The Analysis and Design of Data Quantization Schemes for Stochastic-Signal Detection Systems

The optimal design and performance analysis of non-uniform quantizers are considered in the context of data quantization in detection systems for stochastic signals. The case of detection with small signal-to-noise ratio is treated using two different statistical models for the presence of the signal in this situation. A general data-quantized detection system is proposed, and analytical expressions are presented for the asymptotic performance comparison of such systems within each of the two signal models. A design procedure for the optimal choice of quantizer parameters is also discussed, and optimal parameter values are presented for the particular case of four-level quantization for a class of noise probability densities exhibiting generalized exponential decay. Two suboptimal quantizer-detectors are also proposed, one based on minimum-distortion quantization and the other based on an approximation to the quadratic detector, and the performance of the optimal quantization scheme relative to these is analyzed with the result that the optimal quantizer-detector generally exhibits considerable performance improvement over the suboptimal schemes.