Penalties of Sample-and-Sum and Weighted Partial Decision Detectors in Gaussian Noise

The deterioration in performance, measured in the probability of error sense, of sample-and-sum and weighted partial decision detectors are analyzed for arbitrary signal-to-noise ratios. These suboptimal detectors have more modest computational requirements than the optimal digital matched filter making them amenable to simple digital implementations. The effects on the penalties of the signaling waveform employed, the number of samples processed, and the signal-to-noise ratio are considered in detail. Included are the penalties for the optimum weighted partial decision detector. The optimum weighted partial decision detector is the optimum detector, in the minimum probability of error sense, for hard-limited samples. The penalty of the optimum weighted partial decision detector relative to the digital matched filter detector represents the fundamental loss in signal detectability due to hard-limiting in a sampled system.