research article performance analysis of a two-hop mimo...

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 935609 10 pageshttpdxdoiorg1011552013935609

Research ArticlePerformance Analysis of a Two-Hop MIMOMobile-to-Mobile via Stratospheric-Relay LinkEmploying Hierarchical Modulation

Nikolaos Nomikos1 Emmanouel T Michailidis2

Demosthenes Vouyioukas1 and Athanasios G Kanatas2

1 Department of Information and Communication Systems Engineering University of the Aegean 83200 Karlovassi Samos Greece2 Department of Digital Systems University of Piraeus 80 Karaoli amp Dimitriou Street 18534 Piraeus Greece

Correspondence should be addressed to Demosthenes Vouyioukas dvouyiouaegeangr

Received 12 March 2013 Revised 21 May 2013 Accepted 27 May 2013

Academic Editor Fernando Perez Fontan

Copyright copy 2013 Nikolaos Nomikos 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

Next generation wireless communication networks intend to take advantage of the integration of terrestrial and aerospaceinfrastructures Besides multiple-inputmultiple-output (MIMO) architecture is the key technology which has brought the wirelessgigabit vision closer to reality In this direction high-altitude platforms (HAPs) could act as relay stations in the stratospheretransferring information from an uplink to a downlink MIMO channel This paper investigates the performance of a noveltransmission scheme for the delivery of mobile-to-mobile (M-to-M) services via a stratospheric relay It is assumed that thesource relay and destination nodes are equipped with multiple antennas and that amplify-and-forward (AF) relaying is adoptedThe performance is analyzed through rigorous simulations in terms of the bit-error rate (BER) by using a recently proposed 3Dgeometry-based reference model in spatially correlated flat-fading MIMO channels employing a hierarchical broadcast techniqueand minimum mean square error (MMSE) receivers

1 Introduction

Mobile-to-mobile (M-to-M) communications are expectedto be a fundamental component of future mobile ad hocnetworks intelligent highway vehicular systems (IHVS)broadband mobile multimedia services and relay-based cel-lular networks Although the radio links of M-to-M systemsare usually dominated by harsh multipath fading effectsapplying cooperative diversity techniques by utilizing singleormultiple intermediate relays (119877) between a source (119878) and adestination (119863) can preserve the end-to-end communication[1ndash3] As the evolution of next-generation networks (NGN)promises the integration of heterogeneous wireless terrestrialand aerospace technologies [4ndash6] employing quasistationaryhigh altitude platforms (HAPs) [7] as radio-relay nodes inthe stratosphere is a potential and attractive solution for theinterconnection of existing infrastructures [8ndash10] Previouswork on relaying through HAPs considered a multitude of

scenarios such as the provision of surveillance monitoringmaritime and third-generation (3G) cellular servicesline-break [10ndash14]

To provide appreciable diversity and spatial multiplex-ing gains over multipath environments the applicationof multiple-input multiple-output (MIMO) technology andspace-time coding schemes is suggested in current andfuture wireless standards [15 16] Nevertheless the successfuldesign and deployment of MIMO M-to-M via stratosphericrelay (MMSR) systems require a detailed knowledge of theunderlying radio channel and the mechanisms of radiowave propagation Using this knowledge communicationsystems can be constructed to obtain optimal or near optimalperformance Notwithstanding the MIMO benefits maynot be attained in practice due to the channel specificity[17] for example system geometry fading type correlationat the transmit andor receive antennas and transceiverimpairments In addition the adaptation of themodulation at

2 International Journal of Antennas and Propagation

the transmitter side according to the channel characteristicsallows the reduction of the transmission power andor theenhancement of the data rates [18] Besides adaptive usage ofthe resources offered by the various modulation and codingschemes is mandatory for a systemrsquos efficiency and economyTherefore using detectors the effect of fading and correlationcan be overcome [19] while taking advantage of the adaptivetechniques thus leading to adaptive operation of the receiverwithout any control commands

In this paper the performance analysis of a MIMOMMSR system is analyzed through simulations in terms ofbit-error-rate (BER) so as to estimate the complementary roleofHAPs in conjunctionwith terrestrial networks and reap thebenefits of MIMOMMSR communications It is well knownthat spatial multiplexing systems that employ linear receiverschemes either zero-forcing (ZF) or minimum mean squareerror (MMSE) are practically important because of theirminimal complexity requirements [20 21]This paper focuseson the performance of MMSE detectors at the receivers overspatially correlated double-Rician flat-fading MIMO MMSRchannels since these receivers offer better performance thanZF receivers and avoid the noise-enhancement effect It isconsidered that hierarchically modulated symbols [22] aretransmitted in each time slot through the stratospheric relayin order to distinguish receivers and offer upgraded servicequality to those with better reception conditions as well asbackward compatibility

Since impairments of the signal are mainly caused by theenvironment near the user the starting point of the perfor-mance evaluation is a recently proposed three-dimensional(3D) reference geometry-based model for MIMO MMSRchannels in dual-hop amplify-and-forward (AF) networks[23] This model enables a realistic positioning of the scat-terers in the vicinity of the source and the destination andassumes that these scatterers are nonuniformly distributedwithin two cylinders which reflect the influence of twoheterogeneous 3D nonisotropic scattering environmentsThecommunication between the source and the destination isonly feasible through a relay due to high attenuation in thepropagation medium While the utilized carrier frequenciesare below 10GHz both line-of-sight (LoS) and non-line-of-sight (NLoS) propagation conditions may exist in thetransmission links from the source to the destination via thestratospheric relay whereas rain effects are insignificant

The remainder of this paper is organized as followsSection 2 outlines the MIMO MMSR system model andthe modulation techniques employed Section 3 presents theMIMO MMSR channel model and analyzes the propagationcharacteristics The performance analysis along with thecorresponding results is presented in Section 4 Finally con-clusions and future research directions are given in Section 5

2 System Model

The system model employed throughout this chapter con-siders a narrowband MIMO MMSR fading channel with 119871

119878

antenna elements at a terrestrial source mobile station 119871119877

antenna elements at a half-duplex stratospheric relay station

Low priority (LP) bit

High priority (HP) bit

Figure 1 Hierarchical modulation of order 416QAM

free of local scattering supporting a two-hop communicationand 119871

119863antenna elements at a terrestrial destination mobile

station All antennas are omnidirectional and are numberedas 1 le 119901 le 1199011015840 le 119871

119878 1 le 119902 le 1199021015840 le 119871

119877 and 1 le 119897 le

1198971015840le 119871119863 respectively The source and destination arrays are

equipped with low-elevation antennas while the relay flies ata height ℎ

119877asymp 20 km above the ground The relatively short

endurance due to fuel constraints and human factors limitsthe deployment of mannedHAPs as relay nodesTherefore itis assumed that the relay is a solar-powered unmanned quasi-stationary airship

Let us consider that the destination receives data fromthe source only through the relay since the direct source-destination transmission link is totally obstructed Thus thecommunication takes place in two time slots The relayreceives the source signal in each time slot and sends it tothe destination through an AF process In each transmissionthe source employs hierarchical modulation with two pri-ority streams where the high-priority (HP) robust symbolsare QPSK modulated while the low-priority (LP) symbolsare 16QAM modulated The constellation diagram of the416QAM hierarchically modulated symbols is illustrated inFigure 1 where the bits corresponding to each priority streamare distinguished Each time slot is divided in 119873 symbolperiods where 119873 is the size in symbols of each transmittedsource signal vector These streams are fed to the sourceand after the two-hop transmission the destination will tryto decode either the LP stream if channel conditions arefavorable or the HP which is more robust to bad link quality

Assuming frequency-flat fading channels and constantchannel coefficients for duration equal to119873 symbol periodsthat is one time slot in the source-relay (119878-119877) and relay-destination (119877-119863) links the signal received at the relay is

y119877= H119878119877x + n119877 (1)

