Signal Detection in Fractional Gaussian Noise and an RKHS (Reproducing Kernel Hilbert Space) Approach to Robust Detection and Estimation

摘要

This report is divided into two parts. In the first part, the problem of signal detection in fractional Gaussian noise is considered. To facilitate the study of this problem, several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is characterized completely, and an alternative characterization for the restriction of this class of functions to a compact interval, O,T is given. Infinite-interval whitening filters for fractional Brownian motion are also developed. Application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional Gaussian noise. Also, a formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed. Finally, some results concerning detector performance in the presence of additive fractional Gaussian noise are presented. Signal detection, Fractal noise, Reproducing kernel Hilbert spaces, Robust detection, Radio communications. (jes)