Reducing the Control Overhead of Intelligent Reconfigurable Surfaces via a Tensor-Based Low-Rank Factorization Approach

Intelligent reconfigurable surface IRS are becoming an attractive component of cellular networks due to their ability to shape the propagation environment and thereby improve coverage. While IRS nodes incorporate a great number of phase-shifting elements and a controller entity, the phase shifts are typically determined by the cellular base station (BS) due to its computational capability. Since controlling a large number of phase shifts may become prohibitive in practice, it is important to reduce the control overhead between the BS and the IRS controller. To this end, in this paper, we propose a low-rank modeling approach for the IRS phase shifts. The key idea is to represent the IRS phase shift vector using a low-rank tensor approximation model, where each rank-one component is modeled as the Kronecker product of a predefined number of factors of smaller sizes, obtained via tensor decomposition algorithms. We show that the proposed low-rank models drastically reduce the required feedback requirements associated with the BS-IRS control links. Our simulation results indicate that the proposed method is especially attractive in scenarios with a strong line of sight component, in which case nearly the same spectral efficiency is reached as in the cases with near-optimal phase shifts, but with significantly lower feedback overhead.