Novel Relax-and-Retract Algorithm for Intelligent Reflecting Surface Design

In this paper, a novel relax-and-retract algorithm is proposed to tackle the nonconvex unit-modulus constraint in the joint intelligent reflecting surface (IRS) and multiuser multiple-input multiple-output (MU-MIMO) transceiver design. The conventional method to tackle the unit-modulus constraint is semidefinite relaxation (SDR), and its computational complexity is large. By using the symbol detection mean square error (MSE) as the quality of service (QoS), the proposed relax-and-retract approach enables us to get convex quadratically constrained quadratic programming (QCQP) subproblems, which have a much lower computational complexity than the conventional SDR approach. Simulation results show that the proposed relax-and-retract approach has excellent performance in terms of computational complexity, while the transmit power and the unit-modulus hardware implementation are the same as those of the SDR approach.