performance of mobile mimo ofdm systems with application to utran lte downlink

2696 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 8, AUGUST 2012

Transactions Papers

Performance of Mobile MIMO OFDM SystemsWith Application to UTRAN LTE Downlink

Alexandra Oborina, Member, IEEE, Martti Moisio, Member, IEEE, and Visa Koivunen, Fellow, IEEE

Abstract—This paper analyzes the performance of multiple-input multiple-output (MIMO) orthogonal frequency divisionmultiplexing (OFDM) technology through the ergodic capacity.The capacity is represented based on the mean of the effectivesignal-to-interference-and-noise ratio (SINR) values. The asymp-totic distribution of the effective SINR in the case of independentand m-dependent quality measures, i.e., post-processed SINRs, isestablished analytically. The asymptotic distribution is applicablefor the size of post-processed SINRs of at least 1000 samplesor more and m = 10. The mean value of the effective SINRbased on the moment generating function of post-processedSINR is derived. Additionally, the impact of mobility on thesystem performance is characterized through the ergodic capacityand a system level factor which measures user mobility. Theperformance of MIMO OFDM system is validated by fullydynamic 3GPP Long Term Evolution network simulations indownlink under realistic mobility scenarios with low (3 km/h),medium (30 km/h) and high (120 km/h) user speeds. Thesimulations verify that the derived asymptotic distributions ofthe effective SINR for the independent and m-dependent casesare very accurate in all mobility scenarios. The simulated ergodiccapacity show clear loss in the average MIMO spectral efficiencyespecially in high mobility scenarios.

Index Terms—Mobile MIMO, OFDM, Long Term Evolution,SINR analysis, capacity.

I. INTRODUCTION

MULTIPLE-input multiple-output (MIMO) orthogonalfrequency division multiplexing (OFDM) based system

with multi-stream multi-carrier transmission capability is akey element in the current and near future standards, such as3GPP Long Term Evolution (LTE) and IEEE 802.16 WiMAX,to achieve higher peak throughputs and increased spectralefficiency. However, to gain the full benefit from MIMOOFDM technology, the specific transmission support needs to

Manuscript received April 20, 2010; revised December 3, 2010, September28, 2011, and March 12, 2012; accepted March 15, 2012. The associate editorcoordinating the review of this paper and approving it for publication was Y.-C. Ko.

A. Oborina and V. Koivunen are with the Department of Signal Processingand Acoustics, SMARAD CoE, Aalto University School of Electrical En-gineering, P.O. Box 13000, FI-00076 AALTO, Finland (e-mail: {aoborina,visa}@signal.hut.fi).

M. Moisio is with the Nokia Research Center, Helsinki, P.O. Box 407,FI-00045 Nokia Group, Finland (e-mail: [email protected]).

This work was supported in part by a grant from Nokia Foundation.Digital Object Identifier 10.1109/TWC.2012.060412.100656

be taken into account in the design of many physical layer,data link layer and radio resource management functions.Also, multi-stream multi-carrier transmission has to be takeninto account in the design of interaction between the linkand system level (link-to-system (L2S) interface). Therefore,conventional, single stream single carrier L2S interface, e.g.,Average Value Interface [1], [2], is optimized by effectiveSINR mapping methods in order to support efficiently multi-stream multi-carrier transmission with a large number of linkquality measures.

In this paper we analyze the performance of mobile MIMOOFDM technology on the system level though the ergodic sys-tem capacity. The expressions for the capacity for MIMO per-formance evaluation have been proposed earlier, for example,based on the instantaneous signal-to-noise ratio (SNR) [3], theunified SNR [4], the maximum SNR [5], the wideband averagesignal-to-interference-and-noise ratio (SINR) [6] or the sum ofthe instantaneous SNR using Taylor series expansion [7]. Inthis paper we analyze the ergodic system capacity based onthe mean value of the effective SINR. Such representation ofergodic capacity is beneficial for the system level studies, sinceit includes both system level and link level quality measuresto evaluate MIMO OFDM performance and shows explicitlymapping method used for the L2S interface.

Using analytical tools the following contributions are madein the paper. The ergodic capacity model using the mean ofthe effective SINR mapping for MIMO system performanceevaluation is presented. The asymptotic distribution of theeffective SINR in case of independent and m-dependent post-processed SINRs is established to be normal. The smallestnumber of post-processed SINR used in the effective SINRmapping and the largest number of dependency, m, such thatasymptotic approximation hold in the ε-neighborhood, arederived. The mean value of the effective SINRs based onthe moment generation function of post-processed SINR isderived. As a result, the expression for the ergodic capacitybased on the moment generation function of post-processedSINR is found.

In addition, in this paper we compare the impact of usermobility on average performance of 3GPP LTE with varyingUE speed from low (3 km/h), medium (30 km/h) to high

1536-1276/12$31.00 c© 2012 IEEE

OBORINA et al.: PERFORMANCE OF MOBILE MIMO OFDM SYSTEMS WITH APPLICATION TO UTRAN LTE DOWNLINK 2697

(120 km/h). Earlier the performance of 3GPP LTE undermobility has been studied in [8] and references therein. In[8] the throughput and spectral efficiency as a function ofsignal–to–noise ratio (SNR) estimated in different mobilityscenarios have been considered to evaluate the impact of userspeed. In this paper we introduce the system level factor basedon the mean value of the effective SINRs to measure theimpact of mobility to the system performance. As a result,the performance of 3GPP LTE under mobility is analyzed byestablishing ergodic capacity as a function of the system levelmobility factor evaluated in different mobility scenarios.

Conventionally, system level performance studies are doneusing stationary or quasi-static simulations. In this study,however, an advanced, fully dynamic system level simulator[9] is used where user mobility is explicitly modeled, includinghandovers. This advanced approach gives more insights anda realistic view of MIMO OFDM performance, especially inhigh mobility scenarios.

The theoretical results are verified with the simulationsusing 1000 post-processed SINR mapped to the effective SINRand m = 10. The simulation results demonstrate very highaccuracy of the normal approximations for the asymptoticdistribution of the effective SINR as well as representedcapacity model. The simulation experiments carried out indifferent mobility scenarios and using 3GPP LTE systemmodel show clear impact of mobility on the average spectralefficiency.

This paper is organized as follows. Section II introducesthe MIMO system model. In section III we represent theergodic system capacity based on the mean of the effectiveSINR and establish the asymptotic distribution of the effectiveSINR. Furthermore, in section III we introduce the systemlevel factor based on the mean of the effective SINR andanalyze the impact of mobility on the system capacity. SectionIV describes the simulation methodology and presents thesimulation results. The conclusions drawn from the theoreticalresults and simulations are given in Section V.