International Journal of Antennas and Propagation 3

where y119877isin C119871119877times119873 H

119878119877isin C119871119877times119871119878 are the complex channel

coefficients in the 119878-119877 link x isin C119871119878times119873 is the transmittedsource signal vector and n119877 isin C119871119877times119873 sim 119862N(0 I119871119877) isthe additive white Gaussian noise (AWGN) at the relaywith I119871119877the identity matrix of size 119871119877 times 119871119877 The relayamplifies y119877 with a factor 119860 thus the received signal vectorat the destination in the second time slot is

y119863= H119877119863119860y119877+ n119863= H119877119863119860 (H119878119877x + n119877) + n119863

= H119877119863119860H119878119877x +H119877119863119860n119877 + n119863(2)

where y119863 isin C119871119863times119873 H119877119863 isin C119871119863times119871119877 are the complex channelcoefficients in the 119877-119863 link and n

119863isin C119871119863times119873 sim 119862N(0 I

119871119863) is

the AWGN at the destination with I119871119863

the identity matrix ofsize 119871

119863times 119871119863 At the destination the reception is based on

minimum mean square error (MMSE) equalization whichuses the knowledge of the noise variance in order tomaximizethe signal-to-interference-plus-noise ratio (SINR) Retrievalof the source signal is based on matrix WMMSE which isdenoted as

WMMSE = (H119867H + 1205902

119908I119871119878)minus1

H119867 (3)

where (sdot)119867 denotes the Hermitian matrixH = H119877119863119860H119878119877

isthe end-to-end 119878-119877-119863 channel matrix [24] and 1205902

119908is the

variance of the total noise n119882= H119877119863119860n119877+ n119863which

contains both the amplified version of noise n119877and the noise

at the destination n119863 The 119894th row of WMMSE is derived by

solving the optimization equation

119908119894MMSE = argmax

119908=(1199081 119908119871119878)

1003816100381610038161003816wh1198941003816100381610038161003816

2119864119909

119864119909sum119871119878

119895=1119895 = 119894

10038161003816100381610038161003816wh119895

10038161003816100381610038161003816

2

+ w21205902119908

(4)

where sdot stands for the Euclidean norm of a vector h119894is the

119894th column of the channel matrix H and 119864119909is the power of

the source signal The output of the MMSE equalizer will be

x =WMMSEy = x + (H119867H + 1205902119908I119871119878)minus1

H119867n119908 (5)

Since H = H119877119863119860H119878119877 one can first derive the matrices

H119878119877 andH119877119863 and then derive the matrixH The 119878-119877MIMOchannel is Rician in general Hence H119878119877 can be modeled as[15]

H119878119877= radic

119870119878119877

119870119878119877 + 1H119878119877LoS + radic

1

119870119878119877 + 1H119878119877NLoS (6)

where H119878119877LoS is the matrix containing the free-space(LoS) responses between all source-relay elementsH119878119877NLoS accounts for the scattered (NLoS) signals and119870119878119877 is the Rician factor The elements of H119878119877LoS aredeterministic and can be directly obtained using thereference model in [23] while the matrix H

119878119877NLoS can beevaluated as follows [25]

vec (H119878119877NLoS) = R12

119878119877NLoS vec (H119908) (7)

where R119878119877NLoS is the 119871

119877119871119878times 119871119877119871119878correlation matrix asso-

ciated with the NLoS component of the 119878-119877 MIMO sub-system R12

119878119877NLoS is the square root of R119878119877NLoS that satisfies

R12119878119877NLoSR

1198672

119878119877NLoS = R119878119877NLoSH119908 is a 119871

119877times 119871119878stochastic

matrix with independent and identically distributed (iid)zero mean complex Gaussian entries and vec(sdot) denotesmatrix vectorization (The vectorization of a matrix is a lineartransformation which converts the matrix into a columnvector Specifically the vectorization of a 119898 times 119899 matrix 119860denoted by vec(119860) is the 119898119899 times 1 column vector obtained bystacking the columns of the matrix119860 on top of one another)Since H119908 is stochastic H

119878119877NLoS varies for each simulationtrial and converges to the desired one in the statistical sensethat is when averaged over a sufficiently large number ofsimulation trials Note that H119877119863 can be derived by followinga similar procedure to that used to deriveH119878119877

3 Propagation Characteristics and ChannelModeling

In this section the 3D model for MIMO MMSR channelsproposed in [23] is described and the corresponding propaga-tion characteristics are underlined Based on this model theMIMO channel matrix of the 119878-119877-119863 system can be achievedand then the performance investigation of theMIMOMMSRsystem can be accomplished

It is considered that the source and the destination arelocated within two separate cylindrical regions of scatteringelements Specifically the scatterers in the vicinity of thesource and the destination are nonuniformly distributedwithin two cylinders which reflect the influence of twoheterogeneous 3D scattering environments The radius ofcylinder 1 (2) corresponds to the maximum distance betweenthe source (destination) and an effective scatterer in theazimuth domain while the maximum scatterer height cor-responds to the height of cylinder 1 (2) The waves emittedfrom the source (relay) antennas travel over paths of differentlengths and impinge the relay (destination) antennas fromdifferent directions due to the 3D non-isotropic scatteringconditions within cylinder 1 (2)

The geometrical characteristics of this model are dis-cussed in Figures 2 and 3 Figure 2 presents the LoS pathsof the 3D model for a 2 times 2 times 2 MIMO MMSR channelOne observes that the location of the relay seen from thesource (destination) can be specified by the azimuth angle120596119878(120596119863) and the elevation angle 120573

119878(120573119863) relative to the 119909119910

plane The antenna interelement distance at the source relayand destination is denoted by 120575

119878120575119877 and 120575

119863 respectively In

addition the orientation of the antenna arrays at the sourcerelay and destination is described by the angles 120579

119878 120579119877 and

120579119863 respectively while 120595

119878and 120595

119863denote the elevation angle

of the 119901th source and the 119897th destination antenna elementFigure 3 presents the single-bounce NLoS paths for

the channel in Figure 2 It is assumed that 119872 rarr

infin (119873 rarr infin) scatterers are situated within a cylinder ofradius 119877119878max(119877119863max) and height 119867119878max(119867119863max) around thesource (destination) Let 119878(119898)

119878(119878(119899)

119863) be the119898th (119899th) scatterer

in the vicinity of the source (destination)The radial distance


Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

p120595S

120573S

120587 minus 120579S120596S

p998400

q998400

120579R

120595D120573D

120587 minus 120596D

120579D

RSmax

HSmax

RDmax

HDmax

l998400

Figure 2 LoS paths of the 3D model for a 2 times 2 times 2MIMOMMSRchannel

Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

RSmax

HSmax p

120595S

a(m)S

120587 minus 120579S

R(m)S

H(n)D

S(n)D

R(n)D

120587 minus a(n)Dp998400

q998400

120579R

RDmax

HDmax120595D

120579Dl998400

S(m)S

H(m)S

Figure 3 NLoS paths of the 3Dmodel for a 2times2times2MIMOMMSRchannel

of 119878(119898)119878(119878(119899)

119863) from the axis of the cylinder around the source

(destination) is denoted by 119877(119898)119878(119877(119899)

119863) and119867(119898)

119878(119867(119899)

119863) stands

for its height Furthermore 119886(119898)119878

is the azimuth angle ofdeparture (AAoD) of the transmitted waves from the sourceto 119878(119898)119878

and 119886(119899)119863

is the azimuth angle of arrival (AAoA) of thewaves scattered from 119878(119899)

119863and received at the destination It is

assumed that 119886(119898)119878

119886(119899)119863 119877(119898)119878

119877(119899)119863119867(119898)119878

and119867(119899)119863

are randomvariables and mutually independent

The LoS component ℎ119878119877LoS119901119902

= [H119878119877LoS]119902119901 of the impulse

response for the transmission link from the 119901th sourceantenna element to the qth relay antenna element (119878-119877subsystem) can be approximated as [23]

ℎ119878119877-LoS119901119902

= 120577119878119877119887(119901)

119878119887(119902)

119878119877 (8)

where

120577119878119877= exp(minus1198952120587

120582

ℎ119877

sin120573119878

) (9)

119887(119901)

119878= exp[119895

(3 minus 2119901) 120587120575119878 cos120595119878 cos (120579119878 minus 120596119878)120582 cos120573

119878

] (10)

