Keywords: Multiple-Input Multiple-Output (MIMO), BPSK, QPSK, QAM, STBC, Spatial Modulation.

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1 ISSN Vol.06,Issue.04, June-2014, Pages: Performance Analysis of STBC-SM over Orthogonal STBC SHAIK ABDUL KAREEM 1, M.RAMMOHANA REDDY 2 1 PG Scholar, Dept of ECE, P.B.R.Visvodaya Institute of Technology and Sciences, Kavali, Nellore, AP, India, abdulkareem@gmail.com. 2 Asst Prof, Dept of ECE, P.B.R. Visvodaya Institute of Technology and Sciences, Kavali, Nellore, AP, India, ramumadithati@gmail.com. Abstract: Space-time block coding (STBC) is a Multiple-Input Multiple Output (MIMO) Transmit strategy which exploits transmits diversity and high reliability. STBC have been shown to perform well with other MIMO systems. MIMO transmission scheme, called space-time block coded spatial modulation (STBC-SM), is compared extensively with all MIMO transmission schemes. STBC combines spatial modulation (SM) and space-time block coding (STBC) to take advantage of the benefits of both while avoiding their drawbacks. In the STBCSM scheme, the transmitted information symbols are expanded not only to the space and time domains but also to the spatial (antenna) domain which corresponds to the on/off status of the transmit antennas available at the space domain, and therefore both core STBC and antenna indices carry information. A general technique is presented for the design of the STBC-SM scheme for any number of transmits antennas besides the high spectral efficiency advantage provided by the antenna domain; the proposed scheme is also optimized by deriving its diversity and coding gains to exploit the diversity advantages of STBC. The performance advantages of the STBC-SM over simple OFDM, CDMA, BPSK, QPSK, QAM and PSK are shown by simulation results for various spectral efficiencies and number of channels, which are supported by the comparison for the bit error probability for different time intervals. Along with above stated MIMO techniques new version of STBC are analyzed with existing STBC-SM, like distributed STBC and Orthogonal STBC. Keywords: Multiple-Input Multiple-Output (MIMO), BPSK, QPSK, QAM, STBC, Spatial Modulation. I. INTRODUCTION MIMO technology means multiple antennas at both the ends of a communication system, that is, at the transmitting end and receiving end. The idea behind MIMO is that the transmit antennas at one end and the receive antennas at the other end are connected and combined in such a way that the bit error rate (BER), or the data rate for each user is improved.mimo has the capacity of producing independent parallel channels and transmitting multipath data streams and thus meets the demand for high data rate wireless transmission. This system can provide high frequency spectral efficiency and is a promising approach with tremendous potential. The use of multiple antennas at both transmitter and receiver has been shown to be an effective way to improve capacity and reliability over those achievable with single antenna wireless systems. Consequently, multiple-input multiple-output (MIMO) transmission techniques have been comprehensively studied over the past decade by numerous researchers, and two general MIMO transmission strategies, a space-time block coding1 (STBC) and spatial multiplexing, have been proposed. The low-complexity sub optimum linear decoders, such as the minimum mean square error (MMSE) decoder, degrade the error performance of the system significantly. On the other hand, STBCs offer an excellent way to exploit the potential of MIMO systems because of their implementation simplicity as well as their low decoding complexity. A. STBC-SM It has been shown that the symbol rate of an OSTBC is upper bounded by ¾ symbols per channel use (PCU) for more than two transmit antennas. Several high rate STBCs have been proposed in the past decade, but their ML decoding complexity grows exponentially with the constellation size, which makes their implementation difficult and expensive for future wireless communication systems. Recently, a novel concept known as spatial modulation (SM) has been introduced to remove the ICI completely between the transmit antennas of a MIMO link. The basic idea of SM is an extension of two dimensional signal constellations (such as M-ary phase shift keying (M- PSK) and M-ary quadrature amplitude modulation (M- QAM), where M is the constellation size) to a third dimension, which is the spatial (antenna) dimension. Therefore, the information is conveyed not only by the amplitude/phase modulation (APM) techniques, but also by the antenna indices. However, SSK modulation does not provide any performance advantage compared to SM. In both of the SM and SSK modulation systems, only one transmit antenna is active during each transmission interval, and therefore ICI is totally eliminated, where different 2014 SEMAR GROUPS TECHNICAL SOCIETY. All rights reserved.

