Optimum Detection of Random Signal in Non-Gaussian Noise for Low Input Signal-to-Noise Ratio

摘要

Optimum detection of a weak stationary random signal in independent non-Gaussian noise requires knowledge of the first-order probability density function of the noise and the covariance function of the signal. More precisely, the first and second derivatives of the input noise probability density function must be known to realize the optimum processor. When these two derivatives must be estimated from a finite segment of noise-only data, a severe demand is placed on the amount of required data. Estimation of higher derivatives of histograms is not accomplished reliably without considerable amounts of data. The presence of heavy-tailed noise data exacerbates this issue. The situation improves when Gaussian noise is considered, mainly because the second derivative of the noise density is not relevant or required for Gaussian noise; all other noise densities must have this information to achieve optimum detection. The samples of the random input signal process need not be taken at an independent rate. However, the covariance of the signal process must be known for optimum processing. The joint probability density function of the input signal is not required for low input signal-to-noise ratios. A simple example of a multipath signal is presented in this report that indicates the need for knowledge of the relative path strengths and the multipath delay time. Lack of knowledge of these parameters in this model requires multiple guesses at their values and parallel processors; the amount of degradation depends on the uncertainty of the medium characteristics.