119887(119902)

119878119877= exp[minus119895

(3 minus 2119902) 120587120575119877 cos (120579119877 minus 120596119878)120582 cos120573

119878

] (11)

1198952= minus1 and 120582 is the carrierwavelengthThen using (8)ndash(11)

the deterministic elements ofH119878119877LoS can be obtained as

H119878119877LoS =[[[

[

ℎ119878119877-LoS11

ℎ119878119877-LoS1119871119879

d

ℎ119878119877-LoS1198711198771

sdot sdot sdot ℎ119878119877-LoS119871119877119871119879

]]]

]

(12)

TheMIMOchannelmatrixH119877119863LoS can be defined in a similar

way as inH119878119877LoS by replacing the index 119878 by119863

The reference model assumes that the number of scatter-ers within cylinder 1 is infinite Thus the discrete randomvariables 119886(119898)

119878 119877(119898)119878

and 119867(119898)119878

can be replaced with contin-uous random variables 119886

119878 119877119878 and 119867

119878with joint probability

density function (pdf) 119891(119886119878 119877119878 119867119878) Since 119886(119898)

119878 119877(119898)119878

and119867(119898)

119878are independent the joint pdf 119891(119886

119878 119877119878 119867119878) can be

decomposed to the product 119891(119886119878)119891(119877119878)119891(119867119878)

The vonMises pdf [26] (also known as the circular normaldistribution) is used to characterize the AAoD 119886

119878and is

defined as

119891 (119886119878) =

exp [119896119878cos (119886

119878minus 120583119878)]

21205871198680(119896119878)

minus120587 le 119886119878le 120587 (13)

where 1198680(sdot) is the zeroth-order modified Bessel function of

the first kind 120583119878is the mean angle at which the scatterers

within cylinder 1 are distributed in the 119909-119910 plane and 119896119878ge 0

controls the spread around the mean This pdf is empiricallyjustified in urban and suburban areas in [27] Based on theexperimental results in [28 29] the hyperbolic pdf [30] isused to characterize 119877

119878and is defined as

119891 (119877119878) =119906119878

tanh (119906119878119877119878max) cosh

2(119906119878119877119878) 0 lt 119877

119878 le 119877119878max

(14)

The parameter 119906119878controls the spread (standard deviation)

of the scatterers around the source and its applicable valueis in the interval (0 1) Decreasing 119906

119878increases the spread

of the pdf of 119877119878 Finally the log-normal pdf [31] is used to

characterize119867119878and is defined as

119891 (119867119878) =

exp [minus[ln (119867119878) minus ln (119867

119878mean)]2 (2120590119878

2)]

119867119878120590119878radic2120587

(15)

where the parameters 119867119878mean and 120590

119878are the mean and

standard deviation of 119867119878 This pdf matched geographical

data values obtained from measurements of building heightsconducted in different areas [32 33]


Using (13)ndash(15) and after extensive calculation the nor-malized NLoS component of the spatial correlation function(SCF) of the 119878-119877 subsystem is approximated as follows [23]

119877119878119877-NLoS11990111990211990110158401199021015840 (120575119878 120575119877)

=

Ε [ℎ119878119877-NLoS119901119902

ℎ119878119877-NLoSlowast11990110158401199021015840 ]

radic119864 [10038161003816100381610038161003816ℎ119878119877-NLoS119901119902

10038161003816100381610038161003816

2

] 119864 [100381610038161003816100381610038161003816ℎ119878119877-NLoS11990110158401199021015840

100381610038161003816100381610038161003816

2

]

= 1199011198781198771 int

119867119878max

0

int

119877119878max

0

11990111987811987721198680(radic1199012

1198781198773+ 1199012

1198781198774) 119889119877119878119889119867119878

(16)

where ℎ119878119877-NLoS119901119902

is the NLoS component of the impulseresponse for the transmission link from the 119901th sourceantenna element to the 119902th relay antenna element (119878-119877MIMO subsystem) (sdot)lowast denotes complex conjugate opera-tion

1199011198781198771

=119906119878119887(119902)

119878119877119887(1199021015840)lowast

119878119877

120590119878radic2120587 tanh (119906

119878119877119878max) 1198680 (119896119878)

1199011198781198772

=

exp [minus[ln (119867119878)minusln (119867

119878mean)]2 (2120590119878

2)]

119867119878cosh2 (119906

119878119877119878)

times exp1198952120587120582(1199011015840minus 119901) 120575119878 sin120595119878

times sin [arctan(119867119878

119877119878

)]

1199011198781198773

= 1198952120587

120582 (1199011015840minus119901) 120575

119878sin 120579119878cos120595119878

times cos [arctan(119867119878

119877119878

)]

+ 1198952120587

120582[

(1199021015840minus119902) 120575119877119877119878sin120573119878cos120596119878sin (120579119877minus120596119878)

ℎ119877cos2120573

119878

]

+ 119896119878 sin 120583119878

1199011198781198774

= 1198952120587

120582 (1199011015840minus119901) 120575

119878cos 120579119878cos120595119878


119877119878

)]

minus 1198952120587

120582[

(1199021015840minus119902) 120575119877119877119878sin120573119878sin120596119878sin (120579119877minus120596119878)

ℎ119877cos2120573

119878

]

+ 119896119878cos 120583119878

(17)

The double integral in (16) has to be numerically evaluatedsince there is no closed-form solutionThe elements of corre-lation matrix R

119878119877NLoS associated with the NLoS componentof the 119878-119877MIMO subsystem can be obtained using (16)ndash(20)as

R119878119877NLoS =

[[[[[[[

[

119877119878119877-NLoS1111

119877119878119877-NLoS1121

sdot sdot sdot 119877119878119877-NLoS11119871119877119871119879

119877119878119877-NLoS2111

d 119877119878119877-NLoS21119871119877119871119879

d

119877119878119877-NLoS11987111987711987111987911


]]]]]]]

]

(18)

Since the number of scatterers within cylinder 2 is alsoinfinite the correlation matrix R

119877119863NLoS associated with theNLoS component of the 119877-119863 MIMO can be derived byfollowing a similar procedure to that used to derive R

119878119877NLoS

4 Results and Discussion

In this section the previously described theoretical deriva-tions are demonstrated and the performance of a MIMOMMSR network over spatially correlated fading channels andMMSE receivers is studied in terms of BER for differentsystem parameters and channel conditions Unless indicatedotherwise the values of the model parameters used aredepicted in Table 1 Note that we consider a typical denselybuilt-up district (London [31]) to be the scattering regionthat is the surrounding buildings act as scatterers and weset 119867119878mean = 119867119863mean = 176m and 120590119878 = 120590119863 =

031 We also assume that 119906119878= 119906119863= 001 As shown

in Figure 4 this value corresponds to a reasonable averagedistance between the source (destination) and an effectivescatterer of approximately 60mTheuplink (119878-119877 link) and thedownlink (119877-119863 link) may experience either symmetric thatis double-Rayleigh (RayleighRayleigh) or double-Rician(RicianRician) or asymmetric [34] that is RayleighRicianor RicianRayleigh fading phenomena depending on thestrength of the LoS component To clearly present theinfluence of the spatial correlation on the BER we set theRician factor of the 119878-119877 and 119877-119863 subsystems equal to zerothat is 119870

119878119877= 119870119878119877= 0 (double-Rayleigh channel) Each

transmitted frame is hierarchically modulated using QPSKfor the high-priority (HP) stream and 16QAM for the low-priority (LP) stream Furthermore each frame is furtherdivided into 100 symbols which are 416 hierarchicallymodulated and the channel is considered static during oneframe period Receivers with good reception conditions candecode successfully all 4 bits of each symbol while receiverswith bad conditions can decode only the high priority streamwhich consists of the two first bits of each symbol

The degree of spatial correlation is a complicated functionof the degree of scattering in a specific propagation environ-ment and the antenna inter-element spacing at the sourcerelay and destination Figure 5 examines the effect of theRician factor on the BER performance One observes that byincreasing the Rician factors 119870

119878119877(119878-119877 subsystem) and 119870

119877119863

(119877-119863 subsystem) there is a substantial degradation in BERfor both streams This is explained by the high correlation


