On adaptive minimum probability of error linear filter receivers for DS-CDMA channels

Receiver architectures in the form of a linear filter front-end followed by a hard-limiting decision maker are considered for DS-CDMA communication sy stems. Based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front-end in t he minimum BER sense, The recursive form is decision driven and distributio n free, For additive white Gaussian noise (AWGN) channels, theoretical anal ysis of the BER surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a forma l proof of guaranteed global optimization with probability one for the two- user case. To the extent that the output of a linear DS-CDMA filter can be approximated by a Gaussian random variable, a minimum-mean-square-error opt imized linear filter approximates the minimum BER solution, Numerical and s imulation results indicate that for realistic AWGN DS-CDMA systems with rea sonably low signature cross-correlations the linear minimum BER filter and the MMSE filter exhibit approximately the same performance, The linear mini mum BER receiver is superior, however, when either the signature cross-corr elation is high or the background noise is non-Gaussian.