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IETE Technical Review

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Analysis of TAS/MRC based MIMO Systems over η −µ Fading Channels

Brijesh Kumbhani & Rakhesh Singh Kshetrimayum

To cite this article: Brijesh Kumbhani & Rakhesh Singh Kshetrimayum (2015) Analysis of TAS/MRC based MIMO Systems over η − µ Fading Channels, IETE Technical Review, 32:4, 252-259,DOI: 10.1080/02564602.2015.1010612

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Analysis of TAS/MRC based MIMO Systems overh ¡ m Fading Channels

Brijesh Kumbhani and Rakhesh Singh KshetrimayumDepartment of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, Guwahati, India

ABSTRACT

In this paper, we derive expressions for exact, approximate, and asymptotic symbol error rate (SER) of trans-mit antenna selection with maximal ratio combining (TAS/MRC) multiple input multiple output (MIMO) systemsfor several modulation schemes. We have assumed independent and identically distributed h ¡ m fadingchannels. We use a moment generating function (MGF) based approach to derive the expressions of SER.The expression for approximate SER is derived by approximating Q Function as a sum of exponentials. Theexpressions of SER are in the form of sum of converging infinite series for all values of fading parameters. Theanalytical expressions derived in this paper are also applicable to the SER performance analysis of TAS withselection combining at receiver (TAS/SC) systems. The analytical results are validated by comparing themwith the results of extensive Monte Carlo simulations for different values of fading parameters. Finally, the SERperformance of TAS/MRC systems and TAS/SC systems has been compared and superiority of TAS/MRCsystems over TAS/SC systems has been demonstrated.

Keywords:Fading channels, h ¡ m distribution, MIMO, Symbol error rate, TAS/MRC systems.

1. INTRODUCTION

Multiple input multiple output (MIMO) wireless com-munication system is considered as the promisingwireless technology that gives higher transmissionrates and improved performances. Vertical-Bell Labo-ratories Layered Space-Time (V-BLAST) is a MIMOarchitecture proposed to give very good spectral effi-ciencies and better error performance [1,2]. V-BLASTsystems transmit blocks of information bits using par-allel radio frequency (RF) chains at the transmitter,which makes system bulky and adds cost in terms ofhardware complexity, power, and size [3]. Space timecodes in MIMO systems can further improve the per-formance by using time diversity [4]. Simultaneoustransmissions from multiple antennas have inherentdisadvantages of inter-antenna interference, therequirement of synchronization, etc. [5]. The techniqueof antenna selection at the transmitter, receiver or bothhas been widely explored by the researchers across theglobe to overcome these disadvantages. Transmitantenna selection with maximal ratio combining at thereceiver (TAS/MRC) is one of the popular MIMO sys-tems with antenna selection. TAS with selection com-bining at the receiver (TAS/SC) MIMO systems isequally important as the system complexity is furtherreduced by deploying a single RF chain also at thereceiver.

The analysis of TAS/MRC systems in Rayleigh fadingis presented in [6]. It is also shown that TAS/MRC sys-tems exhibit full diversity order (same as product ofnumber of antennas at transmitter and receiver). Muchwork is reported in literature about outage probabilityand bit error rate (BER) analysis of TAS/MRC systemsover Nakagami-m fading channels. In [7], the exactexpression for BER is derived for TAS/MRC systemswith binary phase shift keying (BPSK) modulationscheme over Nakagami-m fading channels for integervalues of m. In [8], MIMO systems with joint transmitand receive antenna selection are analysed for errorperformance over Nakagami-m fading channels forinteger values of m. Expressions for exact and approxi-mate error probability are derived for BPSK and M-aryphase shift keying (MPSK), respectively. The analysisof joint transmit and receive antenna selection overnon-identical Nakagami-m fading channels has beeninvestigated in [9]. Outage probability and error per-formance of TAS/MRC systems is investigated forNakagami-m fading channels for real values of m in[10]. In [11], the outage probability analysis of multi-user TAS/MRC systems over Nakagami-m fadingchannels has been analysed. Recently, the performanceof TAS/MRC systems over Hoyt fading channels isinvestigated for two receiving antennas in [12]. TAS/MRC systems are combined with cooperative relaying

