Geometry-Aware Meta-Learning Neural Network for Joint Phase Shift and Precoder Optimization in Reconfigurable Intelligent Surface-Aided Multi-User MISO Systems

核心概念

A complex-valued, geometry-aware meta-learning neural network that maximizes the weighted sum rate in an RIS-aided multi-user MISO system by leveraging the complex circle geometry for phase shifts and spherical geometry for the precoder, leading to faster convergence and higher weighted sum rates compared to existing approaches.

摘要

The paper proposes a complex-valued, geometry-aware meta-learning neural network algorithm for joint optimization of the precoder matrix at the base station and the phase shifts of the reconfigurable intelligent surface (RIS) elements in an RIS-aided multi-user MISO (MU-MISO) system.

Key highlights:

1. The optimization problem is formulated to maximize the weighted sum rate, which is a non-convex and NP-hard problem.
2. The proposed algorithm leverages the complex circle geometry for the phase shifts and the spherical geometry for the precoder, performing the optimization on Riemannian manifolds to achieve faster convergence.
3. A complex-valued neural network is used for the phase shift optimization, and an Euler equation-based update is employed for the precoder network design.
4. The meta-learner updates the weights of the phase-learner and precoder-learner networks through backpropagation, minimizing the overall cost function (negative weighted sum rate).
5. The proposed GAMN algorithm outperforms existing neural network-based approaches, offering higher weighted sum rates, lower power consumption, and significantly faster convergence (nearly 100 epochs faster) compared to the state-of-the-art algorithm.

統計資料

The paper reports a 0.7 bps improvement in weighted sum rate and a 1.8 dBm power gain when comparing the proposed GAMN algorithm with the existing GMML algorithm.

引述

"By leveraging the complex circle geometry for phase shifts and spherical geometry for the precoder, the optimization occurs on Riemannian manifolds, leading to faster convergence."
"Our approach outperforms existing neural network-based algorithms, offering higher weighted sum rates, lower power consumption, and significantly faster convergence."

從以下內容提煉的關鍵洞見

Geometry Aware Meta-Learning Neural Network for Joint Phase and Precoder Optimization in RIS

by Dahlia Devap... 於 arxiv.org 09-18-2024

https://arxiv.org/pdf/2409.11270.pdf

深入探究

How can the proposed geometry-aware meta-learning approach be extended to other communication systems beyond RIS-aided MU-MISO, such as multi-cell or multi-tier networks?

The geometry-aware meta-learning approach proposed in the context of RIS-aided MU-MISO systems can be effectively extended to other communication systems, including multi-cell and multi-tier networks, by leveraging the inherent geometric properties of these systems. In multi-cell networks, the optimization of precoder matrices and phase shifts can be framed similarly to the RIS scenario, where the optimization occurs on Riemannian manifolds. The key steps for extension include:

Manifold Representation: Each cell in a multi-cell network can be treated as a separate entity with its own precoder and phase shift optimization problem. The geometry of the optimization can be defined using the complex circle manifold for phase shifts and the sphere manifold for precoder constraints, similar to the RIS case.

Interference Management: In multi-cell scenarios, inter-cell interference becomes a significant factor. The proposed approach can incorporate interference management techniques by modeling the interference as part of the optimization objective, thus allowing the geometry-aware meta-learning framework to adaptively optimize the precoders and phase shifts while considering the impact of neighboring cells.

Hierarchical Learning: For multi-tier networks, where different tiers (e.g., macro, micro, and pico cells) have varying capabilities and coverage, a hierarchical learning structure can be implemented. The meta-learner can be designed to optimize the parameters at different tiers, ensuring that the optimization process respects the unique constraints and objectives of each tier.

Dynamic Adaptation: The geometry-aware approach can be enhanced with dynamic adaptation mechanisms that allow the system to respond to changing channel conditions and user distributions in real-time. This can be achieved through online learning techniques that continuously update the neural network parameters based on the latest channel state information (CSI).

