Hermitian Toeplitz Covariance Tensor Completion With Missing Slices for Angle Estimation in Bistatic MIMO Radars

The performances of the angle estimation algorithms may be significantly deteriorated by the missing samples caused by array element failures in bistatic multiple-input–multiple-output (MIMO) radar systems. When array elements fail, the received signal can be characterized as a high-dimensional incomplete tensor with entire slices missing. Although most existing tensor completion methods successfully recover the randomly distributed missing entries, they are incapable of completing the MIMO radar signal tensor containing structurally missing entries. For bistatic MIMO radar, we propose a Hermitian Toeplitz tensor completion approach for estimating the joint direction of departure (DOD) and direction of arrival (DOA) under element failures. In particular, by exploiting the Hermitian Toeplitz property hidden in the covariance tensor, we formulate a structurally incomplete covariance tensor completion model via CANDECOMP/PARAFAC decomposition. In the proposed model, the regularizations of the low-rankness and Hermitian Toeplitz structure priors are jointly imposed on the slice-missing covariance tensor to capture more hidden correlations of the tensor data. We then present a treatable convex minimization problem with the nuclear norm and develop an implementation algorithm for solving this problem by employing the alternating direction method of multipliers. Finally, the DODs and DOAs are extracted from the restored factor matrices using the shift invariance technique. The simulation results reveal that the proposed algorithm is preferable to alternative matrix- and tensor-based algorithms with respect to both estimation accuracy and computational efficiency.