II. SYSTEM MODEL

Let us consider a frequency–selective L-tap fading singleuser MIMO channel with Nt transmit and Nr receive an-tennas. OFDM modulation with K sub-carriers turns such abroadband channel into a set of frequency flat channels. Herewe assume that the channels experienced by each transmit–receive antenna pair are independent. Also the channels be-tween transmit and receive antennas are uncorrelated andrandomly varying in time. Consequently, the received signalvector y ∈ CNr in the k-th sub-carrier is given by

yk = HkWksk + nk, (1)

where the matrix Hk ∈ CNr×Nt consists of complex Gaussianentries and represents flat frequency fading MIMO channel,vector sk ∈ CNs contains the transmitted symbols with co-variance E(sks

Hk ) = P

NsINs , P is the total transmitted power

and Ns ≤ min (Nt, Nr) is the number of spatially multiplexeddata streams. Here, the subscript (.)H stands for Hermitiantranspose. The matrix Wk ∈ CNt×Ns is a unitary precoder[10] satisfying the transmit constraints WH

k Wk = INs . The

vector nk ∈ CNr contains the additive white Gaussian noise(AWGN) and inter-cell interference. It is assumed to be zero–mean Gaussian with covariance E(nkn

Hk ) = Rk. Perfect

channel estimation is assumed at the receiver.

III. SYSTEM CAPACITY OF MIMO TRANSMISSION

For multi-carrier transmission in the presence of coloredGaussian noise, the ergodic capacity for the system in (1) canbe written as shown in [11]

C = EH

(1

K

K∑k=1

log2 det

(INs +

P

NsWH

k HHk R−1

k HkWk

)).

(2)

In order to include the post-processed interference remainingafter the linear receiver [3], [12] the system capacity can beexpressed in terms of the post-processed SINR as

C = E

(1

K

K∑k=1

Ns∑n=1

log2 (1 + γn,k)

), (3)

where γn,k is the post-processed SINR of the n-th data streamon the k-th sub-carrier. By using the linearity property ofexpectation and applying Jensen’s inequality to the systemcapacity (3), we get

C ≤ 1

K

K∑k=1

Ns∑n=1

log2 (1 + E(γn,k)) . (4)

Let us introduce the Exponential Effective SINR mapping(EESM) [13]–[16] that is proposed for OFDM system levelperformance evaluation [17] to estimate the link performance.The EESM method is widely used and accepted as a validtool within the 3GPP community [18] and is standardized asa link quality prediction model for 3GPP LTE system levelsimulations [19], [20].

The link quality model based on the EESM method accu-rately predicts the packet error rate at the receiver by mappingmultiple sub-carrier post-processed SINR values to a so-calledeffective SINR value with equivalent error rate of a packet inthe AWGN channel.

The effective SINR γeff in the EESM method is defined in[17] for the n-th data stream as follows

γeffn = −βn ln

(1

K

K∑k=1

e−γn,kβn

), (5)

where γn,k is the post-processed SINR of the n-th data streamon the k-th sub-carrier, the scaling parameter βn is determinedfrom the link level simulations for each modulation and codingscheme (MCS) and a bandwidth [13]. The parameter βn fora given MCS level scales the effective SINR for the n-th datastream to match the mapping table constructed for the AWGNchannel.

The effective SINR value provides a quantitative measurefor the link performance characterization of a multi–statechannel. The EESM method realizes the interface betweenthe link and the system level simulations with the reducedcomplexity. The EESM approach is general enough to enablea comparison of a large variety of system realizations withdifferent multiple access strategies and transceiver types in


various deployment scenarios. The effective SINR value isadaptive to the instantaneous channel and interference condi-tions that allows to take into account fast resource schedulingand fast link adaptation obtained in the system level simula-tions.

The expectation of effective SINR is bounded from below

E(γeffn ) ≥ −βn lnE

(e−

γn,kβn

)≥ −βn ln e−

E(γn,k)

βn = E(γn,k).

(6)So, the upper bound of ergodic system capacity may beevaluated by substituting E(γeff

n ) from (6) to (4)

C ≤Ns∑n=1

log2(1 + E(γeff

n )).

Since the block error rate is defined as a function of effectiveSINR, and scheduling is done aiming at maximizing thethroughput, ergodic system capacity can be determined by itsupper bound

C ≈Ns∑n=1

log2(1 + E(γeff

n )). (7)

The ergodic capacity (7) is based on classical Shannon ca-pacity [3] for the MIMO system. Capacity expression (7) isan alternative representation of the ergodic system capacityby means of the effective SINR. This representation is morepractical for the the system level performance evaluation sinceon the system level the quality of the link is estimated throughthe effective SINR, not post-processed SINR. The capacityexpression (7) includes directly system level quality measure(effective SINR) and indirectly link level quality measure(post-processed SINR, βn scaling parameter, that are used tomap to the effective SINR). Other system level capacity eval-uations presented in [6] and used for 3GPP LTE performanceevaluation in [8] involve additional tuning coefficients and donot take into account L2S interface model, that is heavily usedin the system level.

In order to show that the obtained model for ergodicsystem capacity (7) is reasonable, let us consider the followingexample.

Example. Nr = Nt = Ns, HkWk = INs , Rk = N0INs .N0 is the thermal noise variance. Then on the n-th streamthe SNR value in each sub-carrier k is γn,k = P

NsN0and the

effective SNR is

γeffn = − ln

(1

K

K∑k=1

e− P

NsN0

)=

P

NsN0.

In this example βn = 1 according to the definition of theeffective SINR mapping for the case HkWk = INs , Rk =N0INs .

The capacity evaluated through equation (7) is the same asthe capacity after the linear receiver (3) and is confirmed bythe example provided in [3]

C =

Ns∑n=1

log2

(1 +

P

NsN0

)= Ns log2

(1 +

P

NsN0

). (8)

A. Impact of Mobility on the Capacity

Let us first introduce the scalar αn that can be determinedas scaling factor between the mean value of the effective SINRand the mean value of the effective SINR in AWGN channel

αn :=E(γeff

n )

E(γeff, AWGNn )

=E(γeff

n )

γeff, AWGNn

=E(γeff

n )

γAWGN=E(γeff

n )NsN0

P. (9)

The link performance model for the MIMO OFDM systemcaptures fast channel variations in the frequency domainand determines an instantaneous packet error rate based oninstantaneous fading profile [13], [17]. Instantaneous link layerperformance captures the channel information by the linklevel factor βn through the mapping to the AWGN channelperformance [13]. However, the link level factor does nottake into account the mobility in general. The ratio betweenthe expectation of the effective SINR and the expectation ofthe effective SINR in AWGN channel is chosen to indirectlycapture the mobility in multi-cell environment, i.e., on thesystem level. The system level effects which depend onmobility can be described as follows.

• Handover and cell selection inefficiency. The high mobil-ity reduces the optimality in the channel selection. Thiseffect is included in the sub-carrier post-processed SINRsamples of the effective SINR mapping.

• Feedback inaccuracies. In high mobility scenarios ad-ditional channel feedback inaccuracies due to outdatedinformation cause suboptimal link and rank adaptationperformance as well as suboptimal scheduling.

