Tensor beamforming for multilinear translation invariant arrays

In the past few years, multidimensional array processing emerged as the generalization of classic array signal processing. Tensor methods exploiting array multidimensionality provided more accurate parameter estimation and consistent modeling. In this paper, multilinear translation invariant arrays are studied. An M-dimensional translation invariant array admits a separable representation in terms of a reference subarray and a set of M - 1 translations, which is equivalent to a rank-1 decomposition of an Mth order array manifold tensor. We show that such a multilinear translation invariant property can be exploited to design tensor beamformers that operate multilin-early on the subarray level instead of the global array level, which is usually the case with a linear beamforming. An important reduction of the computational complexity is achieved with the proposed tensor beamformer with a negligible loss in performance compared to the classical minimum mean square error (MMSE) beamforming solution.