Receiver performance evaluation using photocounting cumulants with application to atmospheric turbulence

A new technique for evaluating optical communication system performance directly from the photocounting cumulants is presented. This technique is most useful in situations where exact, explicit, closed form solutions exist for the photocounting cumulants, but do not exist for the photocounting distribution, such as in the generalized case of communication through lognormal atmospheric turbulence. Using this technique, theoretical probability of error curves are presented for communication through lognormal atmospheric turbulence, for a superposed coherent-in-chaotic signal, embedded in additive independent Poisson noise, with arbitrary ratio of sampling time to source coherence time, arbitrary ratio of coherent to chaotic component, arbitrary mean frequencies of the coherent and chaotic components, and where the chaotic component need not be stationary and may have arbitrary spectral distribution. Since no solution exists for the photocounting distribution itself in this generalized case, the corresponding performance calculation has not previously been possible. The case described applies to the detection of radiation originating from a multimode laser or scattered from a rough target, and passing through atmospheric turbulence. A special case of these results is shown to be in excellent agreement with previous calculations [Rosenberg and Teich, Applied Optics12, 2625 (1973)] for a lognormally modulated coherent signal.