Bayesian channel estimation in chaos based DS-CDMA system Meher Krishna Patel, Stevan M. Berber, Senior Member, IEEE, and Kevin W. Sowerby, Senior Member, IEEE Abstract—This paper proposes maximum a priori (MAP) channel estimation technique in chaos based code division mul- tiple access (CDMA) system. Two different cases are considered for estimating the fading channel. In the first case, channel coefficients are estimated with the help of chaotic sequences. In the second case estimation is performed without including the chaotic sequence in the estimation algorithm. Simulation results shows that the MAP estimation algorithms performance is better for the first case. Index Terms—Channel estimation, CDMA, Chaotic sequence, Bayesian estimation, MAP I. I NTRODUCTION Fading is the phenomena which makes wireless communica- tion more difficult as compare to other communication systems e.g. optical fiber communication and wired communication etc. For many wireless systems, independent of whether time division multiple access (TDMA) or code division multiple access (CDMA) is employed, estimation of channel fading coefficient is necessary for high speed communication. Chan- nel estimates can be updated frame by frame for slower fading rate as compare to frame rate. If channel coefficients changes significantly within the frame then it is necessary to update coefficients iteratively based on symbol by symbol basis [1], [2]. Various estimation methods have been studied in last few decades and each method has its own advantages and dis- advantages. Minimum mean square estimators (MMSE) [3], [4], [5] are easy to implement and perform well in flat fading environment. But these estimators require correlation computation and have poor performance for time varying channel estimation. Bayesian estimators [6], [7], [8], [9] used prior knowledge of data to generate posterior analysis. There- fore performance extensively depends on prior informations. On the other hand, neural networks [10], [11], [12] do not require prior knowledge of channel statistic, but there is huge computational burden for training process. Finally, particle filters [13], [14], [15], [16] use the sequential Monte Carlo sampling method to implement recursive Bayesian filter. But these filters have very high computational load for correcting each particle, which results in higher energy consumption. Therefore hardware implementation of these filters are dif- ficult. The chaotic signals generated from the same chaotic map has high auto correlation and very low cross correlation values. Further, these signals are very sensitive to initial conditions, therefore infinite number of chaotic sequences can be generated from a chaotic map. Hence, chaos based CDMA system gains significant interest among the researchers in last decade [17], [18], [12], [19], [20], [21], [22], [23], [24], [25]. Each user in CDMA system is distinguish by it’s spreading code. Bayesian estimators i.e. MAP and maximum likelihood (ML) are extensively studied for CDMA systems with binary spreading codes [26], [27], [28], [29], [30], [31]. However, to our best knowledge, performance of these estimators never studied for chaos based CDMA system. Objective of this research work is to study the Bayesian channel estimator for chaos based CDMA system for downlink communication. MAP estimator equation is derived for these systems, which needs a prior knowledge of channel statistics. Further, we have also derived the ML estimation equation for considering the case where the mean and variance of the channel is unknown at the receiver. Two algorithms are derived to consider the multiplexed pilot-data case and added pilot- data case. In multiplexed pilot-data case, after demultiplexing, channle estimation can be performed directly on the extracted pilot signal. Whereas for added pilot-data case, pilot needs to be extracted by multiplying corresponding chaotic sequence, before channel estimation process. Performance difference in these two methods have been shown using simulation results. This paper is organized as follows. In section II chaos based CDMA system with Bayesian estimator is shown. MAP and ML estimation algorithms are derived in section III. Simulation results are shown in section IV. Finally some concluding remarks are given in section V. II. SYSTEM MODEL Fig. 1 shows the baseband representation of the chaos based CDMA system with Bayesian channel estimator. In this figure channel estimation is performed after multiplying the chaotic signal to received signal. The wireless channel is assume to be quasi-static fading channel i.e. path gains are constant over a symbol duration. Then the received signal at user can be described as: y(n)=  N  k=1 s T k (n)C k (n)  h(n)+ w(n) (1) where s(n)=[s(n),s(n − 1), ··· ,s(n − L + 1)] T is the transmitted signal, h(n)=[h 0 (n),h 1 (n), ··· ,h L−1 (n)] T is the quasi-static time varying channel for k th user and w(n) is the zero mean White Gaussian noise with variance of σ 2 w . L and N represents the total number of paths and users respectively. C(n)= diag[c(n), c(n − 1), ··· , c(n − L +1)] is the diagonal matrix with elements c(·) of length 2β known as Recent Advances on Electroscience and Computers ISBN: 978-1-61804-290-3 60