Multiuser beamforming optimization for IRS‐aided systems with discrete phase shifts

Abstract

Here, the beamforming design for multiuser multiple-input and multiple-output (MIMO) downlink transmission aided by an intelligent reflecting surface (IRS) with discrete phase shifts is studied. The authors deduce a minimum signal-to-interference-plus-noise-ratio (SINR) maximization fairness problem with the transmit beamformer, the receive beamformer and IRS phase shifts as optimization variables, which is generally NP-hard. Hence, an alternating optimization algorithm based on the gradient extrapolated majorizationminimization (GEMM) approach is employed to solve the above problem. Specifically, when the transmit beamformer and reflective phase shift are fixed, the authors give an optimal closed expression for the receive beamformer. Then, the receive beamformer is fixed, and the minimum SINR maximization problem at the transmitter is transformed into a power minimization problem. Finally, under the zero-forcing (ZF) transmitter beamformer, the GEMM algorithm is used to optimize the reflective phase shift. Simulation results show that by comparing to existing methods, the proposed GEMM algorithm can almost achieve the same performance with lower complexity.

Resource Allocation for Active IRS-Assisted Multiuser Communication Systems

“…We note that due to the coupling between W and B and the binary feasible set introduced by constraint C3b, problem ( 9) is a combinatorial optimization problem which is NP-hard [1], [4], [5], [8]. Suboptimal algorithms for this non-convex combinatorial optimization problem have been developed based on the AO technique in [4], [5], but cannot reveal the best possible performance. In the next section, we develop a GBD-based iterative algorithm to optimally solve the resource allocation problem in ( 9) with guaranteed convergence.…”

“…In fact, practical largescale IRSs usually employ 1-bit on-off phase shifters or 2-bit quadruple-level phase shifters, as these architectures are more cost-effective [4]. Some initial works have considered discrete IRS phase shifters, e.g., [4] and [5]. For instance, the authors in [4] focused on a single-user scenario and determined the optimal BS beamformer and discrete IRS phase shifts by employing an enumeration-based algorithm.…”

“…Yet, this result is not applicable to multiuser systems since the optimal multiuser beamforming matrix cannot be obtained in closed form. Besides, in [5], a suboptimal algorithm based on alternating optimization (AO) was developed to promote user fairness for an IRS-assisted multiuser system with discrete phase shifts. However, the AObased algorithm in [5] cannot guarantee joint optimality of the BS beamformer and the IRS phase shifts, as its performance highly depends on the selection of the initial point, which may result in unsatisfactory performance [2], [6].…”

“…Besides, in [5], a suboptimal algorithm based on alternating optimization (AO) was developed to promote user fairness for an IRS-assisted multiuser system with discrete phase shifts. However, the AObased algorithm in [5] cannot guarantee joint optimality of the BS beamformer and the IRS phase shifts, as its performance highly depends on the selection of the initial point, which may result in unsatisfactory performance [2], [6]. Thus, in this paper, we investigate for the first time the jointly optimal BS beamforming and IRS reflection coefficient design for multiuser IRS-assisted systems with discrete phase shifters to fully reveal the potential of IRS-assisted systems.…”

“…‚ To handle the coupling between the discrete IRS phase shift matrix and the BS beamforming matrix, we propose a series of transformations that convert the problem at hand to a more tractable mixed integer nonlinear programming (MINLP) problem. ‚ We develop an iterative algorithm based on the generalized Bender's decomposition (GBD) that obtains the globally optimal solution for the joint design problem and can serve as a performance benchmark for any corresponding suboptimal design, e.g., [4], [5]. ‚ Numerical results reveal that the proposed optimal joint design outperforms the commonly adopted suboptimal solution based on AO employing semidefinite relaxation.…”