119899119896s119899119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

T119896

+ sum

119897isinMM119888

sum

119895isinKK119897

H119897119896s119897119895+ n

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(1)

where H119897119906isin C119873119903times119873119905

119897

is the channel matrix between 119897th BSand 119906th UE The vector s

119897119906= b119897119906radic

119901119897119906x119906isin C119873119905

119897times1 denotes

the precoded signal x119906with the precoding vector b

119897119906and

transmit power 119901119897119906le 119875119904limited by a sum power constraint

119875119904 The vector n represents C119873119903times1 Additive White Circular

Symmetric Complex Gaussian Noise (AWCSCGN) samplesat the receiver with covariance Enn119867 = 1205902

119899I119873119903 For clarity

we clustered the receive signal of user 119896 into the 4 followingparts (1) L

119896the effective channel for the desired UE 119896 (2)

S119896interstream (or multiuser) interference caused by spatially

multiplexed users at the serving cell 119898 (3) T119896intracluster

interference which is caused by other cells within the sameclusterM

119888 119898 and (4) Z

119896intercluster interference from the

surrounding tiersM M119888in addition to thermal noise

The resulting Signal to Interference and Noise Ratio(SINR) of user 119896 used to obtain the spectral efficiency withShannonrsquos formula is thus given as follows

SINR119896=

10038161003816100381610038161003816w119867119896H119898119896

b119898119896radic

119901119898119896

10038161003816100381610038161003816

2

10038161003816100381610038161003816w119867119896S119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Stream IF

+

10038161003816100381610038161003816w119867119896T119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Intra Cluster IF

+

10038161003816100381610038161003816w119867119896Z119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Cluster IF

(2)

where w119896is the postcoder (receive beamformer) at 119896th UE

Using optimal linear equalization the MMSE postcoder w119896is

given by

w119896= (Q119896)

minus1

L119896 (3)

where the covariance matrixQ119896comprises

Q119896=S119896S119867119896+T119896T119867119896+Z119896Z119867119896+L119896L119867119896 (4)

In this paper we also inspect the case of imperfect CSI andwe model the channel after adding the error as follows

H = radic1 minus 120576H + radic120576H119890 (5)

where H represents the channelwith error whileH representsthe original channel 120576 is the channel error variance andH

119890isin

C119873119903times119873119905(0 120590) represents the error added to the channel

3 Algorithms

The basic concept in this paper is exceeding the macrodegrees of freedom (DoF) by serving a number ofUEs simul-taneously within the cluster which is greater than the numberof transmit antennas at the macro BS Then we inspectthe effect of this on the hierarchical precoding schemespresented in [15] and whether we can still achieve a gainover the uncoordinated case or not In the uncoordinatedcase the macro BS only applies BD without taking intoaccount the interference towards the underlying small cellsHowever with applying the hierarchical precoding schemesat the macro BS it can utilize the free spatial dimensionsavailable to align its interference towards the underlyingsmall cells Here in this section we will give an introductionfor the schemes with further discussion of the coordinationmechanism between the macro BS small cells and the UEswithin the cluster

31 Macrointerference Subspace Reduction This algorithmreferred to as BDIA requires two stages of precoding in ahierarchical way The first precoding stage is applying BD[12] in order to mitigate the interstream interference betweenthe spatially multiplexed macro UEs The second stage isapplying iterative IA [11] precoding to reduce the rank of themacrointerference subspace towards the small cell connectedUEs while preserving the orthogonal streams towards theserved macro UEs Then the two-stage precoder can becalculated as follows

b119898119896= V0119896f119896 (6)

where V0119896is the common null space of the scheduled macro

UEs K119903derived from the BD algorithm and f

119896from the

IA algorithm This second part of (6) f119896effectively reduces

the interference subspace from the macrocell towards thesmall cell connected UEs in the same cluster M

119888to a

single dimension so our objective here can be modelledas minimizing the interference leakage from the macro BStowards the small cell connected UEs as follows

min sum

119895isinK119899

sum

119896isinK119888119896 =119895

10038171003817100381710038171003817

H119895119896f119896minus c119896c119867119896H119895119896f119896

10038171003817100381710038171003817

2

119865 (7)

whereK119899isin K119888K119901 represents the macro UEs connected

to BS 119899 within the cluster and c119896is rank 1 orthonormal basis

for the received interference subspaceΩ119896and is calculated as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896) (8)

4 International Journal of Antennas and Propagation

while H119895119896

represents the effective channels such that thetransmitting macro BSs are considered as K

119899transmitters

causing interference towards the small cell connected UEsand these new virtual effective channels can be calculated as

H119895119896= H119899119896V0119895 (9)

then the corresponding postcoder for each user 119896 isin K119888is

given as follows

w119896= I119873119903minus c119896c119867119896 (10)

Then the IA precoder is calculated as

f119895cong 120585min( sum

119896isinK119888 119896 =119895

H119867119895119896w119896H119895119896) (11)

Then both the precoding filter at the macro BS and theinterference subspace at the receivers of the UEs are updatediteratively until convergence Here in Figure 2 themechanismof the BDIA algorithm is shown

Algorithm 2 (macrointerference subspace reduction)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (8)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

32 Macrointerference Subspace Reduction with ConsideringUncoordinated Interference The ldquoBDIA uncordrdquo algorithmis similar to Algorithm 2 but it is more sophisticatedbecause it takes into account the uncoordinated interferenceas mentioned in [13] As uncoordinated interference weconsider the undesired signal from the small cells towardsthe macro UEs and other small cells UEs in the case whenonly one cooperation area is active When the multiplesurrounding tiers are active also then all the interferencefrom BSs outside the cluster is added to the uncoordinatedinterference Simply by replacing (8) by (12) in step (3) inAlgorithm 2 this uncoordinated interference is taken intoaccount in the hierarchical precoding framework Hence-forth the orthonormal basis c

119896for the received interference

subspace is now calculated as the maximum eigenvector ofthe uncoordinated interference added to the interferencesubspace from themacro BS towards the small cell connectedUEs In this addition the macro BS transmitting powercannot be directly normalized as in (8) because of addingthe uncoordinated interference to the macro interferenceleakageThis uncoordinated interference is arising from boththe macrocells and the small cells and each of them hasdifferent transmitting power Thus the orthonormal basisc119896for the received interference subspace is represented as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895119901119899f119867119895H119867119895119896+P119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

) (12)

where P119896represents the uncoordinated interference from the

small cells towards the macro UEs and other small cells UEswithin the same cluster and is calculated as

P119896= sum

119903isinM119888M119903

H119903119896f119903119901119903f119867119903H119867119903119896 (13)

while R119896represents the uncoordinated interference from the

other BSs outside the cluster (intercluster interference) in casemulticluster (MC) scenario is applied and is calculated as

R119896= sum

119897isinMM119888

H119897119896f119897119901119897f119867119897H119867119897119896 (14)

Algorithm 3 (macrointerference subspace reduction withconsidering uncoordinated interference)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (12)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

33 Macrointerference Subspace Reduction Using IterativeMMSE Transmit and Receive Structure Here in this algo-rithm referred to as BDIA MMSE JTR the idea of iterativesubspace refinement where both the precoding filter at themacro BS and the interference subspace at the receivers ofthe UEs are updated iteratively is utilized again but this timeusing MMSE transmit and receive structures as in [13] withthe target of taking the macro UE signal level into accountthus aligning the interference towards the small cells and atthe same time keeping the macro UEs signal at a high levelabove the noise

First the algorithm starts iterating in the forward direc-tion by calculating the interference covariance matrix asfollows

Q119896= 1205902I119873119903+ sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896+R119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(15)

where the effective channel here is given by H119895119896

=

H119899119896V0119895radic119901119899119896 With this the dominant interference subspace

is obtained by

Q119896cong 120585max (Q119896) (16)

then calculating the signal subspace Φ119896as the whole receive

space excluding the dominant interference subspace as in [11]

Φ119896= I119873119903minusQ119896Q119867119896 (17)

The signal subspace is obtained in a different way in (17)in [13] where it is calculated as the minimum eigenvectorof the interference subspace but for consistency we stickthroughout the whole work to the methodology in [11]

International Journal of Antennas and Propagation 5

Available space

Null space

Maximizing signal

Available space

Null space

Minimizing interference

Block diagonalization

Cancelled by block diagonalizationInterference

alignment

Macro base station

Pico base station

Macrouser

Macrouser

Picouser

Block diagonalization

Macrointerferencerank

reduction by interference

alignment

1 2

3

11

33

1323

2212

21

111

222

333

Figure 2 Macrointerference subspace reduction mechanism

Then calculating the receive beamformer using theMMSE strategy for K

119888cluster UEs where each macro UE is

represented as 119895 isin K119899and every small cell UE is given as

119904 isin Kc K119899 and a small cell within the coordinated clusteris given as 119901 isin M

119888M119903 therefore the postcoder for the

macro UEs is given as follows

w119895= (Q119895)

minus1

H119895119895f119895 (18)

while for the small cell connected UEs is calculated as

w119904= (Q119904)minus1H119901119904f119904radic119901119901119904 (19)

