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Best Arm Identification Based Beam Acquisition in Stationary and Abruptly Changing Environments

Gourab Ghatak

TL;DR

A novel algorithm called concurrent beam exploration, <monospace>CBE</monospace>, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user, and it is proved that <monospace>CBE</monospace> outperforms the state-of-the-art strategies in this metric.

Abstract

We study the initial beam acquisition problem in millimeter wave (mm-wave) networks from the perspective of best arm identification in multi-armed bandits (MABs). For the stationary environment, we propose a novel algorithm called concurrent beam exploration, CBE, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user. The best beam is then identified using a Hamming decoding strategy. For the case of orthogonal and highly directional thin beams, we characterize the performance of CBE in terms of the probability of missed detection and false alarm in a beam group (BG). Leveraging this, we derive the probability of beam selection error and prove that CBE outperforms the state-of-the-art strategies in this metric. Then, for the abruptly changing environments, e.g., in the case of moving blockages, we characterize the performance of the classical sequential halving (SH) algorithm. In particular, we derive the conditions on the distribution of the change for which the beam selection error is exponentially bounded. In case the change is restricted to a subset of the beams, we devise a strategy called K-sequential halving and exhaustive search, K-SHES, that leads to an improved bound for the beam selection error as compared to SH. This policy is particularly useful when a near-optimal beam becomes optimal during the beam-selection procedure due to abruptly changing channel conditions. Finally, we demonstrate the efficacy of the proposed scheme by employing it in a tandem beam refinement and data transmission scheme.

Best Arm Identification Based Beam Acquisition in Stationary and Abruptly Changing Environments

TL;DR

A novel algorithm called concurrent beam exploration, <monospace>CBE</monospace>, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user, and it is proved that <monospace>CBE</monospace> outperforms the state-of-the-art strategies in this metric.

Abstract

We study the initial beam acquisition problem in millimeter wave (mm-wave) networks from the perspective of best arm identification in multi-armed bandits (MABs). For the stationary environment, we propose a novel algorithm called concurrent beam exploration, CBE, in which multiple beams are grouped based on the beam indices and are simultaneously activated to detect the presence of the user. The best beam is then identified using a Hamming decoding strategy. For the case of orthogonal and highly directional thin beams, we characterize the performance of CBE in terms of the probability of missed detection and false alarm in a beam group (BG). Leveraging this, we derive the probability of beam selection error and prove that CBE outperforms the state-of-the-art strategies in this metric. Then, for the abruptly changing environments, e.g., in the case of moving blockages, we characterize the performance of the classical sequential halving (SH) algorithm. In particular, we derive the conditions on the distribution of the change for which the beam selection error is exponentially bounded. In case the change is restricted to a subset of the beams, we devise a strategy called K-sequential halving and exhaustive search, K-SHES, that leads to an improved bound for the beam selection error as compared to SH. This policy is particularly useful when a near-optimal beam becomes optimal during the beam-selection procedure due to abruptly changing channel conditions. Finally, we demonstrate the efficacy of the proposed scheme by employing it in a tandem beam refinement and data transmission scheme.
Paper Structure (33 sections, 13 theorems, 71 equations, 12 figures, 2 tables, 2 algorithms)

This paper contains 33 sections, 13 theorems, 71 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Context and Background
  3. Related Work
  4. Motivation
  5. Contributions and Organization
  6. System Model and Problem Statement
  7. Stationary Environment Problem
  8. Abruptly Changing Environment Problem
  9. Indexed Exploration for Stationary Environment
  10. Beam Grouping
  11. Rewards
  12. Beam Selection Strategy
  13. Characterization of the Test Statistic
  14. Probability of Missed Detection
  15. Probability of False Alarm
  16. ...and 18 more sections

Key Result

lemma 1

For single beam activation, with $T_{i} \in \mathbb{N}$ observations, the estimate $\hat{\mu}_i$ of $\mu_i$ is $\epsilon$ close to $\mu_i$ is given by

Figures (12)

  • Figure 1: Illustration of BG
  • Figure 2: Probability of beam selection error and error bounds with respect to the UE distance.
  • Figure 3: Impact of sidelobe gain $g$ on the probability of beam-selection error.
  • Figure 4: Bound on $p_{K}(r_{\rm c})$ with respect to $\Delta_{\rm min}$ for different change distributions.
  • Figure 5: Comparison in terms of beam selection error. Here $T = 1024 = 2^{10}$ and $K$ belongs to the top 20 percent of the beams.
  • ...and 7 more figures

Theorems & Definitions (15)

  • lemma 1
  • Corollary 1: Chernoff-type bound
  • lemma 2
  • lemma 3
  • Theorem 1
  • lemma 4
  • lemma 5
  • Example 1
  • Corollary 2
  • lemma 6
  • ...and 5 more