  We address the problem of tensor decomposition in application to
direction-of-arrival (DOA) estimation for transmit beamspace (TB)
multiple-input multiple-output (MIMO) radar. A general 4-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 subarrays. Specifically, the
received signal of TB MIMO radar is expressed as a 4-order tensor. Depending on
the target Doppler shifts, the constructed tensor is reshaped into two distinct
3-order tensors. A computationally efficient tensor decomposition method is
proposed to decompose the Vandermonde factor matrices. 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 target
DOA. It is further shown that our proposed method can be used in a more general
scenario where the subarray structures can be arbitrary but identical. The
proposed DOA estimation method requires no prior information about the tensor
rank and is guaranteed to achieve precise decomposition result. Simulation
results illustrate the performance improvement of the proposed DOA estimation
method as compared to conventional DOA estimation techniques for TB MIMO Radar.