2 combinations of the transmit antenna indices are used to convey information for further design flexibility. B. Related work MIMO is an effective way to improve the capacity and reliability, comparing with single antenna wireless systems[1],[2].several MIMO techniques have been comprehensively studied recently studied among which the space time block code (STBC) for two transmit antennas. Offers a low- complexity maximum likelihood (ML) decoding due to its orthogonal structure. Based on this property of orthogonality, orthogonal space time block codes (OSTBCs) was presented in [3],[4].OSTBCs are special class of space time codes which exploits the spatial diversity and offer low complexity ML decoding. However,rate one OSTBC exists for two transmit antennas only to increase the data rate a new class of semi-orthogonal codes was proposed in [5],[6] known as quasi orthogonal space time block codes (QOSTBCs) they are all full rate codes with pair wise decoding complexity. However, the QOSTBCs of [5],[6] cannot achieve full diversity. To achieve full diversity, QOSTBC in [7],[8] was proposed by talking half of the symbols from rotated constellation. To further reduce the decoding complexity without compromising on the data rates, a new and distinct class of codes were designed using the concept of co-ordinate interleaving.these codes are popularly known as coordinate interleaved orthogonal designs(ciods) [9],[10]. The CIODs are full rate codes which achieve single-symbol decidability. In [9], [10] CIODs for PAM and QAM constellation are discussed. The existing STBCs retransmit each symbol in space and time which reduce the capacity of the system. This reduction in capacity can be improved by using a mapping function for 16- QAM constellation in Alamouti STBC [2], in this M-PAM constellation and extended it to square QAM constellations. Using this mapping function I proposed an STBC for four transmit antennas which achieves high coding gain and full diversity. II. SPACE-TIME BLOCK CODED SPATIAL MODULATION (STBC-SM) A new MIMO transmission scheme, called STBC-SM, is proposed, in which information is conveyed with an STBC matrix that is transmitted from combinations of the transmit antennas of the corresponding MIMO system. The Alamouti code [3] is chosen as the target STBC to exploit. As a source of information, we consider not only the two complex information symbols embedded in Alamouti s STBC, but also the indices (positions) of the two transmit antennas employed for the transmission of the Alamouti STBC. A general technique is presented for constructing the STBC-SM scheme for any number of transmits antennas. A low complexity ML decoder is derived for the proposed STBC-SM system, to decide on the transmitted symbols as well as on the indices of the two transmits antennas that are used in the STBC transmission. It is shown by computer simulations that the proposed STBC- SHAIK ABDUL KAREEM, M.RAMMOHANA REDDY SM scheme has significant performance advantages over the SM with an optimal decoder, due to its diversity advantage. A closed form expression for the union bound on the bit error probability of the STBCSM scheme is also derived to support our results. The derived upper bound is shown to become very tight with increasing signal-to-noise (SNR) ratio. Fig1. Block Diagram of Space-Time Coding. In the STBC-SM scheme, both STBC symbols and the indices of the transmit antennas from which these symbols are transmitted, carry information. We choose Alamouti s STBC, which transmits one symbol PCU, as the core STBC due to its advantages in terms of spectral efficiency and simplified ML detection. In Alamouti s STBC, two complex information symbols (x1 and x2) drawn from an M-PSK or M-QAM constellation are transmitted from two transmit antennas in two symbol intervals in an orthogonal manner by the codeword. X= X1, X2 = X1, X2 space -X2 X1 time Where columns and rows correspond to the transmit antennas and the symbol intervals, respectively. For the STBC SM scheme we extend the matrix in to the antenna domain. A. Multiple Input Multiple Output (MIMO) MIMO system is commonly used in today s wireless technology, including n Wi Fi, WiMAX, LTE, etc. Multiple antennas (and therefore multiple RF chains) are put at both the transmitter and the receiver. A major concern in MIMO systems is the integration of several antennas into small handheld devices. Finding feasible antenna configurations is an integral part of enabling the MIMO technology. Fig2. Block Diagram of MIMO.

