Data-adaptive algorithms for signal detection in impulsive noise modeled as a subGaussian, alpha-stable process

We address the problem of coherent detection of a signal embedded in heavy-tailed noise modeled as a subGaussian, alpha-stable process. We assume that the signal is a complex-valued vector of length L, known only within a multiplicative constant. The dependence structure of the noise, i.e., the underlying matrix of the sub Gaussian process, is not known. The intent is to implement a generalized likelihood ratio detector which employs robust estimates of the unknown noise underlying matrix and the unknown signal strength. The performance of the proposed adaptive detector is compared to that of an adaptive matched filter that uses Gaussian estimates of the noise underlying matrix and the signal strength and is found to be clearly superior. The proposed new algorithms an evaluated via Monte-Carlo simulation