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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 Performance Evaluation of Space-Time Turbo Code Concatenated With Block Code MC-CDMA Systems Lokesh Kumar Bansal Aditya Trivedi Department of Electronics & Comm. Engg., Department of Information and Comm. Technology N.I.E.M., Mathura, India ABV-IIITM, Gwalior, India e-mail: lokesh_bansal@rediffmail.com e-mail: atrivedi@iiitm.ac.in Abstract—In this paper, performance of a space-time turbo emphasizes the need for improved spectral efficiency and code (STTuC) in concatenation with space-time block code higher Quality of Service (QOS) over current systems [5]- (STBC) in multi-carrier code-division multiple-access (MC- [7]. The above requirements can be fulfilled by multicarrier CDMA) system with multi-path fading channel is considered. modulation techniques. Single carrier systems give good data The performance in terms of bit error rate (BER) is evaluated rate but are limited in performance in multi path fading through simulations. The corresponding BER of the channels. Improved performance in multipath fading channel concatenated STTuC-STBC-MC-CDMA system is compared conditions, high data rates and efficient bandwidth usage are with STTuC-MC-CDMA system and STBC-MC-CDMA the main advantages of multicarrier modulation. Space-time system. The simulation results show that the STTuC-MC- coding (STC) techniques incorporate the methods of CDMA system performance is better the STBC-MC-CDMA transmitter diversity, channel coding, and provide significant system and it can be further improved by employing capacity gains over the traditional communication systems in concatenation technique i.e. STTuC-STBC-MC-CDMA the fading wireless channels. Here, STC has been developed system. along two major directions: space-time block coding (STBC) and space-time turbo coding (STTuC). Keywords-MMSE; Multi-path channel; MAP Decoder; MIMO; Space-time code; Space-time turbo-code; Space-time In this paper, the STBC, STTuC, and STTuC-STBC code trellis-code; Viterbi Decoder techniques are studied and applied in MC-CDMA systems. These techniques are employed with multiple input multiple output (MIMO) antenna diversity in multi-path fading I. INTRODUCTION channel. At the receiver side minimum mean-square error The wireless communication market is increased detection (MMSE) technique is used by employing exponentially in recent years. A lot of interest has been maximum a posteriori (MAP) algorithm for turbo code developed in modulation techniques like Orthogonal decoding purpose on full load. The performance in terms of Frequency Division Multiplexing (OFDM), Code Division bit error rate probability (BER) is obtained in presence of Multiple Access (CDMA) and Multicarrier Code Division perfect channel state information (CSI). Multiple Access (MC-CDMA). MC-CDMA is seen as a possible candidate for Fourth Generation (4G) wireless The rest of the paper is organized as follows: in Section communication systems that demand higher data rate for II, MC-CDMA system is presented. In Section III, space- voice and data transmissions. CDMA technique is widely time coding technique is described. The space-time block used in current Third Generation (3G) wireless code scheme is given in section IV. In Section V, the communication systems. The principle of spread spectrum mathematical representation for the space-time turbo code is technology behind CDMA was popularly used in military explained. Space-Time turbo code in concatenation with communications for improving secrecy and low probability space-time block code MC-CDMA system model is given in of interception during transmission. Now, CDMA section VI. Simulation for error rate performance of MC- technology is also increased in civilian markets due to high CDMA systems in presence of perfect CSI are carried out in capacity and better performance. The rapid growth of video, Section VII. The conclusions are presented in Section VIII. voice and data transmission through the internet and the increased use of mobile telephony in today’s life have the II. MC-CDMA SYSTEMS necessity for higher data rate transmissions over the wireless CDMA communication system allows multiple users to channels [1]-[4]. transmit at the same time in the same frequency band. In 3G systems we have higher data rate i.e. 64kbps – Traditional multiple access techniques like time division 2Mbps as compared to 9.6kbps – 14.4kbps used in 2G multiple access (TDMA) and frequency division multiple systems. The 4G systems that include broadband wireless access (FDMA) are based on the philosophy of letting no services require data rate up to 20Mbps. This also more than one transmitter occupy a given time-frequency 