Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication (1810.06934v5)

Abstract: The adoption of a Reconfigurable Intelligent Surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements, subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to $300\%$ higher energy efficiency, in comparison with the use of regular multi-antenna amplify-and-forward relaying.

• The paper presents two iterative algorithms (gradient descent and SFP) that jointly optimize RIS phase shifts and transmit power to enhance energy efficiency.
• It demonstrates that RIS-assisted systems can outperform traditional AF relay systems, achieving up to 300% higher energy efficiency at high transmit powers.
• The study underscores the practicality and scalability of RIS deployments for green wireless networks and suggests future research in robust channel models and advanced hardware designs.

Energy Efficiency in Wireless Communication: Reconfigurable Intelligent Surfaces versus Conventional Relaying

The paper authored by Chongwen Huang et al., titled "Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication," rigorously investigates the implementation of Reconfigurable Intelligent Surfaces (RIS) in downlink multi-user MISO systems. Specifically, it aims to optimize the energy efficiency through joint design of transmit power and phase shifts of RIS reflecting elements. Herein, we provide a detailed analysis of the methodologies, results, and implications of this paper.

The focus of the research is on the development of energy-efficient designs to maximize resource allocation in RIS-assisted wireless communication scenarios. To address this multifaceted problem, the authors introduce two computational algorithms grounded in alternating maximization methodology: gradient descent and sequential fractional programming (SFP). These algorithms are employed to iteratively solve the non-convex optimization problem related to RIS phase shifts and transmit power allocation.

Methodology

Problem Formulation

The SINR for each user is mathematically derived, factoring in the influence of RIS, which serves to reflect and phase-shift incident signals constructively. The paper formalizes the EE maximization problem in a constrained optimization framework considering transmit power limits and minimum QoS constraints. Given the non-convex nature of this problem, the authors implement alternating maximization:

1. RIS Phase Optimization: The gradient descent-based approach iteratively adjusts RIS coefficients, aiming to minimize a suitably defined objective function. Each iteration involves computing the descent direction and step size, ensuring that the RIS coefficients adhere to the unit modulus constraint.
2. Transmitter Power Optimization: Transmit power allocation is optimized using Dinkelbach's iterative algorithm to handle fractional programming efficiently, while ensuring QoS constraints and minimizing power consumption.

Computational Algorithms

• Gradient Descent Approach: This method involves iterative refinement of RIS phase shifts, optimizing a non-convex function via conjugate gradients. The gradient calculations incorporate Hadamard and Kronecker products to handle the complexity of phase optimization effectively.
• Sequential Fractional Programming: The SFP approach leverages the majorization-minimization technique, reformulating the optimization problem into a sequence of simpler subproblems. The convergence properties of the solution sequence are analytically guaranteed through convex surrogate functions.

Numerical Results and Analysis

The paper evaluates the efficacy of the proposed algorithms through extensive simulations. It compares the performance of RIS-assisted systems with traditional Amplify-and-Forward (AF) relaying systems across different configurations:

• Spectral Efficiency (SE) Analysis: The results indicate that while AF relay systems outperform RIS in SE due to active amplification, RIS structures still achieve competitive performance, particularly as the available transmit power increases.
• Energy Efficiency (EE) Analysis: RIS-based systems significantly outperform AF relay systems in EE. Notably, the RIS structures can provide up to 300% higher EE for large transmit powers, highlighting the absence of active amplification as a significant energy-saving factor.

Among the notable findings, the impact of the number of RIS elements (N) is investigated. Although larger RIS arrays provide better SE performance due to increased signal combinations, the associated power consumption also rises. Thus, an optimal N exists to maximize EE, balancing the benefit of additional elements against their power costs.

Implications and Future Directions

The paper provides strong evidence that RIS technology can offer substantial EE improvements in multi-user MISO systems compared to traditional relaying methods. The practical implications include:

• Deployment: RIS configurations could be integrated into existing infrastructure efficiently due to their low hardware footprint and passive design.
• Scalability: The scalable nature of the proposed algorithms renders them feasible for various network sizes, promoting practical deployment of large-scale RIS.

Future Research Directions

The current research opens new avenues for further exploration:

• Enhanced Channel Models: Including the direct BS-to-user channel, which the current paper neglects, could provide more realistic performance insights.
• Advanced Hardware Designs: Investigating RIS with continuous distributed elements or higher phase shift discretization levels could yield additional performance gains.
• Robustness Analysis: Studying the robustness of RIS-assisted communication against channel estimation errors and environmental dynamics remains a critical challenge.
• Joint Optimization Frameworks: Exploring joint optimization of transmit power, RIS phase shifts, and potentially new design parameters in more complex network scenarios will provide deeper insights.

Conclusion

Chongwen Huang et al.'s work on RIS for energy-efficient wireless communication offers a substantial contribution to the growing body of research on green communication technologies. By demonstrating the significant potential of RIS in enhancing EE over conventional relay systems, the paper paves the way for sustainable advancements in wireless network design. The rigorous methodologies and insightful findings provide a robust foundation for future innovations in the domain of reconfigurable intelligent surfaces.