| Density estimation is a critical part of many statistical and signal processing tasks from pattern recognition to signal prediction to detection to separation. Neural networks are powerful approximators by virtue of their universal approximation property. We develop some neural networks for density estimation. More specifically, we propose a hybrid radial basis function/sigmoid network with efficient estimation properties. We also consider distribution estimation, conditional density estimation, and density estimation using the EM algorithm, all using neural nets. We then attempt to apply density estimation with neural networks to several problems involving network traffic monitoring.; Finally, we consider the major thrust of the thesis: the application of density estimation to blind signal separation. In particular, we derive the Cramer-Rao bound for the Bell-Sejnowski infomax signal separation algorithm, and make some heuristic separation algorithms that use kernel density estimators under varying kernels, and show that optimal (Epanechnikov) kernels provide superior convergence rates. We then apply blind signal separation using density estimation to separation of FH-CDMA signals received through an antenna array. This reduces to density estimation of complex signals mixed with a complex mixing matrix and carrying complex additive white Gaussian noise. We also propose a novel method for compensation of the frequency hopping so that the antenna steering vector remains stationary. We then consider the use of a projection pursuit index, used in projection pursuit density estimation, to blind signal separation and compare its performance to a standard signal separation index. We show that the PPI has equivalent performance for small rotation angles and much better performance at large rotation angles compared to an alternative index. |
