[Paper Review] Joint User Association and Power Allocation in Heterogeneous Ultra Dense Network via Semi-Supervised Representation Learning

Xiangyu Zhang, Zhengming Zhang+1 more|arXiv (Cornell University)|Mar 29, 2021

Advanced MIMO Systems Optimization45 references8 citations

TL;DR

This paper proposes a graph neural network (GNN)-based semi-supervised representation learning framework to jointly optimize user association and power allocation in heterogeneous ultra-dense networks (HUDNs). By modeling HUDNs as a heterogeneous graph and training a GNN with both unsupervised and supervised components—enhanced by entropy regularization—the method achieves high computational efficiency and superior performance compared to traditional optimization, with a two-stage learning approach (generalization-representation learning and specialization-representation learning) enabling fast online adaptation.

ABSTRACT

Heterogeneous Ultra-Dense Network (HUDN) is one of the vital networking architectures due to its ability to enable higher connectivity density and ultra-high data rates. Rational user association and power control schedule in HUDN can reduce wireless interference. This paper proposes a novel idea for resolving the joint user association and power control problem: the optimal user association and Base Station transmit power can be represented by channel information. Then, we solve this problem by formulating an optimal representation function. We model the HUDNs as a heterogeneous graph and train a Graph Neural Network (GNN) to approach this representation function by using semi-supervised learning, in which the loss function is composed of the unsupervised part that helps the GNN approach the optimal representation function and the supervised part that utilizes the previous experience to reduce useless exploration. We separate the learning process into two parts, the generalization-representation learning (GRL) part and the specialization-representation learning (SRL) part, which train the GNN for learning representation for generalized scenario quasi-static user distribution scenario, respectively. Simulation results demonstrate that the proposed GRL-based solution has higher computational efficiency than the traditional optimization algorithm, and the performance of SRL outperforms the GRL.

Motivation & Objective

• Address the challenge of high computational complexity and non-convexity in joint user association and power allocation (UAPA) in heterogeneous ultra-dense networks (HUDNs).
• Overcome the limitations of traditional optimization methods, which are slow and struggle with the coupling and scalability of UAPA problems.
• Develop a data-driven, end-to-end learning framework that generalizes across diverse user distributions while enabling fast online adaptation to quasi-static conditions.
• Integrate semi-supervised learning with graph neural networks to leverage both unlabeled network configurations and prior labeled experiences for efficient and robust representation learning.

Proposed method

• Model the HUDN as a heterogeneous graph where nodes represent users and base stations (BSs), and edges encode channel state information and precoding matrices.
• Train a Graph Neural Network (GNN) to learn a representation function that maps network parameters to optimal user association and transmit power configurations.
• Employ a two-stage learning strategy: Generalization-Representation Learning (GRL) for offline pre-training on diverse scenarios, followed by Specialization-Representation Learning (SRL) for online fine-tuning on specific user distributions.
• Design a semi-supervised loss function combining unsupervised contrastive learning (to learn general representations) and supervised learning (to incorporate prior knowledge and reduce initial exploration).
• Apply entropy regularization to the GNN’s output to encourage effective exploration in the high-dimensional configuration space during training.
• Use the GNN’s output to directly infer user association and power control decisions in an end-to-end differentiable manner, avoiding iterative optimization.

Experimental results

Research questions

• RQ1 Can a graph neural network effectively learn a representation function that maps HUDN parameters to optimal user association and power allocation decisions?
• RQ2 How does combining unsupervised and supervised learning in a semi-supervised GNN framework improve convergence and performance compared to purely supervised or unsupervised methods?
• RQ3 To what extent does the two-stage GRL/SRL training strategy enhance computational efficiency and performance in dynamic HUDN environments?
• RQ4 How does entropy regularization contribute to more effective exploration in the configuration space during GNN training?

Key findings

• The proposed GRL-based solution achieves significantly higher computational efficiency than traditional optimization algorithms, reducing runtime while maintaining high-quality solutions.
• The SRL fine-tuning stage consistently outperforms the GRL baseline in terms of spectral efficiency and interference suppression, demonstrating the value of online adaptation.
• The semi-supervised GNN framework with entropy regularization reduces the need for extensive exploration in the initial training phase, accelerating convergence.
• The GNN-based approach generalizes well across diverse user distributions due to the offline GRL pre-training, enabling fast deployment in new scenarios.
• Simulation results confirm that the joint optimization via GNN achieves near-optimal performance with lower complexity than conventional iterative methods.
• The method effectively handles the non-convex, coupled nature of the UAPA problem by learning a direct end-to-end mapping from network state to resource allocation.