[Paper Review] Optimization of RIS-aided MIMO Systems via the Cutoff Rate

Nemanja Stefan Perović, Marco Di Renzo+2 more|arXiv (Cornell University)|Dec 9, 2020

Advanced Wireless Communication Technologies19 references39 citations

TL;DR

This paper proposes using the channel cutoff rate (CR) as a tractable surrogate metric to optimize mutual information (MI) in RIS-aided MIMO systems with discrete signaling, which is otherwise intractable. It introduces two optimization methods—projected gradient method (PGM) and successive convex approximation (SCA)—to jointly optimize precoding and RIS phase shifts, achieving significant CR and MI gains over conventional Gaussian signaling optimization, especially for small constellations.

ABSTRACT

International audience

Motivation & Objective

• To address the intractability of optimizing mutual information (MI) in RIS-aided MIMO systems with discrete signaling.
• To propose the channel cutoff rate (CR) as a tractable, reliable surrogate metric for MI optimization.
• To develop efficient local optimization methods for joint precoding and RIS phase shift design under perfect CSI.
• To demonstrate that CR-based optimization outperforms conventional achievable rate optimization for Gaussian signaling in practical discrete modulation systems.

Proposed method

• Uses the channel cutoff rate (CR) as a practical lower bound on mutual information, enabling tractable optimization.
• Proposes a projected gradient method (PGM) with closed-form updates for joint precoding and RIS phase shift optimization.
• Develops a successive convex approximation (SCA) method by convexifying the non-convex unit-modulus constraints on RIS elements without loss of optimality.
• Derives complex-valued gradients of the CR with respect to phase shifts and precoding matrix using matrix calculus and vectorization.
• Employs line search in PGM and CVX with MOSEK for solving convex subproblems in SCA.
• Assumes perfect channel state information (CSI) and uses discrete M-ary modulation with unit energy symbols.

Experimental results

Research questions

• RQ1 Can the cutoff rate serve as a reliable and tractable surrogate for mutual information optimization in RIS-aided MIMO systems with discrete signaling?
• RQ2 How do PGM and SCA methods compare in optimizing the joint precoding and RIS phase shift design?
• RQ3 Does CR-based optimization yield higher mutual information than conventional Gaussian signaling-based optimization in practical discrete modulation systems?
• RQ4 What performance gains are achievable in terms of CR and MI when using the proposed methods under direct link presence and blockage?
• RQ5 Can the proposed methods avoid poor local optima due to the non-convex nature of the problem?

Key findings

• The proposed PGM and SCA methods achieve nearly identical performance, converging in just a few iterations.
• CR-based optimization increases mutual information by approximately 2 bpcu when the direct link is present and 3 bpcu when blocked.
• For M = 4, CR-based optimization yields significantly higher MI than Gaussian signaling-based optimization, with a gap of over 1 bpcu.
• The achievable rate for Gaussian signaling remains higher than MI, but the gap narrows to less than 0.2 bpcu for M = 16.
• The CR is shown to be a suitable substitute metric, as MI trends closely follow CR and always exceeds it.
• Theoretical analysis confirms that scaling phase shifts beyond unit modulus improves the objective, justifying the use of unit-modulus constraints in optimization.