STAP Based on Toeplitz Covariance Matrix Reconstruction for Airborne Radar

We consider the problem of clutter covariance matrix (CCM) estimation for space-time adaptive processing (STAP) radar in the small sample. In this paper, a fast efficient algorithm for CCM reconstruction is proposed to overcome this shortcoming for the linear structure. Particularly, we present a low-rank matrix recovery (LRMR) question about CCM estimation based on the Toeplitz structure of CCM and the prior knowledge of the noise. The closed-form solution is obtained by relaxing the nonconvex LRMR problem that the trace norm replaces the rank norm. The target can then be efficiently detected by using the recovered CCM according to the STAP theorem. We also analyze the algorithm model under the linear structure in the presence of unknown mutual coupling. It is shown that our method can obtain accurate CCM in the small sample, with even higher accuracy than the traditional algorithms in the same number of samples. It also can reduce the coupling effect and obtain more degrees of freedom (DOF) with limited sensors and pulses by utilizing sparse linear structure (SLS) and improve angle and Doppler resolutions. Finally, numerical simulations have verified the effectiveness of the proposed method in comparison with some of the existing methods.