Performance Analysis of Downlink MIMO WCDMA Systems Using Antenna Selection in Transmitter and MRC Plus LDD in Receiver Over Correlated Nakagami-Fading Channels

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Wireless Sensor Network, 2010, 2, 555-561 doi:10.4236/wsn.2010.27067 Published Online July 2010 (http://www.SciRP.org/journal/wsn)

Performance Analysis of Downlink MIMO WCDMA Systems Using Antenna Selection in Transmitter and MRC Plus LDD in Receiver over Correlated Nakagami-Fading Channels

Siavash Ghavami1, Mahmood Mohassel Feghhi2, Bahman Abolhassani2 1School of Electrical & Computer Engineering, University of Tehran, Tehran, Iran 2School of Electrical Engineering, Iran University of Science and technology, Tehran, Iran E-mail: [email protected], [email protected], [email protected] Received April 9, 2010; revised May 4, 2010; accepted May 12, 2010

Abstract

In this paper bit error rate (BER) performance is analyzed for multiple input-multiple output (MIMO) communications systems using antenna selection in the transmitter, maximal ratio combining (MRC) and linear de-correlating detector (LDD) in the receiver in wide band code division multiple access (WCDMA) downlink channels with correlated Nakagami fading. The MRC maximizes signal to noise ratio of the received signal, then the LDD cancels out multiple access interference (MAI). Theoretical results are validated using computer simulations. Moreover, a pilot based estimation method is proposed to jointly estimate the channel gains and the rows of the LDD operator. Simulation results show that using this proposed method, diversity order is maintained in the receiver. Furthermore, our analysis shows the spectral efficiency degra- dation due to the pilot based strategy is negligible.

Keywords: MIMO, Transmitter Antenna Selection, WCDMA, Maximum Ratio Combining

1. Introduction ity by increasing the number of transmitting and receiv- ing antennas. Transmitter antenna selection (TAS) can Wide band code division multiple accesses (WCDMA) reduce the cost of multiple antennas and at the same time has been proposed to satisfy ever-increasing demands for can retain many advantages of MIMO systems. A com- higher data rates, as well as to allow more users to sim- bined transmitter antenna selection and maximal ratio ultaneously access the network [1]. So, it is employed in combining (MRC) has been proposed in [7]. This method the third generation mobile networks to provide multi- selects the transmitter antenna that maximizes the total media services with required qualities. Multiuser detec- received signal power at the receiver. Inactivating other tors (MUDs) are used to detect the desired signal and to transmitter antennas reduces the hardware complexity; simultaneously cancel out interferences coming from co- furthermore, this method reduces the number of radio users in WCDMA systems [2]. In downlink scenario, channels used in a MIMO system. Bit error rate (BER) blind multiuser detectors are proposed for multiple ac- performance of this method has been analyzed in inde- cess interference (MAI) cancellation [3], but use of these pendent and correlated Rayleigh fading channels, respec- detectors increases computational complexity of mobile tively in [8] and [9]. As well, recently a BER perform- stations (MSs). Another approach for MAI cancellation ance analysis of TAS/MRC has been studied in corre- in downlink multiuser scenario is the precoding method lated Nakagami fading channels [10], however it is for a at the base station (BS) [4], but it requires error free links single user scenario in a non CDMA system. between each MS and the BS, which is not the case in In this paper, the downlink scenario of MIMO WCD- practical scenarios. MA systems using TAS/MRC plus LDD has been stud- Multiple input-multiple-output (MIMO) systems sig- ied. MIMO is a strong tool for capacity increasing and nificantly increase system capacity and improve perfor- performance improvement. But the limitation in the size mance [5,6] at the cost of increasing hardware complex- of a MS necessitates employing receiver antennas with a