Then going backward step to calculate the interferencecovariance matrix Q

119895

Q119895= 1205902IDoF119895 + sum

119896isinK119888 119896 =119895

H119867119895119896w119896w119867119896H119895119896 (20)

where DoF119895represents the available DoF at the macro BS

for serving UE 119895 and is calculated as DoF119895= 119873

119879minus

sum119906isinK119888K119901 119906 =119895

119904119906 where 119904

119906is the number of the spatial streams

assigned for UE 119906 then the macro precoder f119895is calculated as

follows

f119895= (

Q119895)

minus1H119867119895119895w119895 (21)

Then the objective function is modelled as in (7)

min sum119895isinK119899

sum

119896isinK119888 119896 =119895

100381710038171003817100381710038171003817

H119895119896f119895minusQ119896Q119867119896H119895119896f119895

100381710038171003817100381710038171003817

2

119865

(22)

This algorithm is different from the one in Figure 2 Themacro BS chooses the precoding vectors for its UE within thenull space that minimizes the interference towards the smallcell connectedUEs together withmaximizing the signal levelfor the macro UEs

Algorithm 4 (macrointerference subspace reduction usingiterative MMSE transmit and receive structure)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) CalculateQ119896for all 119896 isinK

119888using (15)

(4) Calculate w119895for all 119895 isinK

119899using (18)

(5) Calculate w119904for all 119904 isin K

119888K119899 using (19)

(6) Backward step calculate Q119895for all 119895 isinK

119899using (20)

(7) Calculate f119895for all 119895 isinK

119899using (21)

(8) Repeat steps from (3) to (7) until convergence

4 Complexity Analysis

In this section we analyze the computational complexity ofthe presented IA based algorithms including BDIA BDIAuncord and BDIA MMSE JTR respectively

First we provide the reasons that show the importanceof the computational complexity analysis of the proposedalgorithms [17] which are

(1) IA based algorithms can exploit the channel reci-procity to calculate the transmit precoders andreceiver beamformers in a distributed manner Reci-procity is based on the Time Division Duplex (TDD)operation mode with synchronized time-slot Prac-tical wireless channel is time varying Henceforthassuming perfect reciprocity is not always accurateand can result in residual interference at the receiverside thus algorithms with low computational com-plexity (short computing time) are required to avoidperformance loss arising from imperfect reciprocityin practical systems [18] In our scenario we present

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

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DistributedSensor Networks

International Journal of

2 International Journal of Antennas and Propagation

Hence we propose a two-stage hierarchical precod-ingbeamforming approach to protect the small cell con-nected UEs from the macrointerference while serving themacro UEs simultaneously This is achieved by combiningthe idea of interference alignment (IA) [9 10] by iterativeminimization [11] with operating in the null space of macroUEs served by Block Diagonalization (BD) [12] in a two-stage or hierarchical precoding approach This is achievedby modifying an iterative IA algorithm introduced in [1113 14] to operate in the joint null space of the macro UEsobtained using BD Thus we ensure interference decouplingof macro and small cell connected UEs In [15] we presentedtwo extensions of the algorithm presented in [14] In thefirst algorithm called ldquoBlock Diagonalization-InterferenceAlignment (BDIA) uncoordinatedrdquo uncoordinated interfer-ence from small cells or surroundingmacroBSs is consideredIn the second algorithm the iterative IA objective is changedto Minimum Mean Square Error (MMSE) called ldquoBDIAMMSE Joint Transmit and Receive (JTR) structurerdquo

These algorithms require that Channel State Information(CSI) at the transmitter (CSIT) from the macro and smallcell connected UEs is available As a baseline we assumehaving perfect knowledge of the CSI and then we extendour work to include the imperfect CSI scenario We alsoextend our work in [15] by evaluating the spatial hierarchicalprecoding schemes in a more realistic ultradense HetNetThus we exceed the macro BS degrees of freedom withup to 10 small cells in the coverage area of a macro BSMoreover we consider the out-of-cell interference fromothermacro BSs tiers in the hierarchical precoding frameworkThis can be achieved by utilizing the advantage of addingthe MMSE pre- and postcoder to the proposed hierarchicalframework Finally we provide a comprehensive study on thecontradicting effects of the proposed hierarchical algorithmson both the signal and interference received power as wellas spectral efficiency separately for macro and small cellattached UEs

The novel contributions in this work are summarized asfollows

(1) A complexity analysis and comparison of the algo-rithms are presented In this analysis we separatethe required steps of the algorithms and provide thecomplexity required in each of the steps

(2) Furthermore we investigated the trade-off on thesystem spectral efficiency exceeding the degrees offreedom available at the macro BS In an UDN thenumber of small cells can easily exceed the numberof antennas at the macro BS

(3) Finally we analyze the ldquorobustnessrdquo of our proposedalgorithms In [11 13ndash16] perfect channel knowledgeis considered which is why we introduce a channeluncertainty and investigate in this work its impact onthe system spectral efficiency Additionally we alsotake into account the impact frommultiplemacro BSsand show the advantage of our proposed algorithmsincreasing the number of antennas and thereforedegrees of freedom at the macro BS

19 hexagonal macrocell network deployments with with three-sector sites

MacrouserPicouser

Sector of interestPicocell

Coordinated cluster

Figure 1 Deployment and transmissionmode of the heterogeneousnetwork

Remark 1 Throughout our work all the processing for thehierarchical precoding scheme is handled at the macro BSwhich enables independent transmission at the small cellsThis implies that no user data or feedback exchange isrequired between transmit nodes

For notational convenience throughout the whole papera scalar is denoted as119909 a vector as x and amatrix asXMatrixconjugate transpose is denoted as (sdot)119867 The most dominanteigenvector of a matrix (sdot) is expressed as 120585max(sdot) which isthe eigenvector corresponding to the largest eigenvalue whilethe least dominant one is expressed as 120585min(sdot) The Frobeniusnorm is represented as (sdot)2

119865 The matrix I

119873denotes 119873 times 119873

identity matrix Esdot stands for the expectation operator

2 System Model

In this work we consider the HetNet deployment shown inFigure 1 and investigate the downlink scenario within coher-ent channel bandwidthThe system considered is a Multiuser(MU-) MIMO Orthogonal Frequency Division Multiplexing(OFDM) system with constant CSI per Resource Block (RB)The deployment is a central macro BS serving a specifiedset of UEs within its transmission range and surroundedby multiple tiers of macrosites Each macrosite is dividedinto three 120∘ sectors and within each sector small cellsare deployed Each macrosector and each small cell has anindependent cell identity (ID) such that we have a total set ofcells M with cardinality 119872 = |M| We can split the set Minto the disjoint subsetsM

119903subM andM

119901subM representing

macrocells and small cells within the system respectivelysuch thatM

119903cupM119901=M andM

119903capM119901= 0

Further we assume that a macrosector together with theunderlying small cells forms a cluster given byM

119888subM with

cardinality119872119888= |M

119888| for example Figure 1 Coordination

between the macrocell and small cells is only done within thesame cluster Since we are assuming full spectral frequencyreuse within M other macrosectors (and small cells) cause

International Journal of Antennas and Propagation 3

residual uncoordinated interference henceforth referred toas intercluster interference (ICI)

The setK represents all UEs located within the coveragearea of a cluster (connected to a cell within the cluster)and K

119898sub K a subset of UEs connected to 119898th BS

Consequently the subsetK119903subK represents UEs connected

to a macrocell and K119901sub K are the users attached to

the small cells Furthermore we denote with K119888sub K the

UEs selected (scheduled) for simultaneously spatial downlinktransmission on the same time-frequency resource in clusterM119888 The number of antennas at macrocells small cells and

UEs is set to 119873119898119905 119873119901119905 and119873

119903 respectively

With these assumptions the received signal of user 119896 isinK connected to cell 119898 on a time-frequency resource (RB) isdefined as follows

y119896= H119898119896

b119898119896radic

119901119898119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

L119896

x119896+ sum

119895isinK119898119896

H119898119896

s119898119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

S119896

+ sum

119899isinM119888119898

sum

119895isinK119899

H119899119896s119899119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

T119896

+ sum

119897isinMM119888

sum

119895isinKK119897

H119897119896s119897119895+ n

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(1)

where H119897119906isin C119873119903times119873119905

119897

is the channel matrix between 119897th BSand 119906th UE The vector s

119897119906= b119897119906radic

119901119897119906x119906isin C119873119905

119897times1 denotes

the precoded signal x119906with the precoding vector b

119897119906and

transmit power 119901119897119906le 119875119904limited by a sum power constraint

119875119904 The vector n represents C119873119903times1 Additive White Circular

Symmetric Complex Gaussian Noise (AWCSCGN) samplesat the receiver with covariance Enn119867 = 1205902

119899I119873119903 For clarity

we clustered the receive signal of user 119896 into the 4 followingparts (1) L

119896the effective channel for the desired UE 119896 (2)

S119896interstream (or multiuser) interference caused by spatially

multiplexed users at the serving cell 119898 (3) T119896intracluster

interference which is caused by other cells within the sameclusterM

119888 119898 and (4) Z

119896intercluster interference from the

surrounding tiersM M119888in addition to thermal noise

The resulting Signal to Interference and Noise Ratio(SINR) of user 119896 used to obtain the spectral efficiency withShannonrsquos formula is thus given as follows

