Hybrid Beamforming for Reconfigurable Intelligent Surface based Multi-user Communications: Achievable Rates with Limited Discrete Phase Shifts (1910.14328v1)

Abstract: Reconfigurable intelligent surface (RIS) has drawn considerable attention from the research society recently, which creates favorable propagation conditions by controlling the phase shifts of the reflected waves at the surface, thereby enhancing wireless transmissions. In this paper, we study a downlink multi-user system where the transmission from a multi-antenna base station (BS) to various users is achieved by the RIS reflecting the incident signals of the BS towards the users. Unlike most existing works, we consider the practical case where only a limited number of discrete phase shifts can be realized by the finite-sized RIS. Based on the reflection-dominated one-hop propagation model between the BS and users via the RIS, a hybrid beamforming scheme is proposed and the sum-rate maximization problem is formulated. Specifically, the continuous digital beamforming and discrete RIS-based analog beamforming are performed at the BS and the RIS, respectively, and an iterative algorithm is designed to solve this problem. Both theoretical analysis and numerical validations show that the RIS-based system can achieve a good sum-rate performance by setting a reasonable size of RIS and a small number of discrete phase shifts.

• The paper introduces a novel HBF scheme that merges digital beamforming at the base station with RIS analog beamforming using limited discrete phase shifts.
• An iterative algorithm decomposes the non-convex optimization problem into digital beamforming and RIS configuration, achieving near-optimal sum-rate performance.
• The framework reduces hardware complexity by halving RF chains and establishes design criteria for effective RIS deployment under LoS conditions.

Hybrid Beamforming for Reconfigurable Intelligent Surface Based Multi-user Communications: Achievable Rates with Limited Discrete Phase Shifts

The research presented in the paper focuses on the deployment of Reconfigurable Intelligent Surfaces (RIS) in a downlink multi-user communication system. The architecture described integrates a multi-antenna base station (BS) with an RIS to optimize the communication rates under practical conditions, where only a limited number of discrete phase shifts are realizable.

Overview of the Proposed Framework

The core of the paper's contribution lies in the hybrid beamforming (HBF) scheme designed for multiple user communication facilitated through an RIS. In this system, continuous digital beamforming is conducted at the BS while discrete RIS-based analog beamforming is performed by the RIS. This design stands out by addressing realistic conditions—specifically the finiteness of discrete phase shifts that can be implemented on the RIS.

Problem Formulation

The authors construct a mathematical model comprising a reflection-dominated one-hop propagation model. A mixed-integer optimization problem is formulated to maximize the sum-rate performance of the communication system. This includes the novel addition of RIS configuration into the HBF framework by manipulating discrete phase shifts—a notable distinction from prior models which often assume continuous phase shifts.

Key Contributions and Findings

1. Iterative Algorithm Development: To tackle the non-convex optimization challenge, a decomposition approach is employed. The problem is split into two subproblems: digital beamforming and RIS configuration-based analog beamforming. The authors propose an iterative algorithm combining Zero-Forcing (ZF) beamforming with specific power allocation strategies and an outer approximation method to converge towards optimal RIS configuration.
2. Achievable Sum Rate Analysis: The mathematical analyses and numerical validations illustrate that the proposed RIS-based system can maintain high sum-rate performances by optimizing the size of the RIS and its discrete phase adjustments. This provides a significant advantage over traditional systems without RIS support, particularly when considering the constraint of discrete phase values.
3. Resource Efficiency: As part of the theoretical analysis, the paper contrasts RIS-based HBF with traditional beamforming techniques, showcasing that the proposed approach drastically reduces hardware complexity, specifically cutting down the RF chains in half compared to standard methods while achieving similar digital beamforming capabilities.
4. Special Case and RIS Design: The paper further explores pure Line-of-Sight (LoS) scenarios revealing how RIS design parameters like size and element spacing influence the orthogonality of communication links. This exploration directs a specific design criterion to enhance rate performance under these conditions.

Implications and Future Work

This research highlights the potential of RIS to fundamentally alter multi-user communication efficiency via low-cost, energy-efficient transmission enhancements. The paper establishes a reference point for deploying RIS with discrete phase shifts in real-world wireless communication systems.

Future investigations might focus on extending these findings to broader environmental conditions, integrating stochastic and adaptive elements that respond to variable atmospheric or mobility-induced challenges. Further refinement of the RIS model to account for more intricate electromagnetic interactions and optimizing phase discretization levels could enhance practical deployments further.

Overall, this document provides a solid framework for future deployment of intelligent surfaces in communication systems, encouraging further investigation into RIS technologies and their integration into existing network infrastructures.