Copyright © 2010 SciRes. WSN 556 S. GHAVAMI ET AL. small distance among them; therefore the correlation 1 N1 among channel gains should be considered even in rich htij,,() cmptmT k [ ] ij ( c ), (2) scattering environments. For hardware complexity re- N m0 duction and keeping diversity order in the base station, where N is the processing gain, TTNc  is the chip TAS in the transmitter is a good candidate, which is con- time, pt() is the convolution of three components: sidered in this paper. Furthermore for reducing effect of ij, MAI, a linear de-correlating detector (LDD), which is a the chip pulse shaping waveform, the channel filter be- sub optimum multi user detector, is used in the receiver. tween the ith transmitter antenna and the jth receiver The LDD has simple structure with good performance antenna (which represents the channel echoes) and the for MAI mitigation [2]. In this paper, the BER perform- receiver filter, with unit energy. cmk [] is the value of ance of a downlink WCDMA system in the correlated the mth chip of kth user’s spreading sequence with Nakagami fading channels is analyzed, and theoretical cm[] 1. Data symbols dl[] of different users are results are validated using computer simulations. MAI k k independent with identical distributions (i.i.d). The cancellation using MUDs needs to know the user’s and co-users’ spreading sequences, which increases the com- channel between the ith transmitter and the jth receiver jij, ()t plexities of MSs. In this paper, we consider the case in antenna denotes as ij,,()tte ij () , is assumed to which the links between each MS and the BS are error be a quasi-static fading and its envelope  ()t follows prone. So, precoding techniques can not be applied. Fur- ij, thermore, we give up the blind MUDs for their high Nakagami-m distribution m computational complexities [11]. In this paper, we pro- 2 mmx 2 pose a low complexity pilot based channel estimation 21m px ()  x exp( ) (3) method for the joint estimation of the channel gains and ij, m  the rows of the LDD operator in order to cancel out the 2 MAI. The proposed method does not require the spread- 22  2 where mEij, ,  E  ij,  , ing sequences of all active users (which are not available   in the MS), as well as the calculation of the inverse cross  nu1 2 nuedu. Therefore    has gamma correlation matrix. So, using this estimation method, the 0 ij,, ij MSs can cancel out the MAI with-out prior knowledge distribution, about spreading sequences of co-users by decorrelating m m1 users’ signals. mx mx px ()  exp( ). (4) The remaining of this paper is organized as follows. In ij, m Section 2, system models are considered. BER performance analysis has been presented in Section 3. Joint estimation of channel and the LDD operator is proposed in 2.1. Transmitter Antenna Selection Section 4. Simulation results are presented in Section 5 in order to validate our performance analysis and evalu- The TAS is performed so that the total received signal ate the performance of our proposed joint estimation power is maximized. Mathematically, it is equivalent to method. Finally conclusions are presented in Section 6. selection antenna such that:

L r 2 2. System Model isij arg max , . (5) 1iL  t j 1 We consider the downlink scenario of a WCDMA sys- The MS sends i using only log (L ) bits, where tem. The jth antenna of the MS receives signals of K s 2 t users which have been sent by the ith transmitter antenna  denotes ceiling operation. In performance analysis, in the base station. It is given by channel estimation is assumed to be performed perfectly

K  at the receiver, also the feedback link between the receiver and the transmitter is considered to be perfect and rtij,,,() AdlhtlT k k [] ij ( s ij ) nt (), (1) kl1 without delay (using forward error correction (FEC) it is

possible to send a few flag bits, i.e., log2 (Lt ) , without where Ak, dk[l], Ts and  are, respectively, the re- ij, error even in error prone link). The size of a Ms limits ceived amplitude, lth data symbol of kth user, symbol the use of antenna diversity and this makes the channels period and path delay between ith transmitter antenna correlated. The covariance matrix among channel power and jth receiver antenna and nt() is additive white T gains, e.g., δ  ...  in the receiver is iiss,1 iL sr , Gaussian noise. The hij, is expressed by:  

Copyright © 2010 SciRes. WSN S. GHAVAMI ET AL. 557 given by noise variance in the receiver side is increased to 22 2 H    , where  is variance of n[]l , which is Ωδδ E , (6) nLDD, k n n iiss equal to N0 2 . H where, E and , respectively denote expectation and In the first step of the BER performance analysis, the Hermitian operations. probability density function (PDF) of maximum channel gains, which has been selected by criterion given by (5) 2.2. BER Performance Analysis Lr must be obtained,  max  maxi , where    . 1iL iij , t j1

