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Physics-Informed Parametric Bandits for Beam Alignment in mmWave Communications

Hao Qin, Thang Duong, Ming Li, Chicheng Zhang

TL;DR

This work tackles efficient beam alignment in mmWave systems by formulating the problem as a physics-informed parametric bandit that leverages the sparse multipath nature of mmWave channels. It introduces two algorithms, PR-ETC and PR-Greedy, which estimate the channel parameters via maximum likelihood and select beams based on the learned reward function, avoiding reliance on unimodality assumptions. A regret analysis shows PR-ETC achieves sublinear regret that scales as $O\left(T^{2/3}\right)$ with a path-dependent constant, independent of the beam count, and the methods demonstrate superior sample efficiency and robustness on DeepMIMO and DeepSense6G datasets under stationary and nonstationary conditions. The results establish strong practical potential for real-time beam tracking and motivate future work on reducing time cost, extending to near-field scenarios, and developing adaptive restart strategies for highly dynamic environments.

Abstract

In millimeter wave (mmWave) communications, beam alignment and tracking are crucial to combat the significant path loss. As scanning the entire directional space is inefficient, designing an efficient and robust method to identify the optimal beam directions is essential. Since traditional bandit algorithms require a long time horizon to converge under large beam spaces, many existing works propose efficient bandit algorithms for beam alignment by relying on unimodality or multimodality assumptions on the reward function's structure. However, such assumptions often do not hold (or cannot be strictly satisfied) in practice, which causes such algorithms to converge to choosing suboptimal beams. In this work, we propose two physics-informed bandit algorithms \textit{pretc} and \textit{prgreedy} that exploit the sparse multipath property of mmWave channels - a generic but realistic assumption - which is connected to the Phase Retrieval Bandit problem. Our algorithms treat the parameters of each path as black boxes and maintain optimal estimates of them based on sampled historical rewards. \textit{pretc} starts with a random exploration phase and then commits to the optimal beam under the estimated reward function. \textit{prgreedy} performs such estimation in an online manner and chooses the best beam under current estimates. Our algorithms can also be easily adapted to beam tracking in the mobile setting. Through experiments using both the synthetic DeepMIMO dataset and the real-world DeepSense6G dataset, we demonstrate that both algorithms outperform existing approaches in a wide range of scenarios across diverse channel environments, showing their generalizability and robustness.

Physics-Informed Parametric Bandits for Beam Alignment in mmWave Communications

TL;DR

This work tackles efficient beam alignment in mmWave systems by formulating the problem as a physics-informed parametric bandit that leverages the sparse multipath nature of mmWave channels. It introduces two algorithms, PR-ETC and PR-Greedy, which estimate the channel parameters via maximum likelihood and select beams based on the learned reward function, avoiding reliance on unimodality assumptions. A regret analysis shows PR-ETC achieves sublinear regret that scales as with a path-dependent constant, independent of the beam count, and the methods demonstrate superior sample efficiency and robustness on DeepMIMO and DeepSense6G datasets under stationary and nonstationary conditions. The results establish strong practical potential for real-time beam tracking and motivate future work on reducing time cost, extending to near-field scenarios, and developing adaptive restart strategies for highly dynamic environments.

Abstract

In millimeter wave (mmWave) communications, beam alignment and tracking are crucial to combat the significant path loss. As scanning the entire directional space is inefficient, designing an efficient and robust method to identify the optimal beam directions is essential. Since traditional bandit algorithms require a long time horizon to converge under large beam spaces, many existing works propose efficient bandit algorithms for beam alignment by relying on unimodality or multimodality assumptions on the reward function's structure. However, such assumptions often do not hold (or cannot be strictly satisfied) in practice, which causes such algorithms to converge to choosing suboptimal beams. In this work, we propose two physics-informed bandit algorithms \textit{pretc} and \textit{prgreedy} that exploit the sparse multipath property of mmWave channels - a generic but realistic assumption - which is connected to the Phase Retrieval Bandit problem. Our algorithms treat the parameters of each path as black boxes and maintain optimal estimates of them based on sampled historical rewards. \textit{pretc} starts with a random exploration phase and then commits to the optimal beam under the estimated reward function. \textit{prgreedy} performs such estimation in an online manner and chooses the best beam under current estimates. Our algorithms can also be easily adapted to beam tracking in the mobile setting. Through experiments using both the synthetic DeepMIMO dataset and the real-world DeepSense6G dataset, we demonstrate that both algorithms outperform existing approaches in a wide range of scenarios across diverse channel environments, showing their generalizability and robustness.
Paper Structure (29 sections, 4 theorems, 42 equations, 28 figures, 3 algorithms)

This paper contains 29 sections, 4 theorems, 42 equations, 28 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem formulation
  4. System Model
  5. Beam Alignment as a Parametric Bandit Problem
  6. Algorithms
  7. Algorithms for the Stationary Reward Distribution Setting
  8. Channel Estimation using Maximum Likelihood Estimate (MLE)
  9. Regret guarantee for $\textsc{PR-ETC}$
  10. Performance Evaluation
  11. Evaluation Metrics and Baselines
  12. Evaluation on DeepMIMO simulation environment
  13. Distribution of cumulative regret over different BS-UE pairs
  14. Case Study in one BS-UE location
  15. Spatial distribution of normalized regret
  16. ...and 14 more sections

Key Result

Theorem 4

Suppose Assumptions assum:quadratic-lower-bound, and assum:lip hold. The regret of $\textsc{PR-ETC}$ satisfies: Furthermore, with $M = T^{2/3} \left(k\sigma^2 (\log |B| + \log|\Theta|)\right)^{1/3}$, where $O(\cdot)$ hides constants that depends on $C_i, i =1,\ldots,4$.

Figures (28)

  • Figure 1: The expected reward function of a bandit instance from the DeepSense 6G dataset (scenario 17). Such a reward function is not unimodal, and thus algorithms that rely on unimodality assumptions may converge to choosing a suboptimal beam.
  • Figure 2: An overview of our system model.
  • Figure 3: The right-hand side (in green) vs the left-hand side (in orange) of Eq. \ref{['eqn:RHS-assumption1']}, verified on the DeepMIMO scenario 4 Base Station 1 User Equipment $(0, 843)$.
  • Figure 4: The left-hand side (in green) vs the right-hand side (in orange) of Eq. \ref{['eqn:rhs-assumption2']}, verified on the DeepMIMO scenario 4 Base Station 1 User Equipment $(0, 843)$, with a fixed beam $a = 0$.
  • Figure 5: Distribution of normalized regret over all BS-UE pairs at the first $50$ steps.
  • ...and 23 more figures

Theorems & Definitions (7)

  • Theorem 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Lemma 8: Concentration of Data Norm
  • Lemma 9: Chernoff's inequality
  • Lemma 10: Instantaneous Regret of the Committed Beam