This study investigates a virtual multiuser multiple-input multiple-output (MU-MIMO) system with PSK modulation, realized with a reconfigurable intelligent surface (RIS)-based transmitter. The study focuses on minimizing transmit power under quality-of-service (QoS) constraints while addressing the associated computational complexity. A discrete phase-shift RIS model is considered, and the power minimization problem is formulated in two scenarios. First, for QPSK user data, the symbol-error probability (SEP) is adopted as the QoS criterion. Second, for generalM-PSK modulation, the union-bound SEP (UBSEP) is used to define the QoS constraints. Based on the considered formulations, a partial branch-and-bound (PBB) approach is developed, which improves on full branch-and-bound (FBB) methods in the sense of allowing for favorable complexity performance trade-offs. For the special case of high-resolution RIS, the discrete phase-shift set is approximated by its continuous counterpart, enabling the reformulation of the original problems as constrained optimizations on an oblique manifold, which are solved with reduced computational complexity with the proposed bisection method. Numerical results demonstrate the effectiveness of the proposed approaches in minimizing the transmit power for different SEP requirements and showcase the balance between power efficiency and computational complexity.

The present study considers a virtual multiuser multiple-input multiple-output system with PSK modulation realized via the reconfigurable intelligent surface-based passive transmitter setup. The study considers a discrete phase shift reconfigurable intelligent surface model where the reflecting elements' coefficients are restricted to a discrete set. With this, a symbol-level precoding power minimization problem under the condition that the union-bound symbol-error probability is below a given requirement is formulated. The corresponding mixed integer problem is solved via the utilization of a sophisticated branch-and-bound strategy. Numerical results show that the proposed power minimization approach yields reduced average transmit power when compared to state-of-the-art techniques.

This study focuses on the development of low-resolution symbol-level precoding techniques for multiuser MIMO downlink systems with PSK modulation. While for QPSK the established minimum symbol error probability criterion is used, a criterion for PSK modulation, in general, is proposed based on the minimum union-bound symbol-error probability. Based on these criteria different low-resolution precoding approaches are proposed. First, suboptimal solutions are computed via a partial greedy search method. Then the suboptimal solutions are utilized as initialization for a novel branch-and-bound algorithm that can exploit knowledge of the system’s quality-of-service demands. Different than existing branch-and-bound approaches the proposed quality-of-service branch-and-bound method searches for a solution that attains a target symbol-error probability while going in the direction of the global optimal solution. In this sense, the proposed branch-and-bound method allows for tunable complexity performance trade-offs. Numerical results confirm that the proposed quality-of-service branch-and-bound algorithm yields reduced symbol-error probability with significantly smaller computational complexity than other state-of-the-art branch-and-bound designs.

We propose an optimal MMSE precoding technique using quantized signals with constant envelope. Unlike the existing MMSE design that relies on 1-bit resolution, the proposed approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. We also propose robust MMSE designs where we exploit second order statistics of a channel state information mismatch. Moreover, unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding. Besides an exact approach for computing the extrinsic information, we propose two approximations with reduced computational complexity. Numerical simulations show that utilizing the MMSE criterion instead of the established maximum-minimum distance to the decision threshold yields a lower bit-error-rate in many scenarios. Furthermore, when using the MMSE criterion, a smaller number of bound evaluations in the branch-and-bound method is required for low and medium SNR. Finally, results based on an LDPC block code indicate that the proposed receive processing schemes yield a lower bit-error-rate compared to the conventional design.