Optimum Multiuser Asymptotic Efficiency

The degradation in bit error rate due to the presence of multiple-access interference in a white Gaussian channel can be measured by the multiuser asymptotic efficiency, defined as the ratio between the SNR required to achieve the same uncoded bit error rate in the absence of interfering users and the actual SNR. In this paper, the asymptotic efficiency of the optimum multiuser demodulator (a bank of matched filters followed by a Viterbi algorithm) is investigated and compared to that of the conventional single-user matched filter receiver. The computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the Euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user. It is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1, and therefore the optimum demodulator does not become multiple-access limited in contrast to the single-user receiver. A class of signal constellations with moderate cross-correlation requirements is shown to achieve unit optimum multiuser efficiencies and, hence, to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector.