Detection performance of normalizer for multiple signals subject to partially correlated fading with chi-squared statistics

The false alarm and detection probabilities for a multipulse signal subject to partially correlated fading, in the presence of Gaussian noise of unknown level, are derived in closed form. The number K of signal pulses, as well as the number L of noise‐only pulses used to estimate the noise background power level, are arbitrary. The power fading is characterized by a chi‐squared distribution with 2m degrees of freedom and a normalized set of covariance coefficients {ρkt}, all of which can be selected arbitrarily, in order to match an experimental realization or an actual measured situation. The performance capability of this processor depends additionally on the received signal‐to‐noise ratio. This study covers the case of a nonconstant threshold; comparisons of this normalizer with earlier results (for L = ∞) enable a quantitative evaluation of the losses incurred by lack of knowledge of the noise level. The important capability of constant false alarm rate is achieved by this normalizer.