Multiple-access channels with point-process observations: Optimum demodulation

The derivation and analysis of optimum multiuser detectors for additive-rate and additive-light Poisson multiple-access channels are studied. The observed point process models the output of an ideal photodetector illuminated by several synchronous or asynchronous users who modulate coherent light of the same frequency. Dynamic programming-based decision rules for the asynchronous multiple-access channel exhibit the same computational complexity as their synchronous counterparts and are shown to be optimum under the criteria of minimum error probability and maximum likelihood sequence detection. Upper and lower bounds on the minimum uncoded bit error rate achievable with arbitrary signal constellations are obtained in terms of the error probability of binary hypothesis testing problems. A particular case of these results, namely, the single-user finite-length intersymbol interference problem, solves the error rate analysis of optimum direct-detection systems for dispersive optical fibers.