3 A MIMO system with same amount of antennas at both the transmitter and the receiver in a point-to-point (PTP) link is able to multiply the system throughput linearly with every additional antenna. For example, a 2x2 MIMO will double up the throughput. In radio, multiple-input and multiple-output, or MIMO is the use of multiple antennas at both the transmitter and receiver to improve communication performance. It is one of several forms of smart antenna technology. Note that the terms input and output refer to the radio channel carrying the signal, not to the devices having antennas. MIMO technology has attracted attention in wireless communications, because it offers significant increases in data throughput and link range without additional bandwidth, though extra transmit power is needed since multiple transmit antennas are employed instead of only one as in SISO systems. MIMO systems exploit the multipath structure of the propagation channel. The antennas are adapted to the propagation channel. For a comprehensive study, both antennas and propagation channel have to be treated together and described statistically to take many channel realizations of a propagation environment into account. Correlations among channel coefficients are influenced by the antenna properties. As the antennas are collocated in a MIMO array, mutual coupling effects may occur. All these effects should be considered when designing an antenna array for MIMO systems. In this contribution, a method will be presented for accurately modeling both antennas and the propagation channel. III. STBC-SM SYSTEM MODELING In the STBC-SM scheme, both STBC symbols and the indices of the transmit antennas from which these symbols are transmitted, carry information. We choose Alamouti s STBC, which transmits one symbol per channel use (pcu), as the core STBC due to its advantages in terms of spectral efficiency and simplified ML detection. In Alamouti s STBC, two complex information symbols (x1 and x2) drawn from an -PSK or - QAM constellation are transmitted from two transmit antennas in two symbol intervals in an orthogonal manner by Where columns and rows correspond to the transmit antennas and the symbol intervals, respectively. For the STBC-SM scheme we extend the matrix in (1) to the antenna domain. Example (STBC-SM with four transmit antennas, BPSK modulation). Consider a MIMO system with four transmit antennas which transmit the Alamouti STBC using one of the following four code words: Performance Analysis of STBC-SM over Orthogonal STBC (1) Where,, = 1, 2 are called the STBC-SM codebooks each containing two STBC-SM codeword s, = 1, 2 which do not interfere to each other. The resulting STBC- SM code is A Non-interfering codeword group having elements is defined as a group of codeword s satisfying that is they have no overlapping columns. In (2), is a rotation angle to be optimized for a given modulation format to ensure maximum diversity and coding gain at the expense of expansion of the signal constellation. However, if is not considered, overlapping columns of codeword pairs from different codebooks would reduce the transmit diversity order to one. Assume now that we have four information bits to be transmitted in two consecutive symbol intervals by the STBCSM technique. The mapping rule for 2 bits/s/hz transmission is given by Table I for the codebooks of (2) and for binary phase-shift keying (BPSK) modulation, where a realization of any codeword is called a transmission matrix. We have four different codeword s each having M2 different realizations. Consequently, the spectral efficiency of the STBC-SM scheme for four transmit antennas becomes = (1/2) log24m2 = 1 + log2 M bits/s/hz, where the factor 1/2 normalizes for the two channel uses spanned by the matrices in (2). For STBCs using larger numbers of symbol intervals such as the quasi-orthogonal STBC for four transmit antennas which employs four symbol intervals, the spectral efficiency will be degraded substantially due to this normalization term since the number of bits carried by the antenna modulation (log2c), (where c is the total number of antenna combinations) is normalized by the number of channel uses of the corresponding STBC. A. System Design and Optimization 1. STBC-SM Transmitter In this subsection, we generalize the STBC-SM scheme for MIMO systems using Alamouti s STBC to transmit antennas by giving a general design technique. An important design parameter for quasi-static Rayleigh fading channels is the minimum coding gain distance (CGD) between two STBC-SM codeword s and, where is transmitted and, is erroneously detected, is defined as (3) Minimum CGD between two codebooks xi and xj is defined as (2) (4) And the minimum CGD of an STBC-SM code is defined by

