Waveform Optimization for Channel Matrix-Based Cognitive Radar/Sonar

Cognitive radar systems, driven by adaptive wave-form design, enhance target detection and tracking in complex environments. In the context of channel matrix-based cognitive radar, the asymptotic distribution of the generalized likelihood ratio test (GLRT) statistic for adaptive target detection exhibits a non-central chi-square distribution. We formulate this problem as a semidefinite programming instance and propose a waveform optimization algorithm that maximizes the non-centrality parameter and hence enhances the probability of detection of the target. The proposed algorithm also incorporates power and peak-to-average power ratio (PAPR) constraints, which are crucial for ensuring practical and efficient radar operation.