Scalable Graph Neural Network for Joint Active and Passive Beamforming Optimization in Distributed STAR-RIS-Assisted Multi-User MISO Systems

Core Concepts

A scalable graph neural network (GNN) framework is proposed to jointly optimize active beamforming at the base station and passive beamforming at the distributed simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) in a multi-user MISO system.

Abstract

The paper investigates a joint active and passive beamforming design for distributed STAR-RIS-assisted multi-user MISO systems, where the energy splitting (ES) mode is considered for the STAR-RIS. The goal is to design the active beamforming vectors at the base station (BS) and the passive beamforming at the STAR-RIS to maximize the user sum rate under transmit power constraints.
The key highlights are:

The formulated problem is non-convex and challenging to obtain the global optimum due to the coupling between active beamforming vectors and STAR-RIS phase shifts.

To efficiently solve the problem, a novel graph neural network (GNN)-based framework is proposed. The interactions among users and network entities are modeled using a heterogeneous graph representation.

A heterogeneous graph neural network (HGNN) implementation is introduced to directly optimize beamforming vectors and STAR-RIS coefficients with the system objective.

The proposed HGNN approach demonstrates scalability to various system configurations by preserving the permutation equivariance property.

Numerical results show that the proposed HGNN approach yields efficient performance compared to the previous benchmarks, including an alternating optimization (AO) algorithm based on successive convex approximation (SCA).

Stats

The received signal at the k-th user is expressed as:
yk = ∑L
l=1 hH
kldiag(ββ
βχ
l )diag(Θχ
l )Glx + nk
The SINR at the k-th user is represented as:
γk = (∑L
l=1 hH
klΦΦ
Φχ
l Glwk)2 / (∑j∈K,j≠k (∑L
l=1 hH
klΦΦ
Φχ
l Glwj)2 + σ2)

Quotes

"Compared to a centralized STAR-RIS system, the distributed RISs gain the potential for increased spatial diversity, enhanced interference mitigation by cooperatively optimizing STAR-RIS phase shifts over multiple channel realizations."
"The potential gain is in the order of O(L2M2) thanks to the coherent signal processing."

Key Insights Distilled From

Graph Neural Network based Active and Passive Beamforming for Distributed STAR-RIS-Assisted Multi-User MISO Systems

by Ha An Le,Tri... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2405.01979.pdf

Deeper Inquiries

How can the proposed HGNN framework be extended to handle dynamic environments where the number of users and STAR-RIS elements change over time

To extend the proposed HGNN framework to handle dynamic environments with varying numbers of users and STAR-RIS elements, we can introduce a dynamic graph construction mechanism. This mechanism would allow the graph structure to adapt to changes in the system configuration. When the number of users or STAR-RIS elements changes, new vertices can be added to the graph, and the message passing algorithm can be updated to accommodate these changes. Additionally, the mapping functions in the BHGNN model can be designed to be flexible and capable of handling different input dimensions. By incorporating dynamic graph construction and flexible mapping functions, the HGNN framework can effectively adapt to dynamic environments.

What are the potential challenges and limitations of the HGNN approach compared to the AO-based algorithm in terms of convergence guarantees and optimality of the solution

One potential challenge of the HGNN approach compared to the AO-based algorithm is the lack of theoretical guarantees on convergence and optimality. While the AO-based algorithm follows a well-defined optimization procedure with convergence guarantees, the HGNN approach relies on the training of neural networks, which may not always converge to the global optimum. Additionally, the complexity of the neural network model and the training process can introduce challenges in terms of interpretability and computational efficiency. Despite these challenges, the HGNN approach offers scalability and flexibility in handling complex and dynamic systems, which may outweigh the limitations in convergence guarantees.

Can the HGNN framework be adapted to incorporate other objectives beyond sum rate maximization, such as energy efficiency or fairness, and how would that impact the design of the message passing algorithm

The HGNN framework can be adapted to incorporate other objectives beyond sum rate maximization by modifying the objective function and updating the message passing algorithm accordingly. For example, to optimize for energy efficiency, the objective function can be redefined to include energy consumption metrics, and the message passing algorithm can be adjusted to consider energy-efficient beamforming strategies. Similarly, for fairness objectives, the objective function can be formulated to maximize fairness metrics among users, and the message passing algorithm can be designed to promote fairness in resource allocation. By customizing the objective function and message passing algorithm, the HGNN framework can be tailored to address a variety of optimization goals while maintaining its scalability and adaptability.