Low Complexity Polynomial Expansion Multiuser Detector for CDMA Systems

The polynomial expansion (PE) multiuser detector can iteratively approximate the linear decorrelating and MMSE multiuser detectors. This is a very promising approach since the complexity of the PE detector is considerably less than that of the decorrelating and MMSE detectors. The concept of the PE multiuser detector is a weighted matrix polynomial for which optimal weighting has been suggested in the literature. Unfortunately, the optimal weights apply only to a specific correlation matrix. As soon as the correlation between the users changes (and hence also the correlation matrix), a new set of optimal weights has to be calculated. The calculation of these weights is computationally very intense. In this paper, an approach is presented where the weights are predefined and apply for all matrices. Furthermore, a normalization factor is needed to ensure convergence. It will be shown how this factor has to be chosen to obtain the optimal convergence speed. For the optimal normalization factor the minimum and maximum eigenvalues are needed. A low complexity and accurate method to estimate these eigenvalues is derived which can be applied to all correlation matrices and therefore to any code division multiple access (CDMA) scenario. Hence, the matrix-dependent optimal normalization factor can easily be calculated and ensures a good bit error rate (BER) performance, even if the correlation between the users changes quickly (e.g., in time-variant channels). Furthermore, it will be shown how to enhance the PE detector such that it has a high near-far resistance. Additionally, for the first time it can be proven that the approximation error of the proposed detector diminishes exponentially with the number of iterations. Finally, simulations verify the fast convergence of the proposed PE detector and its flexible usage in a variety of scenarios.