108 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 slot. In a CDMA based system, users are assigned different demonstrated to significantly increase system performance signature wave forms or codes. Each transmitter sends its as well as capacity. The merit of using multiple antennas or data stream by modulating its own signature waveform as in space diversity is that no bandwidth expansion or increase in a single-user digital communication system. The receiver transmitted power is required for capacity and performance does not need to concern itself with the fact that the signature improvements [14]. waveforms overlap both in frequency and time, because their orthogonality ensures that they will be transparent to the III. S-T CODING TECHNIQUE output of the other user's correlator [8], [9]. CDMA still has In most wireless communication systems, the number of a few drawbacks, the main one being that capacity is limited diversity methods are used to get the required performance. by the multiple access interference (MAI). The W-CDMA According to the domain, the diversity techniques are supports high data rate transmission, typically 384 kbps for classified into time, frequency, and space diversity [15]. S-T wide area coverage and 2 mbps for local coverage for coding technique is designed for use with multiple transmit multimedia services. Thus, W-CDMA is capable of offering antennas. There are various techniques in coding structures, the transmission of voice, text, data, picture (still image) and which include Alamouti STC, STBC, STTC, STTuC, and video over a single platform. However, in addition to the layered space-time (LST) codes. S-T coding with multiple drawbacks arising from the mobile environment and multiple transmit and receive antennas minimizes the effect of multi- access interference, high bit rate transmission causes inter- path fading and improves the performance and capacity of symbol interference (ISI) to occur. The ISI, therefore, has to digital transmission over wireless radio channels [16]. be taken into account during transmission. STBC can achieve a maximum possible diversity Multi-carrier modulation is being proposed for 4G advantage with a simple decoding algorithm. It is very wireless communication systems for high data rate attractive because of its simplicity. However, no coding gain application to reduce the effect of ISI and adapt to channel can be provided by STBC. STTuC is able to combat the conditions. A number of MC-CDMA systems have been effects of fading. However, STTuC have a potential proposed lately. These systems solve the ISI problem by drawback due to the fact that its decoder complexity (MAP transmitting the same data symbol over a large number of decoder) grows with the number of iterations. narrow band orthogonal carriers. The number of carriers equals or exceeds the pseudo-noise (PN) code length [10]- A base band S-T coded system with nT transmit [12]. In MC-CDMA system, each data symbol is transmitted over N narrowband sub-carriers, where each sub-carrier is antennas and n R receive antennas is shown in Figure 1. The encoded with a 0 or π phase offset. An MC-CDMA signal is transmitted data are encoded by a S-T encoder. At each time composed of N narrowband sub-carrier signals each with instant, a block of m binary information symbols, denoted by symbol duration, Tb, much larger than the delay spread, Td, hence MC-CDMA signal does not experience significant ISI. a ( n ) = ( a1 (n),a 2 (n),a 3 (n),.....,a m ( n) ) is fed into the Multiple access is achieved with different users transmitting S-T encoder. The S-T encoder maps the block of m binary at the same set of sub-carriers but with spreading codes that input data into nT modulation symbols from a signal set of are different to the codes of other users. Initially, the data M =2m points. The coded data are applied to a serial to stream is serial to parallel converted to a number of lower rate streams. Each stream feeds a number of parallel streams parallel (S/P) converter producing a sequence of nT parallel with the same rate. On each of the parallel streams, bits are symbols, arranged into a nT × 1 column vector interleaved and spread by a PN code with a suitable chip rate. Then, these streams modulate different or orthogonal carriers with a successively overlapping bandwidth. ( X(n) = x1 (n), x 2 (n),........., x nT (n) )T In a MC-CDMA system, the numbers of carriers are where T denotes the transpose of a matrix. The nT parallel typically chosen to be large enough so that the signal on outputs are simultaneously transmitted by nT different each sub-carrier is propagated through a channel, which i behaves in a nonselective manner. The fading processes on antennas, where by symbol x (n), 1 ≤ i ≤ nT , is each sub-carrier for each user must be estimated, which can transmitted by antenna i and all transmitted symbols have be used in forming the MMSE filter. This approach is the same duration of T sec . The vector of coded modulation shown to perform close to ideal for sufficiently high vehicle symbols from different antennas is called a S-T symbol. The speeds, up to which the normalized Doppler rate is about 1percent [13]. rb spectral efficiency of the system =mis η= Providing high data rate transmission of the order of B several megabits per second (mbps) is important for future bits / sec/ Hz ,where rb is the data rate and B is the wireless communications. In recent years, antenna systems which employ multiple antennas at both the base station channel bandwidth. This spectral efficiency is equal to the (BS) and mobile station (MS), have been proposed and spectral efficiency of a reference uncoded system with one transmit antenna. 109 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 x1 (n) r 1 (n) R 2 x ( n) 2 e X(n) r ( n) a(n) a (n ) c Information Space-Time . e Source Encoder S/P . . . i . v . e x nT (n) r nR (n ) r Figure 1- A base band system model The multiple antennas at both the transmitter and the receiver create a MIMO channel. For wireless mobile ( r (n) = r 1 (n), r 2 (n),........., r nR (n) )T communications, each link from a transmit antenna to a receive antenna can be modeled by flat fading, if we assume Thus, the received signal vector can be represented as, that the channel is memoryless. The MIMO channel r ( n ) = H ( n ) X (n ) + v ( n ) (2) with nT transmit and n R receive antennas can be represented It is assumed that the decoder at the receiver uses a by an (n R × nT ) channel matrix H and it can be given as maximum likelihood algorithm to estimate the transmitted information sequence with receiver has perfect channel state h1,1 (n ) h1, 2 (n) ..... h1,nT (n) information (CSI) on the MIMO channel. At the receiver, the decision metric is computed based on the squared Euclidean h2,1 (n) h2,2 (n ) ...... h2.nT (n) distance between the hypothesized received sequence and the H ( n) = : : : : actual received sequence as : : : : nR nT 2 hnR ,1 (n) hnR ,2 (n ) ...... hnR ,nT (n) ∑r j =1 j (n) − ∑ h j ,i (n) x (n) i =1 i (3) where the ( ji ) element, denoted by h j ,i ( n) , is the fading th The decoder select a codeword with the minimum decision attenuation coefficient for the path from transmit antenna metric as the decoded sequence [4], [16]. i to receive antenna j . IV. SPACE-TIME BLOCK CODE (STBC) It is further assumed that the fading coefficients h j ,i ( n) STBC first introduced by Alamouti with two transmit are independent complex Gaussian random variables. At the antennas. Figure 2 shows the block diagram of the Alamouti receiver, the signal at each of the n R receive antennas is a S-T encoder. It is assumed that a M − ary modulation noisy superposition of the nT transmitted signals degraded scheme is used. In the Alamouti S-T encoder, each group of by channel fading. The n th received signal at m information bits is first coded, where m = log 2 M . j Here, the encoder takes a block of two modulated symbols antenna j ( j = 1,2,...., nR ) denoted by r ( n) , is given by x1 and x 2 in each encoding operation and maps them to the nT transmit antennas according to a code matrix given by r j (n) = ∑ h j ,i (n)x i (n) + v j (n) (1) i =1 x − x2 * X= 1 * (4) j where v (n) is the noise component of receive antenna j x2 x1 at time n , which is an independent noise sample of the zero- The encoder outputs are transmitted in two consecutive mean complex Gaussian random variable with the one sided transmission periods from two transmit antennas. During the power spectral density of N o . r ( n) is the received signal first transmission period, two signals x1 and x 2 are sequence from n R receive antennas of n R × 1 column transmitted simultaneously from antenna one and antenna two, respectively. vector 110 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 TX1 1 [ * X = x1 − x 2 ] [x1 x2 ] Encoder Data Modulator x − x2 * TX2 Sequence [x1 x2 ] → 1 * 2 X = x2 [ * x1 ] x2 x1 Figure 2- Block diagram of the Alamouti space-time encoder * In the second transmission period, signal − x 2 is transmitted STBC. The rows of the transmission matrix X n T are * orthogonal to each other. This means that in each block, the from transmit antenna one and signal x from transmit 1 signal sequences from any two transmit antennas are antenna two [7], [16]. The main principle of the Alamouti orthogonal. For example, if we assume that scheme is that the transmit sequences from the two transmit antennas are orthogonal, since the inner product of the ( ) X i = xi ,1 , xi , 2 ,...., xi , p is the transmitted sequence from sequences x1 and x2 is zero, i.e. th the i antenna, i = 1,2,.........., nT , we have 1 2 * * X ⋅ X = x1 ⋅ x − x ⋅ x1 = 0 2 2 p This scheme may be generalized to an arbitrary number of Xi ⋅ X j = ∑ xi ,t ⋅x*j ,t = 0, transmit antennas by applying the theory of orthogonal t =1 designs. The generalized schemes are referred to as STBC. The STBC can achieve the full transmit diversity specified i ≠ j, i, j ∈ { ,2,...., nT } 1 by the number of the transmit antennas nT , while allowing a where X i ⋅ X j denotes the inner product of the sequences very simple maximum-likelihood decoding algorithm, based only on linear processing of the received signals [8], [16]. X i and X j . The orthogonality enables to achieve the full transmit diversity for a given number of transmit antennas. In In general, a STBC is defined by a nT × p transmission addition, it allows the receiver to decouple the signals matrix X. Here nT represents the number of transmit transmitted from different antennas and consequently, a simple maximum likelihood decoding, based only on linear antennas and p represents the number of time periods for processing of the received signals [8], [16]. transmission of one block coded symbols. It is assumed that the signal constellation consists of 2m points. At each encoding operation, a block of km information bits are V. SPACE-TIME T URBO CODE (STTUC) mapped into the signal constellation to select k modulated Space-Time Turbo code can achieve outstanding signals x1 , x 2 ,........, x k , where each group of m bits selects performance gain because it uses specific coding and decoding structure. Here, in turbo code parallel a constellation signal. The k modulated signals are encoded concatenation convolutional code is used, which is a recent by a S-T block encoder to generate nT parallel signal scheme of channel code developed, whose bit error sequences of length p according to the transmission matrix performance is close to the limit predicted by Shannon. In coding side it uses a particular concatenation of two X. These sequences are transmitted through nT transmit Recursive Convolutional Codes (RCC), associated together antennas simultaneously in p time periods. by the inter-leaver, while in decoding it delivered soft ( 2 2 X ⋅ X H = α x1 + x 2 + .... + x k 2 )I nT information between two decoder components to make soft- input and soft-output iterative decoding. The first decoder must deliver a weighted soft decision to the second decoder. where α is a constant, XH is the Hermitian of X and I n T is The Logarithm of Likelihood Ratio (LLR) an nT × nT identity matrix. The element of X in the i row th L1 (an ) associated with each decoded bit an by first decoder th is a relevant piece of information for the second decoder. For and j column, xi , j , i = 1,2,....., nT , j = 1, 2,........, p, information bit an , It’s LLR is defined as the natural log of represents the signal transmitted from the antenna i at its base probabilities. time j . The orthogonal designs are applied to construct 111 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 P(an = +1 ) P(s',s, y) = P(yf s)P(s',s, yp , yn ) . L(an )= ln P(an = -1 ) Now apply Baye’s rule to the last term P(s',s, yp , yn ) = P(s, yn s ', yp )P(s ', yp ) If an has two values +1 and -1, with equally likely, then this ratio is equal to zero. If the binary variable is not equally P(s',s,y)= P(y f s)P(s,yn s' ,yp )P(s',yp ) likely then P(an = -1)= 1- P(an = +1 ) . Let αn-1(s') = P(s ', yp ) βn (s) = P( y f s) , , P(a n = +1) and γ n (s',s) = P(s, yn s ', yp ) L(an ) = ln 1-P(a n = +1) Then P(s ', s, y) = αn−1 (s')βn (s)γ n (s',s) The LLR of N bit sequence is formulated as below. The The LLR equation for MAP algorithm can be written as lower indicator of y means it starts at time 1 and the upper indicator means the ending point at N. ∑α an =+1 n−1 (s')βn (s)γ n (s',s) L(a ) = , where α n−1 ( s ') is called L1(an )= ln P(an = +1 y1N ) (5) n ∑α an =−1 n−1 (s')βn (s)γ n (s',s) P(an = -1 y1N ) Here, first the S-T Turbo encoder encodes the source data. the Forward metric, β n ( s) is called the Backward metric, Next, the encoded data is applied to interleaver, and then and γ n ( s ', s ) is called Transition metric. At the receiver, mapped according to the desired signal constellation. the received data sequence is combined according to the Finally at each time interval, the signals are modulated and combining techniques described for STC-MC-CDMA transmitted simultaneously over different transmit antennas system. The soft output of the combiner is applied directly [16]-[18]. Using Baye’s rule, the above equation can be to the deinterleaver, and then finally, it is applied to S-T reformulated as Turbo decoder, such as the MAP algorithm, to decode the P(y1N ,an =+1)/P(y1N ) P(y N ,a =+1) data. L(an )=ln =ln 1N n P(y1N ,an = -1)/P(y1N ) P(y1 ,an = -1) L1(an )= L(a - priori) + L(channel) + L(extrinsic) This LLR includes joint probabilities between the received The L(a - priori) is a-priori information about an , bits and the information bit, the numerator of which can be L(channel) is the channel value calculated from the written as knowledge of the SNR and received signal. The third term is ∑P(a n = +1, y1 ) = ∑P(s ', s, y1N ) N called the a-posteriori term, also called the extrinsic L value. u r r ∑α N N e where s’ is starting state and s is ending state of trellis. (s').