Block-Term Tensor Decomposition in Array Signal Processing: Uniform Rectangular Arrays

Tensor-based methods have attracted significant interest also in array signal processing (ASP) given the inherently multi-dimensional nature of the problems involved therein. The ability of tensor decomposition (TD)-based techniques to recover latent information, including channel parameters and transmitted symbols in the ASP context, in a deterministic manner and with little or no training overhead fits well with the data efficiency needs of future-generation multi-user massive multiple-input multiple-output (MU-mMIMO) systems. They have mostly relied, however, on a few classical TD models, notably canonical polyadic decomposition (CPD). In this paper, a generalized CPD model, known as block-term decomposition (BTD), which has been increasingly adopted in a wide range of applications, is re-visited in the context of ASP, and shown to be the natural choice in sensor arrays of increased dimensionality and channel multipath. Semi-blind joint channel estimation/data detection (JCD) is addressed in the special but important case of the uniform rectangular array (URA), via efficient algorithms that wed existing JCD schemes with BTD approximation. Their performance, at various noise levels, array sizes, and numbers of users and paths, is evaluated via simulation results and favorably compared with that of the training-only-based solution.