Limited Complexity Maximum-Likelihood Detection for CDMA

A variety of trellis search algorithms have been suggested for multiuser CDMA detection. Breadth-first algorithms have shown especially promising results, e.g., maximum-likelihood detection can be performed by the Viterbi breadth-first algorithm. It has previously been shown that for traditional trellis-structured single-user applications, the family of breadth-first algorithms working on a maximum-likelihood metric performs complexity-constrained maximum-likelihood detection. For multiuser CDMA detection a similar maximum-likelihood metric has not yet been developed. In this paper we derive a general, recursive, additive metric for complexity-constrained maximum-likelihood detection for multiuser CDMA using detection algorithms from this family. The metric requires linear filtering of the matched-filtered received signal vector. This general filter must have full rank and result in a (in some sense) “causal” multiple-access interference pattern in the filtered statistic. It is shown that, in terms of maximising the signal-to-noise ratio subject to the filter constraints, the optimal filter is the well known partially-decorrelating noise-whitening filter. Simulation results are obtained to confirm the analytical results.