Chernoff bounds on the error probability for the detection of non-Gaussian signals

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Abstract
Chernoff bounds on the error probability for the detection of non-Gaussian stochastic signals in additive white Gaussian noise are computed. By the use of Fokker-Planck (F-P) equations and a certain conditional expectation, the quasi-transition function, an equation for time evolution of the Chernoff bound is obtained. This time evolution equation is solved exactly to give all previously known results. Although the general non-Gaussian case cannot be conveniently solved for short time duratio ns, in the important special case of stationary processes and long integration times, bounding the error probability reduces to solving for the largest eigenvalue\lambda_0of a differential operator. In particular,P(error) \leq \exp (\lambda_0T), whereTis the observation period. By iteratively determining\lambda_0via the Galerkin variational procedure, we compare the performance of different receiver forms for a specific problem involving the detection of non-Gaussian random signal processes.