Chernoff bounds for Class A noise

The goal is, using a very large passive array, to determine the performance limits of a detector. The signal of interest is narrowband with a Gaussian envelope, and the contaminating noise is multivariate Class-A. Two different multivariate models for the Class-A family are presented. The data are spatially dependent and temporally independent. It is shown, in the spatially independent case, that the Chernoff approximation does closely approximate the performance of the optimal detector. It is shown that the approximation improves as the number of samples increases. It is also shown that the Chernoff approximation requires numerical evaluation of a M-dimensional integral. For the application, M may be as large as 150, ruling out this approach. Two alternative approaches are examined. First, approximating the Class-A model by a Gaussian model is shown to result in a poor approximation. Second, the exact likelihood ratio is approximated by a piecewise function. Although the approximation can be done with very good accuracy, the bound must be evaluated numerically