• Radio Resource Management (RRM) performance degra-dation. In high mobility scenarios additional inaccuraciesin the measurement reports cause degradation in perfor-mance of RRM algorithms which depend on them, e.g.,power control and handover.

These system level aspects are captured in αn scalar, and inthe context of constant system load it can be called systemlevel mobility factor, αn = αn(v).

As a result, the ergodic capacity can be determined byincorporating mobility factor αn(v) as

C =

Ns∑n=1

log2(1 + αn(v)γ

AWGN)

=

Ns∑n=1

log2

(1 + αn(v)

P

NsN0

). (10)

B. Distribution of the SINR Values

Independent separation and detection for each symbolstream is achieved based on the linear equalizer G, x = Gy.For multiple stream transmission, the linear minimum meansquare error (MMSE) receiver reduces the interference andimproves the system performance. In single stream trans-mission case, in order to mitigate inter-cell interference, theinterference rejection combining (IRC) [21] is used.

The equivalent channel matrix in the k-th sub-carrier afterapplying unitary precoding is Hk = HkWk and the MMSE


receiver can be expressed as

G(MMSE) = minG

E(‖Gy − x‖2F

),

G(MMSE)k = HH

k

(HkH

Hk +Rk

Ns

P

)−1

∗=

(Ns

PINt + HH

k R−1k Hk

)−1

HHk R−1

k .

Equality (*) follows from the application of the matrix in-version lemma (A + BX−1C)−1 = A−1 − A−1B(X +CA−1B)−1CA−1 in the case Ns = Nt = Nr.

The SINR value γ on the n-th spatial stream per sub-carrierk after the MMSE receiver is given by

γ(MMSE)n,k =

∣∣∣∣[GkHk

](n,n)∣∣∣∣2∑

1≤m≤Ntm�=n

∣∣∣∣[GkHk

](n,m)∣∣∣∣2 + Ns

P[GkRkGH

k ](n,n)

,

(11)

where the notation A(n,n) stands for the (n, n) element ofmatrix A. At the same time, this SINR value after the MMSEreceiver (Ns = Nt = Nr) can be expressed as

γ(MMSE)n,k =

1[(INs +

PNs

HHk R−1

k Hk

)−1](n,n) − 1. (12)

The IRC receiver G and SINR value γ for the k-th sub-carrierafter the IRC receiver are given by

G(IRC)k = HH

k R−1k ,

γ(IRC)k =

P

NsHH

k R−1k Hk

Ns=1= P HH

k R−1k Hk. (13)

The distribution of post-processed sub-carrier SINR value forboth receivers belongs to an exponential distribution family,since the SINR value after the IRC receiver can be consideredas a particular one–dimensional case of the SINR value afterthe MMSE receiver. The SINR can be decomposed into twoindependent random variables, SINR = SINRZF + T, whereSINRZF corresponds to the SINR for a zero-forcing receiverand has an exact Gamma distribution G(ρ1, θ1). The randomvariable T, that captures the remaining SINR after zero-forcing receiver, can be approximated by Gamma distributionG(ρ2, θ2) as shown in [22]. Hence, the sub-carrier SINR valuesγn,k obey a distribution that is a convolution of two Gammadistributions G(ρ1, θ1) and G(ρ2, θ2). As a result, the momentgenerating function (MGF) of γn,k can be given by

φγ(t) := E(etγ)= (1− θ1t)

−ρ1(1− θ2t)−ρ2 . (14)

C. Distribution of the Effective SINR Values

In this section we first derive the expressions for the

moments of e−γeffn

βn to estimate the MGF and the cumulantgenerating function of the effective SINR. Then the cumulantsof the effective SINR are calculated and the asymptoticnormality of the effective SINR is established. Finally, themean value and the variance of the effective SINR for normalapproximation are derived.

Let us rewrite the effective SINR value (5) for the n-th

data stream in the exponential form e−γeffn

βn = 1K

∑Kk=1 e

− γn,kβn ,

where the numberK of mapped SINRs, γn,k, tends to be large.

Defining the MGF for γeffn as ψγ(t) := E

(etγ

effn

)the

moments Ms, s ≥ 1, of e−γeffn

βn can be expressed as

M1 = E(e−γeffn

βn ) = ψγ

(− 1

βn

)= φγ

(− 1

βn

),

Ms = E(e−sγeff

nβn ) = ψγ

(− s

βn

)−−−→K→∞

φsγ

(− 1

βn

),

∀ s ≥ 2, ε > 0, K >s− 1

1− s−1√1− ε

,

as shown in Appendix A for independent and identicallydistributed SINR values γn,k. The smallest number of SINRsmapped to the effective SINR, where the asymptotic resultsstart to hold in ε-neighborhood, are derived in Appendix C.

In the case of m-dependent SINR values γn,k the moments

Ms, s ≥ 1, of e−γeffn

βn can be expressed as

M1 = φγ

(− 1

βn

),

Msm�K−−−−→K→∞

φsγ

(− 1

βn

),

∀ s ≥ 2, ε > 0, K > K0 =s− 1

1− s−1√1− ε

,

∀ m < m0 :cm0

K0< ε,

as shown in Appendix B for m-dependent SINR values γn,k.The smallest number of SINRs mapped to the effective SINRand the largest number of m, where the asymptotic resultsstart to hold in ε-neighborhood, are derived in Appendix C.

Denoting t = − sβn

and ψγ(t) −−−→K→∞

φ−tβnγ (− 1

βn), the

cumulant generating function of effective SINR is estimated as−tβn lnφγ(− 1

βn). Thus, the cumulants of the effective SINR

are given as

κ1 = −βn ln(φγ

(− 1

βn

)),

κs −−−→K→∞

0, s ≥ 2.

Figure 1 validates the tendency of the third and the higherorder cumulants to go to zero for an increasing K value. Sincefor the normal distribution all cumulants beyond the secondorder are zero, the normal approximation for the effectiveSINR is well justified here. Furthermore, by showing that thehigher order cumulants are zero, not only Gaussianity, but alsosymmetry and unimodality of the distribution are establishedhere. The mean μN ,n of the effective SINR for the n-th datastream for normal approximation is equal to the first cumulant

μN ,n = −βn ln(φγ

(− 1

βn

)), (15)

and the variance σ2N ,n is calculated from the M1 and M2


100 200 300 400 500 600 700 800 900 1000 1100−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

K

3

4

5

6

(a) Ns = 1.

100 200 300 400 500 600 700 800 900 1000 1100−5

0

5

10

15

20x 10

−3

K

3

4

5

6

(b) Ns = 2.

