Conjugate gradient persymmetric adaptive matched filter

The rank corresponding to interferences and clutter is commonly much smaller than the size of the covariance matrix due to the sparsity of detection environment, which results in the approximate low-rank correction structure of the transformed estimated covariance matrix in the persymmetric adaptive matched filter (PS-AMF). As a result, the conjugate gradient (CG) algorithm is an efficient iterative algorithm in the calculation of the weight vector of PS-AMF and produces the projection of PS-AMF weight vector to the Krylov subspace with the dimension increasing with the CG iterations. Therefore, we focus on the case that CG algorithm is used in PS-AMF in this paper, which leads to a family of reduced-rank detectors in Krylov subspace for PS-AMF. These detectors are referred to as the CG-PS-AMF detectors. Firstly, the expected value of the output signal-to-interference-and-noise ratio (SINR) of CG-PS-AMF detector is analyzed, and then its approximation expression is given. Finally, numerical results are presented to verify our theoretical analysis of CG-PS-AMF. Meanwhile, compared with its counterparts, CG-PS-AMF detector shows better detection performance. Besides, it is shown that CG-PS-AMF has a low computational cost.