SINR119896=

10038161003816100381610038161003816w119867119896H119898119896

b119898119896radic

119901119898119896

10038161003816100381610038161003816

2

10038161003816100381610038161003816w119867119896S119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Stream IF

+

10038161003816100381610038161003816w119867119896T119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Intra Cluster IF

+

10038161003816100381610038161003816w119867119896Z119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Cluster IF

(2)

where w119896is the postcoder (receive beamformer) at 119896th UE

Using optimal linear equalization the MMSE postcoder w119896is

given by

w119896= (Q119896)

minus1

L119896 (3)

where the covariance matrixQ119896comprises

Q119896=S119896S119867119896+T119896T119867119896+Z119896Z119867119896+L119896L119867119896 (4)

In this paper we also inspect the case of imperfect CSI andwe model the channel after adding the error as follows

H = radic1 minus 120576H + radic120576H119890 (5)

where H represents the channelwith error whileH representsthe original channel 120576 is the channel error variance andH

119890isin

C119873119903times119873119905(0 120590) represents the error added to the channel

3 Algorithms

The basic concept in this paper is exceeding the macrodegrees of freedom (DoF) by serving a number ofUEs simul-taneously within the cluster which is greater than the numberof transmit antennas at the macro BS Then we inspectthe effect of this on the hierarchical precoding schemespresented in [15] and whether we can still achieve a gainover the uncoordinated case or not In the uncoordinatedcase the macro BS only applies BD without taking intoaccount the interference towards the underlying small cellsHowever with applying the hierarchical precoding schemesat the macro BS it can utilize the free spatial dimensionsavailable to align its interference towards the underlyingsmall cells Here in this section we will give an introductionfor the schemes with further discussion of the coordinationmechanism between the macro BS small cells and the UEswithin the cluster

31 Macrointerference Subspace Reduction This algorithmreferred to as BDIA requires two stages of precoding in ahierarchical way The first precoding stage is applying BD[12] in order to mitigate the interstream interference betweenthe spatially multiplexed macro UEs The second stage isapplying iterative IA [11] precoding to reduce the rank of themacrointerference subspace towards the small cell connectedUEs while preserving the orthogonal streams towards theserved macro UEs Then the two-stage precoder can becalculated as follows

b119898119896= V0119896f119896 (6)

where V0119896is the common null space of the scheduled macro

UEs K119903derived from the BD algorithm and f

119896from the

IA algorithm This second part of (6) f119896effectively reduces

the interference subspace from the macrocell towards thesmall cell connected UEs in the same cluster M

119888to a

single dimension so our objective here can be modelledas minimizing the interference leakage from the macro BStowards the small cell connected UEs as follows

min sum

119895isinK119899

sum

119896isinK119888119896 =119895

10038171003817100381710038171003817

H119895119896f119896minus c119896c119867119896H119895119896f119896

10038171003817100381710038171003817

2

119865 (7)

whereK119899isin K119888K119901 represents the macro UEs connected

to BS 119899 within the cluster and c119896is rank 1 orthonormal basis

for the received interference subspaceΩ119896and is calculated as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896) (8)

4 International Journal of Antennas and Propagation

while H119895119896

represents the effective channels such that thetransmitting macro BSs are considered as K

119899transmitters

causing interference towards the small cell connected UEsand these new virtual effective channels can be calculated as

H119895119896= H119899119896V0119895 (9)

then the corresponding postcoder for each user 119896 isin K119888is

given as follows

w119896= I119873119903minus c119896c119867119896 (10)

Then the IA precoder is calculated as

f119895cong 120585min( sum

119896isinK119888 119896 =119895

H119867119895119896w119896H119895119896) (11)

Then both the precoding filter at the macro BS and theinterference subspace at the receivers of the UEs are updatediteratively until convergence Here in Figure 2 themechanismof the BDIA algorithm is shown

Algorithm 2 (macrointerference subspace reduction)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (8)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

32 Macrointerference Subspace Reduction with ConsideringUncoordinated Interference The ldquoBDIA uncordrdquo algorithmis similar to Algorithm 2 but it is more sophisticatedbecause it takes into account the uncoordinated interferenceas mentioned in [13] As uncoordinated interference weconsider the undesired signal from the small cells towardsthe macro UEs and other small cells UEs in the case whenonly one cooperation area is active When the multiplesurrounding tiers are active also then all the interferencefrom BSs outside the cluster is added to the uncoordinatedinterference Simply by replacing (8) by (12) in step (3) inAlgorithm 2 this uncoordinated interference is taken intoaccount in the hierarchical precoding framework Hence-forth the orthonormal basis c

119896for the received interference

subspace is now calculated as the maximum eigenvector ofthe uncoordinated interference added to the interferencesubspace from themacro BS towards the small cell connectedUEs In this addition the macro BS transmitting powercannot be directly normalized as in (8) because of addingthe uncoordinated interference to the macro interferenceleakageThis uncoordinated interference is arising from boththe macrocells and the small cells and each of them hasdifferent transmitting power Thus the orthonormal basisc119896for the received interference subspace is represented as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895119901119899f119867119895H119867119895119896+P119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

) (12)

where P119896represents the uncoordinated interference from the

small cells towards the macro UEs and other small cells UEswithin the same cluster and is calculated as

P119896= sum

119903isinM119888M119903

H119903119896f119903119901119903f119867119903H119867119903119896 (13)

while R119896represents the uncoordinated interference from the

other BSs outside the cluster (intercluster interference) in casemulticluster (MC) scenario is applied and is calculated as

R119896= sum

119897isinMM119888

H119897119896f119897119901119897f119867119897H119867119897119896 (14)

Algorithm 3 (macrointerference subspace reduction withconsidering uncoordinated interference)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (12)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

33 Macrointerference Subspace Reduction Using IterativeMMSE Transmit and Receive Structure Here in this algo-rithm referred to as BDIA MMSE JTR the idea of iterativesubspace refinement where both the precoding filter at themacro BS and the interference subspace at the receivers ofthe UEs are updated iteratively is utilized again but this timeusing MMSE transmit and receive structures as in [13] withthe target of taking the macro UE signal level into accountthus aligning the interference towards the small cells and atthe same time keeping the macro UEs signal at a high levelabove the noise

First the algorithm starts iterating in the forward direc-tion by calculating the interference covariance matrix asfollows

Q119896= 1205902I119873119903+ sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896+R119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(15)

where the effective channel here is given by H119895119896

=

H119899119896V0119895radic119901119899119896 With this the dominant interference subspace

is obtained by

Q119896cong 120585max (Q119896) (16)

then calculating the signal subspace Φ119896as the whole receive

space excluding the dominant interference subspace as in [11]

Φ119896= I119873119903minusQ119896Q119867119896 (17)

The signal subspace is obtained in a different way in (17)in [13] where it is calculated as the minimum eigenvectorof the interference subspace but for consistency we stickthroughout the whole work to the methodology in [11]

International Journal of Antennas and Propagation 5

Available space

Null space

Maximizing signal

Available space

Null space

Minimizing interference

Block diagonalization

Cancelled by block diagonalizationInterference

alignment

Macro base station

Pico base station

Macrouser

Macrouser

Picouser

Block diagonalization

Macrointerferencerank

reduction by interference

alignment

1 2

3

11

33

1323

2212

21

111

222

333

Figure 2 Macrointerference subspace reduction mechanism

Then calculating the receive beamformer using theMMSE strategy for K

119888cluster UEs where each macro UE is

represented as 119895 isin K119899and every small cell UE is given as

119904 isin Kc K119899 and a small cell within the coordinated clusteris given as 119901 isin M

119888M119903 therefore the postcoder for the

macro UEs is given as follows

w119895= (Q119895)

minus1

H119895119895f119895 (18)

while for the small cell connected UEs is calculated as

w119904= (Q119904)minus1H119901119904f119904radic119901119901119904 (19)

Then going backward step to calculate the interferencecovariance matrix Q

119895

Q119895= 1205902IDoF119895 + sum

119896isinK119888 119896 =119895

H119867119895119896w119896w119867119896H119895119896 (20)

where DoF119895represents the available DoF at the macro BS

for serving UE 119895 and is calculated as DoF119895= 119873

119879minus

sum119906isinK119888K119901 119906 =119895

119904119906 where 119904

119906is the number of the spatial streams

assigned for UE 119906 then the macro precoder f119895is calculated as

follows

f119895= (

Q119895)

minus1H119867119895119895w119895 (21)

Then the objective function is modelled as in (7)

min sum119895isinK119899

sum

119896isinK119888 119896 =119895

100381710038171003817100381710038171003817

H119895119896f119895minusQ119896Q119867119896H119895119896f119895

100381710038171003817100381710038171003817

2

119865

(22)

This algorithm is different from the one in Figure 2 Themacro BS chooses the precoding vectors for its UE within thenull space that minimizes the interference towards the smallcell connectedUEs together withmaximizing the signal levelfor the macro UEs

Algorithm 4 (macrointerference subspace reduction usingiterative MMSE transmit and receive structure)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) CalculateQ119896for all 119896 isinK

119888using (15)

(4) Calculate w119895for all 119895 isinK

119899using (18)

(5) Calculate w119904for all 119904 isin K

119888K119899 using (19)