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systems to take benefit of both the spatial diversity andthe time diversity and cognitive radio systems [13,14].Generalized fading channel models have attracted theattention of researchers because of their capability tomodel classical fading channels as special cases andthe accurate fit to practical scenario [15�18]. Besidesthe popularity and practical advantage of h ¡ m fadingchannels, to the best of our knowledge, the BER ofTAS/MRC systems has not been investigated over h ¡m fading channels. Recently, the error performanceand capacity of selection diversity combining arereported over h ¡ m fading channels in [19]. However,it considered only the integer values of m.

In this paper, we analyse the symbol error rate (SER)performance of TAS/MRC systems over h ¡ m fadingchannels. We derive expressions for exact, approxi-mate, and asymptotic SER performance for severalmodulation schemes. For our analysis, we use amoment generating function (MGF) based approach toderive the expressions of SER. We derive expression ofapproximate SER by approximating the Gaussian Q-function as a sum of two exponential functions [20].The analytical expressions are also applicable to theperformance analysis of TAS/SC systems in whichonly the best link is active at a time. The exactness ofall the expressions has been validated with the help ofMonte Carlo simulation results. Finally, the BER per-formance of TAS/MRC systems and TAS/SC systemshas been compared and superiority of TAS/MRC sys-tems over TAS/SC systems has been demonstrated.

The remainder of this paper is organized as follows. Inthe next section, we describe system and channelmodel. We derive the probability density function(pdf) and MGF of received signal to noise ratio (SNR).The expression for approximate SER for various mod-ulation schemes is derived in Section 3.1. The expres-sions for exact and asymptotic error probabilities ofTAS/MRC systems for various modulation schemesover h ¡ m fading channels have been derived inSection 3.2 and Section 3.3, respectively. In Section 4,we present the analytical and simulation results withrelated discussion and the paper is concluded in Sec-tion 5.

2. SYSTEMAND CHANNELMODEL

We considered a MIMO system having Nt antennas attransmitter side and Nr antennas at the receiver sidethat has only one RF chain at the transmitter. Thetransmitter antenna which maximizes the SNR atreceiver is selected at the transmitter to transmit infor-mation. Let the fading coefficients from ith transmit-ting antenna to jth receiving antenna is denoted by hj,ifor i 2 (1,Nt) and j 2 (1, Nr). Selection of the best

antenna at the transmitter can be used with either SCor MRC strategy at the receiver. Antenna selection cri-terions for both the receiver strategies are described insubsequent subsections.

(a) SC at the receiver � in this case, we select only oneantenna at the receiver that receives the highest SNR.We refer such systems as TAS/SC (Nt,1;Nr,1) systemsThe link which gives the highest received SNR is deter-mined by

Iji D argmax1�i�Nt

1�j�Nr

fht;ji D j hj;i j 2g; (1)

where j and i represent the antennas corresponding tothe best link at receiver and transmitter respectivelyand Iji denotes the best link. Only the antennas thatcorrespond to the best link are active at a time in thiscase.

(b) MRC at the receiver � in this case, it is assumedthat number of RF chains at the receiver is same as thenumber of receiver antennas. The resulting receivedSNR for MRC scheme is given by gt D

PNr

nD 1gn, weregn is the instantaneous SNR of the nth branch.The transmitting antenna that maximizes SNR at thereceiver can be determined by

Ii D argmax1�i�Nt

(ht;i D

XNr

jD 1

j hj;i j 2); (2)

where Ii is the transmitting antenna that maximizes thereceived SNR. Such systems are referred as TAS/MRC(Nt, 1; Nr) systems.

