Filters for the Detection of Binary Signaling: Optimization Using the Chernoff Bound

The probability of error in the detection of binary signaling by a linear receiver is upper bounded by the Chernoff bound, and a general relationship is obtained whose solution gives a receiver filter and threshold which minimize this bound. As an example, the detection of Poisson signaling in the presence of additive white-Gaussian noise is considered and the resulting filter lies between the optimum filter for Poisson signaling and a matched filter.