Table 1 System parameters used in the performance evaluation

Wireless network Two-hop AF MMSR

Transmission mode MIMO with two antennas at each node119871119878= 119871119877= 119871119863= 2

Frame size (119873) 100 symbolsModulation Hierarchical 416QAMChannel model 3D geometry-based MIMOMMSR [23]Channel conditions Static for one frame periodOperating carrier frequency 119891 = 2GHzCarrier wavelength 120582 = 015mRician factor of the S-R and R-D subsystems respectively 119870SR = 0119870RD = 0 (Double-Rayleigh)Height of the relay antennas ℎ

119877= 20 km

Azimuth angle of the relay with respect to the source and destinationrespectively 120596

119878= 1205874 120596

119863= 31205874

Elevation angle of the relay with respect to the source and destinationrespectively 120573

119878= 1205873 120573

119863= 1205873

Antenna spacing at the source relay and destination respectively 120575119878= 120582 120575

119877= 200120582 120575

119863= 120582

Orientation of antenna arrays at the source relay and destinationrespectively 120579

119878= 1205872 120579

119877= 1205872 120579

119863= 1205872

Εlevation angle of the 119901th source and the 119897th destination antennaelement respectively 120595

119878= 12058718 120595

119863= 12058718

The radius of cylinders 1 and 2 respectively 119877119878max = 180m 119877

119863max = 180mThe height of cylinders 1 and 2 respectively 119867

119878max = 70m119867119863max = 70m

The spread of the scatterers within cylinders 1 and 2 respectivelyaround the mean azimuth angle 119896

119878= 5 119896

119863= 5

Mean azimuth angle at which the scatterers are distributed withincylinders 1 and 2 respectively 120583

119878= 1205876 120583

119863= 1205876

The spread of scatterers around the source and destinationrespectively 119906

119878= 001 119906

119863= 001

Mean height of the scatterers within cylinders 1 and 2 respectively 119867119878mean = 176m119867

119863mean = 176mStandard deviation of scatterers height within cylinders 1 and 2respectively 120590

119878= 031 120590

119863= 031

of the MIMO channels due to the increased strength ofthe LoS components As the spatial correlation increasesan SNR loss is induced [35] and the BER deterioratesdue to the difficulties experienced by the MMSE receiverwhich tries to successfully separate the incoming streamsHence switching to single-input single-output (SISO) modeis suggested in this case On the other hand double-Rayleighfading offers the required rich scattering environment thatbenefitsMIMO transmission and then the streams are ideallydecoded at the MMSE receiver Moreover a slight differenceon the performance in the asymmetric cases exists wherethe RicianRayleigh fading offers better results This findingis further supported by the work in [34] which studiedasymmetric fading conditions for an SISO system Since AFrelaying is considered in this cooperative mode the channelconditions are mainly dominated by the first hop Likewisein our system we employ AF relaying and the signal reachesthe relay with higher power in the RicianRayleigh caseAfterwards in the 119877-119863 link prior to detection the signalexperiences richer scattering which leads in less decodingerrors compared to the RayleighRician case

In Figure 6 the BER performance versus increasingvalues of antenna spacing at the source and destination isdepicted for a fixed SNR of 20 dB The values of the antennaspacing are ranging from 1205824 to 2120582 For this variation ofthe antenna spacing the spatial correlation remains low andamounts to nearly uncorrelated links Therefore the BER isnot significantly affected for both streams

Figure 7 investigates the effect of antenna spacing at theHAP that is 10120582 50120582 100120582 and 200120582 on the BER ofthe network for fixed SNR of 20 dB The results for bothstreams are depicted after theMMSEdetection and decodingThese results indicate less channel correlation for increasingantenna spacing and this dramatically reflects on the BER ofthe network

Figure 8 illustrates the BER performance for increasingvalues of the parameters 119896

119878(cylinder 1) and 119896

119863(cylinder

2) of the von Mises distribution in (13) for a fixed SNR of20 dB The performance of the network does not experiencean important degradation as the degree of scattering increasesfrom 0 (isotropic scattering) to 10 and theMMSE receiver hasalmost stable performance This increase has an analogouseffect on channel correlation [36] which slightly increases


001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)

Figure 4 The mean distance between the source (destination)and the scatterers within cylinder 1 (2) for different values of theparameter 119906

119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)

LP Rician-Rayleigh (KSR = 1dB KRD = 0)HP Rician-Rayleigh (KSR = 1dB KRD = 0)LP double-Rician (KSR = KRD = 5dB)HP double-Rician (KSR = KRD = 5dB)

HP double-Rayleigh (KSR = KRD = 0)LP double-Rayleigh (KSR = KRD = 0)LP double-Rician (KSR = KRD = 1dB)HP double-Rician (KSR = KRD = 1dB)LP Rayleigh-Rician (KSR = 0 KRD = 1dB)HP Rayleigh-Rician (KSR = 0 KRD = 1dB)

Figure 5 BER for increasing the strength of the LoS component atthe 119878-119877 and 119877-119863 subsystems

Figure 9 illustrates the BER for a fixed SNR of 20 dBand for different spread of the scatterers in the vicinity ofthe source and destination which is directly related withthe hyperbolic distribution in (14) As the parameters 119906

119878

(cylinder 1) and 119906119863(cylinder 2) increase the spread value

decreases and the correlation drastically increases [36]Thusthe incoming streams are suboptimally demodulated at the

BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP

Figure 6 BER for increasing values of antenna inter-elementspacing at the source and destination

BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP

Figure 7 BER for increasing values of the antenna spacing at thestratospheric relay

MMSE receiver and the BER performance is significantlydegraded

In Figure 10 different values for the mean height of thescatterers located within cylinders 1 and 2 that is different119867119878mean and119867119863mean respectively are considered (log-normaldistribution) while the elevation angle of the source anddestination antennas takes two different values first theelevation angles of the 119901th source and the 119897th destinationantenna element are 120595

119878= 120595119863= 1205872 and second these

angles are 120595119878= 120595119863= 12058718 As a general remark increasing

scatterersrsquomean height values that is increasing the degree ofurbanization leads to an insignificant decrease in the spatialcorrelation which in turn explains the minor increase in the

8 International Journal of Antennas and PropagationBE

R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)

Figure 8 BER for increasing values of the degree of scatteringwithin cylinders 1 and 2

BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)

Figure 9 BER for increasing values of the average spread ofscatterers around the source and destination

BER performance for a fixed SNR of 20 dB Furthermore for120595119878= 120595119863= 12058718 better channel conditions are obtained as

indicated by the BER curves Overall Figure 10 asseveratesthe inclusion of the third dimension of the model in [23]

5 Conclusions and Future Research Directions

HAPs could be used to relay information between a sourceand one or many destinations providing the means for

BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24

HSmean (HDmean ) (m)

LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)

Figure 10 BER for increasing values of the mean height of thescatterers within cylinders 1 and 2

integrated service provision in conjunction with terres-trial networks Therefore this paper has analyzed the BERperformance of MIMO MMSR systems employing MMSEreceivers in spatially correlated double-Rician fading chan-nelsThrough rigorous simulations the BER of the hierarchi-cally modulated transmitted symbols has been investigatedin various scenarios Results have revealed the relationshipbetween channel correlation and BER for varying fadingcondition and distribution of the scatterers thus illustratingvaluable information for a stratospheric relay system imple-mentation

Future directions include the use of the 3D channelmodelin more complex scenarios where integrated satellite-HAP-terrestrial architectures are considered Also other relayingprotocols such as decode-and-forward (DF) could be inves-tigated in order to examine the effect of channel correlationin this type of operation Finally employing opportunisticrelaying either in HAP selection or in relay selection on theground is an attracting research field and the use of the 3Dscattering model could provide interesting results dependingon channel correlation conditions

Acknowledgments

This work has been co-financed by the European Union(European Social FundmdashESF) and Greek national fundsthrough the Operational Program ldquoEducation and LifelongLearningrdquo of the National Strategic Reference Framework(NSRF)mdashResearch Funding Program THALES MIMOSA(MIS 380041) Investing in knowledge society through theEuropean Social Fund


