Multi-User Beamforming and Transmission Based on Intelligent Reflecting Surface

Abstract

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 amplitudeunconstrained 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.

Intelligent Reflecting Surface Networks With Multiorder-Reflection Effect: System Modeling and Critical Bounds

“…The received signal of Rx 𝑖 in Eq. ( 3) can be rewritten as [38] 𝑦 𝑖 = w 𝐻 A 𝐶,𝑖 s + 𝑛 𝑖 , 𝑖 = 1, 2, ..., 𝑁 ,…”

Intelligent Reflecting Surface Networks with Multi-Order-Reflection Effect: System Modelling and Critical Bounds

“…The received signal of Rx 𝑖 in Eq. ( 3) can be rewritten as [37] 𝑦 𝑖 = w 𝐻 A 𝐶,𝑖 s + 𝑛 𝑖 , 𝑖 = 1, 2, ..., 𝑁 ,…”

“…This is due to smaller spacing resulting in fewer channel ranks and larger beamwidth. Still, the redundant beam, causing energy waste in trivial directions, will less likely occur [37]. Thus, the actual spacing can be less than this value based on different design criteria.…”

“…The second scheme still transmit through the C-LoS channel with random weights but a 4 by 4 joint decoding matrix at Rxs' side using the zero-forcing (ZF) algorithm is leveraged as a benchmark (though it may not be practically implemented). The third one transmit through the C-LoS channel with weights obtained by multi-user linearly constrained minimum variance (MU-LCMV) algorithm [37], which can simultaneously support multiple streams by a single IRS. For a specific realization, 4 pairs of transceivers are distributed uniformly around an IRS and transmit normalized power.…”

“…Although ULA is adopted, the proposed IRS framework can be generalized to URA[37] or any other geometry.…”