Achieving Interference-Free Degrees of Freedom in Cellular Networks via RIS

TL;DR

This paper demonstrates that Reconfigurable Intelligent Surfaces (RIS) can theoretically achieve interference-free Degrees of Freedom in cellular networks, even with direct links, by quantifying the number of RIS elements needed.

Contribution

It provides a theoretical analysis showing RIS can boost DoF in cellular networks with direct links and quantifies the RIS elements required, addressing algebraic feasibility probabilistically.

Findings

RIS can achieve interference-free DoF with direct links.

Number of RIS elements needed is quantified as a function of system parameters.

Numerical results confirm the theoretical predictions.

Abstract

It's widely perceived that Reconfigurable Intelligent Surfaces (RIS) cannot increase Degrees of Freedom (DoF) due to their relay nature. A notable exception is Jiang \& Yu's work. They demonstrate via simulation that in an ideal $K$-user interference channel, passive RIS can achieve the interference-free DoF. In this paper, we investigate the DoF gain of RIS in more realistic systems, namely cellular networks, and more challenging scenarios with direct links. We prove that RIS can boost the DoF per cell to that of the interference-free scenario even \textit{ with direct-links}. Furthermore, we \textit{theoretically} quantify the number of RIS elements required to achieve that goal, i.e. $max\left\{ {2L, (\sqrt L + c)\eta+L } \right\}$ (where $L=GM(GM-1)$, $c$ is a constant and $\eta$ denotes the ratio of channel strength) for the $G$-cells with more single-antenna users $K$ than base station antennas $M$ per cell. The main challenge lies in addressing the feasibility of a system of algebraic equations, which is difficult by itself in algebraic geometry. We tackle this problem in a probabilistic way, by exploiting the randomness of the involved coefficients and addressing the problem from the perspective of extreme value statistics and convex geometry. Moreover, numerical results confirm the tightness of our theoretical results.