(6) Backward step calculate Q119895for all 119895 isinK

119899using (20)

(7) Calculate f119895for all 119895 isinK

119899using (21)

(8) Repeat steps from (3) to (7) until convergence

4 Complexity Analysis

In this section we analyze the computational complexity ofthe presented IA based algorithms including BDIA BDIAuncord and BDIA MMSE JTR respectively

First we provide the reasons that show the importanceof the computational complexity analysis of the proposedalgorithms [17] which are

(1) IA based algorithms can exploit the channel reci-procity to calculate the transmit precoders andreceiver beamformers in a distributed manner Reci-procity is based on the Time Division Duplex (TDD)operation mode with synchronized time-slot Prac-tical wireless channel is time varying Henceforthassuming perfect reciprocity is not always accurateand can result in residual interference at the receiverside thus algorithms with low computational com-plexity (short computing time) are required to avoidperformance loss arising from imperfect reciprocityin practical systems [18] In our scenario we present

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

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Active and Passive Electronic Components

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 3

residual uncoordinated interference henceforth referred toas intercluster interference (ICI)

The setK represents all UEs located within the coveragearea of a cluster (connected to a cell within the cluster)and K

119898sub K a subset of UEs connected to 119898th BS

Consequently the subsetK119903subK represents UEs connected

to a macrocell and K119901sub K are the users attached to

the small cells Furthermore we denote with K119888sub K the

UEs selected (scheduled) for simultaneously spatial downlinktransmission on the same time-frequency resource in clusterM119888 The number of antennas at macrocells small cells and

UEs is set to 119873119898119905 119873119901119905 and119873

119903 respectively

With these assumptions the received signal of user 119896 isinK connected to cell 119898 on a time-frequency resource (RB) isdefined as follows

y119896= H119898119896

b119898119896radic

119901119898119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

L119896

x119896+ sum

119895isinK119898119896

H119898119896

s119898119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

S119896

+ sum

119899isinM119888119898

sum

119895isinK119899

H119899119896s119899119895

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

T119896

+ sum

119897isinMM119888

sum

119895isinKK119897

H119897119896s119897119895+ n

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(1)

where H119897119906isin C119873119903times119873119905

119897

is the channel matrix between 119897th BSand 119906th UE The vector s

119897119906= b119897119906radic

119901119897119906x119906isin C119873119905

119897times1 denotes

the precoded signal x119906with the precoding vector b

119897119906and

transmit power 119901119897119906le 119875119904limited by a sum power constraint

119875119904 The vector n represents C119873119903times1 Additive White Circular

Symmetric Complex Gaussian Noise (AWCSCGN) samplesat the receiver with covariance Enn119867 = 1205902

119899I119873119903 For clarity

we clustered the receive signal of user 119896 into the 4 followingparts (1) L

119896the effective channel for the desired UE 119896 (2)

S119896interstream (or multiuser) interference caused by spatially

multiplexed users at the serving cell 119898 (3) T119896intracluster

interference which is caused by other cells within the sameclusterM

119888 119898 and (4) Z

119896intercluster interference from the

surrounding tiersM M119888in addition to thermal noise

The resulting Signal to Interference and Noise Ratio(SINR) of user 119896 used to obtain the spectral efficiency withShannonrsquos formula is thus given as follows

SINR119896=

10038161003816100381610038161003816w119867119896H119898119896

b119898119896radic

119901119898119896

10038161003816100381610038161003816

2

10038161003816100381610038161003816w119867119896S119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Stream IF

+

10038161003816100381610038161003816w119867119896T119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Intra Cluster IF

+

10038161003816100381610038161003816w119867119896Z119896

10038161003816100381610038161003816

2

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Inter Cluster IF

(2)

where w119896is the postcoder (receive beamformer) at 119896th UE

Using optimal linear equalization the MMSE postcoder w119896is

given by

w119896= (Q119896)

minus1

L119896 (3)

where the covariance matrixQ119896comprises

Q119896=S119896S119867119896+T119896T119867119896+Z119896Z119867119896+L119896L119867119896 (4)

In this paper we also inspect the case of imperfect CSI andwe model the channel after adding the error as follows

H = radic1 minus 120576H + radic120576H119890 (5)

where H represents the channelwith error whileH representsthe original channel 120576 is the channel error variance andH

119890isin

C119873119903times119873119905(0 120590) represents the error added to the channel

3 Algorithms

The basic concept in this paper is exceeding the macrodegrees of freedom (DoF) by serving a number ofUEs simul-taneously within the cluster which is greater than the numberof transmit antennas at the macro BS Then we inspectthe effect of this on the hierarchical precoding schemespresented in [15] and whether we can still achieve a gainover the uncoordinated case or not In the uncoordinatedcase the macro BS only applies BD without taking intoaccount the interference towards the underlying small cellsHowever with applying the hierarchical precoding schemesat the macro BS it can utilize the free spatial dimensionsavailable to align its interference towards the underlyingsmall cells Here in this section we will give an introductionfor the schemes with further discussion of the coordinationmechanism between the macro BS small cells and the UEswithin the cluster

31 Macrointerference Subspace Reduction This algorithmreferred to as BDIA requires two stages of precoding in ahierarchical way The first precoding stage is applying BD[12] in order to mitigate the interstream interference betweenthe spatially multiplexed macro UEs The second stage isapplying iterative IA [11] precoding to reduce the rank of themacrointerference subspace towards the small cell connectedUEs while preserving the orthogonal streams towards theserved macro UEs Then the two-stage precoder can becalculated as follows

b119898119896= V0119896f119896 (6)

where V0119896is the common null space of the scheduled macro

UEs K119903derived from the BD algorithm and f

119896from the

IA algorithm This second part of (6) f119896effectively reduces

the interference subspace from the macrocell towards thesmall cell connected UEs in the same cluster M

119888to a

single dimension so our objective here can be modelledas minimizing the interference leakage from the macro BStowards the small cell connected UEs as follows

min sum

119895isinK119899

sum

119896isinK119888119896 =119895

10038171003817100381710038171003817

H119895119896f119896minus c119896c119867119896H119895119896f119896

10038171003817100381710038171003817

2

119865 (7)

whereK119899isin K119888K119901 represents the macro UEs connected

to BS 119899 within the cluster and c119896is rank 1 orthonormal basis

for the received interference subspaceΩ119896and is calculated as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896) (8)

4 International Journal of Antennas and Propagation

while H119895119896

represents the effective channels such that thetransmitting macro BSs are considered as K

119899transmitters

causing interference towards the small cell connected UEsand these new virtual effective channels can be calculated as

H119895119896= H119899119896V0119895 (9)

then the corresponding postcoder for each user 119896 isin K119888is

given as follows

w119896= I119873119903minus c119896c119867119896 (10)

Then the IA precoder is calculated as

f119895cong 120585min( sum

119896isinK119888 119896 =119895

H119867119895119896w119896H119895119896) (11)

Then both the precoding filter at the macro BS and theinterference subspace at the receivers of the UEs are updatediteratively until convergence Here in Figure 2 themechanismof the BDIA algorithm is shown

Algorithm 2 (macrointerference subspace reduction)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (8)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

32 Macrointerference Subspace Reduction with ConsideringUncoordinated Interference The ldquoBDIA uncordrdquo algorithmis similar to Algorithm 2 but it is more sophisticatedbecause it takes into account the uncoordinated interferenceas mentioned in [13] As uncoordinated interference weconsider the undesired signal from the small cells towardsthe macro UEs and other small cells UEs in the case whenonly one cooperation area is active When the multiplesurrounding tiers are active also then all the interferencefrom BSs outside the cluster is added to the uncoordinatedinterference Simply by replacing (8) by (12) in step (3) inAlgorithm 2 this uncoordinated interference is taken intoaccount in the hierarchical precoding framework Hence-forth the orthonormal basis c

119896for the received interference

subspace is now calculated as the maximum eigenvector ofthe uncoordinated interference added to the interferencesubspace from themacro BS towards the small cell connectedUEs In this addition the macro BS transmitting powercannot be directly normalized as in (8) because of addingthe uncoordinated interference to the macro interferenceleakageThis uncoordinated interference is arising from boththe macrocells and the small cells and each of them hasdifferent transmitting power Thus the orthonormal basisc119896for the received interference subspace is represented as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895119901119899f119867119895H119867119895119896+P119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

) (12)

where P119896represents the uncoordinated interference from the

small cells towards the macro UEs and other small cells UEswithin the same cluster and is calculated as

P119896= sum

119903isinM119888M119903

H119903119896f119903119901119903f119867119903H119867119903119896 (13)

while R119896represents the uncoordinated interference from the

other BSs outside the cluster (intercluster interference) in casemulticluster (MC) scenario is applied and is calculated as

R119896= sum

119897isinMM119888

H119897119896f119897119901119897f119867119897H119867119897119896 (14)

Algorithm 3 (macrointerference subspace reduction withconsidering uncoordinated interference)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (12)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

33 Macrointerference Subspace Reduction Using IterativeMMSE Transmit and Receive Structure Here in this algo-rithm referred to as BDIA MMSE JTR the idea of iterativesubspace refinement where both the precoding filter at themacro BS and the interference subspace at the receivers ofthe UEs are updated iteratively is utilized again but this timeusing MMSE transmit and receive structures as in [13] withthe target of taking the macro UE signal level into accountthus aligning the interference towards the small cells and atthe same time keeping the macro UEs signal at a high levelabove the noise

