Performance Analysis of Optical Receivers by the Saddlepoint Approximation

Determining the minimum error probability of a binary communication receiver embodying a photoelectric detector requires calculating both the probability p
k
that
k
output electrons are counted and the cumulative probability that the number
k
exceeds a certain decision level. A saddlepoint method is described for both setting the decision level and approximating the error probability on the basis of the probability generating function of the p
k
's. The method is applied to the avalanche photodiode. The cumulative probabilities so calculated are compared with the Chernoff bound, which in typical cases is found to be too high by an order of magnitude or more. The error probabilities of a class of avalanche diodes having the same mean gain are compared with that of a receiver with no amplification at all.