Accurate Evaluation of the Average Probability of Error of Pulse Position Modulation in Amplified Optical Wireless Communications under Turbulence

We present exact and approximate results on the average probability of error (PER) for pulse position modulation (PPM) in pre-amplified optical wireless communication systems with diversity. The approximate results are obtained by combining a new mathematical formula that we derive for binary PPM and an existing formula that associates higher-order PPM PERs with their binary PPM counterpart. The approximate results are compared with the exact in weak, moderate, and strong turbulence, and it is demonstrated that they are in good agreement under all fading conditions. Moreover, the accuracy of the approximation improves with the optical signal-to-noise ratio and the number of diversity branches that are used, which correspond to implementation scenarios that are typically anticipated in practice.