First the algorithm starts iterating in the forward direc-tion by calculating the interference covariance matrix asfollows

Q119896= 1205902I119873119903+ sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896+R119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(15)

where the effective channel here is given by H119895119896

=

H119899119896V0119895radic119901119899119896 With this the dominant interference subspace

is obtained by

Q119896cong 120585max (Q119896) (16)

then calculating the signal subspace Φ119896as the whole receive

space excluding the dominant interference subspace as in [11]

Φ119896= I119873119903minusQ119896Q119867119896 (17)

The signal subspace is obtained in a different way in (17)in [13] where it is calculated as the minimum eigenvectorof the interference subspace but for consistency we stickthroughout the whole work to the methodology in [11]

International Journal of Antennas and Propagation 5

Available space

Null space

Maximizing signal

Available space

Null space

Minimizing interference

Block diagonalization

Cancelled by block diagonalizationInterference

alignment

Macro base station

Pico base station

Macrouser

Macrouser

Picouser

Block diagonalization

Macrointerferencerank

reduction by interference

alignment

1 2

3

11

33

1323

2212

21

111

222

333

Figure 2 Macrointerference subspace reduction mechanism

Then calculating the receive beamformer using theMMSE strategy for K

119888cluster UEs where each macro UE is

represented as 119895 isin K119899and every small cell UE is given as

119904 isin Kc K119899 and a small cell within the coordinated clusteris given as 119901 isin M

119888M119903 therefore the postcoder for the

macro UEs is given as follows

w119895= (Q119895)

minus1

H119895119895f119895 (18)

while for the small cell connected UEs is calculated as

w119904= (Q119904)minus1H119901119904f119904radic119901119901119904 (19)

Then going backward step to calculate the interferencecovariance matrix Q

119895

Q119895= 1205902IDoF119895 + sum

119896isinK119888 119896 =119895

H119867119895119896w119896w119867119896H119895119896 (20)

where DoF119895represents the available DoF at the macro BS

for serving UE 119895 and is calculated as DoF119895= 119873

119879minus

sum119906isinK119888K119901 119906 =119895

119904119906 where 119904

119906is the number of the spatial streams

assigned for UE 119906 then the macro precoder f119895is calculated as

follows

f119895= (

Q119895)

minus1H119867119895119895w119895 (21)

Then the objective function is modelled as in (7)

min sum119895isinK119899

sum

119896isinK119888 119896 =119895

100381710038171003817100381710038171003817

H119895119896f119895minusQ119896Q119867119896H119895119896f119895

100381710038171003817100381710038171003817

2

119865

(22)

This algorithm is different from the one in Figure 2 Themacro BS chooses the precoding vectors for its UE within thenull space that minimizes the interference towards the smallcell connectedUEs together withmaximizing the signal levelfor the macro UEs

Algorithm 4 (macrointerference subspace reduction usingiterative MMSE transmit and receive structure)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) CalculateQ119896for all 119896 isinK

119888using (15)

(4) Calculate w119895for all 119895 isinK

119899using (18)

(5) Calculate w119904for all 119904 isin K

119888K119899 using (19)

(6) Backward step calculate Q119895for all 119895 isinK

119899using (20)

(7) Calculate f119895for all 119895 isinK

119899using (21)

(8) Repeat steps from (3) to (7) until convergence

4 Complexity Analysis

In this section we analyze the computational complexity ofthe presented IA based algorithms including BDIA BDIAuncord and BDIA MMSE JTR respectively

First we provide the reasons that show the importanceof the computational complexity analysis of the proposedalgorithms [17] which are

(1) IA based algorithms can exploit the channel reci-procity to calculate the transmit precoders andreceiver beamformers in a distributed manner Reci-procity is based on the Time Division Duplex (TDD)operation mode with synchronized time-slot Prac-tical wireless channel is time varying Henceforthassuming perfect reciprocity is not always accurateand can result in residual interference at the receiverside thus algorithms with low computational com-plexity (short computing time) are required to avoidperformance loss arising from imperfect reciprocityin practical systems [18] In our scenario we present

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

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VLSI Design

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Volume 2014

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International Journal of

4 International Journal of Antennas and Propagation

while H119895119896

represents the effective channels such that thetransmitting macro BSs are considered as K

119899transmitters

causing interference towards the small cell connected UEsand these new virtual effective channels can be calculated as

H119895119896= H119899119896V0119895 (9)

then the corresponding postcoder for each user 119896 isin K119888is

given as follows

w119896= I119873119903minus c119896c119867119896 (10)

Then the IA precoder is calculated as

f119895cong 120585min( sum

119896isinK119888 119896 =119895

H119867119895119896w119896H119895119896) (11)

Then both the precoding filter at the macro BS and theinterference subspace at the receivers of the UEs are updatediteratively until convergence Here in Figure 2 themechanismof the BDIA algorithm is shown

Algorithm 2 (macrointerference subspace reduction)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (8)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

32 Macrointerference Subspace Reduction with ConsideringUncoordinated Interference The ldquoBDIA uncordrdquo algorithmis similar to Algorithm 2 but it is more sophisticatedbecause it takes into account the uncoordinated interferenceas mentioned in [13] As uncoordinated interference weconsider the undesired signal from the small cells towardsthe macro UEs and other small cells UEs in the case whenonly one cooperation area is active When the multiplesurrounding tiers are active also then all the interferencefrom BSs outside the cluster is added to the uncoordinatedinterference Simply by replacing (8) by (12) in step (3) inAlgorithm 2 this uncoordinated interference is taken intoaccount in the hierarchical precoding framework Hence-forth the orthonormal basis c

119896for the received interference

subspace is now calculated as the maximum eigenvector ofthe uncoordinated interference added to the interferencesubspace from themacro BS towards the small cell connectedUEs In this addition the macro BS transmitting powercannot be directly normalized as in (8) because of addingthe uncoordinated interference to the macro interferenceleakageThis uncoordinated interference is arising from boththe macrocells and the small cells and each of them hasdifferent transmitting power Thus the orthonormal basisc119896for the received interference subspace is represented as

follows

c119896cong 120585max( sum

119895isinK119899119895 =119896

H119895119896f119895119901119899f119867119895H119867119895119896+P119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

) (12)

where P119896represents the uncoordinated interference from the

small cells towards the macro UEs and other small cells UEswithin the same cluster and is calculated as

P119896= sum

119903isinM119888M119903

H119903119896f119903119901119903f119867119903H119867119903119896 (13)

while R119896represents the uncoordinated interference from the

other BSs outside the cluster (intercluster interference) in casemulticluster (MC) scenario is applied and is calculated as

R119896= sum

119897isinMM119888

H119897119896f119897119901119897f119867119897H119867119897119896 (14)

Algorithm 3 (macrointerference subspace reduction withconsidering uncoordinated interference)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) Calculate c119896for all 119896 isinK

119888using (12)

(4) Calculate f119895for all 119895 isinK

119899using (11)

(5) Repeat (3) and (4) until convergence

33 Macrointerference Subspace Reduction Using IterativeMMSE Transmit and Receive Structure Here in this algo-rithm referred to as BDIA MMSE JTR the idea of iterativesubspace refinement where both the precoding filter at themacro BS and the interference subspace at the receivers ofthe UEs are updated iteratively is utilized again but this timeusing MMSE transmit and receive structures as in [13] withthe target of taking the macro UE signal level into accountthus aligning the interference towards the small cells and atthe same time keeping the macro UEs signal at a high levelabove the noise

First the algorithm starts iterating in the forward direc-tion by calculating the interference covariance matrix asfollows

Q119896= 1205902I119873119903+ sum

119895isinK119899119895 =119896

H119895119896f119895f119867119895H119867119895119896+R119896+R119896⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Z119896

(15)

where the effective channel here is given by H119895119896

=

H119899119896V0119895radic119901119899119896 With this the dominant interference subspace

is obtained by

Q119896cong 120585max (Q119896) (16)

then calculating the signal subspace Φ119896as the whole receive

space excluding the dominant interference subspace as in [11]

Φ119896= I119873119903minusQ119896Q119867119896 (17)

The signal subspace is obtained in a different way in (17)in [13] where it is calculated as the minimum eigenvectorof the interference subspace but for consistency we stickthroughout the whole work to the methodology in [11]

International Journal of Antennas and Propagation 5

Available space

Null space

Maximizing signal

Available space

Null space

Minimizing interference

Block diagonalization

Cancelled by block diagonalizationInterference

alignment

Macro base station

Pico base station

Macrouser

Macrouser

Picouser

Block diagonalization

Macrointerferencerank

reduction by interference

alignment

1 2

3

11

33

1323

2212

21

111

222

333

Figure 2 Macrointerference subspace reduction mechanism

Then calculating the receive beamformer using theMMSE strategy for K

119888cluster UEs where each macro UE is

represented as 119895 isin K119899and every small cell UE is given as

119904 isin Kc K119899 and a small cell within the coordinated clusteris given as 119901 isin M