Fig. 1. The third and the higher order cumulants for the independent SINRvalues, speed is 3 km/h, number of streams Ns = 1, 2. The tendency ofthe third and higher order cumulants towards zero for the large number ofthe mapped post-processed SINRs justifies the normal approximation of theeffective SINR.

moments applying the normal MGF for ψγ(t)⎧⎨⎩M1 = ψγ

(− 1

βn

)= e

− 1βn

μN ,n+ 12β2

nσ2N ,n

M2 = ψγ

(− 2

βn

)= e

− 2βn

μN ,n+ 2β2nσ2N ,n

σ2N ,n = β2

n ln(M2)− 2β2n ln(M1). (16)

The knowledge of the distribution of the effective SINR allowsto fully quantify statistics of the SINR, e.g., the confidence ofthe mean value.

D. Impact of the Mobility on the Capacity Through the MeanValue of the Effective SINR

The mean of the effective SINR is approximated by (15)without requiring the independence assumption of the SINRvalues. Thus, the system level factor αn(v) (9) for each MCSis evaluated through the mean value of the effective SINRas αn(v) =

μN ,nNsN0

P := αN ,n(v) also regardless of theindependence assumption of the SINR values.

Finally, the ergodic capacity can be modeled using thesystem level factor evaluated through the mean value of theeffective SINR as follows

CN =

Ns∑n=1

log2 (1 + μN ,n)

=

Ns∑n=1

log2

(1− βn ln

(φγ

(− 1

βn

)))(17)

=

Ns∑n=1

log2

(1 + αN ,n(v)

P

NsN0

).

IV. SIMULATION METHODOLOGY AND RESULTS

The multi-stream transmission performance is evaluatedbased on the E-UTRA LTE downlink assumptions and pa-rameters agreed in [23]. Unlike in the earlier studies thesimulation methodology here is a fully dynamic time-drivencellular model. All the evaluated simulations are performedin a three tier diamond-pattern macrocell scenario with 19sites of 3 sectors. Uniformly distributed User Equipments (UE)move within 21 cells in the middle (inside tiers 1-2) with aconstant speed but can make random turns. The 36 cells at theedge of the scenario produce the interference at the same levelas the average load in the center cells. The exact macro cellmobility model is described in [24]. The simulation parametersare summarized in detail in Table I.

The scheduling is organized as follows. First, the spatialdomain is scheduled through the dynamic rank adaptation. Atthe receiver side, the rank and the best suitable precodingmatrix Wk is selected over the whole bandwidth for the nexttransmission. The selection criteria for the transmission rankand precoding matrix can be designed in many ways [10],[25], [26] leading to different computational complexity andperformance. Here, the rank and precoding matrix is selectedaccording to the maximum estimated instantaneous capacityfor all possible ranks and precoding matrix combinations [25].

In order to take into account the impact of rank adaptationon the ergodic capacity we propose to model the resultingergodic capacity in the following way

C = p1C1 + p2C2, (18)

where p1 and p2 are the proportions of time for single streamand dual stream transmission, respectively, p1 + p2 = 1. Theproportions can be obtained from the system level simulations,where wide variety of channel conditions are experienced.Hence, these proportions can be considered representative ortypical in this type of scenario. C1 and C2 are the ergodiccapacities for single stream and dual stream transmission,respectively. The precoding is done using the closed loopcodebook based approach with the predefined precoding ma-trixes given in [10]. The codebook is known both at thereceiver and at the transmitter side. The feedback of thetransmission rank and the index of the precoding matrix areideal.

After rank and precoding matrix selection, the UEs are firstscheduled in the time domain and in the frequency domainlater. The scheduler algorithm selects the users with maximumthroughput. The scheduler closely co-operates with Hybrid


TABLE ISIMULATION PARAMETERS.

Parameter description Parameter value

Scenario / Network 57 cells, synchronized downlink

FDD, Reuse 1, 20 MHz bandwidth

1732 meters inter-site distance

10 dB penetration loss

Simulation time 3M steps (about 214 seconds)

1 ms simulation time step

Total number of UEs 210

UE speed 3 km/h, 30 km/h, 120 km/h

Channel model modified ITU Vehicular A

Traffic model Infinite Buffer

L1 parameters 14 symbols per TTI

1 ms sub-frame length

12 sub-carriers per PRB with 15 kHz spacing

Number of antennas Nt = 2, Nr = 2

Receivers LMMSE (dual stream transmission)

IRC (single stream transmission)

Link Adaptation dual stream transmission Link Adaptation

outer loop Link Adaptation

0.2 BLER target

MCSs (β) QPSK 1/3 (1.3322)

16QAM 1/2 (4.7817)

16QAM 2/3 (6.3860)

16QAM 4/5 (6.9970)

CQIs 5 ms measurement period

1 dB error variance

1 dB quantization step

2 ms reporting delay

2 resource blocks per CQI

Packet scheduling maximizing the throughput

Hybrid ARQ dual stream Asynchronous Chase Combining

blanking

6 stop-and-wait processes per stream

max 3 retransmissions per stream

ARQ Off

Power Control Off

Handovers hard handovers with hysteresis

based on reference signal pathloss

200 ms sliding window

3 dB handover margin

ARQ and Link Adaptation (LA) that need to be adjustedfor multi-stream transmission. In dual stream transmissionindependent LA is applied for each stream. The selection ofMCS (LA) for the next transmission is based on the ChannelQuality Indicator (CQI) estimates. The separate CQI values aremeasured for each data stream with independent measurementand quantization errors. The CQI measurements are calculatedfrom the downlink reference signals of the physical resourceblocks [27]. A report of the CQI measurements for the selectedtransmission mode is then transmitted to the eNodeB, whichcauses a reporting delay and may make the feedback outdatedin highly time-varying scenarios.

A. Results

In this section we first validate the analytical results of thedistribution of the effective SINR presented in Section III-Cby simulations. Then, we present the ergodic system capacityresults and compare them with the proposed model (17).

Let us assume that single optimal MCS is used for theeffective SINR mapping both in analytical derivations andin simulations. The optimal MCS is chosen as a statisticalmaximum of all possible MCSs used in the system levelsimulations for each mobility scenario. Hence, only one βnscaling parameter is utilized for the γeff

n calculation (5) for thespecified number of data streams and user speed. The valuesof the scaling parameter βn for the set of considered MCSsare presented in Table I.

The parameters for the MGF of sub-carrier SINR (14) areestimated from the simulated data by solving the followingsystem of equations for the first four moments, the mean μand variance σ2 and central moments m3 and m4{μ = ρ1θ1 + ρ2θ2, σ2 = ρ1θ

21 + ρ2θ

22,

m3 = 2(ρ1θ31 + ρ2θ

32), m4 = 3σ4 + 6(ρ1θ

41 + ρ2θ

42)).