4 Note that, corresponds to the determinant criterion, since the minimum CGD between non-interfering codeword s of the same codebook is always greater than or equal to the right hand side of above equation (4) SHAIK ABDUL KAREEM, M.RAMMOHANA REDDY (5) Each codebook must be composed of codeword s with antenna combinations that were never used in the construction of a previous codebook. 5. Determine the rotation angles for each, that maximize for a given signal constellation and antenna configuration; that is, where. As long as the STBC-SM codeword s are generated by the algorithm described above, the choice of other antenna combinations is also possible but this would not improve the overall system performance for uncorrelated channels. Since we have antenna combinations, the resulting spectral efficiency of the STBC-SM scheme can be calculated as Fig3. Block diagram of the STBC-SM transmitter. Unlike in the SM scheme, the number of transmit antennas in the STBC-SM scheme need not be an integer power of 2, since the pair wise combinations are chosen from available transmit antennas for STBC transmission. This provides design flexibility. However, the total number of codeword combinations considered should be an integer power of 2. In the following, we give an algorithm to design the STBC-SM scheme: 1. Given the total number of transmit antennas, calculate the number of possible antenna combinations for the transmission of Alamouti s STBC, i.e., the total number of STBC-SM codeword s from, where is a positive integer. 2. Calculate the number of codeword s in each codebook, from and the total number of codebooks from. Note that the last codebook does not need to have codeword s, i.e., its cardinality is. 3. Start with the construction of which contains non interfering codeword s as (7) The block diagram of the STBC-SM transmitter is shown in Fig. 3. During each two consecutive symbol intervals, 2 bits. Enter the STBC- SM transmitter, where the first log2 bits determine the antenna-pair position l = that is associated with the corresponding antenna pair, while the last bits determine the symbol pair. If we compare the spectral efficiency (7) of the STBC-SM scheme with that of Alamouti s scheme, we observe an increment of provided by the antenna modulation. We consider two different cases for the optimization of the STBC-SM scheme. Case 1: : We have, in this case, two codebooks and and only one non-zero angle, say, to be optimized. It can be seen that is equal to the minimum CGD between any two interfering codeword s from and. Without loss of generality, assume that the interfering codeword s are chosen as (8) Where is transmitted and is erroneously detected. We calculate the minimum CGD between from (3) as (6) 4. Using a similar approach, construct for by considering the following two important facts: Every codebook must contain non-interfering codeword s chosen from pair wise combinations of available transmit antennas. (9)

5 Where for BPSK and quadrature phase-shift keying (QPSK) constellations, it becomes unmanageable for 16-QAM and 64- QAM which are essential modulation formats for the next generation wireless standards such as LTE-advanced and WiMAX. We compute Performance Analysis of STBC-SM over Orthogonal STBC. Although maximization of Similar results are obtained for BPSK signaling except with respect to is analytically possible that is replaced by in (12) and (13). We obtain the corresponding maximum as as a function of [0, /2] for BPSK, QPSK, 16-QAM and 64-QAM signal constellations via computer search and plot them in Fig. 2. These curves are denoted by for = 2, 4, 16 and 64, respectively. Values maximizing these functions can be determined from Fig. 2 as follows:. On the other hand, for 16-QAM and 64-QAM signaling, the selection of s in integer multiples of /2 would not guarantee to maximize the minimum CGD for the STBC-SM scheme since the behavior of the functions and for QPSK and 16-QAM. Similarly, max is calculated for BPSK, QPSK and 16-QAM constellations as (15) (10) Case 2: : In this case, the number of codebooks,, is greater than 2. Let the corresponding rotation angles to be optimized be denoted in ascending order by, where for BPSK and for QPSK. For BPSK and QPSK signaling, choosing According to the design algorithm, the codebooks can be constructed as follows: (11) For guarantees the maximization of the minimum CGD for the STBC-SM scheme. This can be explained as follows. For any, we have to maximize as (13) Where,, for and the minimum CGD between codebooks and is directly determined by the difference between their rotation angles. This can be easily verified from (9) by choosing the two interfering codeword s as and with the rotation angles and, respectively. Then, to maximize min ( ), it is sufficient to maximize the minimum CGD between the consecutive codebooks and. For QPSK signaling, this is accomplished by dividing the interval into equal sub-intervals and choosing, The resulting maximum (11) as can be evaluated from (14) (16) B. Optimal ML Decoder for the STBC-SM System In this subsection, we formulate the ML decoder for the STBC-SM scheme. The system with transmit and receive antennas is considered in the presence of a quasi-static Rayleigh flat fading MIMO channel. The received signal matrix Y can be expressed as (17) Where is the STBC-SM transmission matrix, transmitted over two channel uses and is a normalization factor to ensure that is the average SNR at each receive antenna. H and N denote the channel matrix and 2 noise matrix, respectively. The entries of H and N are assumed to be independent and identically distributed (i.i.d.) complex Gaussian random variables with zero means and unit variances. We assume that H remains constant during the transmission of a codeword and takes independent values from one codeword to another. We further assume that H is known at the receiver, but not at the transmitter. Assuming transmit antennas are employed; the STBCSM code has c codeword s, from which different transmission matrices can be constructed. An ML decoder must make an

6 exhaustive search over all possible transmission matrices, and decides in favor of the matrix that minimizes the following metric: (17) The minimization in (6) can be simplified due to the orthogonality of Alamouti s STBC as follows. The decoder can extract the embedded information symbol vector from (5), and obtain the following equivalent channel model: (18) Where is the equivalent channel matrix of the Alamouti coded SM scheme, which has cdifferent realizations according to the STBC-SM codeword s. In (7), y and n represent the equivalent received signal and noise vectors, respectively. Due to the orthogonality of Alamouti s STBC, the columns of are orthogonal to each other for all cases and, consequently, no ICI occurs in our scheme as in the case of SM. Consider the STBC-SM transmission model as described in Table I for four transmit antennas. Since there are c = 4 STBC-SM codeword s. Generally, we have equivalent channel matrices, and for the lth combination, the receiver determines the ML estimates of and using the decomposition as follows, resulting from the orthogonality of hl,1 and hl,2: x SHAIK ABDUL KAREEM, M.RAMMOHANA REDDY complexity is rewarded with significant performance improvement provided by the STBC-SM over SM. The last step of the decoding process is the demapping operation based on the look-up table used at the transmitter, to recover the input bits from the determined spatial position (combination) ˆl and the information symbols ˆ 1 and ˆ 2. The block diagram of the ML decoder described above is given in Fig. 3. As a result, the total number of metric calculations in (6) is reduced from to, yielding a linear decoding complexity as is also true for the SM scheme, whose optimal decoder requires metric calculations. Obviously, since C for, there will be a linear increase in ML decoding complexity with STBC-SM as compared to the SM scheme. However, as we will show in the next section, this in signisficant increase in decoding complexity