Independent Code Division Multiple Access in DS-CDMA System

Abstract

Orthogonality of different spreading codes is considered extremely important in Code Division Multiple Access (CDMA) systems to separate individual users’ message symbols from the mixtures. Spreading codes having minimum cross correlation and single auto-correlation peaks are preferred. Independent compo nent analysis (ICA) based CDMA receivers utilize the statistical independence of users’ message symbols and exploit orthogonality of the spreading codes in user signal separation. ICA based CDMA receivers are deemed superior to con ventional CDMA receivers; however, these rely on the orthogonality of spreading codes. Standard ICA-CDMA receivers utilize Gram-Schmidt orthogonalization to produce mutually orthogonal separating vectors. This orthogonalization ensures that multiple components do not converge to the same extrema. Mutually orthog onal separating vectors are extracted by taking projections in Euclidean space, equivalent to exploiting only Second order Statistics (SoS) of separating vectors. The utilization of SoS of separating vectors leaves a performance margin that can DRSML QAU be realized if statistically independent separating vectors are extracted by utilizing Higher order Statistics (HoS). In this thesis, we propose to exploit independence of spreading codes in conjunction with independent CDMA receivers. Indepen dent Code Division Multiple Access (i-CDMA) receivers are such that they are capable of incorporating the statistical independence of codes in addition to the independence of sources. Two independent CDMA receivers are proposed, in this connection. As a first solution, an independent Gram-Schmidt based deflationary i-CDMA receiver is presented. This receiver replaces the deflationary Gram Schmidt orthogonalization with the independent Gram-Schmidt process. This process introduces nonlinear decorrelation in a nonlinearly transformed, possibly higher dimensional, Hilbert space. The performance of the proposed receiver is investigated for commonly used nonlinearities, and the appropriate nonlinear ity is optimized numerically according to the channel parameters. Simulations are carried out to evaluate the performance of the proposed receiver for various users and signal-to-noise ratio (SNR) levels. It is observed that the independent Gram-Schmidt based deflationary i-CDMA receiver outperforms the deflationary Gram-Schmidt orthgonalization based standard ICA-CDMA receiver in terms of bit error rate. Moreover, the introduction of nonlinearity does not adversely affect algorithmic convergence. As a second solution, symmetric independence based symmetric i-CDMA receiver is proposed. In symmetric i-CDMA receiver, ix DRSML QAU independent separating vectors are extracted in parallel. In order to utilize the independence of spreading codes, complete signal plus noise subspace is utilized. Standard whitening transform is redefined such that it performs the necessary dimension reduction and restores the noise plus signal subspace for further pro cessing. This enhanced signal plus noise subspace offers more dimensions to extract independent separating vectors. In order to produce independent separating vectors, it is proposed to replace the symmetric Gram-Schmidt orthogonalization with the standard ICA algorithm. Simulations are carried out to evaluate the performance of the proposed receiver for various parameters in CDMA uplink and CDMA downlink systems. It is demonstrated that the symmetric i-CDMA receiver outperforms the symmetric Gram-Schmidt orthogonalization based stan dard ICA-CDMA receiver. Comparison is carried out for various SNR levels and different number of users. Moreover, during simulations, it is observed that the performance margin increases with increasing the processing gain. As final part of this study, we attempt to bring to the fore relative statistical independence of spreading codes. It is argued that family of chaotic codes may render statis tically more independent spreading codes. These codes are obtained through chaotic maps and usually belong to a relatively large ensemble having additional information in their higher order moments as compared with conventional Gold codes. It is proposed to utilize independent chaotic codes in conjunction with x DRSML QAU the independent CDMA receivers. Due to the utilization of the independence of codes in addition to the independence of sources in independent CDMA receivers, superior performance results can be achieved. For comparison, chaotic codes having minimum cross-correlation with other codes are selected, and results are compared with the Gold codes. Simulation results depict comparable performance of chaotic codes with Gold codes, offering an alternative to the conventional codes due to their easy generation, arbitrary length, and possibly unlimited ensemble size. However, more work is needed to determine subset of chaotic codes that fully utilize the proposed receivers’ capabilities.