A Semiclassical Analysis of Optical Code Division Multiple Access

in this paper, we consider a noncoherent, optical, asynchronous, code division multiple access (CDMA) system. We present an analysis of the error rate for a single-user matched-filter receiver that applies for arbitrary photomultipliers and signature sequence sets, adheres fully to the semiclassical model of light, and does not depend on approximations for large user groups, strong received optical fields, or chip synchronism. We compare the exact minimum probability of error and optimal threshold to those obtained with popular approximations on user synchronism or on the distribution of the multiple access interference (MAI). For the special case of unity-gain photodetectors and prime sequences, we show that the approximation of chip synchronism yields a weak upper bound on the exact error rate. We demonstrate that the approximations of perfect optical-to-electrical conversion and Gaussian-distributed MAI yield a poor approximation to the minimum error rate and an underestimate of the optimal threshold. In this paper, we also develop arbitrarily tight bounds on the error rate for unequal energies per bit. In the case when the signal energies coincide, these bounding expressions are considerably easier to compute than the exact error rate.