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Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning

Hassaan Hashmi, Spyridon Pougkakiotis, Dionysis Kalogerias

TL;DR

This work addresses ultra-reliable downlink beamforming in a MISO system under fading by introducing a CVaR-based risk-aggregated WSR objective. It develops a WMMSE-like equivalence to a weighted risk-averse MSE and designs an unfolded Graph Neural Network, $\alpha$RGNN, as a model-aided policy function approximator to maximize lower-tail rates. Empirical results show that $\alpha$RGNN eliminates deep fade events per user and significantly reduces rate variability, achieving robust, reliable performance while maintaining substantial ergodic throughput. Overall, the framework provides a principled trade-off between average performance and reliability and can be extended to other QoS metrics and model-based PFAs.

Abstract

We consider the problem of maximizing weighted sum rate in a multiple-input single-output (MISO) downlink wireless network with emphasis on user rate reliability. We introduce a novel risk-aggregated formulation of the complex WSR maximization problem, which utilizes the Conditional Value-at-Risk (CVaR) as a functional for enforcing rate (ultra)-reliability over channel fading uncertainty/risk. We establish a WMMSE-like equivalence between the proposed precoding problem and a weighted risk-averse MSE problem, enabling us to design a tailored unfolded graph neural network (GNN) policy function approximation (PFA), named α-Robust Graph Neural Network (αRGNN), trained to maximize lower-tail (CVaR) rates resulting from adverse wireless channel realizations (e.g., deep fading, attenuation). We empirically demonstrate that a trained αRGNN fully eliminates per user deep rate fades, and substantially and optimally reduces statistical user rate variability while retaining adequate ergodic performance.

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning

TL;DR

This work addresses ultra-reliable downlink beamforming in a MISO system under fading by introducing a CVaR-based risk-aggregated WSR objective. It develops a WMMSE-like equivalence to a weighted risk-averse MSE and designs an unfolded Graph Neural Network, RGNN, as a model-aided policy function approximator to maximize lower-tail rates. Empirical results show that RGNN eliminates deep fade events per user and significantly reduces rate variability, achieving robust, reliable performance while maintaining substantial ergodic throughput. Overall, the framework provides a principled trade-off between average performance and reliability and can be extended to other QoS metrics and model-based PFAs.

Abstract

We consider the problem of maximizing weighted sum rate in a multiple-input single-output (MISO) downlink wireless network with emphasis on user rate reliability. We introduce a novel risk-aggregated formulation of the complex WSR maximization problem, which utilizes the Conditional Value-at-Risk (CVaR) as a functional for enforcing rate (ultra)-reliability over channel fading uncertainty/risk. We establish a WMMSE-like equivalence between the proposed precoding problem and a weighted risk-averse MSE problem, enabling us to design a tailored unfolded graph neural network (GNN) policy function approximation (PFA), named α-Robust Graph Neural Network (αRGNN), trained to maximize lower-tail (CVaR) rates resulting from adverse wireless channel realizations (e.g., deep fading, attenuation). We empirically demonstrate that a trained αRGNN fully eliminates per user deep rate fades, and substantially and optimally reduces statistical user rate variability while retaining adequate ergodic performance.

Paper Structure

This paper contains 8 sections, 1 theorem, 17 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. An Equivalent WMMSE-like Formulation
  4. A Model-aided Graph Neural Network
  5. Network Realizations as Graph Data
  6. $\alpha$RGNN architecture
  7. Simulations
  8. Conclusions

Key Result

Lemma 1

For every $\bm{V}\left(\cdot\right)$, $\bm{H} \in \mathcal{H}$, and $t_{i}\in\mathbb{R}$, $i\in\mathcal{I}$, it holds that where $R_{i}\left(u_{i},w_{i},\bm{V}(\bm{H}),\bm{h}_{i}\right)\triangleq\log w_{i}-w_{i}e_{i}\left(u_{i},\bm{V}(\bm{H}),\bm{h}_{i}\right)$.

Figures (4)

  • Figure 1: A depiction of $-\text{CVaR}_{\alpha}(-Z)$
  • Figure 2: Simulated MISO downlink network configuration.
  • Figure 3: User rate densities achieved by WMMSE wmmse, risk-neutral$\alpha$RGNN, and $\alpha$RGNN with $\alpha=0.7$ on 50,000 channel realizations and 200 bins; vertical dotted lines represent sample averages (rate and density axes ranges are kept consistent for all users).
  • Figure 4: User Rate Sharpe ratios sharperatio achieved by $\alpha$RGNN.

Theorems & Definitions (1)

  • Lemma 1