DOA Estimation for Transmit Beamspace MIMO Radar via Tensor Decomposition with Vandermonde Factor Matrix

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general higher-order tensor model that enables computationally efficient DOA estimation is designed. Whereas other tensor decomposition-based methods treat all factor matrices as arbitrary, the essence of the proposed DOA estimation method is to fully exploit the Vandermonde structure of the factor matrices to take advantage of the shift-invariance between and within different transmit subarrays. Specifically, the received signal of TB MIMO radar is expressed as a higher-order tensor. A computationally efficient tensor decomposition method is proposed to decompose the Vandermonde factor matrices of this signal tensor. The generators of the Vandermonde factor matrices are computed to estimate the phase rotations between subarrays, which can be utilized as a look-up table for finding targets DOA. The proposed tensor signal model as well as the DOA estimation algorithm are also straightforwardly applicable for the one-dimensional TB MIMO radar case. It is further shown that our proposed approach can be used in a more general scenario where the transmit subarrays with arbitrary but identical configuration can be non-uniformly displaced. We also show that both the tensor rank of the signal tensor and the matrix rank of a particular matrix derived from the signal tensor are identical to the number of targets. Thus, the number of targets can be estimated via matrix rank determination. Simulation results illustrate the performance improvement of the proposed DOA estimation method as compared to other tensor decomposition-based techniques for TB MIMO radar.