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HoloBeam: Learning Optimal Beamforming in Far-Field Holographic Metasurface Transceivers

Debamita Ghosh, Manjesh Kumar Hanawal, Nikola Zlatanova

TL;DR

HoloBeam tackles the challenge of learning optimal far-field beamforming for holographic metasurface transceivers under a fixed pilot budget. By discretizing two continuous phase-sh shifting parameters and exploiting the unimodal dependence of RSS on each parameter, it frames beamforming as a fixed-budget pure-exploration bandit problem and introduces a two-phase algorithm that learns one parameter at a time. The authors derive an exponential decay bound on misidentification probability and demonstrate through simulations that HoloBeam outperforms state-of-the-art pure-exploration methods in LOS HMT scenarios, with notable gains in throughput. The work suggests significant practical impact for low-cost, scalable mmWave/THz beamforming, while indicating future extensions to multimodal channels with NLOS components.

Abstract

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a {\it fixed-budget multi-armed bandit framework} to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named \Algo exploits the parametric form of channel gains of the beams, which can be expressed in terms of two {\it phase-shifting parameters}. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, {\it\HB} works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of {\it\HB} incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that {\it\HB} outperforms state-of-the-art algorithms through extensive simulations.

HoloBeam: Learning Optimal Beamforming in Far-Field Holographic Metasurface Transceivers

TL;DR

HoloBeam tackles the challenge of learning optimal far-field beamforming for holographic metasurface transceivers under a fixed pilot budget. By discretizing two continuous phase-sh shifting parameters and exploiting the unimodal dependence of RSS on each parameter, it frames beamforming as a fixed-budget pure-exploration bandit problem and introduces a two-phase algorithm that learns one parameter at a time. The authors derive an exponential decay bound on misidentification probability and demonstrate through simulations that HoloBeam outperforms state-of-the-art pure-exploration methods in LOS HMT scenarios, with notable gains in throughput. The work suggests significant practical impact for low-cost, scalable mmWave/THz beamforming, while indicating future extensions to multimodal channels with NLOS components.

Abstract

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a {\it fixed-budget multi-armed bandit framework} to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named \Algo exploits the parametric form of channel gains of the beams, which can be expressed in terms of two {\it phase-shifting parameters}. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, {\it\HB} works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of {\it\HB} incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that {\it\HB} outperforms state-of-the-art algorithms through extensive simulations.
Paper Structure (19 sections, 3 theorems, 27 equations, 6 figures, 2 algorithms)

This paper contains 19 sections, 3 theorems, 27 equations, 6 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Channel Model and Channel Estimation
  4. Channel Model
  5. Channel Estimation
  6. Discretizating Phase-Shifting Parameters
  7. Discretization of the Phase-Shifting Parameters
  8. Problem Formulation
  9. Proposed Algorithm
  10. The Baseline Algorithm: $\beta_i$-HoloBeam
  11. Analysis
  12. Numerical Simulations
  13. Comparison with other pure exploration algorithms
  14. Comparison of throughput performance
  15. Conclusion and future work
  16. ...and 4 more sections

Key Result

Lemma 1

Let $\mathcal{B}_1$ be such that $K_1 = \left\lceil 2/d_1 \right\rceil+1$ and $d_1 = \frac{1}{K_x}$, then $\mu_1(\beta_1)$ is unimodal on $\mathcal{B}_1$. Similarly, let $K_2 = \left\lceil 2/d_2 \right\rceil+1$ and $d_2 = \frac{1}{K_y}$ in $\mathcal{B}_2$, then $\mu_2(\beta_2)$ is unimodal on $\math

Figures (6)

  • Figure 1: The HMT-assisted wireless communication system ghermezcheshmeh2021channel.
  • Figure 2: The optimal value is attained at the highest peak of the central lobe of $|H^{ff}(\beta_1,\beta_2)|$, i.e. $(\beta^*_1,\beta^*_2) = (\alpha_1,\alpha_2) = (0.5, -0.5).$
  • Figure 3: Mean RSS vs Discrete and Continuous $\beta_2$, where $\beta^0_1= -0.5$.
  • Figure 4: Different cases of elimination in batch $l$.
  • Figure 5: Error probability performance of HoloBeam vs State-of-the-art Algorithms
  • ...and 1 more figures

Theorems & Definitions (10)

  • Definition 1: Unimodality
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Theorem 1
  • proof
  • proof
  • proof
  • proof