Performance of linear reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

The performance of a set of linear reduced-rank multistage filter banks is studied in the context of multiuser detection for direct-sequence (DS) code-division multiple-access (CDMA) systems. The set of filter banks under consideration is comprised of the minimum mean-square error (MMSE), the minimum output energy (MOE), the best linear unbiased estimator (BLUE), and the maximum-likelihood (ML) detector. Based on a common framework for the multistage implementations of the aforementioned filter banks, the signal-to-interference plus noise ratios (SINRs) and bit-error rates (BERs) of these reduced-rank filter banks are studied for multipath Rayleigh-fading channels. A generic BER formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework. Analysis shows that all of these performance measures are characterized by a kernel matrix K_mmse whose trace forms the output SINR of the MMSE filter bank. Through investigating the recursive structure of K_mmse, the output SINRs are proven to be monotonically increasing with the number of stages and upper-bounded by a number equal to the paths of the desired user´s channel. The condition for asymptotically achieving this upper bound is also provided, which leads to the notion of effective user capacity of linear reduced-rank multiuser detection as well as serves as a test for the existence of a BER floor for coherent detection. In addition, the channel mismatch due to differential detection is also shown to yield a BER floor for noncoherent detection. Based on this analysis, a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection.