Performance Assessment of GLRT Statistics for Channel Matrix-Based Cognitive Radar

In this study, we extend our previous work by providing analytical expressions for the probability distributions governing the Generalized Likelihood Ratio Test (GLRT) statistics within the channel matrix-based sonar/radar data model framework. Building upon the GLRs derived in our previous paper, we delve into two specific cases: (a) The probability distribution of the GLR, when assuming the covariance of waveform-independent colored noise (WICN) to be known, is chi-square. (b) When the covariance of WICN is unknown, we establish that the distribution of the GLR aligns with Wilks lambda, which we estimate using the saddle point approximation method. To validate our theoretical findings, we compare receiver operating characteristic (ROC) curves derived from our analytical framework with those obtained through Monte Carlo simulations. The dependence of non-centrality parameters on waveform characteristics in both cases also highlights the influence of waveform design in target detection.