References

[1] A Nosratinia T E Hunter and A Hedayat ldquoCooperativecommunication in wireless networksrdquo IEEE CommunicationsMagazine vol 42 no 10 pp 74ndash80 2004

[2] J N Laneman D N C Tse and G W Wornell ldquoCooperativediversity in wireless networks efficient protocols and outagebehaviorrdquo IEEE Transactions on InformationTheory vol 50 no12 pp 3062ndash3080 2004

[3] B Paillassa B Escrig R Dhaou M Boucheret and C BesldquoImproving satellite services with cooperative communica-tionsrdquo International Journal of Satellite Communications andNetworking vol 29 no 6 pp 479ndash500 2011

[4] B Evans M Werner E Lutz et al ldquoIntegration of satellite andterrestrial systems in futuremultimedia communicationsrdquo IEEEWireless Communications vol 12 no 5 pp 72ndash80 2005

[5] R Giuliano M Luglio and F Mazzenga ldquoInteroperabilitybetweenWiMAX and broadbandmobile space networksrdquo IEEECommunications Magazine vol 46 no 3 pp 50ndash57 2008

[6] S Kota G Giambene and S Kim ldquoSatellite component ofNGN integrated and hybrid networksrdquo International Journal ofSatellite Communications and Networking vol 29 no 3 pp 191ndash208 2011

[7] A Mohammed A Mehmood F Pavlidou and M MohorcicldquoThe role of high-altitude platforms (HAPs) in the globalwireless connectivityrdquo Proceedings of the IEEE vol 99 no 11pp 1939ndash1953 2011

[8] D Avagnina F Dovis A Ghiglione and P Mulassano ldquoWire-less networks based on high-altitude platforms for the provisionof integrated navigationcommunication servicesrdquo IEEE Com-munications Magazine vol 40 no 2 pp 119ndash125 2002

[9] E Falletti M Laddomada M Mondin and F Sellone ldquoInte-grated services from high-altitude platforms a flexible commu-nication systemrdquo IEEE Communications Magazine vol 44 no2 pp 85ndash94 2006

[10] M Antonini E Cianca A De Luise M Pratesi and MRuggieri ldquoStratospheric relay potentialities of new satellite-high altitude platforms integrated scenariosrdquo in Proceedings ofthe IEEE Aerospace Conference vol 3 pp 3-1211ndash3-1219 March2003

[11] G W Jull A Lillemark and R M Turner ldquoSHARP (stationaryhigh altitude relay platform) telecommunications missions andsystemsrdquo in Proceedings of the IEEE Global TelecommunicationsConference pp 955ndash959 New Orleans La USA December1985

[12] G M Djuknic J Freidenfelds and Y Okunev ldquoEstablishingwireless communications services via high-altitude aeronauti-cal platforms a concept whose time has comerdquo IEEE Commu-nications Magazine vol 35 no 9 pp 128ndash135 1997

[13] M Oodo H Tsuji R Miura et al ldquoExperiments on IMT-2000using unmanned solar powered aircraft at an altitude of 20 kmrdquoIEEE Transactions on Vehicular Technology vol 54 no 4 pp1278ndash1294 2005

[14] P Zhan K Yu and A L Swindlehurst ldquoWireless relay com-munications with unmanned aerial vehicles performance andoptimizationrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 47 no 3 pp 2068ndash2085 2011

[15] A Paulraj R Nabar and D Gore Introduction to Space-Time Wireless Communications Cambridge University PressCambridge UK 2003

[16] H Muhaidat and M Uysal ldquoCooperative diversity withmultiple-antenna nodes in fading relay channelsrdquo IEEE Trans-actions on Wireless Communications vol 7 no 8 pp 3036ndash3046 2008

[17] R U Nabar H Bolcskei and A J Paulraj ldquoDiversity andoutage performance in space-time block coded ricean MIMOchannelsrdquo IEEE Transactions on Wireless Communications vol4 no 5 pp 2519ndash2532 2005

[18] A G Armada L Hong and A Lozano ldquoBit loading for MIMOwith statistical channel information at the transmitter and ZFreceiversrdquo in Proceedings of the IEEE International Conferenceon Communications pp 1ndash5 Dresden Germany June 2009

[19] R W Heath and D J Love ldquoMultimode antenna selectionfor spatial multiplexing systems with linear receiversrdquo IEEETransactions on Signal Processing vol 53 no 8 pp 3042ndash30562005

[20] J G ProakisDigital Communications McGraw-Hill NewYorkNY USA 3rd edition 1995

[21] Y Jiang M K Varanasi and J Li ldquoPerformance analysis of ZFand MMSE equalizers for MIMO systems an in-depth studyof the high SNR regimerdquo IEEE Transactions on InformationTheory vol 57 no 4 pp 2008ndash2026 2011

[22] A Schertz and C Week ldquoHierarchical modulationmdashthe trans-mission of two independent DVB-T multiplexes on a singlefrequencyrdquo EBU Technical Review no 294 13 pages 2003

[23] E T Michailidis P Theofilakos and A G Kanatas ldquoThree-dimensional modeling and simulation of MIMO mobile-to-mobile via stratospheric relay fading channelsrdquo IEEE Transac-tions on Vehicular Technology no 99 1 pages 2012

[24] C S Patel G L Stuber and T G Pratt ldquoStatistical properties ofamplify and forward relay fading channelsrdquo IEEE Transactionson Vehicular Technology vol 55 no 1 pp 1ndash9 2006

[25] D Shiu G J Foschini M J Gans and J M Kahn ldquoFadingcorrelation and its effect on the capacity of multielementantenna systemsrdquo IEEE Transactions on Communications vol48 no 3 pp 502ndash513 2000

[26] A Abdi and M Kaveh ldquoA space-time correlation model formultielement antenna systems inmobile fading channelsrdquo IEEEJournal on Selected Areas in Communications vol 20 no 3 pp550ndash560 2002

[27] A Abdi J A Barger and M Kaveh ldquoA parametric modelfor the distribution of the angle of arrival and the associatedcorrelation function and power spectrum at themobile stationrdquoIEEE Transactions on Vehicular Technology vol 51 no 3 pp425ndash434 2002

[28] S S Mahmoud Z M Hussain and P OrsquoShea ldquoA geometrical-based microcell mobile radio channel modelrdquo Wireless Net-works vol 12 no 5 pp 653ndash664 2006

[29] S S Mahmoud F S Al-Qahtani Z M Hussain andA Gopalakrishnan ldquoSpatial and temporal statistics for thegeometrical-based hyperbolic macrocell channel modelrdquo Dig-ital Signal Processing vol 18 no 2 pp 151ndash167 2008

[30] S S Mahmoud Z M Hussain and P OrsquoShea ldquoA space-timemodel for mobile radio channel with hyperbolically distributedscatterersrdquo IEEE Antennas andWireless Propagation Letters vol1 pp 211ndash214 2002

[31] M Vazquez-Castro F Perez-Fontan and S R Saunders ldquoShad-owing correlation assessment and modeling for satellite diver-sity in urban environmentsrdquo International Journal of SatelliteCommunications vol 20 no 2 pp 151ndash166 2002


[32] M A Vazquez-Castro D Belay-Zelek and A Curieses-Guerrero ldquoAvailability of systems based on satellites with spatialdiversity and HAPSrdquo Electronics Letters vol 38 no 6 pp 286ndash288 2002

[33] C Tzaras E G Evans and S R Saunders ldquoPhysical-statisticalanalysis of land mobilesatellite channelrdquo Electronics Letters vol34 no 13 pp 1355ndash1357 1998

[34] H Suraweera G K Karagiannidis and P J Smith ldquoPerfor-mance analysis of the dual-hop asymmetric fading channelrdquoIEEE Transactions onWireless Communications vol 8 no 6 pp2783ndash2788 2009

[35] M R McKay and I B Collings ldquoError performance ofMIMO-BICM with zero-forcing receivers in spatially-correlated Rayleigh channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 3 pp 787ndash792 2007