2.1 Channel Model

In this paper, we assume the fading envelope (jhj,ij) tobe h ¡ m distributed. The pdf of SNR at any singleantenna output for h ¡ m fading channels is given as[15,16]

pgh¡mðgÞD 2

ffiffiffip

p ðmÞmC 12hmgm¡ 1

2

GðmÞHm¡ 12ðgÞmC 1

2

e¡ 2mgh

g

� �Im¡ 1

2

2mgH

g

� �;

(3)

where h and m are fading parameters, h and H arefunctions of the parameter h defined for two formatsin next subsections, Iy(¢) is the modified Bessel functionof first kind and g is the average SNR. Some of thespecial cases of h ¡ m distribution are Rayleigh distri-bution for h ! 1, m D 0.5, one sided Gaussian distribu-tion for h ! 1, m D 0.25, Nakagami-m distribution for

Kumbhani B and Kshetrimayum R S: Analysis of TAS/MRC based MIMO Systems over h ¡ m Fading Channels

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h ! 1, m D m/2 and Hoyt distribution for h ! q2,m D 0.5.

(a) h¡ m distribution: format 1� in this format, h is theratio of power of in-phase component to quadra-ture phase component. It is assumed that the in-phase and quadrature phase components of afading signal within each cluster are independentof each other. In this case, h D (2 C h¡1 C h)/4 andH D (h¡1¡ h)/4.

(b) h ¡ m distribution: format 2 � in this format, the in-phase and quadrature phase components of afading signal within each multipath component areassumed to have equal power. ¡1 < h< 1 is the cor-relation coefficient between the in-phase and quad-rature components of the scattered waves of eachmultipath component. In this case, h D 1/(1¡h2)and H D h/(1¡h2).

The cumulative distribution function (cdf) of receivedSNR at any single antenna output for h ¡ m fadingchannels is given as

Pgh¡mðxÞD 2

ffiffiffip

p ðmÞmC 12hm

GðmÞHm¡ 12ðgÞmC 1

2

Z x

0

gm¡ 12e

�¡ 2mgh

g

�Im¡ 1

2

2mgH

g

� �dg:

(4)

The integral in the above expression can be solved byusing [21, (8.445), (3.351.1)]. After further mathematicalsimplifications, the cdf can be given as

Pgh¡mðxÞD 21¡ 2m ffiffiffi

pp

hmGðmÞX1iD 0

g inc 2mC 2i; 2mhxg

� �i!GðmC iC 0:5Þ

H

2h

� �2i

; (5)

where ginc(¢, ¢) is lower incomplete gamma function.

2.2 PDF and MGF of Received SNR After AntennaSelection

Each ht,ji or ht,i for i 2 (1, Nt) and j 2 (1, Nr) obtainedfrom (1) or (2) are arranged in ascending order suchthat ht,(1) � ht,(2) �� � � � ht,(N), where ht,(¢) is the randomvariable obtained after the arrangement in ascendingorder and N D Nt Nr or Nt for TAS/SC or TAS/MRCsystems, respectively. In TAS/MRC system, we selectthe transmitting antenna corresponding to the highestchannel gain, ht,(Nt) when the MRC diversity techniqueis used at the receiver. In TAS/SC, the transmit andreceive antenna pair that maximizes the received SNRht,(NtNr) is selected. The pdf of SNR in such a system

can be given by [22]

pgðxÞDN½Ph¡mðxÞ�N¡ 1ph¡mðxÞ

DN21¡ 2m ffiffiffi

pp

hmGðmÞX1iD 0

g inc 2mC 2i;2mhx

g

� �i!GðmC iC 0:5Þ

H

2h

� �2i

2664

3775N¡ 1

2ffiffiffip

p ðmÞmC 12hmxm¡ 1

2

GðmÞHm¡ 12ðgÞmC 1

2

e¡ 2mxh

g

� �Im¡ 1

2

2mxH

g

� �:

(6)

In the above expression, modified Bessel function canbe represented in the series form [21, (8.445)] as

IrðvÞDX1sD 0

1

s!GðrC sC 1Þv

2

� �rC 2s; (7)

and incomplete gamma function can be represented inthe series form using equations (9.236.4), (9.212.1) and(9.210.1) of [21] as follows

g incðs; xÞD e¡ x

s

X1kD 0

xsC k

ðsC 1Þk; (8)

where (a)n is a Pochhammer symbol defined as (a)n DG(aCn)/G(a).

