Gaussian approximation versus nearly exact performance analysis of optical communication systems with PPM signaling and APD receivers

A 25 Mbit/s direct-detection optical communication system that used Q=4 PPM signaling was constructed and its performance measured under laboratory conditions. The system used a single mode AlGaAs laser diode (λ=834 nm) and low-noise silicon avalanche photodiode (APD). A procedure is given to numerically compute system performance which uses the nearly exact Webb´s approximation of the true Conradi distribution for the APD output that does not require excessive amounts of computer time (a few CPU minutes on VAX 8600 per system operating point). Comparison revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10^-12A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain and overestimates of system bit error probability. Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. The measured performance of the system was found to be in excellent agreement with the performance predicted by the nearly exact computational procedure. This system achieved a bit error probability of 10^-6 at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700