[36] E T Michailidis and A G Kanatas ldquoThree-dimensional HAP-MIMO channels modeling and analysis of space-time correla-tionrdquo IEEE Transactions on Vehicular Technology vol 59 no 5pp 2232ndash2242 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



the transmitter side according to the channel characteristicsallows the reduction of the transmission power andor theenhancement of the data rates [18] Besides adaptive usage ofthe resources offered by the various modulation and codingschemes is mandatory for a systemrsquos efficiency and economyTherefore using detectors the effect of fading and correlationcan be overcome [19] while taking advantage of the adaptivetechniques thus leading to adaptive operation of the receiverwithout any control commands

In this paper the performance analysis of a MIMOMMSR system is analyzed through simulations in terms ofbit-error-rate (BER) so as to estimate the complementary roleofHAPs in conjunctionwith terrestrial networks and reap thebenefits of MIMOMMSR communications It is well knownthat spatial multiplexing systems that employ linear receiverschemes either zero-forcing (ZF) or minimum mean squareerror (MMSE) are practically important because of theirminimal complexity requirements [20 21]This paper focuseson the performance of MMSE detectors at the receivers overspatially correlated double-Rician flat-fading MIMO MMSRchannels since these receivers offer better performance thanZF receivers and avoid the noise-enhancement effect It isconsidered that hierarchically modulated symbols [22] aretransmitted in each time slot through the stratospheric relayin order to distinguish receivers and offer upgraded servicequality to those with better reception conditions as well asbackward compatibility

Since impairments of the signal are mainly caused by theenvironment near the user the starting point of the perfor-mance evaluation is a recently proposed three-dimensional(3D) reference geometry-based model for MIMO MMSRchannels in dual-hop amplify-and-forward (AF) networks[23] This model enables a realistic positioning of the scat-terers in the vicinity of the source and the destination andassumes that these scatterers are nonuniformly distributedwithin two cylinders which reflect the influence of twoheterogeneous 3D nonisotropic scattering environmentsThecommunication between the source and the destination isonly feasible through a relay due to high attenuation in thepropagation medium While the utilized carrier frequenciesare below 10GHz both line-of-sight (LoS) and non-line-of-sight (NLoS) propagation conditions may exist in thetransmission links from the source to the destination via thestratospheric relay whereas rain effects are insignificant

The remainder of this paper is organized as followsSection 2 outlines the MIMO MMSR system model andthe modulation techniques employed Section 3 presents theMIMO MMSR channel model and analyzes the propagationcharacteristics The performance analysis along with thecorresponding results is presented in Section 4 Finally con-clusions and future research directions are given in Section 5

2 System Model

The system model employed throughout this chapter con-siders a narrowband MIMO MMSR fading channel with 119871

119878

antenna elements at a terrestrial source mobile station 119871119877

antenna elements at a half-duplex stratospheric relay station

Low priority (LP) bit

High priority (HP) bit

Figure 1 Hierarchical modulation of order 416QAM

free of local scattering supporting a two-hop communicationand 119871

119863antenna elements at a terrestrial destination mobile

station All antennas are omnidirectional and are numberedas 1 le 119901 le 1199011015840 le 119871

119878 1 le 119902 le 1199021015840 le 119871

119877 and 1 le 119897 le

1198971015840le 119871119863 respectively The source and destination arrays are

equipped with low-elevation antennas while the relay flies ata height ℎ

119877asymp 20 km above the ground The relatively short

endurance due to fuel constraints and human factors limitsthe deployment of mannedHAPs as relay nodesTherefore itis assumed that the relay is a solar-powered unmanned quasi-stationary airship

Let us consider that the destination receives data fromthe source only through the relay since the direct source-destination transmission link is totally obstructed Thus thecommunication takes place in two time slots The relayreceives the source signal in each time slot and sends it tothe destination through an AF process In each transmissionthe source employs hierarchical modulation with two pri-ority streams where the high-priority (HP) robust symbolsare QPSK modulated while the low-priority (LP) symbolsare 16QAM modulated The constellation diagram of the416QAM hierarchically modulated symbols is illustrated inFigure 1 where the bits corresponding to each priority streamare distinguished Each time slot is divided in 119873 symbolperiods where 119873 is the size in symbols of each transmittedsource signal vector These streams are fed to the sourceand after the two-hop transmission the destination will tryto decode either the LP stream if channel conditions arefavorable or the HP which is more robust to bad link quality

Assuming frequency-flat fading channels and constantchannel coefficients for duration equal to119873 symbol periodsthat is one time slot in the source-relay (119878-119877) and relay-destination (119877-119863) links the signal received at the relay is

y119877= H119878119877x + n119877 (1)





y119863= H119877119863119860y119877+ n119863= H119877119863119860 (H119878119877x + n119877) + n119863

= H119877119863119860H119878119877x +H119877119863119860n119877 + n119863(2)



119871119863) is





WMMSE = (H119867H + 1205902

119908I119871119878)minus1

H119867 (3)



119908is the






119908=(1199081 119908119871119878)

1003816100381610038161003816wh1198941003816100381610038161003816

2119864119909

119864119909sum119871119878

119895=1119895 = 119894

10038161003816100381610038161003816wh119895

10038161003816100381610038161003816

2

+ w21205902119908

(4)





H119867n119908 (5)



H119878119877= radic

119870119878119877

119870119878119877 + 1H119878119877LoS + radic

1

119870119878119877 + 1H119878119877NLoS (6)



vec (H119878119877NLoS) = R12

119878119877NLoS vec (H119908) (7)





R12119878119877NLoSR

1198672

119878119877NLoS = R119878119877NLoSH119908 is a 119871








119878(120573119863) relative to the 119909119910


119878120575119877 and 120575



119878 120579119877 and


119878and 120595





119878(119878(119899)




Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

p120595S

120573S

120587 minus 120579S120596S

p998400

q998400

120579R

120595D120573D

120587 minus 120596D

120579D

RSmax

HSmax

RDmax

HDmax

l998400


Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

RSmax

HSmax p

120595S

a(m)S

120587 minus 120579S

R(m)S

H(n)D

S(n)D

R(n)D

120587 minus a(n)Dp998400

q998400

120579R

RDmax

HDmax120595D

120579Dl998400

S(m)S

H(m)S


of 119878(119898)119878(119878(119899)



119863) and119867(119898)

119878(119867(119899)

119863) stands



and 119886(119899)119863



assumed that 119886(119898)119878

119886(119899)119863 119877(119898)119878

119877(119899)119863119867(119898)119878

and119867(119899)119863





ℎ119878119877-LoS119901119902

= 120577119878119877119887(119901)

119878119887(119902)

119878119877 (8)

where

120577119878119877= exp(minus1198952120587

120582

ℎ119877

sin120573119878

) (9)

119887(119901)

119878= exp[119895


119878

] (10)

119887(119902)

119878119877= exp[minus119895


119878

] (11)



H119878119877LoS =[[[

[

ℎ119878119877-LoS11

ℎ119878119877-LoS1119871119879

d

ℎ119878119877-LoS1198711198771


]]]

]

(12)




119878 119877(119898)119878

and 119867(119898)119878


119878 119877119878 and 119867



119878 119877(119898)119878

and119867(119898)


119878 119877119878 119867119878) can be



119878and is

defined as

119891 (119886119878) =

exp [119896119878cos (119886

119878minus 120583119878)]

21205871198680(119896119878)

minus120587 le 119886119878le 120587 (13)






119891 (119877119878) =119906119878

tanh (119906119878119877119878max) cosh

2(119906119878119877119878) 0 lt 119877

119878 le 119877119878max

(14)






119891 (119867119878) =


119878mean)]2 (2120590119878

2)]

119867119878120590119878radic2120587

(15)







119877119878119877-NLoS11990111990211990110158401199021015840 (120575119878 120575119877)

=

Ε [ℎ119878119877-NLoS119901119902

ℎ119878119877-NLoSlowast11990110158401199021015840 ]

radic119864 [10038161003816100381610038161003816ℎ119878119877-NLoS119901119902

10038161003816100381610038161003816

2

] 119864 [100381610038161003816100381610038161003816ℎ119878119877-NLoS11990110158401199021015840

