Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise

Abstract

We consider a fading channel in which a multi-antenna transmitter communicates with a multi-antenna receiver through a reconfigurable intelligent surface (RIS) that is made of $N$ reconfigurable passive scatterers impaired by phase noise. The beamforming vector at the transmitter, the combining vector at the receiver, and the phase shifts of the $N$ scatterers are optimized in order to maximize the signal-to-noise-ratio (SNR) at the receiver. By assuming Rayleigh fading (or line-of-sight propagation) on the transmitter-RIS link and Rayleigh fading on the RIS-receiver link, we prove that the SNR is a random variable that is equivalent in distribution to the product of three (or two) independent random variables whose distributions are approximated by two (or one) gamma random variables and the sum of two scaled non-central chi-square random variables. The proposed analytical framework allows us to quantify the robustness of RIS-aided transmission to fading channels. For example, we prove that the amount of fading experienced on the transmitter-RIS-receiver channel linearly decreases with $N$. This proves that RISs of large size can be effectively employed to make fading less severe and wireless channels more reliable.

References in corpus (4)

• Wireless Communications with Reconfigurable Intelligent Surface: Path Loss Modeling and Experimental Measurement
• Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
• Reconfigurable Intelligent Surfaces vs. Relaying: Differences, Similarities, and Performance Comparison
• Spectral and Energy Efficiency of IRS-Assisted MISO Communication with Hardware Impairments

Cited by in corpus (4)

• A Novel Physics-based Channel Model for Reconfigurable Intelligent Surface-assisted Multi-user Communication Systems
• Reconfigurable Intelligent Surfaces Assisted Communications with Discrete Phase Shifts: How Many Quantization Levels are Required to Achieve Full Diversity?
• Reconfigurable Intelligent Surfaces Aided mmWave NOMA: Joint Power Allocation,Phase Shifts, and Hybrid Beamforming Optimization
• Battery Recharging Time Models for Reconfigurable Intelligent Surface-Assisted Wireless Power Transfer Systems