In this section, BER performance of TAS/MRC plus The PDF of max is obtained as [12] LDD in the downlink scenario of WCDMA systems is pxLFxfx() ( ())Lt 1 (), (11) analyzed. In the following, a bold capital letter denotes a max t ii matrix (A), a bold small letter denotes a vector (a), and where F ()x and f ()x are respectively, the cumula- an unbolded letter denotes a scalar (a or A). Samples of i i the channel are considered to be constant for each sym- tive distribution function (CDF) and PDF of  . F ()x i i bol; such that for the lth symbol defined as and f ()x for multi user scenario over correlated Na-  []llT  ( ) . Defining A  diag(A ,...,A ) , i ij,, ij 1 k kagami fading channels are extracted similar to those of Cc [TT , ... ,c ] , c  NN0.5 cc[0],..., [ 1] , 1 K kkka single user scenario over correlated Nakagami fading T T channels, which proposed in [10]. d[]ldldl [],..., [] and n[]lnlnl 0 [],...,N 1 [] ,  1 K  j j The TAS in the transmitter and MRC in the receiver which contains the noise samples in the jth receiver an- increase the received SNR of kth user to tenna, the received signal form the ith transmitter an- Lr  || 2 , (12) tenna to the jth receiver antenna is given by kk ijs i1

rnij,,[]llll  ij []CAd [] []. (7) 2 in which kbkn E   , where Eb is average energy For any linear detector combined with MRC, the deci- per bit in the transmitter. For the BPSK modulation the sion variable, dˆ[]l is obtained by a linear combination instantaneous BER of the kth user is obtained as Q 2 , where Q  is the Q-function. The BER is of rij, []l , i.e.,  k    obtained by integration of instantaneous BER from zero Lr ˆ * to infinity, as [13] dDr[]lll sign{Re(ij,, [] ij []))}, (8) j 1   PQpd (2 ) ( ) . (13) ek,  kk k k where the matrix D represents the operation of the mul- 0 tiuser detector. For the LDD, D is the Moore-Penrose Since k in (12) is kmax , the PDF of k is also generalized inverse of the code matrix C [2], given by obtained similar to (11), e.g., pp() () . Hence, k max T1T 1T DCCCRCLDD () , (9) calculation of integral in (13) can be performed using p () . Calculation of above integral, which is related where R=CT C is a KK matrix containing the max autocorrelation coefficients of the users’ spreading codes. to BER performance of multi-user scenario, is similar to In (9), it is assumed that K users’ codes are linearly in- the calculation of BER performance in a single user sce- 1 nario, which has been performed in [10]. The final BER dependent, to guarantee the existence of R . The re- is obtained as (14), where, ! denotes the factorial opera- ceiver output is obtained as follows tion andlr,1lL are the eigenvalues of the matrix Lr -1T * v[lll ]  Rr Cij, [ ] [ ]  m . As well,  lr is defined as (15), and the ex- j1 pressions of abcj ,,jj can be obtained using the multi- Lr -12 TT -1 nomial theorem [14].  RdRnij, []lll CCA[] C [] (10) j1 Lr 2 -1 T 3. Joint Estimation of Channel Gains and  ij, []ll AdRn [] C [] l . j1 LDD Operator

1 The  kkk()R , 1 is the noise enhancement fac- In this section, effect of joint estimation of the channel tor produced by the de-correlating operation, therefore gains and the rows of the LDD operator is investigated.

cr mm(1) cr j (1)(LLtr 1) j Lr m 2   lr lE b  l PLek,  tr  a j cr j 12! 1 lr11()  ()r j  0 b   Eb N l jl bjlk0 s (14) crj 1 cr1 s s j Ebl  21 s0 s Eb N bjlk0

m  L r   1k , rm kkl1, i   1 d mr  (1s )m , rm (15) lr mr mr k s1/l ()!()mrl ds kl    0, rm 

