Mitigating Spatial-Wideband and Beam-Split Effects via Distributed IRSs: Design and Analysis

This paper addresses the mitigation of spatial-wideband (SW) and the resulting beam-split (B-SP) effects in intelligent reflecting surface (IRS)-aided wideband systems. The SW effect occurs when the signal delay across the IRS aperture exceeds the system’s sampling duration, causing the user equipment’s (UE) channel angle to vary with frequency. This leads to the B-SP effect, wherein the IRS cannot coherently beamform to a given UE over the entire bandwidth, reducing array gain and throughput. We first show that partitioning a single IRS into multiple smaller IRSs and distributing them in the environment can naturally mitigate the SW effect (and hence the B-SP effect) by parallelizing the spatial delays and exploiting angle diversity benefits. Next, by determining the maximum number of elements at each smaller IRS to limit B-SP effects and analyzing the achievable sum-rate, we demonstrate that our approach ensures a minimum positive rate over the entire bandwidth of operation. However, distributed IRSs may introduce temporal delay spread (TDS) due to the differences in the path lengths through the IRSs and this may reduce the achievable flat channel gain. To minimize TDS and maintain the full array gain, we show that the optimal placement of the IRSs is on an ellipse with the base station (BS) and UE as the focal points. We also analyze the impact of the optimal IRS placement on TDS and throughput for a UE that is located within a hotspot served by the IRSs. Finally, we illustrate that distributed IRSs enhance angle diversity, which exponentially reduces the outage probability due to B-SP effects as the number of IRSs increases. Numerical results validate the efficacy and simplicity of our method compared to the existing solutions.