We validate the normal approximation for the effectiveSINR mapping by comparing the cumulative distributionfunction (CDF) of the simulated effective SINR values withthe normal cumulative distribution function. First, the inde-pendent SINR values are considered for the effective SINRcalculation (5), next, the m-dependent SINRs are used forthe effective SINR mapping. The m-dependency is necessaryin the analyses since in the wideband OFDM system highlycorrelated SINRs are obtained in the adjacent sub-carriers andslightly correlated SINRs are collected in the distant sub-carriers. The number of post-processed SINRs mapped to theeffective SINR is chosen to be 1000 to ensure that the third andhigher order cumulants of the effective SINR tend to zero asshown in Fig. 1, and the second and higher order moments of

e−γeffn

βn hold in ε-neighborhood of asymptotic limit for ε = 0.1as shown in Appendix C. The number of dependency m iscalculated to be 10 to provide convergence towards the normalapproximation for 1000 post-processed mapped SINRs andε = 0.1 as shown in Appendix C.

Figure 2 presents the CDF of the simulated effective SINRand the CDF of normal distribution for single stream anddual stream transmission for the mobile speeds of 3, 30 and120 km/h. Here, only independent SINR values generate theeffective SINR values. The CDF plots show that the simulatedeffective SINR distribution is very accurately approximated bythe normal distribution. The Kolmogorov–Smirnov test witha = 0.05 level of significance accepts the goodness of thenormal approximation fit with the mean (15) and variance (16)in all mobility cases.

In order to demonstrate the accuracy of the normal ap-proximation the mean of the simulated effective SINR andmean of the normal approximation (15) as well as the varianceof the simulated effective SINR and variance of the normalapproximation (16) are presented in Table II. The approxi-mation is very accurate. The mean of normal approximationis at most only 0.03% lower than the mean of the simulatedeffective SINR in all mobility cases. The variance of normal


2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

effective SINR (linear scale)

cum

ulat

ive

dist

ribut

ion

func

tion

normal app., 3 kmph, = 6.9977

eff. SINR, 3 kmph, = 6.9977


eff. SINR, 30 kmph, = 6.9977


eff. SINR, 120 kmph, = 1.3322

(a) Ns = 1.

4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


cum

ulat

ive

dist

ribut

ion

func

tion

normal app., 3 kmph, = 4.7817eff. SINR, 3 kmph, = 4.7817normal app., 30 kmph, = 4.7817eff. SINR, 30 kmph, = 4.7817normal app., 120 kmph, = 4.7817eff. SINR, 120 kmph, = 4.7817

(b) Ns = 2.

Fig. 2. The cumulative distribution function of simulated effective SINRscompared with the cumulative distribution function of normal approximation.SINR values are independent, speeds are 3, 30 and 120 km/h, numberof streams Ns = 1, 2. The simulated effective SINR distribution is veryaccurately approximated by the normal distribution with the derived meanand variance.

approximation is at most only 1% lower the variance of thesimulated effective SINR in all mobility cases. So, the meanand the variance of the effective SINR are very accuratelyapproximated by the derived mean (15) and variance (16). Bycombining the CDF’s and the validation results for the meanand variance, it can be concluded that the effective SINRdistribution constructed on the independent SINR values isaccurately approximated by normal distribution.

Next, we validate the normal approximation for the effectiveSINR mapped from the m-dependent SINR values. Figure 3presents the CDF of the simulated effective SINR and theCDF of normal distribution for single stream and dual streamtransmission for the speeds of 3, 30 and 120 km/h. TheKolmogorov–Smirnov test with a = 0.05 level of significanceaccepts the goodness of the normal approximation fit with themean (15) and variance (16) for all mobility cases.

Results for the mean and variance of the simulated effectiveSINRs as well as for the mean and variance for normalapproximation in the case of m-dependent SINR values are

TABLE IITHE MEAN μ AND VARIANCE σ2 OF THE SIMULATED EFFECTIVE SINRS

AND THE MEAN μN (15) AND VARIANCE σ2N (16) OF NORMAL

APPROXIMATION. THE RESULTS FOR INDEPENDENT AND m-DEPENDENT

SINR VALUES, MOBILITY CASES WITH SPEED v OF 3, 30, 120 KM/H AND

NUMBER OF STREAMS Ns = 1, 2.

Ns=1 independent case m-dependent case

v (km/h) 3 30 120 3 30 120

μ 8.9922 6.3496 2.6747 8.9926 6.3498 2.6748

μN 8.9879 6.3472 2.6730 8.9879 6.3472 2.6730

σ2 0.0595 0.0328 0.00465 0.1714 0.0953 0.0110

σ2N 0.0593 0.0327 0.00461 0.1740 0.0951 0.0115

Ns=2 independent case m-dependent case

v (km/h) 3 30 120 3 30 120

μ 5.1641 4.9867 4.8806 5.1664 4.9869 4.8828

μN 5.1622 4.9848 4.8789 5.1622 4.9848 4.8789

σ2 0.0185 0.01771 0.0167 0.0405 0.0378 0.0375

σ2N 0.0183 0.01767 0.0166 0.0406 0.0380 0.0374

2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


cum

ulat

ive

dist

ribut

ion

func

tion


eff. SINR, 3 kmph, = 6.9977


eff. SINR, 30 kmph, = 6.9977


eff. SINR, 120 kmph, = 1.3322

(a) Ns = 1.

4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


cum

ulat

ive

dist

ribut

ion

func

tion

normal app., 3 kmph, = 6.9977eff. SINR, 3 kmph, = 6.9977normal app., 30 kmph, = 6.9977eff. SINR, 30 kmph, = 6.9977normal app., 120 kmph, = 1.3322eff. SINR, 120 kmph, = 1.3322

(b) Ns = 2.

Fig. 3. The cumulative distribution function of the simulated effective SINRscompared with the cumulative distribution function of normal approximation.SINR values are m-dependent, speeds are 3, 30 and 120 km/h, number ofstreams Ns = 1, 2.

presented in Table II. The mean of normal approximation isat most only 0.08% lower than the mean of the simulated


0 20 40 60 80 100 1201.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

speed (kmph)

ergo

dic

capa

city

ergodic capacity

estimated ergodic capacity

confidence interval

2.98 3 3.023.48

3.482

3.484

29.98 30 30.023.06

3.062

3.064

119.98 120 120.022.106

2.107

2.108

Fig. 4. Ergodic system capacity of MIMO transmission (7) compared withthe proposed ergodic system capacity (17) inside the confidence interval (19)– (20). Speeds are 3, 30 and 120 km/h. The approximation model is verytight.

effective SINR in all mobility cases. The variance of normalapproximation is at most 4% lower than the variance of thesimulated effective SINR in all mobility cases. Both singlestream and dual stream transmissions show that the meanand variance of the effective SINR is slightly less accuratelyapproximated by the derived mean value (15) and variance(16). So, we can conclude that the effective SINR distributionis slightly less accurately approximated by normal distributionin the case of m-dependent SINR values. The main reasonfor lower accuracy is that the number of post-processed sub-carrier SINRs involved in the effective SINR mapping is notsufficiently large to relieve the dependence in the effectiveSINR values.