In the downlink scenario of a WCDMA system, each MS rcFnpilot Al [] , (17) knows only its own spreading sequence and doesn’t have jkijks , k any knowledge about spreading sequence of any other where Fc Dk , n=c  n and  denotes user, however using the LDD in the receiver needs the k k LDD k knowledge of spreading sequences of all other active element by element multiplications of two vectors. If users. Moreover, even if a mobile user knows the code pilot Ak  1 then rj will be equal to ij, []l Fnk   . Fig- matrix of all users (e.g., C ) it needs to calculate the in- s ure 1 shows block diagram of the proposed strategy for verse cross correlation matrix among spreading se- -1 joint channel and LDD operator estimation, in which TSk quences of all active users (e.g., R ), which has high [l] denotes lth symbol of the training sequence of kth computational complexity. Furthermore, the mobile user user. Training sequences for LDD operator estimation is allowed to detect only its own data. On the other hand, have been sent in non-overlapping time slots, hence MAI the total DLDD is not required in the mobile. And the is not produced due to the transmission of pilot signals. kth user requires only the kth row of the DLDD denoted If the pilot symbols length of each user increases, the effect of n in (17) reduces and a better estimation of by Dk in the lth detected data as can be seen in the LDD Dk can be exploited. Error reduction of Dk esti- following equation LDD LDD mation is obtained at the expense of increasing the train- L r 2 v[]llllDk  [] CAd [] n [], (16) ing duration from NTs to qNTs, where q is the number of kij LDD , j1 pilot symbols repetition for the desired user.

In the feedback link, ij, []l F k is sent from the mo- where nDn[]ll k []. To obtain Dk in the receiver, s LDD LDD bile user to the base-station to be used for the TAS. Since, in this paper, a new method is proposed, in which the F is known at the base-station,  []l can be easily k ijs , base station sends Dk through a pilot signal. In the LDD calculated at the base-station. Exactly like the previous proposed method, the base station transmits the Dk section, feedback link is assumed to be error free and LDD without any delay. periodically, whose period is much larger than the sym- Using pilot based strategy for joint estimation of chan- bol time since the number of mobile users changes much nel gains and LDD operator reduce the spectral effi- slower than the symbol time. Moreover, the base station ciency. Hence, effect of using pilot based strategy on the spreads the pilot signal for transmitting Dk using the LDD spectral efficiency is analyzed in this section. The spec- kth spreading sequence. This strategy avoids generating tral efficiency of joint estimation of channel and LDD interference and maintains the system security since only operator is defined as, the kth mobile user can obtain the Dk for detecting its TIB qK LDD  1, (18) data. The received pilot symbol is as follows: TTB Rb

TSk[l] Βi,j[l]

k Βi,j[l] DLDD +n’(t)

TSk[l]

k n(t) ck DLDD ck

Transmitter Module Wireless Channel Receiver Module Figure 1. Block diagram of proposed joint channel estimation and LDD operator method.

4 where, TIB and TTB are transmitted information bits the TAS at Pek,  10 with the diversity order m = 1. and total transmitted bits, respectively; also,  and Rb Figure 3 shows the effect of proposed joint estimation are variation rate of number of arriving user to the cell of channel gains and the LDD operator on the perform- and bit rate, respectively. The spectral efficiency of the ance of the TAS/MRC plus LDD with a training sequence proposed method is analyzed for practical values of q , having length of either 25 or 50, which needs once (q = 1) or twice (q = 2) repetition of D elements, respec- K and  in the next Section. LDD In the next section, the currently explained algorithm tively. From Figure 3, it is obvious that the diversity is used for the joint estimation of channel and the LDD order remains almost constant since the slope of the three operator. Also, the bit error probability performance of -1 this method is evaluated and compared with the bit error 1010-1 m = 1, MRC+ LDD , Sim. m = 1, MRC + LDD, Theo. probability of the same system with the perfect estima- m = 1, TAS/MRC + LDD, Sim. m = 1 TAS/MRC + LDD, Theo. tion of channel and the LDD operator. m = 2, MRC+ LDD , Sim. -2-2 m = 2, MRC + LDD, Theo. 1010 m = 2, TAS/MRC + LDD, Sim. m = 2 TAS/MRC + LDD, Theo. 4. Simulation Results m = 3, MRC+ LDD , Sim. m = 3, MRC + LDD, Theo. m = 3, TAS/MRC + LDD, Sim. -3-3 1010 m = 3 TAS/MRC + LDD, Theo. BER In this section, we validate our analysis, equation (14), BER using computer simulations. We simulate the TAS/MRC plus LDD scheme in flat Nakagami correlated fading -4-4 1010 channels. Furthermore, the effect of the proposed method for joint estimation of channel and the LDD operator is

