New Results on Avalanche Multiplication Statistics with Applications to Optical Detection

In this paper, we derive statistics of the random gain of two types of avalanche diode optical detectors. A simple optical binary receiver which could employ these devices is analyzed. In particular, we determine the moment generating function of the random gain probability density for a diode with equal hole and electron collision probabilities and for a diode with unilateral gain. For the unilateral gain case, we invert the moment generating function to obtain the probability density which turns out to be a shifted Bose Einstein density. Using the Chernoff bound, we analyze the performance of a simple binary receiver using the above devices. In addition, we exactly analyze a receiver with a deterministic gain device. We upper bound the degradation incurred from the use of a random gain rather than a deterministic gain. For the devices above, the degradation can be as small as a dB or less in certain ranges of parameter values discussed in the text.