Adaptive soft limiter bootstrap separator for one-shot asynchronous CDMA channel with singular partial cross-correlation matrix

The adaptive bootstrap separator has been shown to perform better than the conventional decorrelation detector when used for synchronous code division multiple access (CDMA) channels, or with a one-shot matched filter bank for asynchronous channels when the cross-correlation of the partial sequences is nonsingular. In the later case, however, when the “partial cross-correlation” is singular, the separator weights fail to converge. We propose the use of a soft-limiting decision instead of a hard limiter for controlling the adaptive weights of the separator. We show that the algorithm weights converge, provided that the limiting threshold is not zero or not very large. Due to analytical difficulties, the actual steady state weights are not found, but are shown to exist. Simulation results support these claims. The bit error rate (BER) performance of the adaptive soft limiter bootstrap separator are also found by simulation and compared to the performance of the conventional decorrelator that uses the pseudoinverse of the cross-correlation matrix