Directional Estimation of Block-Fading MIMO Channels Using Spherical Harmonics Expansion and Tensor Analysis

The well-known benefits of multiple input multiple output (MIMO) wireless communication systems suppose an efficient use of spatial diversity at both the transmitter and receiver. An important and not well-explored path toward improving MIMO system performance using spatial diversity takes into account the interactions among the antennas and the (physical) propagation medium. In this work, spherical harmonics and tensor analysis are originally combined into the problem of MIMO channel modeling and estimation. The use of spherical harmonics allows to represent the antenna radiation patterns in terms of coefficients of an expansion of spatially orthogonal functions, thus decoupling the transmit and receive antenna array responses from the physical propagation medium. Assuming a single-scattering propagation scenario driven by a finite number of specular multipaths, the parallel factor model is used to decompose the spherical modes of the MIMO channel into a sum of rank-one spherical mode tensors, whose dimensions are transmit modes, receive modes, and time. Then, we extend the tensor modeling framework to double scattering channels by resorting to the PARATUCK model that captures the interactions between multiple-scattering clusters. Capitalizing on the structure of these tensor models, we derive tensor-based alternating least squares algorithms for estimating directional MIMO channels in the spherical harmonics domain, from which the directions of arrival and directions of departure are extracted by means of a MUSIC-based method. Simulation results are provided to assess the performance of the proposed algorithms in selected system configurations. Our results also show the impact of the spherical expansion order on the accuracy of DoD/DoA estimates using the proposed algorithms.