100381610038161003816100381610038161003816

2

]

= 1199011198781198771 int

119867119878max

0

int

119877119878max

0

11990111987811987721198680(radic1199012

1198781198773+ 1199012

1198781198774) 119889119877119878119889119867119878

(16)

where ℎ119878119877-NLoS119901119902


1199011198781198771

=119906119878119887(119902)

119878119877119887(1199021015840)lowast

119878119877

120590119878radic2120587 tanh (119906

119878119877119878max) 1198680 (119896119878)

1199011198781198772

=


119878mean)]2 (2120590119878

2)]

119867119878cosh2 (119906

119878119877119878)



119877119878

)]

1199011198781198773

= 1198952120587

120582 (1199011015840minus119901) 120575

119878sin 120579119878cos120595119878


119877119878

)]

+ 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878 sin 120583119878

1199011198781198774

= 1198952120587

120582 (1199011015840minus119901) 120575

119878cos 120579119878cos120595119878


119877119878

)]

minus 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878cos 120583119878

(17)



R119878119877NLoS =

[[[[[[[

[

119877119878119877-NLoS1111

119877119878119877-NLoS1121


119877119878119877-NLoS2111

d 119877119878119877-NLoS21119871119877119871119879

d

119877119878119877-NLoS11987111987711987111987911


]]]]]]]

]

(18)



119878119877NLoS








119878119877(119878-119877 subsystem) and 119870

119877119863







119877= 20 km


119878= 1205874 120596

119863= 31205874


119878= 1205873 120573

119863= 1205873


119877= 200120582 120575

119863= 120582


119878= 1205872 120579

119877= 1205872 120579

119863= 1205872


119878= 12058718 120595

119863= 12058718



119878max = 70m119867119863max = 70m


119878= 5 119896

119863= 5


119878= 1205876 120583

119863= 1205876


119878= 001 119906

119863= 001



119878= 031 120590

119863= 031





119878(cylinder 1) and 119896

119863(cylinder



001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













y119863= H119877119863119860y119877+ n119863= H119877119863119860 (H119878119877x + n119877) + n119863

= H119877119863119860H119878119877x +H119877119863119860n119877 + n119863(2)



119871119863) is





WMMSE = (H119867H + 1205902

119908I119871119878)minus1

H119867 (3)



119908is the






119908=(1199081 119908119871119878)

1003816100381610038161003816wh1198941003816100381610038161003816

2119864119909

119864119909sum119871119878

119895=1119895 = 119894

10038161003816100381610038161003816wh119895

10038161003816100381610038161003816

2

+ w21205902119908

(4)





H119867n119908 (5)



H119878119877= radic

119870119878119877

119870119878119877 + 1H119878119877LoS + radic

1

119870119878119877 + 1H119878119877NLoS (6)



vec (H119878119877NLoS) = R12

119878119877NLoS vec (H119908) (7)





R12119878119877NLoSR

1198672

119878119877NLoS = R119878119877NLoSH119908 is a 119871








119878(120573119863) relative to the 119909119910


119878120575119877 and 120575



119878 120579119877 and


119878and 120595





119878(119878(119899)




Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

p120595S

120573S

120587 minus 120579S120596S

p998400

q998400

120579R

120595D120573D

120587 minus 120596D

120579D

RSmax

HSmax

RDmax

HDmax

l998400


Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

RSmax

HSmax p

120595S

a(m)S

120587 minus 120579S

R(m)S

H(n)D

S(n)D

R(n)D

120587 minus a(n)Dp998400

q998400

120579R

RDmax

HDmax120595D

120579Dl998400

S(m)S

H(m)S


of 119878(119898)119878(119878(119899)



119863) and119867(119898)

119878(119867(119899)

119863) stands



and 119886(119899)119863



assumed that 119886(119898)119878

119886(119899)119863 119877(119898)119878

119877(119899)119863119867(119898)119878

and119867(119899)119863





ℎ119878119877-LoS119901119902

= 120577119878119877119887(119901)

119878119887(119902)

119878119877 (8)

where

120577119878119877= exp(minus1198952120587

120582

ℎ119877

sin120573119878

) (9)

119887(119901)

119878= exp[119895


119878

] (10)

119887(119902)

119878119877= exp[minus119895


119878

] (11)



H119878119877LoS =[[[

[

ℎ119878119877-LoS11

ℎ119878119877-LoS1119871119879

d

ℎ119878119877-LoS1198711198771


]]]

]

(12)




119878 119877(119898)119878

and 119867(119898)119878


119878 119877119878 and 119867



119878 119877(119898)119878

and119867(119898)


119878 119877119878 119867119878) can be



119878and is

defined as

119891 (119886119878) =

exp [119896119878cos (119886

119878minus 120583119878)]

21205871198680(119896119878)

minus120587 le 119886119878le 120587 (13)






119891 (119877119878) =119906119878

tanh (119906119878119877119878max) cosh

2(119906119878119877119878) 0 lt 119877

119878 le 119877119878max

(14)






119891 (119867119878) =


119878mean)]2 (2120590119878

2)]

119867119878120590119878radic2120587

(15)







119877119878119877-NLoS11990111990211990110158401199021015840 (120575119878 120575119877)

=

Ε [ℎ119878119877-NLoS119901119902

ℎ119878119877-NLoSlowast11990110158401199021015840 ]

radic119864 [10038161003816100381610038161003816ℎ119878119877-NLoS119901119902

10038161003816100381610038161003816

2

] 119864 [100381610038161003816100381610038161003816ℎ119878119877-NLoS11990110158401199021015840

100381610038161003816100381610038161003816

2

]

= 1199011198781198771 int

119867119878max

0

int

119877119878max

0

11990111987811987721198680(radic1199012

1198781198773+ 1199012

1198781198774) 119889119877119878119889119867119878

(16)

where ℎ119878119877-NLoS119901119902


1199011198781198771

=119906119878119887(119902)

119878119877119887(1199021015840)lowast

119878119877

120590119878radic2120587 tanh (119906

119878119877119878max) 1198680 (119896119878)

1199011198781198772

=


119878mean)]2 (2120590119878

2)]

119867119878cosh2 (119906

119878119877119878)



119877119878

)]

1199011198781198773

= 1198952120587

120582 (1199011015840minus119901) 120575

119878sin 120579119878cos120595119878


119877119878

)]

+ 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878 sin 120583119878

1199011198781198774

= 1198952120587

120582 (1199011015840minus119901) 120575

119878cos 120579119878cos120595119878


119877119878

)]

minus 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878cos 120583119878

(17)



R119878119877NLoS =

[[[[[[[

[

119877119878119877-NLoS1111

119877119878119877-NLoS1121


119877119878119877-NLoS2111

d 119877119878119877-NLoS21119871119877119871119879

d

119877119878119877-NLoS11987111987711987111987911


]]]]]]]

]

(18)



119878119877NLoS








119878119877(119878-119877 subsystem) and 119870

119877119863







119877= 20 km


119878= 1205874 120596

119863= 31205874


119878= 1205873 120573

119863= 1205873


119877= 200120582 120575

119863= 120582


119878= 1205872 120579

119877= 1205872 120579

119863= 1205872


119878= 12058718 120595

119863= 12058718



119878max = 70m119867119863max = 70m


119878= 5 119896

119863= 5


119878= 1205876 120583

119863= 1205876


119878= 001 119906

119863= 001



119878= 031 120590

119863= 031





119878(cylinder 1) and 119896

119863(cylinder



001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

p120595S

120573S

120587 minus 120579S120596S

p998400

q998400

120579R

120595D120573D

120587 minus 120596D

120579D

RSmax

HSmax

RDmax

HDmax

l998400


Cylinder 2

Stratospheric relay

Cylinder 1

DestinationSource

q

l

z y

x

RSmax

HSmax p

120595S

a(m)S

120587 minus 120579S

R(m)S

H(n)D

S(n)D

R(n)D

120587 minus a(n)Dp998400

q998400

120579R

RDmax

HDmax120595D

120579Dl998400

S(m)S

H(m)S


of 119878(119898)119878(119878(119899)



119863) and119867(119898)

119878(119867(119899)

