Performance Enhancement of MC-CDMA System through B-STTC based STBC and STBC based B-STTC Site Diversity Techniques * Corresponding author N.Kumaratharan* Department of Information Technology P.Dananjayan Sri Venkateswara College of Engineering Department of Electronics and Communication Engg Sriperumbudur, Tamil Nadu, India Pondicherry Engineering College [email protected] Pondicherry-605014 India

Abstract— The combination of multiple antennas and multi-carrier code division multiple access (MC-CDMA) is a strong candidate for the downlink of future mobile communications. The advancement of such systems, in scenarios that model real life transmissions is an additional step towards an optimised achievement. Nevertheless, when transmitting over fading channel, multi-cell interference occurs and this degrades the performance of the system. Site diversity technique is applied to the system to overcome multi-cell interference. Due to non orthogonality of spreading codes multi-cell interference is not completely eradicated. To overcome this problem, space time block code (STBC) based space time trellis code (STTC) site diversity technique was introduced to reduce multi-cell interference. In this paper, balanced STTC (B-STTC) based STBC site diversity is proposed to further improve the performance of MC-CDMA system by mitigating multi-cell interference and is extended to STBC based B-STTC site diversity technique. Simulation result shows that STBC based B- STTC site diversity outperforms B-STTC based STBC site diversity technique.

Index Terms— MC-CDMA, B-STTC based STBC, STBC based B-STTC, site diversity

I. INTRODUCTION

Broadband wireless access for evolving mobile internet system faces multi-cell interference due to fading channel and multimedia services are driving a surge of research resulting in degradation of bit-error rate (BER). on future wireless communication systems to support Site diversity technique has been proposed for multi-user access and high data rates. Multi-carrier code realising CDMA and orthogonal frequency division division multiple access (MC-CDMA), which suits high multiplexing (OFDM) systems to minimise multi-cell data rate applications with multiplexing technique interference [5-7], where STBC is used to gain diversity appears to be a promising technique in achieving high effect among several base stations. STBC site diversity data rates [1]. MC-CDMA is robust to multi-path fading, system transmits the encoded signals from several base inheriting the advantages of conventional CDMA where stations and these signals are combined at the receiver frequency diversity can be achieved in a broadband with STBC decoding operation. STBC branches and the channel [2]. With its capability of synchronous scrambling codes are assigned to each base station to transmission, MC-CDMA is suitable for downlink of maintain orthogonality of signals between the cells and to cellular communication systems [3]. The challenge of reduce interference among them. The same technique is achieving reliable data transmission over wireless link is extended to MC-CDMA system. However, the more difficult due to the fact that received signals from scrambling codes assigned are generally non orthogonal multi-path add destructively causing multi-cell among cells and hence multi-cell interference still exists. interference which results in serious performance Using STBC with multiple antennas at each base station, degradation. To achieve reliable communication over site diversity was achieved with further reduction in wireless links antenna diversity [4] derived by employing multi-cell interference [8]. STBC does not provide coding spatially separated antennas at the transmitter and gain and in view of this it is worthwhile to consider a receiver was introduced. High data rate MC-CDMA joint design of error control coding, modulation, transmit systems additionally employ multiple input multiple and receive diversity to develop an effective signalling output (MIMO) [5] techniques to mitigate fading. scheme called space time trellis code (STTC), which Data transmission involves spreading operations by the combats the effects of fading [9]. STTC became use of short channelisation code and long scrambling extremely popular as it can simultaneously offer coding code. Short channelisation code helps in separating the gain with spectral efficiency and full diversity over signals of different users present within the cell and long fading channels. STTC was used to obtain site diversity scrambling code mitigates the effects of interference with multiple antennas at base station and it outperformed produced by users belonging to other cells. However, the STBC based site diversity in terms of error rates [10]. A new class of 4-phase shift keying (4-PSK) STTC using points of constellation with same probability called as 骣s1... s 1 ... s 1 ... s 1 balanced STTC (B-STTC) [11] was proposed. B-STTC 琪1,1u ,1 1, v+ 1 u , v + 1 2 2 2 2 with equal probable of constellation points achieves SB=琪s1,1... s u ,1 ... s 1, v+ 1 ... s u , v + 1 (3) 琪 reduced error rate [11] and it is used to achieve site 琪sMT... s M T ... s M T ... s M T diversity for MC-CDMA system to enhance its 桫1,1u ,1 1, v+ 1 u , v + 1 performance. STBC based STTC codes [12] built with set partitioning [13], achieves more diversity gain and For three transmit and receive antenna case, the achieves better error rates and improves the performance encoder with a help of three constellation symbols s1, s 2 of MC-CDMA system. To further enhance the * * * performance of MC-CDMA system, in this work, and s3 generates blocks s1, s 2 , s 3 ,- s 1 , s 2 and -s3 . B-STTC based STBC site diversity is proposed and Signal s1 is transmitted from first antenna, s2 is analysed. The use of B-STTC in STTC based STBC reduces the error rate and pave way for improvement in transmitted from second antenna and s3 is transmitted performance. Furthermore, it is extended to STBC based from third antenna at time t =1. Signals -s*, s * and B-STTC to attain site diversity. 1 2 * -s3 are transmitted from first, second and third antenna II. B-STTC BASED STBC SITE DIVERSITY TECHNIQUE FOR MC- respectively at time t = 2 . CDMA SYSTEM Assuming that the fading remains constant, the B-STTC based STBC site diversity is proposed to received signals from three different antennas are denoted improve the performance of MC-CDMA system in multi- as path fading environment. B-STTC based STBC code exploits diversity gain and channel efficiency y1= h 1 s 1 + h 2 s 2 + h 3 s 3 + n 1 simultaneously without aggravating a bandwidth * * * y2= - h 1 s 1 + h 2 s 2 - h 3 s 3 + n 2 (4) expansion similar to STTC based STBC codes, with y= h s - h s* + h s + n decreased error rate in view of the fact that B-STTC is 3 1 1 2 2 3 3 3 used in replacement to STTC block. Fig.1 represents the block diagram of B-STTC based where STBC site diversity transmitter for MC-CDMA system h1, h 2 and h3 are the path gains modelled as with MT transmitting antennas. The input symbol vectors independent samples of a zero mean complex are modulated by a B-STTC and STBC encoder and Gaussian random variable transmitted as in conventional MC-CDMA system. The n1, n 2 and n are random Gaussian variables with receiver model provided for STBC site diversity [8] can 3 2 be used here as it involves normal STBC decoding zero mean and variance s . operation. In the transmitter, input bits are fed to the encoder The receiver generates soft estimates with the assistance with the help of memoryless source SR = {0, 1} with of perfect channel state information (CSI) [10] as follows equally probable symbols [11], the modulation for a * * given state is denoted as s1= h 1 y 1 + h 2 y 2 + h 3 y 3

2 2 2 * * T iT =h + h + h s + h n + h n + h n X= ( x1 , x 2 ,....., xu ) Z 4 (1) ( 1 2 3) 2 1 1 2 2 3 3

i * * T s2= h 2 y 1 + h 1 y 2 + h 3 y 3 where Z 4 represents the index of quadrature phase shift 2 2 2 (5) keying (Q-PSK) symbols at transmitting antenna of the h h h s h n h n* h * n =( 1 + 2 + 3) 3 + 2 1 + 1 2 + 3 3 shift register realized by (v + 1) blocks of u bits and * * s3= h 3 y 1 + h 2 y 2 + h 1 y 3 x1 x 2 ,...,x u are the modulated symbols. The B-STTC 2 2 2 h h h s h n* h n h * n generated by the STTC encoder with Q-PSK is given by =( 1 + 2 + 3) 1 + 3 1 + 2 2 + 3 3

F= SB X (2) With the first transmitted symbol s1 , the Viterbi decoder builds the following metric for the branch where SB is the generator matrix given by s symbol M R , as given below

2 m( s , s )= h2 + h 2 + h 2 s + d2 (s  , s ) e1 MR( 1 2 3) M R e 1 M R

2 m( s , s )= h2 + h 2 + h 2 s + d2 (s  , s ) e2 MR( 1 2 3) M R e 2 M R (6) 2 Fig. 1 Block diagram of B-STTC based STBC site diversity 2 2 2 2 me( s3 , s M )= h 1 + h 2 + h 3 s M + d e (s  3 , s M ) transmitter for MC-CDMA system R( ) R R -M R -r M where ra a R 骣 2 2 骣E P( S E ) 琪 轾 s- e + s - e s e臌 l l l l+1 琪 2 me denotes the metric of the soft estimates 桫l =1 桫4s

