We analyze the performance of receivers which use envelope detection at IF to detect optical signals with orthogonal modulation formats. We obtain exact closedform expressions for the error probability conditioned on the normalized envelope. The only information necessary for obtaining the unconditional error probability is the set of tilted moments of the envelope. We then provide an approximation to this envelope which is not only accurate to the first order in phase noise strength, but also has the same range as the actual random envelope. We use this approximation to obtain the bit error performance of the three receiver models that we consider. We also provide a tight lower bound in closed-form. Finally we extend the analysis to N-ary FSK to observe the improvement due to increased bandwidth use and transmitter/receiver complexity.
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