Gradient estimation for stochastic optimization of optical code-division multiple-access systems .I. Generalized sensitivity analysis

For optimizing the performance of optical code-division multiple-access (CDMA) systems, there is a need for determining the sensitivity of the bit-error rate (BER) of the system to various system parameters. Asymptotic approximations and bounds, used for system bit-error probabilities, seldom capture the sensitivities of the system performance. We develop single-run gradient estimation methods for such optical CDMA systems using a discrete-event dynamic systems (DEDS) approach. Specifically, computer-aided techniques such as infinitesimal perturbation analysis (IPA) and likelihood ratio (LR) methods are used for analyzing the sensitivity of the average BER to a wide class of system parameters. It is shown that the above formulation is equally applicable to time-encoded and frequency-encoded systems. Further, the estimates derived are unbiased, and also optimality of the variance of these estimates is shown via the theory of common random variates and importance sampling techniques