-ra M R -r M s ra a R associated with M R 骣 2 2 1/ra E 轾 骣 s =琪 sl - e l + s l - e l+1 琪 2 MR is the number of receiving antennas 臌 桫l =1 桫4s d2 ( s , s ) d2 ( s , s ) d2 ( s , s ) e1 M R , e2 M R and e3 M R are (10) the Euclidean distance obtained from where * * ra is the rank of the coded matrix (s1 , sM )( s  1 , s M ) , (s2 , sM )( s  2 , s M ) and R R R R r M is the diversity gain (s , s )( s  , s )* a R 3MR 3 M R respectively ra 2 2 1/ra 轾c- e + c - e is the coding gain 臌l l l l+1 Performance of the system with B-STTC based STBC l =1 site diversity under fading channel remains constant for By this method B-STTC based STBC site diversity two consecutive symbol transmission periods, 2Tp. Analysis of the system is carried out through the technique is realised for the system which obtains coding decoding data E obtained from the maximum likelihood gain without provoking bandwidth expansion. decoder in the receiver when the coded sequence S is transmitted. S and E are defined as III. STTC BASED STBC SITE DIVERSITY TECHNIQUE FOR MC-CDMA SYSTEM S=[ s , s , - s* , s * ,..., s , - s * , s * ] 1 2 2 1 2Tp- 1 2 T p - 1 2 T p - 2 (7) Fig.2 depicts the block diagram of STBC based B- E=[ e , e , - e* , e * ,..., e , - e * , e * ] 1 2 2 1 2Tp- 1 2 T p - 1 2 T p - 2 STTC site diversity transmitter for MC-CDMA system and the receiver can utilise STTC site diversity [10] technique. STBC based B-STTC codes are similar to where e1 and e2 are the decoded data of the symbols s1 STBC based STTC codes with balanced constellation and s2 points in STTC block. Like STBC based STTC codes, The error probability approximation is obtained as STBC based B-STTC codes are also built by set partitioning. The goal of set partitioning is to achieve 2 2 禳 2T - 2 禳轾 p sl- e l + s l - e l+1 better coding gain and is obtained through pair-wise 镲Es 臌 镲 Pe ( S� E h1 , h 2 )- exp 眄 2  distance. As STBC based B-STTC codes have equally 4s 2 2 镲rx =1 轾h+ h 镲 铪 铪臌1 2 probable constellation points at the decoder it reduces the (8) error rate compared to B-STTC based STBC codes. where For STBC codes, the determinant criterion defines the l is the symbol duration pair-wise distance which is used to establish the partitioning rules. If the transmission matrix of space time Tp is the symbol transmission period ⅱ Es is the average energy of the signal code is denoted as , Df ( c1 , c 2 )= G ( s 1 , s 2 ) - G ( s 1 , s 2 ) constellation represents the difference of the transmission matrices for

codewords c1 and c2 , the diversity is defined by the For an independent Rayleigh fading distribution of minimum rank of the matrix D( c , c ) . The minimum of r M and h with probability density of f 1 2 a R 1 the determinant of the matrix P h=2 h exp - h 2 H H ( 1) 1( 1 ) , B( c1 , c 2 )= Df ( c 1 , c 2 ) D f ( c 1 , c 2 ) ,where Df ( c1 , c 2 ) is the Hermition difference of the transmission matrix, over all

2Tp - 2 禳 E 2 2 2 2 possible pairs of distinct codewords c and c [14] P( S E ) E exp -s 轾 s - e + s - e 轾 h + h 1 2 e睚 2 臌 l l l l +1 臌 1 2 l =1 铪 4s corresponds to the coding gain. Using this definition

2Tp - 2 骣 禳 E 2 2 2 CGD between codewords (c1 , c 2 ) is given as =E琪exp 睚 -s 轾 s - e + s - e h O4s2 臌 l l l l+1 1, M R 2 l =1 桫 铪 CGD( c1 , c 2 )= Df ( c 1 , c 2 ) = det( B ( c 1 , c 2 )) (11) (9) where With the aid of equation (8), the error event probability, the coded sequence S is decided to E and is 轾 2z2 - ( z )( z )* ej b ( z ) * ( z ) expressed as 犏 1 2 1 2 1 * -j b2 2 * - j a B( c1 , c 2 )=犏 - ( z 3 ) ( z 2 ) e z 2 + z 3 ( z 2 ) ( z 1 ) e 犏 (z )( z )* ( z ) * ( z ) ej a 2 z 2 臌犏 3 1 3 1 3 ⅱ z1= s 1 - s 1; z 2 = s 2 - s 2 ; z 3 = s 3 - s 3 The STBC orthogonal design coupled via symbol s2 2 骣q2-p 2 det(B(c1 ,c 2 )=64 sinω琪 for three transmit and receive antennas is denoted as 桫 2 2 骣 骣q-p 骣 q -p 琪sinω2琪 +1 sin 1 2 ω 琪 + 2 2 琪 桫2 桫 2 琪 琪 2 骣q3-p 3 琪 sinω琪 桫 桫 2 (15) Fig. 2 Block diagram of STBC based B-STTC site diversity transmitter for MC-CDMA system where w= 2 p / Pc (Pc is the size of the transmit constellation) and w= p / 2 for a Q-PSK constellation. Equation (15) clearly implies that symbols s and s ; s 轾-s* s s * e j b 1 1 2 2 1 1 and s ; s and s have to be different in each coset to 犏 * * 2 3 3 G( s1 , s 2 , s 3 ) =犏 s 1 s 2 - s 3 maintain a non-null CGD. 犏s* ej a s s * (12) After the set partitioning step, a trellis is built 臌3 3 2 affecting a particular STBC from a set of possible candidates to transitions originating from a state. The *j b *j a where s1 e and s3 e enable to optimise the minimum coding gain is optimised within each coset by maximising the distance between codewords. A design with full CGD within each obtained coset, angles (a , b ) belong to diversity is needed to use STBC code given in equation the constellation symbol and are used to separate the (14) into a STTC design and in fact, achieving full triplets of symbols which share the same second symbol. diversity is equivalent to showing the determinant of The set partitioning for Q-PSK constellation is matrices B( c , c ) are nonzero over all possible obtained through the mathematical expression given by 1 2 codewords c1 and c2 . As it is the case, matrices B( c1 , c 2 ) 4 2 2 4 should be checked that they do not loose the full rank det(B ( c1 , c 2 )) = z 1 z 3 + z 1 z 3 (13) value when c1 and c2 belong to different cosets. To solve - 2 Re轾 (z* )3 ( z ) 3 e j ( a-b ) 臌 3 1 this unit transform matrices Θ are assigned to each state to check that the minimum of det( B( c1 , c 2 ) ) is equal to

The choice of (a , b ) , which maximises the minimum zero when c1 belongs to coset 1 and c2 belongs to coset CGD within each coset, is sampled at a rate p /16 . 2. In fact, unitary matrix Θj corresponds to a rotation and However, the obtained values for (a , b ) does not preserves distance among the constellation points i.e., the minimum CGD value is left unchanged by applying a correspond to Q-PSK constellation points [15] and this G( s , s , s ) necessitates the need for constellation expansion to use unitary transform Θj to 1 2 3 within each coset. set partitioning with maximum of minimum CGD values. Search for unitary matrices are done using Applying set partitioning for 16 cosets gives a minimum parameterisation [17], and along with the selected CGD values of 128 and without constellation expansion partitioning level, unit matrices whose number equal to [16], using set partitioning for the same number of cosets the number of cosets with maximum separation distance gives minimum CGD of 8 with (a , b ) = (0,0) . are obtained. The trellis is evenly built by affecting a unitary matrix transform to each coset with each of them A simple STBC structure is used to derive a set corresponding to a trellis state and is transmitted. partitioning rule. This structure will be a basis to obtain a Assuming Rayleigh fading channel between each powerful quasi orthogonal structure which will be pair of transmit and receive antenna, the received signal incorporated into a trellis. The STBC matrix looks like is given as (14) Y= H Qj G( s1 , s 2 , s 3 ) + N (16)

The computation of the determinant of matrix B( c1 , c 2 ) where with jp1ω jp2ω jpω 3 and s1 = e , s2 = e , s 3 = e H is the channel coefficient Θj is the 3 x 3 unitary matrix used in state j 'jq1ω ' jq 2 ω ' jq 3 ω where s1 = e , s 2 = e , s 3 = e N is the vector of additive white Gaussian noise 2 p1, p 2 , p 3 , q 1 , q 2 , q 3 are the integers, and yields the (AWGN) with zero mean and variance s following expression Received signal within three successive time slot intervals, is given by y= - h s* + h s * + h s * ej a + n there is an improvement error rate and hence the 1 1 2 2 1 3 3 1 performance of the system increases due to the y2= h 1 s 1 + h 2 s 2 + h 3 s 3 + n 2 (17) exploitation of diversity in the transmitter and receiver. *j b * * y3= h 1 s 1 e - h 2 s 3 + h 3 s 2 + n 3 TABLE I To compute branch metrics for different symbol SIMULATION PARAMETERS triplets, auxiliary quantities are obtained as below Parameters Descriptions Modulation 4-PSK ' * ja y1 = y 1 -h 3s 3 e Symbol length 64 ' Number of sub- 128 y2 = y 2 -h 3s 3 carriers (18) Channel estimation Perfect estimation y'' = y -h s 2 2 1 1 Channelisation code Walsh-Hadamard code of ' * jb length 63 y3 = y 3 -h 1s 1 e Scrambling code Random code of length 63