is rewarded with significant performance improvement provided by the STBC-SM. The last step of the decoding process is the de-mapping operation, to recover the input bits spatial position (combination) from the determined and the information symbols and. The block diagram of the ML decoder described in Fig.4. (19) Where H l =[ hl,1 hl,2 ],, and is a 2 1 column vector. The associated minimum ML metrics and for and are (20) Since and are calculated by the ML decoder for the lth combination, their summation 1 gives the total ML metric for the lth combination. Finally, the receiver makes a decision by choosing the minimum antenna combination metric as for which. As a result, the total number of ML metric calculations in (15) is reduced from 2 to 2, yielding a linear decoding complexity as is also true for the SM scheme, whose optimal decoder requires metric calculations. Obviously, since for, there will be a linear increase in ML decoding complexity with STBC-SM as compared to the SM scheme. However, as we will show in the next section, this insignificant increase in decoding Fig4. Block diagram of the STBC-SM receiver. C. Performance Analysis Of The Stbc-Sm System In this section, we analyze the error performance of the STBC-SM system, in which 2m bits are transmitted during two consecutive symbol intervals using one of the 2 = 22 different STBC-SM transmission matrices, denoted by X1,X2,...,X here for convenience. An upper bound on the average bit error probability (BEP) is given by the well known union bound Where, deciding STBC-SM matrix (21) is the pair wise error probability (PEP) of given that the STBC SM matrix is transmitted, and, is the number of bits in error between the matrices and. Under the normalization = 1 and in (10), the conditional PEP of the STBC-SM system is calculated as

7 Performance Analysis of STBC-SM over Orthogonal STBC (22) Where,. Averaging (17) over the channel matrix H and using the moment generating function(mgf) approach; the unconditional PEP is obtained as (23) All transmission matrices have the uniform error property due to the symmetry of STBC-SM codebooks, i.e., have the same PEP as that of X1. Thus, we obtain a BEP upper bound for STBC-SM as follows: Fig6. BER performance of STNC scheme for different SNR, with Distributed STBC using CDMA modulation. We obtain the union bound on the BEP as (24) (25) IV.SIMULATION RESULTS AND COMPARISONS In this section, we present simulation results for the STBCSM system with different numbers of transmit antennas and make comparisons with OFDM, CDMA, BPSK, QPSK, QAM, PSK, O-STBC and DSTBC for four transmit antennas. All performance comparisons are made for a BER value of 10 5 and Error probability. We first present the BER upper bound curves of the STBC-SM scheme are evaluated from and depicted in the following Figures. It follows that the derived upper bound becomes very tight with increasing SNR values for all cases and can Fig7. BER performance of STNC scheme for different time intervals, with STBC using QAM modulation. Fig5. BER performance of STNC scheme for different SNR, with Distributed STBC using OFDM modulation. Fig8. BER performance of STNC scheme for different time intervals, with STBC using QPSK modulation.

8 SHAIK ABDUL KAREEM, M.RAMMOHANA REDDY Fig9. BER performance of STNC scheme for different, with Distributed STBC using QPSK modulation. Fig12. The BER performance of the STBC-SM scheme with the orthogonal STBC code scheme. be used as a helpful tool to estimate the error performance behavior of the STBC-SM scheme with different setups. Also note that the BER curves for nt=3,4 and BPSK, QPSK modulations from Fig. 5,6,7,8,9,10,11,12; are shifted to the right while their slope remains unchanged and equal to, with increasing spectral efficiency. We compare the BER performance of the STBC-SM scheme with the orthogonal STBC code scheme which is rate- 3 (transmitting four symbols in two time intervals) STBCS for two and four transmit antennas, respectively. Fig10. BER performance of STNC scheme for different time intervals STBC using BPSK modulation. Fig13. The BER performance of the STBC-SM scheme with = 4 and QPSK. Fig11. BER performance of STNC scheme for different time intervals STBC using OSTBC modulation. In the above figures 12, 13, the BER curves of STBC-SM with =4 and QPSK is evaluated for 3bits/s/Hz transmission. We compare the BER performance of the