By applying these strategies, the geometry-aware meta-learning approach can be tailored to optimize performance in complex multi-cell and multi-tier communication environments, ultimately improving the overall system capacity and user experience.

What are the potential challenges and considerations in applying the complex-valued neural network design to practical hardware implementations?

Implementing complex-valued neural networks in practical hardware settings presents several challenges and considerations that must be addressed to ensure effective deployment:

Hardware Compatibility: Most existing hardware architectures, including GPUs and TPUs, are primarily designed for real-valued computations. Adapting these architectures to efficiently handle complex-valued operations, such as complex multiplications and additions, may require significant modifications or the development of specialized hardware.

Precision and Quantization: Complex-valued neural networks may face issues related to numerical precision, especially when quantizing weights and activations for hardware implementation. Careful consideration must be given to the quantization process to maintain the performance of the network while reducing the computational load.

Training Complexity: The training of complex-valued neural networks can be more complex than their real-valued counterparts due to the need to manage both real and imaginary components. This complexity can lead to longer training times and may require more sophisticated optimization algorithms to ensure convergence.

Integration with Existing Systems: Integrating complex-valued neural networks into existing communication systems may pose challenges in terms of compatibility with legacy systems and protocols. Ensuring seamless integration while maintaining performance and reliability is crucial.

Real-Time Processing: In communication systems, real-time processing is often required. The computational overhead associated with complex-valued operations may hinder the ability to meet real-time constraints, necessitating optimizations in both the algorithm and hardware design.

Robustness to Channel Variability: Practical communication environments are subject to variability in channel conditions. The robustness of complex-valued neural networks to such variations must be thoroughly evaluated to ensure reliable performance in real-world scenarios.

Addressing these challenges will be essential for the successful deployment of complex-valued neural networks in practical communication systems, enabling the realization of their potential benefits in optimizing performance metrics such as sum rate and power efficiency.

Can the insights from the geometry-aware optimization be leveraged to develop novel neural network architectures or training techniques for a broader range of communication and signal processing problems?

Yes, the insights gained from geometry-aware optimization can significantly influence the development of novel neural network architectures and training techniques applicable to a broader range of communication and signal processing problems. Here are several ways in which these insights can be leveraged:

Riemannian Geometry in Neural Networks: The principles of Riemannian geometry can be integrated into neural network architectures to create Riemannian neural networks. These networks can optimize their parameters on curved manifolds, allowing for more efficient learning in scenarios where the parameter space is inherently non-Euclidean, such as in phase shift optimization and beamforming.

Manifold Learning Techniques: The concept of manifold learning can be applied to develop neural networks that are specifically designed to operate on data that lies on low-dimensional manifolds. This can enhance the performance of networks in tasks such as signal classification and feature extraction, where the underlying data structure is complex.

Adaptive Learning Rates: Insights from geometry-aware optimization can inform the design of adaptive learning rate strategies that take into account the curvature of the loss landscape. This can lead to more efficient convergence and improved training stability, particularly in high-dimensional optimization problems common in communication systems.

Multi-Task Learning Frameworks: The geometry-aware approach can be extended to multi-task learning frameworks, where a single neural network is trained to perform multiple related tasks simultaneously. By leveraging shared geometric structures, the network can learn more generalized representations that improve performance across tasks.

Transfer Learning and Meta-Learning: The meta-learning framework proposed in the context of RIS can be adapted for transfer learning scenarios, where knowledge gained from one task is applied to another. This can be particularly useful in communication systems where channel conditions and user distributions vary, allowing for rapid adaptation to new environments.

Robustness to Perturbations: The geometric insights can also be used to enhance the robustness of neural networks against perturbations and adversarial attacks. By understanding the geometry of the loss landscape, networks can be designed to maintain performance even in the presence of noise or interference.

By incorporating these insights into the design and training of neural networks, researchers can develop more effective and efficient solutions for a wide range of communication and signal processing challenges, ultimately leading to improved system performance and user experience.