Bayesian Framework for Target Detection in Noise Environments of FDA-MIMO Radar

For the target detection problem in frequency diverse array multiple input multiple output (FDA-MIMO) radar operating in noise environments (including receiver thermal noise, interference, and clutter after range compensation) with certain prior knowledge available, this paper integrates both training data and prior information of the covariance matrix into the detector design by resorting to Bayesian framework. To model the prior information of the unknown covariance matrix, it is reasonable to assume that it follows a known complex Wishart distribution. Next, this paper designs corresponding detectors within the Bayesian framework based on the one-step and two-step general likelihood ratio test (GLRT) criteria, denoted as OGLRT and TGLRT, as well as the Rao criterion. From the statistical expressions of the detectors, it is evident that the incorporation of prior information about the covariance matrix eliminates the dependency between the number of transmission snapshots and the dimension of the received signals. Specifically, when the number of transmission snapshots is limited, the prior information of the covariance matrix plays a dominant role. Conversely, as the number of transmission snapshots increases, the sample covariance matrix becomes more influential. Simulation results demonstrate that the detectors proposed in this paper exhibit constant false alarm rate (CFAR) characteristics under the null hypothesis. Moreover, even with limited training data, the Bayesian detectors introduced in this paper are still capable of effectively detecting targets and maintain strong robustness against signal mismatches.