Finally, the impact of mobility on the system performanceis evaluated through the ergodic system capacity. The resultsof ergodic system capacity (7) for the mobile speeds of 3, 30and 120 km/h as well as the proposed model (17) inside theconfidence interval are plotted in Fig. 4.

The confidence interval for the capacity is calculated asfollows. Applying the confidence interval definition of themean from [28] to the ergodic system capacity (7) we get

C ≥Ns∑n=1

log2

(1 + μ− t−1

( 1+α2 ,N−1)

σ√N − 1

), (19)

C ≤Ns∑n=1

log2

(1 + μ+ t−1

( 1+α2 ,N−1)

σ√N − 1

), (20)

where μ is the sample mean, σ is the sample standarddeviation, N is the sample size, t−1

(·,N−1) is the inverse t-distribution with N − 1 degrees of freedom.

The ergodic capacity results show that the mobility hasa clear impact on the average MIMO system performance.Using dynamic rank adaptation (18) and feedback aboutthe channel state, the average spectral efficiencies of 3.4821bps/Hz, 3.0617 bps/Hz and 2.1069 bps/Hz are achieved forthe low, medium and high mobility cases, respectively. The

0 20 40 60 80 100 1201

2

3

4

5

6

7

8x 10

−14

speed (kmph)

syst

em le

vel m

obili

ty fa

ctor

Ns = 1

Ns = 2

Fig. 5. System level mobility factor (9). Speeds are 3, 30 and 120 km/h,number of streams Ns = 1, 2.

approximation for the ergodic capacity is equal to 3.4815bps/Hz, 3.0612 bps/Hz and 2.1063 bps/Hz for the speeds of 3,30 and 120 km/h. The confidence interval is very tight for allmobility cases with the width of 0.1% of the ergodic capacity.Hence, the proposed model (17) for ergodic capacity is veryaccurate.

The ergodic capacity results show, that in the high mobilityscenario considered here about 40% lower average spectralefficiency is achieved than in the low mobility scenario. Thesystem level mobility factor (9) plotted in Fig. 5 also confirmsthe degradation of the system performance.

The loss in the ergodic capacity happens due to the loss inthe mean value of the effective SINR. Since the dual streamtransmission takes place only about 10% of time, the lossin the mean value of the effective SINR for single streamtransmission mostly degrades the system performance. Themean value in the case of single stream transmission decreasesdramatically, e.g., at 120 km/h it is about 70% lower than at3 km/h. There are two major causes of the loss in the meanvalue. First, the most robust MCS is chosen by scheduler inthe high mobility scenario, i.e., 16QAM4/3 at 3 km/h andQPSK1/3 at 120 km/h. Second, lower post–processed sub-carrier SINRs are obtained in the high mobility scenario dueto outdated feedback that randomizes the precoding and thescheduling.

In other words, the change in the mobility scenario in-fluences the rank adaptation, link adaptation and schedulerbehavior and, consequently, the mean value of the effectiveSINR. As a result, the change in the mobility scenario in-fluences the whole system behavior that is reflected on theaverage MIMO OFDM system performance.

V. CONCLUSION

A model for the ergodic capacity based on the mean of theeffective SINR values is presented. The asymptotic distributionfor the effective SINR values is analytically derived in twocases, i.e., independent and m-dependent SINR generatingvalues. The simulations verify that the effective SINR mapped


from the independent SINRs is very accurately approximatedby normal distribution. The normal distribution approximationis slightly less accurate in cases where m-dependent SINRs aremapped to the effective SINR for a small dimensional MIMOOFDM system. As a result, a highly accurate approximation ofthe ergodic capacity is derived and validated by simulations.

The impact of mobility on ergodic system capacity isanalyzed for MIMO OFDM system in 3GPP LTE downlinkat different varying user mobility levels, i.e, at low, mediumand high speeds. The impact of mobility is studied by sim-ulations in realistic scenarios taking into account, e.g., theeffect of dynamic rank adaptation, link adaptation as wellas the scheduling of MIMO transmission. The simulationexperiments show about 70% drop in the mean value ofthe effective SINR in the high mobility scenarios caused bychosen robust MCS as well as outdated channel feedback. Thisdrop results in mobility factor decline and in the clear loss ofaverage spectral efficiency of MIMO OFDM system in thehigh mobility scenarios.

APPENDIX AMOMENTS CALCULATION FOR THE INDEPENDENT SINR

VALUES

Let us assume that all post-processed sub-carrier SINRvalues γn,k are independent and identically distributed. Thisassumption is not necessarily true in any practical frequencyselective channel. However, such an idealized channel modelallows evaluating the performance analytically and has beenused in several studies [29]–[31].

The first moment of e−γeffn

βn is given by

M1 := E(e−γeffn

βn ) = E

(1

K

K∑k=1

e−γn,kβn

)

= E(e−γn,kβn )

(14)= φγ

(− 1

βn

). (21)

The second moment can be derived as

M2 := E

(e−

2γeffn

βn

)= E

⎛⎝ 1

K2

{K∑

k=1

e−γn,kβn

}2⎞⎠

=1

K2E

(K∑

k=1

e−2γn,kβn + 2

K∑k=1

K∑l=k+1

e−γn,kβn

−γn,lβn

)

=E(e−

2γn,kβn )

K+

2

K2E2(e−

γn,kβn )

(K∑

k=1

K∑l=k+1

1

)

=E(e−

2γn,kβn )

K+

2

K2E2(e−

γn,kβn )

K2 −K

2

= E2(e−γn,kβn ) +

E(e−2γn,kβn )− E2(e−

γn,kβn )

K

−−−→K→∞

E2(e−γn,kβn )

(14)= φ2γ

(− 1

βn

).

The higher order moments Ms := E

(e−

sγeffn

βn

)of order s can

be found in the same manner using the multinomial theorem

and independence of the SINR values.

Ms = E

(1

Ks

{K∑

k=1

e−γn,kβn

}s)

=1

KsE

⎛⎝ ∑k1,k2,...,ks

s!

k1! · · · ks!e− k1γ1

βn···− ksγn,k

βn

⎞⎠=

s!

KsEs(e−

γn,kβn )

K∑k=1

K∑l=k+1

· · ·K∑

v=p+1︸︷︷︸s sums

1 +O(Ks−1)

Ks

=s!

KsEs(e−

γn,kβn )

K(K − 1) · · · (K − (s− 1))

s!+O(Ks−1)

Ks

−−−→K→∞

Es(e−γn,kβn )

(14)= φsγ

(− 1

βn

).