119888M119903 therefore the postcoder for the

macro UEs is given as follows

w119895= (Q119895)

minus1

H119895119895f119895 (18)

while for the small cell connected UEs is calculated as

w119904= (Q119904)minus1H119901119904f119904radic119901119901119904 (19)

Then going backward step to calculate the interferencecovariance matrix Q

119895

Q119895= 1205902IDoF119895 + sum

119896isinK119888 119896 =119895

H119867119895119896w119896w119867119896H119895119896 (20)

where DoF119895represents the available DoF at the macro BS

for serving UE 119895 and is calculated as DoF119895= 119873

119879minus

sum119906isinK119888K119901 119906 =119895

119904119906 where 119904

119906is the number of the spatial streams

assigned for UE 119906 then the macro precoder f119895is calculated as

follows

f119895= (

Q119895)

minus1H119867119895119895w119895 (21)

Then the objective function is modelled as in (7)

min sum119895isinK119899

sum

119896isinK119888 119896 =119895

100381710038171003817100381710038171003817

H119895119896f119895minusQ119896Q119867119896H119895119896f119895

100381710038171003817100381710038171003817

2

119865

(22)

This algorithm is different from the one in Figure 2 Themacro BS chooses the precoding vectors for its UE within thenull space that minimizes the interference towards the smallcell connectedUEs together withmaximizing the signal levelfor the macro UEs

Algorithm 4 (macrointerference subspace reduction usingiterative MMSE transmit and receive structure)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) CalculateQ119896for all 119896 isinK

119888using (15)

(4) Calculate w119895for all 119895 isinK

119899using (18)

(5) Calculate w119904for all 119904 isin K

119888K119899 using (19)

(6) Backward step calculate Q119895for all 119895 isinK

119899using (20)

(7) Calculate f119895for all 119895 isinK

119899using (21)

(8) Repeat steps from (3) to (7) until convergence

4 Complexity Analysis

In this section we analyze the computational complexity ofthe presented IA based algorithms including BDIA BDIAuncord and BDIA MMSE JTR respectively

First we provide the reasons that show the importanceof the computational complexity analysis of the proposedalgorithms [17] which are

(1) IA based algorithms can exploit the channel reci-procity to calculate the transmit precoders andreceiver beamformers in a distributed manner Reci-procity is based on the Time Division Duplex (TDD)operation mode with synchronized time-slot Prac-tical wireless channel is time varying Henceforthassuming perfect reciprocity is not always accurateand can result in residual interference at the receiverside thus algorithms with low computational com-plexity (short computing time) are required to avoidperformance loss arising from imperfect reciprocityin practical systems [18] In our scenario we present

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 5

Available space

Null space

Maximizing signal

Available space

Null space

Minimizing interference

Block diagonalization

Cancelled by block diagonalizationInterference

alignment

Macro base station

Pico base station

Macrouser

Macrouser

Picouser

Block diagonalization

Macrointerferencerank

reduction by interference

alignment

1 2

3

11

33

1323

2212

21

111

222

333

Figure 2 Macrointerference subspace reduction mechanism

Then calculating the receive beamformer using theMMSE strategy for K

119888cluster UEs where each macro UE is

represented as 119895 isin K119899and every small cell UE is given as

119904 isin Kc K119899 and a small cell within the coordinated clusteris given as 119901 isin M

119888M119903 therefore the postcoder for the

macro UEs is given as follows

w119895= (Q119895)

minus1

H119895119895f119895 (18)

while for the small cell connected UEs is calculated as

w119904= (Q119904)minus1H119901119904f119904radic119901119901119904 (19)

Then going backward step to calculate the interferencecovariance matrix Q

119895

Q119895= 1205902IDoF119895 + sum

119896isinK119888 119896 =119895

H119867119895119896w119896w119867119896H119895119896 (20)

where DoF119895represents the available DoF at the macro BS

for serving UE 119895 and is calculated as DoF119895= 119873

119879minus

sum119906isinK119888K119901 119906 =119895

119904119906 where 119904

119906is the number of the spatial streams

assigned for UE 119906 then the macro precoder f119895is calculated as

follows

f119895= (

Q119895)

minus1H119867119895119895w119895 (21)

Then the objective function is modelled as in (7)

min sum119895isinK119899

sum

119896isinK119888 119896 =119895

100381710038171003817100381710038171003817

H119895119896f119895minusQ119896Q119867119896H119895119896f119895

100381710038171003817100381710038171003817

2

119865

(22)

This algorithm is different from the one in Figure 2 Themacro BS chooses the precoding vectors for its UE within thenull space that minimizes the interference towards the smallcell connectedUEs together withmaximizing the signal levelfor the macro UEs

Algorithm 4 (macrointerference subspace reduction usingiterative MMSE transmit and receive structure)

(1) Initialize f119895isin 119862 forall119895 isin K

119899randomly such that f

119895f119867119895=

1(2) Calculate f

119904isin 119862 forall119904 isinK

119888K119899using BD [12]

(3) CalculateQ119896for all 119896 isinK

119888using (15)

(4) Calculate w119895for all 119895 isinK

119899using (18)

(5) Calculate w119904for all 119904 isin K

119888K119899 using (19)

(6) Backward step calculate Q119895for all 119895 isinK

119899using (20)

(7) Calculate f119895for all 119895 isinK

119899using (21)

(8) Repeat steps from (3) to (7) until convergence

4 Complexity Analysis

In this section we analyze the computational complexity ofthe presented IA based algorithms including BDIA BDIAuncord and BDIA MMSE JTR respectively

First we provide the reasons that show the importanceof the computational complexity analysis of the proposedalgorithms [17] which are

(1) IA based algorithms can exploit the channel reci-procity to calculate the transmit precoders andreceiver beamformers in a distributed manner Reci-procity is based on the Time Division Duplex (TDD)operation mode with synchronized time-slot Prac-tical wireless channel is time varying Henceforthassuming perfect reciprocity is not always accurateand can result in residual interference at the receiverside thus algorithms with low computational com-plexity (short computing time) are required to avoidperformance loss arising from imperfect reciprocityin practical systems [18] In our scenario we present

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

6 International Journal of Antennas and Propagation

PicouserPicouser

MacrouserMacrouser

Obtain channel state information

Calculate the precoders and postcoders

Virt

ual r

ecei

vers

Virt

ual r

ecei

vers

Virt

ual t

rans

mitt

ers

Virt

ual t

rans

mitt

ers

Optimize receive filters

Optimize receive filters

Iterate until convergence

TimeTime

Send pilotsfeedback

Send the precoded data (and postcoders)

TimeTime

Macrobase station

base stationPico

Back

haul

link

PicouserPicouser

MacrouserMacrouser

Optimize receive filters

Figure 3 Macrointerference subspace reduction mechanism

the algorithms in a generic framework to operate inFrequencyDivisionDuplexing (FDD) or TDDmodesas shown in Figure 3

(2) Also the receivers (UEs) have limited processingfunctionalities in practical systems Henceforth theycannot cope with algorithms that need high compu-tational complexity This can impose limitations tothe complexity of the algorithms Thus we need todesign algorithms with low complexity and simplecomputation In our scenario we assume all thecomputations are done within the macro BS whichis equipped with powerful processing capabilitiesthus relaxing this complexity limitations as shown inFigure 3

(3) Moreover for scalability issues algorithmswith lowercomplexity are always favoured in order to extend thealgorithms to large scale problems

Here our complexity criterion is the number of complexmultiplications The computational complexity for BDIABDIA uncord and BDIA MMSE JTR algorithms is analyzedconsidering the BD as a baseline for all of them and thus nottaken into account The main computations in one iterationare listed as follows

(1) The computation of the coordinated interference forall the three algorithms in (8) (12) and (15) thecomplexity is1198702(119904119873

119905119873119903+1199041198732

119903) where 119896 is the number

of UEs 119904 is the number of streams per UE and 119873119905

and119873119903represent the number of transmit and receive

antennas respectively(2) The eigenvalue decomposition carried out by the

three algorithms in (8) (12) and (16) the complexityis 9119870(1198733

119903)

(3) The computation of the intracluster interferencewhich is caused by other cells within the same clusterin both BDIA uncord and BDIA MMSE JTR algo-rithms shown in (13) the complexity is 1198702(119904119873

119905119873119903+

1199041198732

119903)

(4) The computation of the intercluster interference fromthe surrounding tiers in both BDIA uncord andBDIA MMSE JTR algorithms shown in (14) thecomplexity is1198702(119904119873

119905119873119903+ 1199041198732

119903)

(5) The computation of the objective function for all thethree algorithms in (7) and (20) the complexity is119896(119896minus1)119904

2(min(119873

119905 119873119903)+1) given that the interference

terms complexity are already accounted previously(6) The computation of the matrix inversion in BDIA

MMSE JTR algorithm shown in (18) (19) and (21)the complexity for each is119870(119873

119903minus 119904)3

The computational complexity comparison betweenBDIA BDIA uncord and BDIA MMSE JTR is summa-rized in Table 1 It is clear that BDIA MMSE JTR has thehighest computation complexity per iteration followed byBDIA uncord Finally BDIA has the lowest computationalcomplexity per iteration

