Sampling design for Gaussian detection problems

We propose an approach for the design of sampling schemes for Gaussian hypothesis testing problems. Our approach for this design is based on the class of Ali-Silvey (see J. Royal Stat. Soc., Series B, vol.28, p.131-43, 1996) distance measures. Closed forms for the Bhattacharyya distance, the I-divergence, the J-divergence, and the Chernoff distance between the class conditional densities are obtained for the sampling design problem in the strong signal case. A new member of the class of Ali-Silvey distance measures that is suitable for the detection problem in the weak signal case is also derived. Sampling schemes are determined to maximize those four distance measures as well as the new distance measure for the strong signal case and the weak signal case, respectively. The detection performance of our sampling schemes is compared with those of various other sampling schemes by means of numerical examples. Comparisons show that the sampling design based on Ali-Silvey distance measures result in superior performance.