APPENDIX BMOMENTS CALCULATION FOR THE m-DEPENDENT SINR

VALUES

The first moment for the m-dependent SINR values remainsthe same as for the independent SINR values shown in(21), M1 = φγ

(− 1

βn

), since only the linear property of

expectation was used in the calculation. The expression for

the second moment, M2 := E

(e−

2γeffn

βn

), needs to be revised

as

M2 = E

⎛⎝ 1

K2

{K∑

k=1

e−γn,kβn

}2⎞⎠

=1

K2E

(K∑

k=1

e−2γn,kβn + 2

K∑k=1

K∑l=k+1

e−γn,kβn

− γn,lβn

)

=E(e−

2γn,kβn )

K+

2

K2E

(K∑

k=1

K∑l=k+1

e−γn,kβn

− γn,lβn

).

(22)

By definition, a sequence of random variables is said to be m-dependent, if any subset of (X1, X2, . . . , Xr) is independentof any other subset (Xv, Xv+1, . . . ) provided that v− r > m.

So, E(e−

γn,kβn

− γn,lβn

)= E

(e−

γn,kβn

)E(e−

γn,lβn

), if k − l >

m and in this case we can rewrite the expectation of doublesummation Es as

Es := E

(K∑

k=1

K∑l=k+1

e−γn,kβn

− γn,lβn

)

= E

(K∑

k=1

m+k∑l=k+1

e−γn,kβn

−γn,lβn

)+

+ E

(K∑

k=1

K∑l=m+k+1

e−γn,kβn

− γn,lβn

)

= E

(K∑

k=1

m+k∑l=k+1

e−γn,kβn

−γn,lβn

)+

+ E2(e−

γn,kβn

)( K∑k=1

K∑l=m+k+1

1

)


= E

(K∑

k=1

m+k∑l=k+1

e−γn,kβn

− γn,lβn

)+

+ E2(e−

γn,kβn

) (K2 − 2Km−K)

2.

Thus, the second moment (22) can be found as

M2 =E(e−

2γn,kβn )

K+

2

K2E

(K∑

k=1

m+K∑l=k+1

e−γn,kβn

−γn,lβn

)+

+ E2(e−

γn,kβn

)(1− 2m+ 1

K

)m�K−−−−→K→∞

E2(e−γn,kβn )

(14)= φ2γ

(− 1

βn

).

The higher order moments of order s can be established inthe same manner as

Ms = E

(1

Ks

{K∑

k=1

e−γn,kβn

}s)

=s!

KsEs(e−

γn,kβn )

K∑k=1

K∑l=m+k+1

· · ·K∑

v=m+p+1︸︷︷︸s sums

1 +O(Ks−1)

Ks

m�K−−−−→K→∞

Es(e−γn,kβn )

(14)= φsγ

(− 1

βn

).

APPENDIX CLIMITS FOR NUMBER OF QUALITY MEASURES IN THE

EFFECTIVE SINR AND VALUE m

For every real number ε > 0, there exists a natural numberK0 depending on the chosen ε and order of the moments, K0 = K0(ε, s), such that for any K > K0 holds∣∣∣Ms − φsγ

(− 1

βn

)∣∣∣ < ε by definition of the limit. So, thenumber K0 can be found as∣∣∣∣ s!Ks

0

Es(e−γn,kβn )

∏sl=1(K0 − (s− l))

s!− Es(e−

γn,kβn )

∣∣∣∣ < ε,∣∣∣∣K0(K0 − 1) · · · (K0 − (s− 1))

Ks0

− 1

∣∣∣∣ < ε,

1− ε <

(1− 1

K0

)(1− 2

K0

)· · ·(1− s− 1

K0

)< 1 + ε.

Since for any ε > 0 holds(1− s− 1

K0

)s−1

<

(1− 1

K0

)· · ·(1− s− 1

K0

)< 1 + ε,

K0 should be found as

1− ε <

(1− s− 1

K0

)s−1

=⇒ K0 >s− 1

1− s−1√1− ε

. (23)

For each moment of order s exists such a natural num-ber m0 = m0(s, ε,K0) that for any m < m0 holds∣∣∣Ms − φsγ

(− 1

βn

)∣∣∣ < ε in the m-dependent SINR case.This number m0 can be found from cm0

K0< ε, where the

constant c is the coefficient for the mKs−1 term in the sum

1s!

K∑k=1

K∑l=m+k+1

· · ·K∑

v=m+p+1︸︷︷︸s sums

1.

ACKNOWLEDGMENT

The authors would like to thank Dr. Andreas Richter forfruitful discussions.

REFERENCES

[1] J. Wigard and P. Mogensen, “A simple mapping from C/I to FER andBER for a GSM type of air interface,” in Proc. 1996 IEEE PIMRC, pp.78–82.

[2] E. Malkamaki, F. de Ryck, and C. Mourot, “A method for combiningradio link simulations and system simulations for a slow frequencyhopped cellular system,” in Proc. 1994 IEEE VTC – Spring, pp. 1145–1149.

[3] I. Telatar, “Capacity of multi–antenna Gaussian channels,” EuropeanTrans. Telecommun., vol. 10, no. 6, pp. 585–595, Dec. 1999.

[4] N. Wei, T. Sørensen, P. Mogensen, and T. Kolding, “Analysis andevaluation of link adaptation including MIMO adaptation,” in Proc. 2006IEEE VTC – Fall, pp. 1–5.

[5] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channelswith partial side information,” IEEE Trans. Inf. Theory, vol. 51, no. 2,pp. 506–522, Feb. 2005.

[6] P. Mogensen, N. Wei, I. Kovacs, F. Frederiksen, A. Pokhariyal, K. Ped-ersen, T. Kolding, K. Hugl, and M. Kuusela, “LTE capacity compared tothe Shannon Bound,” in Proc. 2007 IEEE VTC – Spring, pp. 1234–1238.

[7] H.-L. Maattanen, O. Tirkkonen, and K. Hugl, “Orthogonalizing trans-mission in MIMO with linear receiver and finite MCS set,” in Proc.2008 IEEE WCNC, pp. 522–527.

[8] H. Holma and A. Toskala, LTE for UMTS – OFDMA and SC-FDMABased Radio Access. John Wiley & Sons, Ltd., 2009.

[9] P. Kela, J. Puttonen, N. Kolehmainen, T. Ristaniemi, T. Henttonen, andM. Moisio, “Dynamic packet scheduling performance in UTRA LongTerm Evolution downlink,” in Proc. 2008 ISWPC, pp. 308–313.

[10] 3GPP, “Evolved universal terrestrial radio access (E-UTRA); physicalchannels and modulation,” 3G Partnership Project, Tech. Rep. TS 36.211TSG RAN, Sep. 2007, rel. 8.

[11] M. Ahmed, A. Alexiou, F. Kharrat, M. Lamarca, R. Pintenet, F. Rey,J. Sala, and D. Samardzija, “MTMR baseband transceivers needsfor intra–system and inter–system (UMTS/WLAN) reconfigurability,”Information Society Technologies FITNESS Project, Tech. Rep. IST-2000-30116 FITNESS Project, Aug. 2007, d3.3.1.

