Optimum Quantization for Binary Hypothesis Testing

In this letter, optimum quantization of samples for use in ultra-wideband (UWB) ranging and communication systems is considered. The necessary conditions which the optimal quantization parameters, i.e. the quantization levels and thresholds, should satisfy are derived based on two optimality criteria of maximizing the detection probability and minimizing the error probability respectively. In particular, the design of optimal quantizers for weak signals is specially explored. To give a concrete example, applications to the case of detecting known signals in additive noise are investigated. Numerical results on four-level quantization demonstrate that the optimal quantizers perform better than suboptimal quantizers thanks to the extra information contained in the optimal parameters.