9 STBC-SM scheme with the orthogonal STBC code scheme which are rate-3 (transmitting four symbols in two time intervals) STBCS for four transmit antennas, and STBC with 8-qam OSTBC with 32 QAM. Performance Analysis of STBC-SM over Orthogonal STBC TABLE I: Comparison With Respect To the Loss Of Signal Fig14. The BER performance at 3bits for STBC-SM scheme with the orthogonal STBC code scheme. We compare the BER performance of the STBC-SM scheme with the orthogonal STBC code scheme which are rate-3 (transmitting four symbols in two time intervals) STBCS for four transmit antennas, and STBC with 16- QAM and OSTBC with 256 QAM. V. CONCLUSION In this paper, we have compared a novel high-rate, low complexity MIMO transmission scheme, called STBC-SM, with an alternative to existing techniques such as orthogonal STBC and DSTBC. A general technique has been presented for the construction of the STBC-SM scheme for any number of transmit antennas in which the STBC-SM system was optimized by deriving its diversity to reach optimum performance. The proposed new transmission scheme employs both APM techniques and antenna indices to convey information and exploits the transmit diversity potential of MIMO channels. From a practical implementation point of view, the RF (radio frequency) front-end of the system should be able to switch between different transmit antennas similar to the classical SM scheme. It has been shown by a theoretical and practical analysis that the STBC-SM offers significant improvements in BER performance compared to OSTBC and DSTBC systems and other standard communication systems (approximately 3-5 db depending on the spectral efficiency) with an acceptable linear increase in decoding complexity. On the other hand, unlike DSTBC in which all antennas are employed to transmit simultaneously, the number of required RF chains is only two in our scheme, and the synchronization of all transmit antennas would not be required. We conclude that the STBC-SM scheme can be useful for high-rate, low complexity, emerging wireless communication systems. Fig15. The BER performance at 6bits for STBC-SM scheme with the orthogonal STBC code scheme. In Fig. 14, 15 the BER curves of STBC-SM with = 4 and QPSK is evaluated for 3 bits/s/hz transmission. Table-I, clearly explains the overall comparison with respect to the loss of signal at the receiver and by calculating the percentage of loss, the loss less communication will be QAM,QPSK and BPSK schemes over OFDM and CDMA. To select the appropriate Modulation Technique we want to simulate for, coding flexibility is provided and comparative values are clearly exhibited, by the MATLAB program. VI. REFERENCES [1] S. M. Alamouti, A simple transmit diversity technique for wireless communications, IEEE J. Sel. Areas Commun., vol. 16, pp , Oct [2] P. Wolniansky, G. Foschini, G. Golden, and R.Valenzuela, an architecture for realizing very high data rates over the rich-scattering wireless channel, in Proc International Symp. Signals, Syst.,Electron., pp [3] H. Jafarkhani, Space-Time Coding, Theory and Practive. Cambridg University Press, [4] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space time block codes from orthogonal designs, IEEE Trans. Inf. Theory, vol. 45, no. 5,pp , July 1999.

10 SHAIK ABDUL KAREEM, M.RAMMOHANA REDDY [5] E.Biglieri, Y. Hong, and E. Viterbo, On fast-decodable space-time block codes, IEEE Trans. Inf. Theory, vol. 55, no. 2, pp , Feb [6] E. Ba ar and Ümit Aygölü, High-rate full-diveristy space-time blocks codes for three and four transmit antennas, IET Commun., vol. 3, no. 8 pp , Aug, [7] Full-rate full-diversity STBCS for three and four transmit antennas, Electron. Lett. vol. 44, no. 18, pp , Aug [8] D. Tse and P. Viswanath, Fundamentals of Wireless Communication Cambridge University Press, [9] J. Jeganathan, A. Ghrayeb, L. Szczecinski, and A. Ceron, Space shift keying modulation for MIMO channels, IEEE Trans. Wireless ommun., vol. 12, pp , July [10] R. Mesleh, H. Haas, S. Sinaovic, C. W. Ahn, and S. Yun, Spatial modulation, IEEE Trans. Veh. Technol., vol. 57, no. 4, pp , July 2008.

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