On Optimum and Nearly Optimum Data Quantization for Signal Detection

The application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered. This application is twofold, allowing for greater simplicity in both analysis and design of quantizers for detection systems. Most computational methods for designing optimum (most efficient) quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions. Companding approximation theory is used here to obtain suitable initial conditions for this problem. Furthermore, the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large. In this design, iteration is not needed to derive the parameters of the quantizer, and the design procedure is very simple. In this paper, we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems.