Tensor-Based Approaches for Channel Estimation in IRS-Assisted MIMO Wireless Communications

Abstract

The fifth-generation (5G) is in its business version, and researchers have started to look at the potential technologies to be employed in the next generation. In this context, intelligent reflecting surface (IRS) is a promising technology for the sixth-generation (6G) of wireless systems by introducing the smart radio environment concept. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. Using a tensor framework, particularly tensor decomposition, we propose different solutions to solve the channel estimation problem for different scenarios. We firstly address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach to solve the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factors (PARAFAC) tensor modeling of the received signals. The first method has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel by solving rank-1 matrix approximation problems, while the second is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station (BS)-IRS and IRS-user terminal (UT)), which provides performance enhancements in comparison to competing methods that are based on unstructured least squares (LS) estimates of the cascaded channel. In this scenario, the numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions. Second, we develop algorithms to jointly estimate the involved channel matrices and the transmitted symbols in a semi-blind fashion. This is achieved by introducing a simple space-time coding scheme at the transmitter, such that the received signal model can be advantageously built using the PARATUCK tensor model. As a result, a semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. In this context, we first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved communication channels – IRS-BS and UT-IRS – and the transmitted symbol matrix. Second, we formulate an enhanced two-stage semi-blind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In addition, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Finally, we formulate a tensor-based semi-blind receiver for an IRS-assisted uplink multi-user MIMO system where the proposed approach relies on a generalized PARATUCK tensor model of the signals reflected by the IRS, based on a two-stage closed-form semi-blind receiver using Khatri-Rao and Kronecker factorizations.