Receiver performance evaluation using photocounting cumulants with application to atmospheric turbulence

A new technique for evaluating optical communication system performance directly from the photocountingcumulants is presented. This technique is most useful in situations where exact, explicit, closed form solutionsexist for the photocounting cumulants, but do not exist for the photocounting distribution, such as inthe 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, witharbitrary ratio of sampling time to source coherence time, arbitrary ratio of coherent to chaotic component, arbitrary mean frequencies of the coherent and chaotic components, andwhere the chaotic component neednot be stationary and may have arbitrary spectral distribution. Since no solution exists for the photocountingdistribution itself in this generalized case, the corresponding performance calculation has not previouslybeen possible. The case described applies to the detection of radiation originating from a multimode laseror scattered from a rough target, and passing through atmospheric turbulence. A special case of these resultsis shown to be in excellent agreement with previous calculations [Rosenberg and Teich, Applied Optics12, 2625 (1973)] for a lognormally modulated coherent signal.