An algorithm for the design of generalized quantizers for detection

A procedure based on the generalized Lloyd algorithm approach using a sequence of independent noise samples to design M-region generalized quantizers for signal detection is presented. Included in this case are the conventional M-interval quantizer detectors. The quantizer parameters for S.A. Kassam´s (1985) four-region generalized quantizer detector are computed using various sample sizes for the known sequence of independent noise samples. Two families of densities which cover a wide spectrum of possible nonGaussian densities are considered: the generalized Gaussian densities and the Johnson S_u family of densities. The performance of the quantizer detector is compared to that of the locally optimum detector, and the results are presented as the asymptotic relative efficiencies of the respective detectors. The case when the noise density is not known before analysis is considered, and the detection performance is examined using an estimate of the density. A mean-squared-error distortion criterion is used in the proposed algorithm to obtain quantizers that yield maximum efficacy. It is shown through numerical examples that the design procedure is simple, fast, and applicable to a wide range of nonGaussian distributions