β n (s).γn (s',s) n-1 ∑ P(s',s,y1N ) + L(extrinsic)= ln a r r u (6) L(an )= ln P(y1N ,an =+1) an=+1 = ∑ e α n-1 (s').β n (s).γn (s',s) P(y1N ,an = -1) ∑ P(s',s,y1N ) a- an =-1 During each iteration the decoder produces the extrinsic value, this extrinsic value becomes the input to the next N N y1 = y1k-1, yn , yn+1 = yp , yk , y f decoder. The decision is made about the bit by looking at r uu We take the N bit data sequence and separate this into three the sign of the L value. an = sign {L1 (an ) , The process pieces, from 1 to n-1, then the nth point, and then from n+1 can continue until the extrinsic values change becomes N insignificant or the algorithm can allow for a fixed number to N. P(s ', s, y1 ) = P(s ', s, y p , yk , y f ) where yp is past , of iterations. sequence, which is the part that came before the current data VI. STTUC CONCATENATED WITH STBC MC-CDMA point. yn current data point and y f is the part that come SYSTEM MODEL after the current point. Using Baye’s rule In order to further improvement in the performance of P(s ', s, y) = P(s ', s, yp , yn , y f ) STTuC-MC-CDMA system, we can use S-T turbo code in concatenation with S-T block code MC-CDMA system. The = P(y f s' ,s, y p , yn )P(s',s, y p , yn ) STTuC-STBC-MC-CDMA system provides both diversity The term y f is the future sequence and we consider that it and coding gain with a reasonable increase in complexity. Figure 3 show the general block diagram of concatenated is independent of the past and only depend on the present system. First, the STTuC encoder encodes the source data. state s. We can remove these dependencies to simplify the Next, the encoded data is applied to S-T block encoder & above equation. 112 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 (k ) c0 × ak ( n ) xk ( n ) STTuC STBC : IFFT P/S Copier Interleaver Encoder Encoder : (k ) cP × Channel h(n) v (n) × xk ( n ) Detector ak ( n ) Decoder (MMSE) Deinterleaver FFT S/P (MAP) Figure 3- Block diagram of STTuC Concatenated with STBC code MC-CDMA System interleaver, and then mapped according to the desired signal constellation. Finally at each time interval, the symbols are s ( k ) (1) = x ( k ) (1) , s ( k ) ( 2 ) = − x ( k )* ( 2 ) where modulated and transmitted simultaneously over different (k ) (k ) transmit antennas. At the receiver, the received data is s (1) = x (k ) ( 2 ) , s ( 2 ) = x( k )* (1) combined according to the combining techniques described for * STBC. The soft output of the combiner is sent directly to the and ( .) denotes the complex conjugate. The two columns deinterleaver, and then finally, it is applied to a STTuC (k) decoder, such as the MAP algorithm, to decode the data. of s ( n ) will be transmitted in two consecutive time slots, Here, a base band system configuration of the STBC-MC- with the first element of each column transmitted from Tx1 CMDA system employing the Alamouti’s S-T coding scheme and the second element from Tx2, respectively. Throughout at the transmitter is depicted in Figure 3, which involves two this paper, is designated to quantities associated with Tx2. transmit antennas, Tx1 and Tx2, and one receive antenna, Rx. In the current system, each user is assigned two distinct At the transmitter, we assume K number of users transmit simultaneously with STTuC in concatenation of STBC over spreading codes to spread symbols transmitted from the two T MC-CDMA system from the two transmit antennas. The c ( ) = c0 ) ,...., c(p −)1 (k k k antennas. Let and frequency selective channel between transmit and receive T antennas is divided into P subchannels such that each = c 0 ,...., c p −1 are two spreading code sequences for (k ) (k ) (k ) c subchannel is approximately flat. Let X ( k ) ( n ) be the S-T { } Turbo encoded output. kth user with processing gain P which spread the symbols transmitted from antenna Tx1 & Tx2 respectively. Define For kth user, the output of S-T Turbo encoder is given to the u ( ) ( n) = s ( k ) ( n)c( ) is the signal associated with Tx1. The k k S-T block encoder that is represented by the following code matrix (k) OFDM modulation can be implemented via IFFT on u (n) s (k ) (k ) (1) s ( 2 ) (k ) −1 ( k ) y ( n ) = F u (n ) (8) S( k) (n) = (k ) (k ) (7) (k ) s (1) s ( 2 ) Similarly we obtain the signal associated with Tx2 as y (n) . 113 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 1, January 2011 At the receiver, the received signal after demodulating via FFT and passing through deinterleaver is given as In Figure 4 we present the BER of STTuC-MC-CDMA K system with different number of iterations, and it is observed Y (n) = ∑ s ( k ) (n)bc( k ) + s ( k ) (n)bc ( k ) + V (n) that the performance is improved by 2 dB from 1 to 2 k =1 iterations and again it is enhanced by around 2 dB from 2 to 5 T iterations at 10-3 BER. From this we can state that the rate of where b = Fh , and h = h ( 0 ) ,...., h ( M − 1) , 0T − M is P improvement in the performance decreases with increasing channel vector between Tx1 & Rx, number of iterations. The performance of STBC-MC-CDMA, T STTuC-MC-CDMA, & STTuC-STBC-MC-CDMA systems and v ( n ) = v0 ( n ) ,...., v p −1 ( n ) contains samples of the versus the SNR in a Rayleigh fading environment for K = 10 2 users and 20000 bit sequences are shown in Figure 5. It is channel noise with zero mean and variance σ v . noted that at 10-3 BER the performance of STTuC-MC-CDMA VII. SIMULATION RESULTS system using MMSE detector is better than STBC-MC- CDMA system by around 1 dB. The performance of STTuC- The simulations are done for STTuC-MC-CDMA, STBC- MC-CDMA system can also be further improved by 1.5dB at MC-CDMA, and STTuC-STBC-MC-CDMA systems with K = 10-3 BER by using STTuC-STBC-MC-CDMA systems in 10 users. The user symbols are drawn from a unit-energy presence of perfect channel state information (CSI). BPSK (binary phase shift keying) constellation. Walsh- Hadamard codes with processing gain P = 32 are used for VIII. CONCLUSION spreading. We assume noise samples as i.i.d. complex 2 In this paper, the performance of concatenated STTuC- Gaussian random variables with zero mean and variance σ n . STBC-MC-CDMA, STTuC-MC-CDMA and STBC-MC- CDMA systems are obtained using MMSE detection 10 0 technique employing MAP algorithm for turbo code decoding. STTuC-MCCDMA-Iter-1 STTuC-MCCDMA-Iter-2 Simulation results are presented in presence of perfect CSI. It STTuC-MCCDMA-Iter-5 is noted that the performance of STTuC-MC-CDMA system 10 -1 increases with more number of iterations. However, the rate of improvement in the performance decreases with increasing number of iterations. 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Benedetto, “Computing the free distance of Turbo Codes and Serially Concatenated Codes with Interleavers: Algorithms and Applications”, IEEE J. on Selected Areas in Comm., vol. 19, no. 5, pp. 800 – 812, May 2001. [17] M. Modarresi and S. Sadough, “Turbo-Trellis Coded Modulation Under Channel Estimation Inaccuracies”, IEEE Proceedings of ICEE 2010, May 11-13, 2010. [18] V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications, vol.47, no. 2, pp. 199- 207, February 1999. 115 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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The International Journal of Computer Science and Information Security (IJCSIS) is a reputable venue for publishing novel ideas, state-of-the-art research results and fundamental advances in all aspects of computer science and information & communication security. IJCSIS is a peer reviewed international journal with a key objective to provide the academic and industrial community a medium for presenting original research and applications related to Computer Science and Information Security.
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The core vision of IJCSIS is to disseminate new knowledge and technology for the benefit of everyone ranging from the academic and professional research communities to industry practitioners in a range of topics in computer science & engineering in general and information & communication security, mobile & wireless networking, and wireless communication systems. It also provides a venue for high-calibre researchers, PhD students and professionals to submit on-going research and developments in these areas.
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IJCSIS invites authors to submit their original and unpublished work that communicates current research on information assurance and security regarding both the theoretical and methodological aspects, as well as various applications in solving real world information security problems.
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Frequency of Publication: MONTHLY
ISSN: 1947-5500 [Copyright � 2011, IJCSIS, USA]

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