Therefore, the PDF and MGF of the received instanta-neous SNR can be given as (9) and (10)

pgtðNÞ ðxÞD 2N‘Xi;j

2jSH2iS

hNmC 2iSYNpD 1

�ip!Gðm 0 Þ�

qe¡ ƛxxr¡ 1

YN¡ 1

pD 1

�ðmC ipÞð2m 0 Þjp� ;

(9)

MgðsÞD 2N‘Xi;j

2jSH2iSqGðrÞðƛC sÞ¡ r

hNmC 2iSYNpD 1

�ip!Gðm 0 Þ�YN¡ 1

pD 1

�ðmC ipÞð2m 0 Þjp�;

(10)

where

Xi;j

DXi

Xj

DX1i1 D 0

X1i2 D 0

� � �X1iN D 0

X1j1 D 0

X1j2 D 0

� � �X1

jN¡ 1 D 0

;

rD 2NmC 2iS C jS; iS DXNpD 1

ip; jS DXN¡ 1

pD 1

jp;

m 0 DmC ip C 1

2; ‘D

ffiffiffip

pGðmÞ� �N

; ƛD 2Nmh

g;

and

qD mh

g

� �r

:

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It should be noted that (9) applies to TAS/MRC as wellas TAS/SC systems. For TAS/MRC gt is h ¡ Nrm dis-tributed as it is the sum of Nr independent and identi-cally distributed h ¡ m square variates [16]. Therefore,in (9), (10) and all subsequent expressions, m shall beinterpreted as Nrm for TAS/MRC systems and Nr

becomes the number of antennas selected at thereceiver, i.e. Nr D 1 for the TAS/SC (Nt, 1; Nr, 1)system.

3. E XACT ANDAPPROXIMATEPROBABILITY OF ERROR

In this section, we derive an expression for the approx-imate and exact SER of TAS/MRC systems over h ¡ mfading channels for various modulation techniques.SER for a wireless communication system can be calcu-lated by averaging the conditional probability of error(CPE) over the pdf of received SNR. Exact CPE for var-ious modulation schemes and approximate CPE forMPSK modulation scheme can be given by

PeðgÞD aQðffiffiffiffiffibg

pÞ¡ cQ2ð

ffiffiffiffiffibg

pÞ; (11)

where Q(¢) is the Gaussian Q-function, g is SNR and a,b, and c are modulation-dependent parameters. Thevalues of a, b, and c are listed inTable 1 for differentdigital modulation techniques. The SER can be givenby

Pe DZ 1

0

PeðgÞpgtðNÞ ðgÞdg: (12)

3.1 Approximate Probability of Error

To analyse approximate probability of error, theGaussian Q-function is approximated as a sum of twoexponential functions [20]. Approximate CPE can be

given as

PeðgÞ ffi a

12e¡

bg2 C a

4e¡

2bg3 ¡ c

144e¡ bg ¡ c

16e¡

4bg3 ¡ c

24e¡

7bg6 ;

(13)

where first two terms and last three terms representthe first term and second term of (11), respectively.

