Robust Matched Filters for Optical Receivers

The problem of designing optical receivers that are robust against uncertainty in the statistics of the observation process in photodetection is investigated. In particular, a modification in the design of the postdetection matched filter is proposed to account for possible uncertainty in the rate function of the incident light, the rate of the dark current, and in the statistics of the additive noise present at the input to the optical receiver. This design is based on a game-theoretic approach in which a filter is sought that has the maximum worst case output signal-to-noise ratio possible over the class of allowable statistics; that is, the design criterion is maximin signal-to-noise ratio. A general characterization of maximin robust matched filters for observed Poisson processes is presented in this context, and specific solutions for several useful uncertainty models are obtained. Numerical results are presented for a specific example to illustrate the performance of the proposed technique.