5 Numerical Results

In order to evaluate the proposed algorithms we simulateda realistic ultradense HetNet scenario where the networkis overloaded with a lot of UEs that need to be servedsimultaneously in the same time-frequency resource withhigh data rates We carried out Monte-Carlo simulationswith 500 runs Each run is an independent (with uniformlydistributed dropped users) channel realization

Here we consider a coordinated cluster to consist ofone macrosector and the underlying small cells which aredeployed randomlywithin the coverage area of themacrosec-torThemacrosector is themain entity in the cluster while thesmall cells are deployed on demand when the number of UEsin the cluster increases The small cell BS is equipped with2 transmit antennas while the macro BS is equipped with8 transmit antennas Throughout our simulation scenarioseach small cell serves only 1UE per RB while the macro BScan serve UEs less than or equal to the number of its transmitantennas A summary for the simulation parameters is shownin Table 2

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 7

Table 1 Comparison of computational complexity

Operation BDIA BDIA uncord BDIA MMSE JTRCoordinated interference (1198702(119904119873

119905119873119903+ 1199041198732

119903))

Eigenvalue decomposition (9119870(1198733119903))

Intracluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Intercluster interference (1198702(119904119873119905119873119903+ 1199041198732

119903))

Objective function (119896(119896 minus 1)1199042(min(119873119905 119873119903) + 1))

Matrix inversion (119870(119873119903minus 119904)3)

Table 2 Simulation parameter

Parameter ValueChannel model QUADRIGA [19]

Scenario Macro BS urban macro (C2)Small cell urban mirco (B1)

Propagation Non-line-of-sightLarge-scale fading Geo-correlated parameters mapsCenter frequency 119891

11988826GHz

Simulation type Monte Carlo (500 runs)Traffic model Full bufferSignal bandwidth 180 kHz per RB 100 RBsIntersite distance(macro) 500m

Number of macro BSs 19 having 3 sectors eachNumber of small cells (1ndash10) per macrosector119873119905 spacing Macro 48 1205822 small cell 2 1205822

Transmit power Macro 49 dBm small cell 26 dBmBS height Macro 32m small cell 5mMin distance betweenmacrocell and small cell 75m

Min distance betweensmall cells 40m

119873119906119890 spacing 2 1205822UE height 2m

UE distribution 10 uniform in macrosector and aroundeach small cell

UE placementMinmax distance to small cells1040mMinimum distance to macro BS 35m

CSI at the transmitter Perfect imperfect

In Figure 4 we introduce two main simulation environ-ments which are the homogeneous environment where onlymacro UEs are served and no small cells are deployed andthe ultradense heterogeneous one where the macro sectoris overloaded with small cells In Figure 5 we compare thecluster sum spectral efficiency for 3 different scenarios Thefirst scenario is the homogeneous one the second scenariois the ultradense heterogeneous one where the macro BSapplies only BD algorithm and the cluster UEs apply theMMSE linear equalizer Thus this scenario is referred toas ultradense uncoordinated scenario since no coordinationoccurs between the macro and small cell BSs The thirdscenario is the coordinated ultradense one where the macro

Macrouser

Macrosector Picocell

Picouser

Homogeneous scenario

Ultradenseheterogeneous

scenario

Figure 4 Homogeneous and ultradense heterogeneous networkdeployments

BS applies the BDIAMMSE JTR algorithm thus coordinationoccurs between the macro and small cell BSs within the samecluster in this case

As we can see in Figure 5 that the HetNet deploymentalways achieves higher sum spectral efficiency than thehomogeneous one even when no coordination takes placebetween the macro and small cell BSs Also we can observethat coordinated ultradense scenario achieves higher spectralefficiency over the uncoordinated ultradense one only whenenough free spatial dimensions are available at the macro BSto align the macrointerference towards the small cells Herewe can see that the coordinated beamforming achieves higherspectral efficiency than the uncoordinated one in ultradensedeployment until the case where 6UEs are served per macroBS and two spatial dimensions are available at the macro BSfor aligning the interference However once we move to thecase where 7UEs are served per macro BS and only 1 spatialdimension is free for interference alignment the sum spectralefficiency drops below the uncoordinated case

In Figure 6 we consider the case where the macro BS hasenough free spatial dimensions for aligning the interferenceHere the macro BS is serving only 2UEs thus having 6 freespatial dimensions while small cells are deployed from 1 to10 and each small cell is serving 1UE We observe that evenwhen the macro BS DoF are exceeded the BDIA achieveshigher spectral efficiency than applying only BD algorithmat the macro BS Moreover the BDIA MMSE JTR which is

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Antennas and Propagation

140

12010 pico UEs

100No pico UEs

80

60

40

BD MMSE Rx (only macro UEs)BDIA MMSE JTR (coordinated)BD MMSE Rx (uncoordinated and macro and pico UEs)

20[1] [2] [3] [4] [5] [6] [7] [8]

Number of users at macrocell

Sum

spec

tral

effici

ency

(bits

sH

z)

Figure 5 Comparing the sum spectral efficiency for homogeneousuncoordinated ultradense and coordinated ultradense scenarioswith 8 transmitting antennas at the macro BS

Sum

spec

tral

effici

ency

(bits

sH

z)

130

120 Less thanthe macro DoF

Exceeding the macro DoF

110

100

90

80

70

BDIA MMSE JTR

60

BDIA uncord

50

BD MMSE Rx

BDIA MMSE Rx

40

BDIABD

30[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]

Number of users at macrocell and picocells [x y]

Figure 6 Evaluating the cluster sum spectral efficiency for serving2macroUEs and deploying small cells from 1 to 10 within the clusterfor the introduced algorithms

referred to as the coordinated beamforming case achieves thehighest spectral efficiency with a gain of 20 bitssHz overthe case when the macro BS applies only BD while each UEwithin the cluster applies MMSE equalizer referred to as theuncoordinated beamforming case

In order to inspect the results in Figure 6 in more detailwe show the coordinated and uncoordinated interferencepower received by the small cell connected UEs in Figures7 and 8 respectively In Figure 7 it is shown that the BDIAalgorithm can perfectly align the macrointerference towards

[2 1] [2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d co

ordi

nate

d in

terfe

renc

e pow

er (d

Bm)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Less than the macro DoF

Exceeding themacro DoF

Number of users at macrocell and small cells [x y]

minus50

minus100

minus150

minus200

minus250

minus300

Figure 7 Evaluating the small cell connected UEs received coor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

[2 2] [2 3] [2 4] [2 5] [2 6] [2 7] [2 8] [2 9] [2 10]Pico

user

s rec

eive

d un

coor

dina

ted

inte

rfere

nce p

ower

(dBm

)

BDIA MMSE JTRBDIA uncordBD MMSE Rx

BDIA MMSE RxBDIABD

Number of users at macrocell and small cells [x y]

minus75

minus80

minus85

minus90

minus95

minus100

minus105

minus110

minus115

minus120

minus125

Figure 8 Evaluating the small cell connected UEs received uncoor-dinated interference power for serving 2 macro UEs and deployingsmall cells from 1 to 10 within the cluster

the small cell connected UEs as long as the number of UEswithin the cluster is less than or equal to the DoF available atthe macro BS When the number of the cluster UEs exceedsthe macro DoF the BDIA can no longer align the macrointerference perfectly towards the small cell connected UEsHowever it can still partially align the macrointerferencethus applying BDIA at the macro BS achieves the lowest

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 9

125

120

115

110

BDIA MMSE JTR BD MMSE Rx BD

BDIA MMSE JTR wo error BD MMSE Rx wo error BD wo error

105

100

95

90

85

80

75

Sum

spec

tral

effici

ency

(bits

sH

z)

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 9 Evaluating the cluster sum spectral efficiency for serving2 macro UEs and deploying 10 small cells within the cluster incoordinated and uncoordinated scenarios (with and without perfectCSI)

received interference power at the small cell connected UEsside compared to all the other introduced algorithms evenwhen the number ofUEswithin the cluster exceeds themacroBS DoF Moving to Figure 8 we can observe that applyingthe BDIA MMSE JTR algorithm at the macro BS achievesthe lowest received uncoordinated interference power at thesmall cell connected UEs side compared to all the otherintroduced algorithms

In order to evaluate our framework in more realisticenvironment we introduce the results for having imperfectCSI and evaluate the sensitivity of the introduced algorithmstowards the channel error In Figure 9 we observe thatincreasing the channel error variance 120598 from minus50 to minus10 dBcauses a drop in the sum spectral efficiency of 30 bitssHz incase of applying the BDIA MMSE JTR algorithm Howeverit causes a drop of 16 bitssHz in case of applying the BDalgorithm at the macro BS side while utilizing the MMSElinear equalizer at the receiver sideWhile in case of applyingonly BD algorithm at themacro BS side a drop of 12 bitssHzoccurs

Figure 10 shows the normalized degradation in sum spec-tral efficiency due to increasing the channel error variance Itis clear that the BDIA MMSE JTR is the most sensitive algo-rithm to channel error such that the sum spectral efficiencydrops by 25 followed by the all other algorithms that utilizethe IA concept (BDIA BDIA uncord and BDIAMMSE Rx)with a degradation of about 21 followed by the BD withMMSE equalizer with a degradation of 17 and finally theBD algorithm with a degradation of 13

