Exploiting Beam-Split Effect in IRS-Aided Systems via Opportunistic OFDMA: Design and Analysis

This paper addresses the challenges caused by employing phased-array-based intelligent reflecting surfaces (IRSs) for wideband beamforming applications at mmWave frequencies. When a large IRS is used in conjunction with a wideband signal, a phenomenon known as the beam-split (B-SP) effect arises wherein the IRS fails to focus its reflected energy toward a single user equipment (UE) across the entire signal bandwidth, resulting in a dramatic reduction in array gain and throughput. While B-SP is commonly regarded as a performance-limiting impairment, in this paper, we take an optimistic viewpoint and exploit the B-SP to improve system performance using orthogonal frequency division multiple access (OFDMA). We first show that, under the B-SP effect, the IRS can inherently exhibit amulti-directional beamformingbehavior, directing its energy toward different spatial angles at different frequency components. Capitalizing on this property, we then propose an opportunistic OFDMA scheme wherein the IRS phase shifts are randomly configured, and multiple UEs areopportunisticallyscheduled over different subcarriers (SCs) using a max-rate scheduling policy. We rigorously prove that, when the number of UEs is large, we can almost surely procure the optimal array gain on all SCs (possibly at different UEs) by exploiting the B-SP effect. Subsequently, we characterize a sufficient condition on the number of UEs to witness near-optimal gains in practical systems. Then, we demonstrate that the proposed OFDMA scheme offers multi-user diversity benefits, resulting in further throughput enhancements beyond those achieved through optimal beamforming. Finally, we also show how our idea extends to near-field propagation scenarios. Numerical simulations reveal that the OFDMA scheme outperforms the existing IRS-aided wideband beamforming solutions at low cost and complexity.