[12] G. Foschini, D. Chizhik, C. Papadias, and R. Valenzuela, “Analysis andperformance of some basic space–time architectures,” IEEE J. Sel. AreasCommun., vol. 21, no. 3, pp. 303–320, Apr. 2003.

[13] K. Brueninghaus, D. Astely, T. Salzer, S. Visuri, A. Alexiou, S. Karger,and G. Seraji, “Link performance models for system level simulations ofbroadband radio access systems,” in Proc. 2005 IEEE PIMRC, vol. 4,,pp. 2306–2311.

[14] X. He, K. Niu, Z. He, and J. Lin, “Link layer abstraction in MIMO-OFDM system,” in Proc. 2007 IEEE IWCLD, pp. 1–5.

[15] R. Sandanalakshmi, T. Palanivelu, and K. Manivannan, “Effective SNRmapping for link error prediction in OFDM based systems,” in Proc.2007 ICTES, pp. 684–687.

[16] F. Cavalcanti and S. Andersson, Optimizing Wireless CommunicationSystems. Springer, 2009.

[17] S. Tsai and A. Soong, “Effective SINR mapping for modeling frameerror rates in multiple–state channels,” 3G Partnership Project, Tech.Rep. 3GPP2-C30-20030429-010, Apr. 2003.

[18] 3GPP, “Feasibility study for orthogonal frequency division multiplexing(OFDM) for UTRAN enhancement,” 3G Partnership Project, Tech. Rep.TR 25.892 TSG RAN, June 2004, rel. 2.

[19] J. Ikuno, M. Wrulich, and M. Rupp, “System level simulation of LTEnetworks,” in Proc. 2010 IEEE VTC – Spring, pp. 1–5.

[20] M. Rupp, S. Caban, C. Mehlfuhrer, and M. Wrulich, Evaluation ofHSDPA and LTE: From Testbed Measurements to System Level Per-formance. Wiley, 2011.

[21] J. Winters, “Optimum combining in digital mobile radio with co–channelinterference,” IEEE J. Sel. Areas Commun., vol. 2, pp. 528–539, July1984.

[22] P. Li, D. Paul, R. Narasimhan, and J. Cioffi, “On the distribution ofSINR for the MMSE MIMO receiver and performance analysis,” IEEETrans. Inf. Theory, vol. 52, no. 1, pp. 271–286, Jan. 2006.


[23] 3GPP, “Physical layer aspects for evolved UTRA,” 3G PartnershipProject, Tech. Rep. TR 25.814 TSG RAN, Sep. 2006, rel. 7.

[24] ETSI, “Universal mobile telecommunications system (UMTS) - selec-tion procedures for the choice of radio transmission technologies of theUMTS,” European Telecommunications Standards Institute, Tech. Rep.TR 101 112, Apr. 1998, v3.2.0.

[25] A. Oborina, M. Moisio, T. Henttonen, E. Pernila, and V. Koivunen,“MIMO performance evaluation in UTRAN Long Term Evolution,” inProc. 2008 CISS, pp. 1179–1183.

[26] I. Kovacs, M. Kuusela, E. Virtej, and K. Pedersen, “Performance ofMIMO aware RRM in downlink OFDMA,” in Proc. 2008 IEEE VTC –Spring, pp. 1171–1175.

[27] N. Kolehmainen, J. Puttonen, P. Kela, T. Ristaniemi, T. Henttonen, andM. Moisio, “Channel quality indication reporting schemes for UTRANLong Term Evolution downlink,” in Proc. 2008 IEEE VTC – Spring,pp. 2522–2526.

[28] H. Stark and J. Woods, Probability and Random Processes with Appli-cations to Signal Processing. Prentice Hall, 2002.

[29] S. Sanayei and A. Nosratinia, “Opportunistic downlink transmissionwith limited feedback,” IEEE Trans. Inf. Theory, vol. 53, no. 11, pp.4363–4372, Nov. 2007.

[30] A. Kuhne and A. Klein, “Throughput analysis of multi–user OFDMA–systems using imperfect CQI feedback and diversity techniques,” IEEEJ. Sel. Areas Commun., vol. 26, no. 8, pp. 1440–1450, Oct. 2008.

[31] R. Agarwal, V. Majjigi, Z. Han, R. Vannithamby, and J. Cioffi, “Lowcomplexity resource allocation with opportunistic feedback over down-link OFDMA networks,” IEEE J. Sel. Areas Commun., vol. 26, no. 8,pp. 1462–1472, Oct. 2008.

Alexandra Oborina received the M.Sc. degreewith distinction in applied mathematics from Saint-Petersburg State University, Russia, in 2003, and theM.Sc. degree with distinction in computer sciencefrom University of Joensuu, Finland, in 2005. Since2006, she has been working towards Ph.D. degreeat Aalto University School of Electrical Engineering(formerly known as Helsinki University of Tech-nology). Her research interests are in the areasof statistical signal processing and future wirelessnetworks system performance.

Martti Moisio received his M.Sc. degree in physicsfrom University of Helsinki in 1995. He has co-authored over 25 conference or journal papers andseveral book chapters in the area of wireless com-munications and has received two excellent paperawards. His research interests include especiallywireless and cellular system performance and sim-ulations. Currently he is Principal Researcher withNokia Research Center, Helsinki, Finland.

Visa Koivunen (IEEE Fellow) received the D.Sc.(EE) degree (with honors) from the Department ofElectrical Engineering, University of Oulu, Finland.From 1992 to 1995, he was a visiting researcher atthe University of Pennsylvania, Philadelphia. Since1999, he has been a Professor of Signal Processingat Aalto University (formerly known as HelsinkiUniversity of Technology), Finland. Since 2009 hehas been Academy professor at Aalto University. Heis one of the Principal Investigators in the SMARAD(Smart Radios and Wireless Systems) Center of

Excellence nominated by the Academy of Finland. He was also AdjunctFull Professor at the University of Pennsylvania, Philadelphia. During hissabbatical leave in 2006-2007, he was a Visiting Fellow at Nokia ResearchCenter, as well as Princeton University. He makes frequent research visits toPrinceton University.

His research interests include statistical, communications, and sensor arraysignal processing. He has published more than 350 papers in internationalscientific conferences and journals. Dr. Koivunen received the Primus Doctor(best graduate) Award among the doctoral graduates in the years 1989 to1994. He is a member of Eta Kappa Nu. He co-authored the papers receivingthe Best Paper Award in IEEE PIMRC 2005, EUSIPCO 2006, and EuCAP2006. He has been awarded the IEEE Signal Processing Society Best PaperAward for 2007 (co-authored with J. Eriksson). He is a member of the editorialboard for the IEEE Signal Processing Magazine. He is also a member of theIEEE Sensor Array Multichannel Signal Processing Technical Committee. Heis also serving at the industrial relations board of the IEEE SP society. Hewas the general chair of the IEEE SPAWC (Signal Processing Advances inWireless Communication) 2007 conference in Helsinki, June 2007.

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