Finally one more step to make the simulation environ-ment more realistic is introducing the MC scenario as shownin Figure 1 where the coordinated cluster is now deployedwithin two tiers of active macro BSs that are causing severeinterference towards the coordinated cluster In Figure 11we compare the cluster sum spectral efficiency in the Single

0

005

01

015

02

025

03

035

Nor

mal

ized

deg

rada

tion

in su

m sp

ectr

al effi

cien

cy

BDIA uncordBDIA MMSE JTRBD MMSE Rx

BDIA MMSE RxBDIABD

minus50 minus45 minus40 minus35 minus30 minus25 minus20 minus15 minus10

Channel error variance (dB)

Figure 10 Evaluating the normalized degradation in cluster sumspectral efficiency for serving 2 macro UEs and deploying 10 smallcells within the cluster with imperfect CSI

Single cluster Multi cluster0

10

20

30

40

50

60

Scenario

Sum

spec

tral

effici

ency

(bits

sH

z)

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 11 Cluster sum spectral efficiency comparison betweenthe single and multicluster scenarios for serving 2 macro UEsand deploying 2 small cells within the cluster with the macro BSemployed with 4 transmitting antennas

Cluster (SC) scenario with the MC one In this deploymentthe macro BS is deployed with 4 transmit antennas andserving 2UEs while 2 small cells are deployed within thecoverage of themacrosector each is deployed with 2 transmitantennas and serving 1UE It is shown in Figure 11 thatmoving from the SC scenario to the MC one causes a severedegradation in the cluster sum spectral efficiency for all theintroduced algorithms specially for the BDIA MMSE JTRalgorithm which suffers from a degradation of 35 bitssHz

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Antennas and PropagationSu

m sp

ectr

al effi

cien

cy (b

itss

Hz)

4 Tx 8 Tx0

5

10

15

20

25

30

35

Number of macro transmit antennas

BDIA MMSE RxBD MMSE RxBDIA MMSE JTR

BDIA uncordBDIABD

Figure 12 The effect of increasing the number of macro transmitantennas on the cluster sum spectral efficiency for serving 2 macroUEs and deploying 2 small cells within the cluster

This degradation makes the BDIA MMSE JTR which isreferred to as coordinated beamforming give a higher sumspectral efficiency of only 05 bitssHz over the BD withMMSE equalizer which is referred to as uncoordinatedbeamforming in the MC case

In order to exploit the gain from using the coordinatedbeamforming we increase the number of macro transmitantennas to 8 The gain from increasing the macrospatialdimensions is shown in Figure 12 We can observe thatincreasing the number of macro transmit antennas results ina gain for all the introduced algorithms and specially for thecoordinated beamforming scheme such that the gain of thecoordinated beamforming scheme over the uncoordinatedone increased to 25 bitssHz instead of only 05 bitssHzin the case when the macro BS was equipped with only4 transmit antennas This result means that increasing themacrospatial dimensions allows us to yield higher gains in thecluster sum spectral efficiencywhen applying the coordinatedbeamforming scheme Henceforth moving to the massiveMIMO regime is expected to achieve high gains for theintroduced hierarchical coordinated beamforming schemes

6 Conclusion

From the results shown in Section 5 we can conclude that thehierarchical precoding framework performs higher spectralefficiency than the uncoordinated beamforming given that aSC scenario is available with enough free spatial dimensionsat the macro BS for aligning the interference This is valideven when the number of the UEs within the cluster exceedsthe DoF available at the macro BS We can also conclude thatrobust coordinated beamforming cannot be totally ensuredwith the introduced hierarchical precoding framework inultradense HetNet scenario due to the high sensitivity to

imperfect CSI even if a SC scenario is available with enoughfree spatial dimensions at the macro BS Moreover we canobserve that a severe degradation happens in the sum spectralefficiency for the hierarchical framework in the MC scenario(when multiple sources of uncoordinated interference existwith high power and different directions) Thus a solutionfor this problem is increasing the number of the availablespatial dimensions at the macro BS This was shown inSection 5 where increasing the number of macro transmitantennas from 4 to 8 achieved a high gain for the coordinatedbeamforming scheme

Therefore as a future work we suggest increasing thenumber of the spatial dimensions by either increasing thenumber of macro BS transmit antennas or increasing thenumber of the UEs receive antennas Concerning the imper-fect CSI scenario we also suggest as a future work to intro-duce adaptive precoding technique enclosing all the proposedalgorithms within the paper and even more algorithms thatare more robust against channel errors Henceforth eachalgorithm can be employed based on a threshold for theaccuracy of the CSI with considering the trade-off betweenthe spectral efficiency the complexity and the overhead ofeach algorithm

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Part of this work has been performed in the framework ofthe Horizon 2020 project Flexible Air iNTerfAce for Scalableservice deliverywiThinwIreless Communication networks ofthe 5th Generation (FANTASTIC-5G) (ICT-671660) whichis partly funded by the European Union The authors wouldlike to acknowledge the contributions of their colleagues inFANTASTIC-5G

References

[1] V Jungnickel K Manolakis W Zirwas et al ldquoThe role of smallcells coordinated multipoint and massive MIMO in 5Grdquo IEEECommunications Magazine vol 52 no 5 pp 44ndash51 2014

[2] J F Monserrat H Droste O Bulakci et al ldquoRethinking themobile and wireless network architecture the METIS researchinto 5Grdquo in Proceedings of the European Conference on Networksand Communications (EuCNC rsquo14) pp 1ndash5 June 2014

[3] N Bhushan J Li D Malladi et al ldquoNetwork densificationthe dominant theme for wireless evolution into 5Grdquo IEEECommunications Magazine vol 52 no 2 pp 82ndash89 2014

[4] S Yunas M Valkama and J Niemela ldquoSpectral and energyefficiency of ultra-dense networks under different deploymentstrategiesrdquo IEEE Communications Magazine vol 53 no 1 pp90ndash100 2015

[5] E G Larsson O Edfors F Tufvesson and T LMarzetta ldquoMas-siveMIMOfor next generationwireless systemsrdquo IEEECommu-nications Magazine vol 52 no 2 pp 186ndash195 2014

[6] T L Marzetta ldquoMassive MIMO an introductionrdquo Bell LabsTechnical Journal vol 20 pp 11ndash12 2015

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 11

[7] T L Marzetta ldquoNoncooperative cellular wireless with unlim-ited numbers of base station antennasrdquo IEEE Transactions onWireless Communications vol 9 no 11 pp 3590ndash3600 2010

[8] 3GPP ldquoPhysical channels and modulationrdquo 3rd GenerationPartnership Project Standard 36 211 3GPP 2016

[9] V Cadambe and S Jafar ldquoInterference alignment and spatialdegrees of freedom for the k user interference channelrdquo inProceedings of the in IEEE International Conference on Commu-nications (ICC rsquo08) pp 971ndash975 May 2008

[10] M Maddah-Ali A Motahari and A Khandani ldquoCommuni-cation over mimo x channels interference alignment decom-position and performance analysisrdquo IEEE Transactions onInformation Theory vol 54 no 8 pp 3457ndash3470 2008

[11] S W Peters and R W Heath Jr ldquoInterference alignment viaalternating minimizationrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo09) pp 2445ndash2448 IEEE Taipei Taiwan April 2009

[12] QH Spencer A L Swindlehurst andMHaardt ldquoZero-forcingmethods for downlink spatial multiplexing inmultiuserMIMOchannelsrdquo IEEE Transactions on Signal Processing vol 52 no 2pp 461ndash471 2004

[13] S W Peters and R W Heath Jr ldquoCooperative algorithms forMIMO interference channelsrdquo IEEE Transactions on VehicularTechnology vol 60 no 1 pp 206ndash218 2011

[14] J Dommel P-P Knust L Thiele and T Haustein ldquoMas-sive MIMO for interference management in heterogeneousnetworksrdquo in Proceedings of the IEEE 8th Sensor Array andMultichannel Signal Processing Workshop (SAM rsquo14) pp 289ndash292 A Coruna Spain June 2014

[15] M Kurras M Shehata K Hassan and L Thiele ldquoSpatialinterference management with hierarchical precoding in ultra-dense heterogeneous networksrdquo in Proceedings of the IEEE 11thInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo15) pp 520ndash526IEEE Abu Dhabi United Arab Emirates October 2015

[16] L Thiele and M Kurras ldquoHierarchical precoding for ultra-dense heterogeneous networksrdquo in Proceedings of the 48thAsilomar Conference on Signals Systems andComputers (ACSSCrsquo15) pp 1286ndash1290 November 2014

[17] C Sun Y Yang and Y Yuan ldquoLow complexity interferencealignment algorithms for desired signal power maximizationproblem of MIMO channelsrdquo Eurasip Journal on Advances inSignal Processing vol 2012 article 137 2012

[18] H G Ghauch and C B Papadias ldquoInterference alignment aonesided approachrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 HoustonTex USA December 2011

[19] S Jaeckel L Raschkowski K Borner and L ThieleldquoQuaDRiGa a 3-D multi-cell channel model with timeevolution for enabling virtual field trialsrdquo IEEE Transactions onAntennas and Propagation vol 62 no 6 pp 3242ndash3256 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of