The approximate SER can be given by

Peappr: ffiXi

zi

Z 1

0

e¡cigpgtðNÞ ðgÞdg; (14)

where

z1 D a

12; z2 D a

4; z3 D ¡ c

144; z4 D ¡ c

16; z5 D ¡ c

24; c1 D b

2;

c2 D 2b

3; c3 D b; c4 D 4b

3; and c5 D 7b

6:

In the above expression, the integral of (14) fits the def-inition of MGF of the received SNR, Mg(ci). Thus,approximate SER can be given as the weighted sum ofMGFs of received SNR. In this case, it can be given as

Peappr: ffiXi

ziMgðciÞ: (15)

3.2 Exact Probability of Error

In this section, we derive expression for exact SER ofTAS/MRC systems over h ¡ m fading channels for var-ious modulation techniques. The exact SER can beevaluated as [25, (4.2), (4.9), (5.3)]

Pe DZ 1

0

½aQðffiffiffiffiffibx

pÞ¡ cQ2ð

ffiffiffiffiffibx

pÞ�pgtðNÞ ðxÞdx (16)

D a

p

Z p2

0

Mgb

2sin2u

� �du

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}I1

¡ c

p

Z p4

0

Mgb

2sin2u

� �du

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}I2

: (17)

The integrals I1and I2 of (17) are evaluated as (18) and(19), respectively, where PFQ({a1, a2, . . ., aP}; {b1, b2, . . .,bQ}; z) is a Hypergeometric function, F(1)A(a; b1, b2; c; x,y) is an Appell Hypergeometric function of two varia-bles and zD b

2ƛ . It shall be noted that the integral I1 issolved by some algebraic simplifications and using(5A.3) of [25] and I2 is solved by putting Sin2uD tfollowed by algebraic simplifications and usingthe definition of Appell Hypergeometric function

Table 1: Modulation parameters for various modulationschemes [23,24].

Modulation scheme a b c

BPSK 1 2 0BFSK 1 1 0

MPSK 2 2sinp

M

� �0

MPAM 2M¡1M

6M2 ¡1

0

QPSK or MSK 2 1 1Coherent DPSK 2 2 2

MQAM 4

ffiffiffiffiffiM

p ¡1ffiffiffiffiffiM

p 3M¡1

4

ffiffiffiffiffiM

p ¡1ffiffiffiffiffiM

p !2

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[26, (7.2.4.42)],

I1 D 2aN

p‘Xi;j

2jSH2iSqGðrÞZ p

2

0

ƛC b

2sin2u

� �¡ rdu

hNmC 2iSYNpD 1

�ip!Gðm 0 Þ�YN¡ 1

pD 1

�ðmC ipÞð2m 0 Þjp�

D aN‘

ffiffiffiz

p

r Xi;j

2jSH2iSqƛ¡ rG rC 12

� �hNmC 2iS

YNpD 1

�ip!Gðm 0 Þ�

2F1�1; rC 1

2 ; rC 1; 11C z

�rð1C zÞrC 1

2

YN¡ 1

pD 1

�ðmC ipÞð2m 0 Þjp� ; (18)

I2 Dffiffiffi2

pcN

p‘Xi;j

2jSH2iSqƛ¡ rGðrÞ

hNmC 2iSYNpD 1

�ip!Gðm 0 Þ�

�Fð1ÞA rC 1

2 ;12 ; r; rC 3

2 ;12 ; ¡ 1

2z

� �YN¡ 1

pD 1

�ðmC ipÞð2m 0 Þjp�ð1C 2rÞð2zÞr

: (19)

3.3 Asymptotic Probability of Error

Asymptotic probability of error is a measure of perfor-mance analysis at high SNR conditions. From (16) and(17), it is clear that I2 corresponds to the term contain-ing squared Gaussian Q-function and can be neglectedat high SNR. The asymptotic error performance can beevaluated by assuming the values of all summationvariables to be zero, i.e. (i1, i2, . . .,iN D 0 and j1, j2, . . .,jN¡1 D 0) in (18). It can be given by

Peasympt Da‘

2

ffiffiffiz

p

rG 2NmC 1

2

� �hNmG mC 1

2

� �NmN

� 2F1�1; 2NmC 1

2 ; 2NmC 1; 11C z

�mhg

� �¡ 2Nm

ƛ2Nmð1C zÞ2NmC 12

: (20)

