New Results on Avalanche Multiplication Statistics with Applications to Optical Detection

Practical optical direct detection receivers can employ detectors with internal gain (more than one output electron on the average per optically or thermally generated primary electron) to overcome thermal noise in amplifying stages following the detector. Since the gain is a random variable, its statistics affect the system performance. In certain systems (e.g., linear analog intensity modulation with linear processing and a mean square error risk criterion) it is sufficient to know the mean and variance of the random gain to determine performance. Various authors1-2 have calculated those statistics for a variety of avalanche multiplier models. In digital systems with a probability of error risk, one needs to know the probability density of the gain to evaluate performance. 167 168 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1971 Up to now, little work has been published on these statistics.* In this paper, we derive the moment generating function (and in one case the density) of the multiplication statistics for two special cases of avalanche diode detectors. We apply results to performance evaluation for a simple binary optical receiver.