119863) stands



and 119886(119899)119863



assumed that 119886(119898)119878

119886(119899)119863 119877(119898)119878

119877(119899)119863119867(119898)119878

and119867(119899)119863





ℎ119878119877-LoS119901119902

= 120577119878119877119887(119901)

119878119887(119902)

119878119877 (8)

where

120577119878119877= exp(minus1198952120587

120582

ℎ119877

sin120573119878

) (9)

119887(119901)

119878= exp[119895


119878

] (10)

119887(119902)

119878119877= exp[minus119895


119878

] (11)



H119878119877LoS =[[[

[

ℎ119878119877-LoS11

ℎ119878119877-LoS1119871119879

d

ℎ119878119877-LoS1198711198771


]]]

]

(12)




119878 119877(119898)119878

and 119867(119898)119878


119878 119877119878 and 119867



119878 119877(119898)119878

and119867(119898)


119878 119877119878 119867119878) can be



119878and is

defined as

119891 (119886119878) =

exp [119896119878cos (119886

119878minus 120583119878)]

21205871198680(119896119878)

minus120587 le 119886119878le 120587 (13)






119891 (119877119878) =119906119878

tanh (119906119878119877119878max) cosh

2(119906119878119877119878) 0 lt 119877

119878 le 119877119878max

(14)






119891 (119867119878) =


119878mean)]2 (2120590119878

2)]

119867119878120590119878radic2120587

(15)







119877119878119877-NLoS11990111990211990110158401199021015840 (120575119878 120575119877)

=

Ε [ℎ119878119877-NLoS119901119902

ℎ119878119877-NLoSlowast11990110158401199021015840 ]

radic119864 [10038161003816100381610038161003816ℎ119878119877-NLoS119901119902

10038161003816100381610038161003816

2

] 119864 [100381610038161003816100381610038161003816ℎ119878119877-NLoS11990110158401199021015840

100381610038161003816100381610038161003816

2

]

= 1199011198781198771 int

119867119878max

0

int

119877119878max

0

11990111987811987721198680(radic1199012

1198781198773+ 1199012

1198781198774) 119889119877119878119889119867119878

(16)

where ℎ119878119877-NLoS119901119902


1199011198781198771

=119906119878119887(119902)

119878119877119887(1199021015840)lowast

119878119877

120590119878radic2120587 tanh (119906

119878119877119878max) 1198680 (119896119878)

1199011198781198772

=


119878mean)]2 (2120590119878

2)]

119867119878cosh2 (119906

119878119877119878)



119877119878

)]

1199011198781198773

= 1198952120587

120582 (1199011015840minus119901) 120575

119878sin 120579119878cos120595119878


119877119878

)]

+ 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878 sin 120583119878

1199011198781198774

= 1198952120587

120582 (1199011015840minus119901) 120575

119878cos 120579119878cos120595119878


119877119878

)]

minus 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878cos 120583119878

(17)



R119878119877NLoS =

[[[[[[[

[

119877119878119877-NLoS1111

119877119878119877-NLoS1121


119877119878119877-NLoS2111

d 119877119878119877-NLoS21119871119877119871119879

d

119877119878119877-NLoS11987111987711987111987911


]]]]]]]

]

(18)



119878119877NLoS








119878119877(119878-119877 subsystem) and 119870

119877119863







119877= 20 km


119878= 1205874 120596

119863= 31205874


119878= 1205873 120573

119863= 1205873


119877= 200120582 120575

119863= 120582


119878= 1205872 120579

119877= 1205872 120579

119863= 1205872


119878= 12058718 120595

119863= 12058718



119878max = 70m119867119863max = 70m


119878= 5 119896

119863= 5


119878= 1205876 120583

119863= 1205876


119878= 001 119906

119863= 001



119878= 031 120590

119863= 031





119878(cylinder 1) and 119896

119863(cylinder



001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119877119878119877-NLoS11990111990211990110158401199021015840 (120575119878 120575119877)

=

Ε [ℎ119878119877-NLoS119901119902

ℎ119878119877-NLoSlowast11990110158401199021015840 ]

radic119864 [10038161003816100381610038161003816ℎ119878119877-NLoS119901119902

10038161003816100381610038161003816

2

] 119864 [100381610038161003816100381610038161003816ℎ119878119877-NLoS11990110158401199021015840

100381610038161003816100381610038161003816

2

]

= 1199011198781198771 int

119867119878max

0

int

119877119878max

0

11990111987811987721198680(radic1199012

1198781198773+ 1199012

1198781198774) 119889119877119878119889119867119878

(16)

where ℎ119878119877-NLoS119901119902


1199011198781198771

=119906119878119887(119902)

119878119877119887(1199021015840)lowast

119878119877

120590119878radic2120587 tanh (119906

119878119877119878max) 1198680 (119896119878)

1199011198781198772

=


119878mean)]2 (2120590119878

2)]

119867119878cosh2 (119906

119878119877119878)



119877119878

)]

1199011198781198773

= 1198952120587

120582 (1199011015840minus119901) 120575

119878sin 120579119878cos120595119878


119877119878

)]

+ 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878 sin 120583119878

1199011198781198774

= 1198952120587

120582 (1199011015840minus119901) 120575

119878cos 120579119878cos120595119878


119877119878

)]

minus 1198952120587

120582[


ℎ119877cos2120573

119878

]

+ 119896119878cos 120583119878

(17)



R119878119877NLoS =

[[[[[[[

[

119877119878119877-NLoS1111

119877119878119877-NLoS1121


119877119878119877-NLoS2111

d 119877119878119877-NLoS21119871119877119871119879

d

119877119878119877-NLoS11987111987711987111987911


]]]]]]]

]

(18)



119878119877NLoS








119878119877(119878-119877 subsystem) and 119870

119877119863







119877= 20 km


119878= 1205874 120596

119863= 31205874


119878= 1205873 120573

119863= 1205873


119877= 200120582 120575

119863= 120582


119878= 1205872 120579

119877= 1205872 120579

119863= 1205872


119878= 12058718 120595

119863= 12058718



119878max = 70m119867119863max = 70m


119878= 5 119896

119863= 5


119878= 1205876 120583

119863= 1205876


119878= 001 119906

119863= 001



119878= 031 120590

119863= 031





119878(cylinder 1) and 119896

119863(cylinder



001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














119877= 20 km


119878= 1205874 120596

119863= 31205874


119878= 1205873 120573

119863= 1205873


119877= 200120582 120575

119863= 120582


119878= 1205872 120579

119877= 1205872 120579

119863= 1205872


119878= 12058718 120595

119863= 12058718



119878max = 70m119867119863max = 70m


119878= 5 119896

119863= 5


119878= 1205876 120583

119863= 1205876


119878= 001 119906

119863= 001



119878= 031 120590

119863= 031





119878(cylinder 1) and 119896

119863(cylinder



001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










001 002 003 004 005 006 007 008 009 010

10

20

30

40

50

60

70

80

90

100

uS (uD)

Mea

n di

stan

ce b

etw

een

sour

ce (d

estin

atio

n) an

d sc

atte

rers

(m)


119878(119906119863)

BER

100

10minus1

10minus2

10minus3

10minus4

0 5 10 15 20 25 30EbNo (dB)





119878



BER

10minus2

10minus3

025 05 075 1 125 15 175 2120575S120582 (120575D120582)

LPHP


BER

100

10minus1

10minus2

10minus30 40 80 120 160 200

120575R120582

LPHP




119878= 120595119863= 1205872 and second these




R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










R

10minus1

10minus2

10minus3

0 1 2 3 4 5 6 7 8 9 10

LPHP

kS (kD)


BER

100

10minus1

10minus2

10minus3

10minus4001 002 003 004 005 006 007 008 009 01

LPHP

uS (uD)






BER

10minus1

10minus2

10minus3

10minus44 6 8 10 12 14 16 18 20 22 24


LP (120595S = 120595D = 1205872)LP (120595S = 120595D = 12058718)

HP (120595S = 120595D = 1205872)HP (120595S = 120595D = 12058718)




Acknowledgments



References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article performance analysis of a two-hop mimo...

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