Channel Rayleigh fading channel with The decoding signal is obtained through combining AWGN floor [18] with equations (17) and (18) and is given by Number of antennas Two, three, four and five

2 2 y* hj +h * y = h + hs +n h * +n * h 1 2 1 2( 1 2) 1 2 1 1 2 2 2 -y* hj +h * y = h + hs +n h * -n * h 1 1 2 2( 1 2) 1 2 2 1 1

2 2 y* h +h * y'' = h + hs +n h * +n * h 3 3 2 2( 2 3) 2 2 2 3 3 2 2 (19) -y* h +h * y'' = h + hs +n h * -n * h 3 2 3 2( 2 3) 3 2 3 3 2

Summing the above equation yields

* * 轾 y1 h 2+ y 2 h 1 犏 * * * 犏-y1 h 1 +2 y 2 h 2 + y 3 h 3 = 犏 -y* h + y h * 臌 3 2 2 3 轾 2 2 * * -j a h1+ h 20 h 3 h 1 + h 2 h 3 e 犏 轾s1 犏h h*+ h h * e -j b h2 +2 h 2 + h 2 h h * + h h * e - j a 犏 s 犏1 2 3 1 1 2 3 3 2 1 3犏 2 Fig. 3 Performance of the system with and without diversity * * -j b 2 2 犏 犏h h+ h h e0 h + h 臌s3 臌犏1 3 2 1 2 3 Performance of MC-CDMA system with STBC based * * STTC site diversity is evaluated by varying the 轾 n1 h 2+ n 2 h 1 犏 * * * transmitting and receiving antennas. Fig.4 illustrates the + -n1 h 1 +2 n 2 h 2 + n 3 h3 犏 performance of the system in terms of SER and Eb/N0 犏 -n* h + n h * 臌 3 2 2 3 with STBC based STTC site diversity for two, three, four (20) and five transmit and receive antennas. It is observed from the plots that the system with five transmit and receive antennas gives better performance in SER when

compared to the system with two, three and four IV. PERFORMANCE ANALYSIS antennas. The improvement in SER for the larger number of antennas is due to the maximum utilisation of The proposed site diversity for MC-CDMA system is diversity. The maximum number of antennas used for simulated using MATLAB and the simulation parameters simulation is restricted to five as further increase of it are given in Table 1. Fig.3 shows the symbol error rate introduces hardware complexity and increases the cost of (SER) performance with bit energy to the spectral noise the system. density (Eb/N0) of the system with and without diversity under Rayleigh fading channel. The diversity technique uses two antennas at the transmitter and receiver terminal. The result indicates that when multiple antennas are used B-STTC based STBC site diversity uses balanced codes in STTC encoder block which reduces the error rate when compared to STBC based STTC site diversity technique.

Fig. 4 Performance of the system with STBC based STTC site diversity for various antennas

Fig.5 depicts SER versus Eb/N0 performance of the system with B-STTC based STBC site diversity for various numbers of antennas. The result portrays that the SER of the system with five transmit and receive Fig. 6 Performance of the system with STBC based B-STTC site diversity for various antennas antennas outperforms two, three and four transmit and receive antennas. Fig.6 renders the same scenario of the system with STBC based B-STTC site diversity for different antennas. Similar conditions of diversity utilisation observed in Fig.4 and 5 are noticed here irrespective of the coding techniques used for site diversity technique i.e. improvement of SER is noticed clearly when there is increase in number of antennas.

Fig. 7 Performance comparison of the system with STBC based STTC and B-STTC based STBC site diversity techniques for various antennas

SER performance of the system is compared between B-STTC based STBC site diversity technique and STBC based B-STTC site diversity technique and is depicted in Fig. 5 Performance of the system with B-STTC based STBC site Fig.8. This figure clearly portrays that STBC based diversity for various antennas B-STTC site diversity technique surpasses B-STTC based STBC site diversity technique. As the STBC based The SER performance of STBC based STTC site B-STTC codes are transmitted in STTC form and diversity is compared with the B-STTC based STBC site moreover in balanced manner (equal probability of diversity in Fig.7. It is clearly visible from this figure that constellation points), significant improvement in error B-STTC based STBC site diversity technique outshines performance is achieved. STBC based STTC site diversity technique of the system. [5] S.M. 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