[Paper Review] On the Achievable Sum-rate of the RIS-aided MIMO Broadcast Channel

Nemanja Stefan Perović, Le‐Nam Tran+2 more|arXiv (Cornell University)|Apr 25, 2021

Advanced Wireless Communication Technologies15 references4 citations

TL;DR

This paper proposes an alternating optimization (AO) algorithm to maximize the achievable sum-rate in a Reconfigurable Intelligent Surface (RIS)-aided MIMO broadcast channel by jointly optimizing users' covariance matrices and RIS phase shifts using BC-MAC duality. The method achieves significant sum-rate gains, especially with direct links and increasing user/antenna counts, due to closed-form solutions for both covariance matrices and phase shifts via dual decomposition and phase optimization.

ABSTRACT

Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation and thus offers a great variety of possible performance and implementation gains. Motivated by this, we investigate the achievable sum-rate optimization in a broadcast channel (BC) that is equipped with an RIS. We exploit the well-known duality between the Gaussian multiple-input multiple-output (MIMO) BC and multiple-access channel (MAC) to derive an alternating optimization (AO) algorithm which optimizes the users' covariance matrices and the RIS phase shifts in the dual MAC. The optimal users' covariance matrices are obtained by a dual decomposition method in which each iteration is solved in closed-form. The optimal RIS phase shifts are also computed using a derived closed-form expression. Furthermore, we present a computational complexity analysis for the proposed AO algorithm. Simulation results show that the proposed AO algorithm can provide significant achievable sum-rate gains in a BC.

Motivation & Objective

• To address the challenge of maximizing achievable sum-rate in RIS-aided MIMO broadcast channels with joint optimization of user precoding and RIS phase shifts.
• To leverage the well-known Gaussian MIMO BC-MAC duality to transform the sum-rate maximization problem into a dual multiple-access channel (MAC) framework.
• To develop an iterative AO algorithm that alternately optimizes users' covariance matrices and RIS phase shifts in the dual MAC domain.
• To derive closed-form expressions for both optimal users' covariance matrices and optimal RIS phase shifts to ensure computational efficiency.
• To analyze the computational complexity of the proposed AO algorithm in terms of complex multiplications.

Proposed method

• Utilizes BC-MAC duality to reformulate the MIMO broadcast channel sum-rate maximization problem into its dual multiple-access channel (MAC) form.
• Applies dual decomposition to compute the optimal users' covariance matrices in each iteration, solving the dual problem in closed-form.
• Derives a closed-form expression for the optimal RIS phase shifts based on the dual MAC structure and channel state information.
• Implements an alternating optimization (AO) framework that iteratively updates users' covariance matrices and RIS phase shifts until convergence.
• Analyzes computational complexity by counting complex multiplications required per iteration, providing a scalable performance metric.
• Employs a system model with a multi-antenna base station, multiple single-antenna users, and a large-scale RIS with phase-shift reconfigurability.

Experimental results

Research questions

• RQ1 How can the achievable sum-rate be maximized in an RIS-aided MIMO broadcast channel with joint optimization of user precoding and RIS phase shifts?
• RQ2 Can BC-MAC duality be effectively leveraged to transform the sum-rate maximization problem into a more tractable dual MAC framework?
• RQ3 What closed-form solutions exist for the optimal users' covariance matrices and RIS phase shifts in the dual MAC domain?
• RQ4 How does the presence of direct links affect the achievable sum-rate gains in RIS-aided MIMO BC systems?
• RQ5 What is the computational complexity of the proposed AO algorithm in terms of complex multiplications?

Key findings

• The proposed AO algorithm achieves significant sum-rate gains, particularly when direct links are present in the broadcast channel.
• Sum-rate increases with the number of users and transmit antennas, but the gain diminishes when K ≥ 4 due to rank saturation of the channel matrix.
• For 6 users and 2 transmit antennas, adding the RIS yields a 99% increase in achievable sum-rate compared to the direct-link-only case.
• The achievable sum-rate curves exhibit an approximately logarithmic growth with respect to the number of transmit antennas.
• The algorithm’s computational complexity is analytically quantified in terms of complex multiplications, enabling scalability assessment.
• The lack of amplitude control in RIS limits interference suppression, making direct links more effective for sum-rate enhancement.