Statistically Optimal Beamforming and Ergodic Capacity for RIS-aided MISO Systems

TL;DR

This paper develops a semidefinite relaxation-based algorithm for optimal beamforming in RIS-aided MISO systems, deriving closed-form solutions and analyzing performance metrics like outage probability and ergodic capacity.

Contribution

It introduces a novel iterative algorithm for statistically optimal beamforming and provides closed-form expressions for key performance metrics under special cases.

Findings

i.i.d. fading outperforms correlated fading with LoS components.

Maximum mean SNR scales linearly with RIS elements without LoS.

Maximum mean SNR scales quadratically with RIS elements with LoS.

Abstract

This paper focuses on optimal beamforming to maximize the mean signal-to-noise ratio (SNR) for a reconfigurable intelligent surface (RIS)-aided MISO downlink system under correlated Rician fading. The beamforming problem becomes non-convex because of the unit modulus constraint of passive RIS elements. To tackle this, we propose a semidefinite relaxation-based iterative algorithm for obtaining statistically optimal transmit beamforming vector and RIS-phase shift matrix. Further, we analyze the outage probability (OP) and ergodic capacity (EC) to measure the performance of the proposed beamforming scheme. Just like the existing works, the OP and EC evaluations rely on the numerical computation of the iterative algorithm, which does not clearly reveal the functional dependence of system performance on key parameters. Therefore, we derive closed-form expressions for the optimal beamforming vector and phase shift matrix along with their OP performance for special cases of the general setup. Our analysis reveals that the i.i.d. fading is more beneficial than the correlated case in the presence of LoS components. This fact is analytically established for the setting in which the LoS is blocked. Furthermore, we demonstrate that the maximum mean SNR improves linearly/quadratically with the number of RIS elements in the absence/presence of LoS component under i.i.d. fading.