-5-5 studied on the BER performance of TAS/MRC plus 10 10 0 2 4 6 8 10 12 LDD system. 0 2 4 SNR[dB] 6 8 10 12 The base station transmits data with equal amplitudes SNR [dB] for each of K = 25 users. Random sequence with length Figure 2. BER performance of MRC plus LDD and TAS/ of 63 has been used for short spreading codes. A rectan- MRC plus LDD. gular pulse shaping waveform pt() is used for shaping filter in the transmitter side. The type of modulation is 10-1 BPSK. Simulations are performed for a MIMO system with 2 transmitter antennas and 3 receiver antennas over correlated Nakagami flat fading channels. The normal- 10-2 ized correlation antenna matrix is the same as the one given in [9], it is given by a 3 × 3 matrix denoted by T 10-3   123,, , where  1  1 0.727 0.913 , BER T T  2  0.727 1 0.913 and  3  0.913 0.913 1 . -4 Figure 2 shows the BER of the TAS/MRC plus LDD 10 in the aforementioned Nakagami correlated fading channels for m = 1, 2 and 3. It is obvious that our analytical result given by (14) is validated by computer simulations. 0 2 4 6 8 10 12 Moreover, the system with TAS/MRC plus LDD has a SNR [dB] better performance so that it has approximately 3.5 dB Figure 3. BER performance of TAS/MRC plus LDD for m SNR gain relative to that of the MRC plus LDD without = 1 with imperfect channel estimation.

Copyright © 2010 SciRes. WSN 560 S. GHAVAMI ET AL. curves are approximately the same, and there is only 4.5 1.002 4 1 dB or 3 dB loss in the SNR at Pek,  10 due to using the proposed joint estimation of channel and the LDD 0.998 operator with training sequence whose length is 25 or 50,

 0.996 respectively. It is notable that by increasing q the SNR k = 10 loss reduces. 0.994 k = 30 The mean square error (MSE) of the proposed joint k = 50 0.992 k = 70 estimation of channel and the LDD operator is defined k = 90 as, 0.99 0 5 10 15 20 25 30 35 40 45 50 2 Training Length, q MSE E DDˆ LDDk,:  LDD (19) k,: (a) λ1 = 10 user/sec 1.005 where ˆ is kth row of the estimated LDD op- DLDD  k,: 1 era- tor, E{} denotes expectation operator and 2 0.995 ˆ denotes square norm of matrix. DDLDD LDD  k,: k,: k = 10 0.99 Figure 4 shows MSE of the proposed joint estimation of k = 30 channel and the LDD operator over AWGN, in terms of k = 50 0.985 k = 70 number of pilot repetition q, for different values of SNR. k = 90 It is obvious that by increasing q, MSE of D 0.98  LDD k,: 0 5 10 15 20 25 30 35 40 45 50 estimation is reduced. Training Length, q Figure 5(a) shows the  in terms of the q for dif- (b) λ2 = 20 user/sec ferent values of active users in the cell with traffic varia- 1 tion of   10 user/ sec and Rb  5 Mbps . It is obvious 0.99 even with q = 50 bits and k = 90 users, the efficiency is greater than 0.99. Figure 5(b) is similar to Figure 5(a) 0.98

with   20 user/ sec . It can be seen with q = 50 bits  k = 10 0.97 and k = 90 users, the efficiency is greater than 0.98. Fig- k = 30 ure 5(c) and 5(d) are similar to Figure 5(a) with k = 50 0.96 k = 70   50 user/ sec and   100 user/ sec , respectively. k = 90 0.95 0 5 10 15 20 25 30 35 40 45 50 SNR = 0 dB Training Length, q 0 SNR = 3 dB 1010 SNR = 6 dB (c) λ = 50 user/sec SNR = 9 dB 3 SNR = 12 dB -1 1 1010-1 SNR = 15 dB

