Semi-Blind Joint Channel and Symbol Estimation for IRS-Assisted MIMO Systems

Intelligent reflecting surface (IRS) is a promising technology for the 6
$\text{th}$
 generation of wireless systems, realizing the smart radio environment concept. This paper presents a novel tensor-based receiver for Intelligent reflecting surface (IRS)-assisted multiple-input multiple-output communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. A semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. We first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved – IRS-base station and user terminal-IRS – communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. We also formulate an enhanced two-stage semi-blind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In particular, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Numerical results are proposed for performance evaluation in several system settings in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate, corroborating the merits of the proposed semi-blind receiver in comparison to competing methods.