Parameter Convergence Radar Detector Based on VAMP Deep Unfolding

Compared with the sparse recovery process in traditional compressed sensing (CS) radar detector CAMP, vector AMP deep unfolding (VAMP-DU) can achieve sparse recovery over a broader range of observation matrices, with faster convergence speed and higher recovery accuracy. However, the distribution of the error term in VAMP-DU remains unknown, which renders the distribution of the test statistic in CS radar detection undetermined and thus hinders threshold setting under a given false alarm rate when VAMP-DU is applied to CS radar detection. In this work, we theoretically prove that the error term in VAMP-DU follows a Gaussian distribution by leveraging a general state evolution (SE). Based on the Gaussianity, we propose a new parameter convergence radar detector (PCRD) as the CS detector to calculate the distribution parameter of the test statistic and realize target detection under a given false alarm rate. Specifically, PCRD exploits the Gaussian property of error term in VAMP-DU to exhibit superior false alarm control capability, while leveraging the improved recovery accuracy of VAMP-DU to further enhance target detection performance. Numerical simulations validate the Gaussianity of the error term in VAMP-DU and show the superiority of the VAMP-DU-based PCRD over existing approaches in both false alarm control accuracy and target detection performance.

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