Operating characteristics for weighted energy detector with Gaussian signals

The performance of several weighted energy detectors of Gaussian signals in noise are investigated, both by exact procedures and by five different approximation procedures. In particular, receiver operating characteristics, for false alarm probabilities ranging from 1E-10 to .1 and detection probabilities ranging from .01 to .999, are quantitatively compared. The standard Gaussian approximation is found to be severely deficient and generally optimistic for small false alarm probabilities, while two different fourth-order approximations have excellent capability over the entire range of probabilities considered. A method of avoiding the calculation of the eigenvalues of a covariance matrix, and yet accurately predicting performance of a fading medium, is presented. It requires only sums of products of the covariance elements directly, the precise number depending on the order of the approximation.