Coded error performance bound for Q-ary PPM signaling over the satellite-to-ground optical channel

In this letter, the proof of the classical Proakis result has been adapted on the probability of error when the decision variable is a quadratic form in Gaussian random variable (RV) to obtain the pairwise error probability (PEP) expression for Q-ary pulse-position modulation (PPM) signaling. Specifically, the expression is derived based on jointly Gaussian model, which is accurate for avalanche photodiode (APD) output in comparison to the additive, white Gaussian noise (AWGN) model for satellite-to-ground optical communication link. The average bit error rate (BER) for convolutional codes with arbitrary Q has been derived. This work can help to approximate the coded performance of Q-ary PPM signaling over the satellite communication system.