-2 0.98 1010-2

0.96 -3-3 1010  k = 10

MSE 0.94 MSE MSE -4 k = 30 1010-4 k = 50 0.92 k = 70 -5 1010-5 k = 90 0.9 0 5 10 15 20 25 30 35 40 45 50 -6-6 1010 Training Length, q

-7-7 (d) λ4 = 100 user/sec 1010 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Training Length, q Figure 5. Efficiency in terms of number of pilot symbols Training Length, q repetition for different number of active users in cell with

Figure 4. Mean Square error of joint estimation of channel (a) variation of input traffic of λ1 =10 user/sec, (b) λ2 =20 and the LDD operator in terms of training length. user/sec, (c) λ 3 =50 user/sec and (d) λ 4 = 100 user/sec.

4. Conclusions 10, No. 6, 1999, pp. 585-595. [6] G. J. Foschini and M. J. Gans, “On Limits of Wireless In this paper, the BER performance analysis of the TAS/ Communications in a Fading Environment When Using Multiple Antennas,” Wireless Personal Communications, MRC plus LDD is performed for the downlink WCDMA Vol. 6, No. 3, March 1998, pp. 311-335. network in correlated Nakagami fading channels. Equa- tion (14), derived in the analysis, was validated using [7] S. Thoen, L. Van der Perre, B. Gyselinckx and M. Eng- computer simulations. Also a pilot based channel estima- els, “Performance Analysis of Combined Transmit-SC/ Receiver-MRC,” IEEE Transactions on Communications, tion method is proposed for joint estimating of the chan- Vol. 49, No. 1, 2001, pp. 5-8. nel gains and the LDD operator. Simulation results show that with joint estimation of channel gains and the LDD [8] Z. Chen, J. Yuan and B. Vucetic, “Analysis of Transmit antenna Selection/Maximal-ratio Combining in Rayleigh operator, diversity order is kept in the receiver. Moreover, Fading Channels,” IEEE Transactions on Vehicular our analysis shows that the spectral efficiency degrada- Technology, Vol. 54, No. 4, 2005, pp. 1312-1321. tion due to using the pilot based strategy for joint estima- [9] L. Yang, D. Tang and J. Qin, “Performance of Spatially tion of channel gains and LDD operator is negligible. Correlated MIMO Channel with Antenna Selection,” IEE Ectronics Letters, Vol. 40, No. 20, 2004, pp. 1281-1282. 5. References [10] B. Y. Wang and W. X. Zheng, “Exact BER of Transmit- ter Antenna Selection/Receiver MRC over Spatially Cor- [1] L. B. Milstein, “Wideband Code Division Multiple Ac- related Nakagami-Fading Channels,” IEEE Conference cess,” IEEE Journal on Selected Areas in Communica- on Circuits and Systems, Kos, May 2006, pp. 1370-1373. tions, Vol. 18, No. 8, August 2000, pp. 1344-1354. [11] Y. Yao and H. V. Poor, “Blind Detection of Synchronous [2] S. Verdu, “Multiuser Detection,” Cambridge University CDMA in Non-Gaussian Channels,” IEEE Transactions Press, Cambirdge, 1998. on Signal Processing, Vol. 52, No. 1, January 2004, pp. [3] X. Wang and H. V. Poor, “Blind Multiuser Detection: A 271-279. Subspace Approach,” IEEE Transactions on Information [12] A. Papoulis, “Probability, Random Variables and Sto- Theory, Vol. 44, No. 2, March 1998, pp. 677-690. chastic Processes,” 4th Edition, McGraw-Hill, New York, [4] B. R. Vojcic and W. M. Jang, “Transmitter Precoding in 2001. Synchronous Multiuser Communications,” IEEE Trans- [13] J. G. Proakis, “Digital Communications,” 4th Edition, actions on Communications, Vol. 46, No. 10, October McGraw-Hill, New York, 2001. 1998, pp. 1346-1355. [14] R. L. Graham, D. B. Knuth and O. Patashnik, “Concrete [5] E. Telatar, “Capacity of Multi-Antenna Gaussian Chann- Mathematics,” Addison-Wesley, New York, 1989. els,” European Transactions on Telecommunications, Vol.