Computing bit-error probabilities for avalanche photodiode receivers by large deviations theory

A bit error probability analysis of direct detection optical receivers employing avalanche photodiodes is presented. An asymptotic analysis for large signal intensities is first presented. This analysis provides some useful insight into the balance between the Poisson statistics, the avalanche gain statistics, and the Gaussian thermal noise. The conjugate distribution is then developed, which is obtained by applying the large deviations exponential twisting formula. It is demonstrated that this conjugate distribution can be used to obtain numerically efficient Monte Carlo estimates of the biterror probability via the importance sampling method.