Locally optimal detection of unknown signals in non-Gaussian Markov noise

The authors address the application of locally optimum (LO) signal detection techniques to environments in which there is no prior knowledge of the noise density and spectral properties. Specific algorithms are introduced, and the performance of these algorithms is examined. Unlike previous algorithms, these techniques place few assumptions on the properties of the noise, and they perform well under a wide variety of circumstances. The algorithms presented were tested using noise with Cauchy, Laplace, and Gaussian mixture density functions. In all cases the LO procedures showed significant improvement over the direct use of the magnitude of the DFT (discrete Fourier transform), at least for small signal levels. In general, the results were most dramatic when testing with noise densities with very heavy tails, such as the Cauchy and Gaussian mixture cases