RIS-Aided Multiuser MIMO-OFDM with Linear Precoding and Iterative Detection: Analysis and Optimization

In this paper, we consider a reconfigurable intelligence surface (RIS) aided uplink multiuser multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, where the receiver is assumed to conduct low-complexity iterative detection. We aim to minimize the total transmit power by jointly designing the precoder of the transmitter and the passive beamforming of the RIS. This problem can be tackled from the perspective of information theory. But this information-theoretic approach may involve prohibitively high complexity since the number of rate constraints that specify the capacity region of the uplink multiuser channel is exponential in the number of users. To avoid this difficulty, we formulate the design problem of the iterative receiver under the constraints of a maximal iteration number and target bit error rates of users. To tackle this challenging problem, we propose a groupwise successive interference cancellation (SIC) optimization approach, where the signals of users are decoded and cancelled in a group-by-group manner. We present a heuristic user grouping strategy, and resort to the alternating optimization technique to iteratively solve the precoding and passive beamforming sub-problems. Specifically, for the precoding sub-problem, we employ fractional programming to convert it to a convex problem; for the passive beamforming sub-problem, we adopt successive convex approximation to deal with the unit-modulus constraints of the RIS. We show that the proposed groupwise SIC approach has significant advantages in both performance and computational complexity, as compared with the counterpart approaches.