Statistical analysis of the Wigner-Ville distribution with applications to wideband detection

A time-frequency statistical description of the Wigner-Ville distribution of random processes that exploits the statistical parameters constituting the Karhunen-Loeve expansion of the original time process is introduced. This provides a method for constructing Wigner-Ville-based detector structures that are of analytical handiness. As an illustration of the utility of this statistical analysis, an algorithm for detection of weak signals of unknown parameters that are obliterated by additive wideband Gaussian noise is proposed. The algorithm utilizes samples from an orthogonal function expansion in the time-frequency domain, the performance measure of which is ascertained. Theoretical evidence of its potential superiority over the radiometer (an energy-detecting device) is presented. Monte-Carlo simulations are then implemented to demonstrate its effectiveness and display probability performance curves