A semiclassical analysis of optical code division multiple access

A model noncoherent, optical, asynchronous, code-division multiple-access (CDMA) system is described. The error rate for a single-user matched-filter receiver that is valid for arbitrary photomultipliers and signature sequence sets, adheres to the semiclassical model of light, and does not depend on approximations for large user groups, strong received optical fields, or chip synchronism is analyzed. The exact minimum probability of error and optimal threshold are compared to those obtained with user-synchronism and multiple-access interference (MAI) distribution approximations. For the special case of unity-gain photodetectors and prime sequences, it is shown that the approximation of chip synchronism yields a weak upper bound on the exact error rate. It is demonstrated 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. Arbitrarily tight bounds are developed 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.