Detection performance characteristics for a system with quantizers, OR-ing, and accumulator
Albert H. Nuttall · The Journal of the Acoustical Society of America · 1983
The false alarm and detection probabilities of an N-channel system subject to L+1 level quantization, OR-ing, and accumulation of M time samples, are evaluated exactly, with no Gaussian assumptions, for arbitrary values of N, L, M, and for a quantizer with arbitrary breakpoint locations. The channel noises are independent but can have arbitrary statistics. The signal occupies one unknown (possibly changing) channel, if present. Two FFTs suffice to sweep out a complete detection probability versus threshold curve. The optimum placement of quantizer breakpoints, for a fixed total number of levels, L+1, is a subtle one and shown to depend on N, M, and the desired level of performance; a simple rule-of-thumb is presented which yields near-optimum capability over the useful range of the operating characteristics.