A Data and Model-Driven Deep Learning Approach to Robust Downlink Beamforming Optimization

TL;DR

This work tackles robust downlink beamforming in MU-MISO under Gaussian CSI uncertainties with outage constraints by introducing a data- and model-driven DL framework. It combines a modified model-based beamforming structure with a bipartite graph neural network to learn interference and power features, and uses data augmentation to estimate the rate quantile for outage-constrained optimization (P1). For the more challenging power minimization problem (P2), it adds a universal power input and employs a bisection algorithm guided by a neural estimator to find the minimum feasible transmit power. The approach yields non-conservative robust performance, higher data rates, improved power efficiency, and faster execution than state-of-the-art convex-relaxation methods and prior DL methods, with strong scalability to larger system sizes and adaptable power budgets.

Abstract

This paper investigates the optimization of the long-standing probabilistically robust transmit beamforming problem with channel uncertainties in the multiuser multiple-input single-output (MISO) downlink transmission. This problem poses significant analytical and computational challenges. Currently, the state-of-the-art optimization method relies on convex restrictions as tractable approximations to ensure robustness against Gaussian channel uncertainties. However, this method not only exhibits high computational complexity and suffers from the rank relaxation issue but also yields conservative solutions. In this paper, we propose an unsupervised deep learning-based approach that incorporates the sampling of channel uncertainties in the training process to optimize the probabilistic system performance. We introduce a model-driven learning approach that defines a new beamforming structure with trainable parameters to account for channel uncertainties. Additionally, we employ a graph neural network to efficiently infer the key beamforming parameters. We successfully apply this approach to the minimum rate quantile maximization problem subject to outage and total power constraints. Furthermore, we propose a bisection search method to address the more challenging power minimization problem with probabilistic rate constraints by leveraging the aforementioned approach. Numerical results confirm that our approach achieves non-conservative robust performance, higher data rates, greater power efficiency, and faster execution compared to state-of-the-art optimization methods.

Figures (12)

• Figure 1: Graph representation and deep learning based BMP inference with $N=2, K=2$.
• Figure 2: The proposed overall neural network framework for $\mathbf \Psi_1(\hat{{\bf H}}; \mathbf \Theta)$.
• Figure 3: Modified framework for $\mathbf \Psi_2(\tilde{{\bf H}},P;\mathbf \Theta)$.
• Figure 4: The achievable robust data rate against the transmit power.
• Figure 5: Comparison of execution time of different rate maximization algorithms.