Multi-User Beamforming and Transmission Based on Intelligent Reflecting Surface

Intelligent Reflecting Surfaces (IRS) show a revolutionary potential for wireless communications. In this paper, a single IRS is used to achieve distributed multi-user beamforming and interference-free transmission. We first establish the IRS assisted multi-user system model and formulate an optimization problem called multi-user linearly constrained minimum variance (MU-LCMV) beamformer, under the criterion of minimizing the overall received signal power subject to a certain level of power response (e.g., unit power response) at desired signal directions and arbitrary low power response (e.g., zero power response) at the interference directions. A closed-form amplitude-unconstrained phase-continuous (AUPC) solution is derived first, then an amplitude-constrained phase-continuous (ACPC) solution is obtained by using sequential quadratic programming (SQP). Given the solutions, the IRS beam pattern shows that to achieve multi-user ( $N$ pairs of transceivers, $N > 1$ ) transmission through a single surface, up to $N-1$ redundant beams are generated, significantly affecting power efficiency. The directions of the redundant beams are mathematically derived. The effect of mutual coupling on IRS is also analyzed to show the characteristic of side lobes. Simulation results verify the existence and accuracy of the redundant beam directions. This work can potentially enhance state-of-the-art wireless communication systems ranging from transceiver design, system and architecture design, network deployment and self-organizing-network operations.