The authors analyze the performance of receivers that use envelope detection at an IF to detect optical signals with orthogonal modulation formats. Exact closed-form expressions for the error probability conditioned on the normalized envelope were obtained. The only information necessary for obtaining the unconditional error probability is a small set of tilted moments of the envelope. The authors 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. This approximation was used to obtain the bit error performance of the three receiver models considered. A tight lower bound in closed form is given. The analysis is extended to the case of N-ary frequency-shift-keying (FSK) to provide very tight upper and lower bounds to the bit error probability.
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