Minimum Probability of Error for Asynchronous Multiple Access Communication Systems

Consider an ideal white gaussian channel shared by K users that transmit independent data streams by modulating antipodally a set of assigned signal waveforms without maintaining relative synchronism among them. This paper investigates the probability of error achievable by an optimum K-user coherent detector. It is shown that unless signals with poor cross-correlation properties are used or the interfering users are comparatively weak, the minimum error probabilities have the same asymptotic behavior as in a single-user communication system, i.e. there is no performance degradation due to the presence of other users. As illustrated by several examples, this implies that in the SNR region of interest, the error probability of the conventional detector is not necessarily close to the minimum even if signals with low cross-correlations are used.