Asymptotic performance of code-reference spatial filters for multicode DS/CDMA

We address the problem of code-reference spatial filtering for multicode DS/CDMA. The large-system analysis of the asymptotic performance of three spatial filters, respectively based on the matched filter, the decorrelator and a projector onto the span of the codes of the desired user, is presented. We derive analytical expressions for the asymptotic covariance and output signal-to-interference-plus-noise ratio (SINR) of these filters, assuming that both the spreading factor and the number of parallel code sequences increase without bound at the same rate. A superior performance of the projecting filter against the other two solutions is revealed: the performance of the spatial filters based on the matched filter and the decorrelator saturates both for increasing values of the input signal-to-noise ratio (SNR), whereas the projecting solution is able to sustain an increasingly high SINR.