Using (9.100) of [21], the above expression can be sim-plified to obtain asymptotic probability of error as

Peasympt Da

2ffiffiffip

pffiffiffip

pGðmÞ� �N ð2NÞ¡ 2NmG 2NmC 1

2

� �hNmmNG mC 1

2

� �N1C bg

4Nmh

� �2Nm:

(21)

4. RESULTS ANDDISCUSSION

We simulated TAS/MRC systems for various values offading parameters (h and m) for BER/SER. We trun-cated the infinite sum series of (18) and (19) while eval-uating SER using (17) up to first P terms such that itgives accurate results at the fifth place of a decimaldigit when the value is represented in scientific nota-tion, i.e. in the form a x 10b. The value of P and corre-sponding SER for some cases is tabulated in Table 2. Itis observed that we can obtain sufficient accuracy bytruncating infinite sums to first 20 terms.

In Figure 1, the results are shown for a TAS/MRC(2,1;1) system for the Nakagami-m fading case withh D 1 and m D m/2 (a special case of h ¡ m fading). Theanalytical (exact, approximate, and asymptotic) andsimulation results of error performance are plotted form D 0.5, 1, 1.5, and 2.5 for the BPSK modulationscheme. As the value of fading parameter, m increasesthe severity of fading decreases and the BER perfor-mance of the system improves. It can be seen from thefigure that the asymptotic BER performance is a lowerbound and approximate BER is an upper bound of theexact BER performance. The analytical and simulationresults can be observed to be in close agreement.

Table 2: Number of terms required for accuracy at fifth placeof decimal digit in scientific notation.

SNRD 5dB SNRD 10dB

h, m, Nt, Nr P SER P SER

1, 0.5, 2, 2 10 1.98186 £ 10¡2 7 9.27794£ 10¡4

0.5, 1.25, 2, 1 18 6.92964 £ 10¡2 11 5.49862£ 10¡3

0.8, 1.5, 3, 1 18 4.58657 £ 10¡2 11 1.52017£ 10¡3

Figure 1: BER performance of TAS/MRC (2, 1; 1) system

over h ¡ m fading channels for h D 1 with BPSK

modulation.

Kumbhani B and Kshetrimayum R S: Analysis of TAS/MRC based MIMO Systems over h ¡ m Fading Channels

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In Figure 2, the results are shown for a TAS/MRC (2, 1;Nr) system for Hoyt (Nakagami-q) fading case withh D 0.01 and m D 0.5 (a special case of h ¡ m fading).The analytical (exact, approximate, and asymptotic)and simulation results of error performance are plottedfor Nr D 1, 2, and 3 for the BPSK modulation scheme.

In Figure 3, the results are shown for a TAS/MRC(Nt, 1; Nr) system and TAS/SC (Nt, 1; Nr, 1) system forh D 1 and m D 1. It compares the performance of theTAS/MRC system and TAS/SC systems. The analyti-cal and simulation results of error performance areplotted for the BPSK modulation scheme. From thefigure, it can be observed that to achieve the same BERof 10¡4 TAS/MRC (2, 1; 2), it requires 2dB less SNR

than TAS/SC (2, 1; 2, 1) system. Similarly, to achievethe BER of 10¡5, TAS/MRC (2, 1; 3) system requires3dB less SNR and TAS/MRC (3, 1; 2) require 2dB lessSNR when compared with the performance of TAS/SC (2, 1; 3, 1) or (3, 1; 2, 1) system. It is important tonote that the BER performance of the TAS/SC (Nt, 1;Nr, 1) system is same as that of the TAS/SC (Nr,1;Nt,1)system. Similarly, it is intuitive to say that the BER per-formance of the TAS/SC (Nt, 1;Nr, 1) system is same asthat of the TAS/SC (NtNr,1;1,1) system or TAS/SC (1,1;NrNt,1) system.

In Figure 4, the results are shown for a TAS/MRC(Nt, 1; Nr) system for different values of fading param-eters h and m with 4-QAM modulation. Analytical andMonte Carlo simulation results are plotted for differentnumbers of transmit and receive antennas. The exact-ness of the analytical results can be seen through theclose agreement of analytical and simulation results.

5. CONCLUSION

In this paper, we derived expressions for the exact,approximate, and asymptotic SER of TAS/MRC sys-tems with the arbitrary numbers of transmitting andreceiving antennas for various modulation schemesover h ¡ m fading channels. The derived expressionscan also be applied for the performance analysis of theTAS/SC systems over h ¡ m fading channels. MonteCarlo simulations of TAS/MRC systems and TAS/SCsystems are carried out for various values of fadingparameters so that the special cases of h ¡ m fadingmodel like Rayleigh, Nakagami-m and Hoytfading scenario are covered. The SER performances ofthe TAS/MRC and TAS/SC systems are compared

Figure 3: Performance comparison of TAS/MRC and TAS/

SC systems.

Figure 4: SER performance of TAS/MRC (Nt, 1; Nr) system

with 4-QAM modulation for different values of fading

parameters.

Figure 2: BER performance of TAS/MRC (2, 1; Nr) system

over h ¡ m fading channels for h D 0.01 and m D 0.5 with

BPSK modulation.

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and the superiority of TAS/MRC systems overTAS/SC systems is demonstrated.

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Kumbhani B and Kshetrimayum R S: Analysis of TAS/MRC based MIMO Systems over h ¡ m Fading Channels

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AuthorsBrijesh Kumbhani received his BE degree inelectronics and communication engineeringfrom Dharmsinh Desai University, Nadiad,India, in 2010. He is currently a PhD candidatein the Department of Electronics and ElectricalEngineering at Indian Institute of TechnologyGuwahati, India. His research interests are inthe areas of wireless communication, UWBcommunication systems and multiple

antenna systems.

Email: k.brijesh@iitg.ernet.in.

Rakhesh Singh Kshetrimayum received PhDdegree from the School of Electrical and Elec-tronic Engineering (EEE), Nanyang Techno-logical University (NTU) Singapore in 2005.Since 2005, he has been with the Departmentof EEE, IIT Guwahati as an associate professor(2010), assistant professor (2006–2010) andsenior lecturer (2005–2006). He worked as apostdoctoral scholar at the Department of EE,

Pennsylvania State University (PSU) USA (2005), research associateprovisional at the Department of Electrical Communication Engineer-ing (ECE), Indian Institute of Science (IISc) Bangalore (2004–2005),teaching assistant at the School of EEE, NTU Singapore (2002–2003)and trainee software engineer at Mphasis Pune, India (2000–2001).Dr. Kshetrimayum is the recipient of SEFOGG Young Engineer Award(2011), Department of Science & Technology India (SERC) Fast TrackScheme for Young Scientists (2007–2010) and NTU Research Schol-arship from 2001–2004. His current areas of research interests are inprinted antennas and circuits, UWB communications and MIMO wire-less communications. He has been involved in organizing severalIEEE international conferences as technical program co-chair, publi-cation chair, program chair, session chair and technical programcommittee. He is the editor-in-chief of Inderscience journal Interna-tional Journal of Ultra Wideband Communications and Systems. Heis a life fellow of the Institution of Electronics and TelecommunicationEngineers (IETE), India, Optical Society of India (OSI) and AntennaTest & Measurement Society (ATMS), India, and a senior member ofInternational Association of Computer Science and Information Tech-nology (IACSIT), Singapore and Institute of Electrical and ElectronicsEngineers (IEEE), USA.

Email: krs@iitg.ernet.in.

DOI: 10.1080/02564602.2015.1010612; Copyright © 2015 by the IETE

Kumbhani B and Kshetrimayum R S: Analysis of TAS/MRC based MIMO Systems over h ¡ m Fading Channels

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