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Reliable Majority Vote Computation with Complementary Sequences for UAV Waypoint Flight Control

Alphan Sahin, Xiaofeng Wang

TL;DR

This work tackles reliable MV computation over fading wireless channels without CSI at transmitters by introducing a non-coherent OAC scheme based on Golay complementary sequences. The method encodes $m$ MV votes into a length-$L=2^m$ CS, preserves PMEPR with a bound of $3$ dB, and uses non-coherent energy detection at the UAV via $E^{+}_n$ and $E^{-}_n$ to recover the MV even under time-varying channels. The authors derive average energy expressions and a CER framework, provide convergence analysis for MV-driven UAV control, and validate performance through extensive simulations, showing CER improvements over Goldenbaum’s approach and robust UAV trajectories under MV-based updates. The results indicate substantial reductions in computation error rate while maintaining hardware-friendly PMEPR, enabling scalable, CSI-free distributed MV computation for UAV guidance and similar control tasks. Overall, the paper advances practical over-the-air MV computation with bounded PMEPR and provable stability, highlighting its potential for real-time wireless control and distributed decision-making.

Abstract

In this study, we propose a non-coherent over-the-air computation scheme to calculate the majority vote (MV) reliably in fading channels. The proposed approach relies on modulating the amplitude of the elements of complementary sequences based on the sign of the parameters to be aggregated. Since it does not use channel state information at the nodes, it is compatible with time-varying channels. To demonstrate the efficacy of our method, we employ it in a scenario where an unmanned aerial vehicle is guided by distributed sensors, relying on the MV computed using our proposed scheme. We show that the proposed scheme notably reduces the computation error rate with a longer sequence length in fading channels while maintaining the peak-to-mean-envelope power ratio of the transmitted orthogonal frequency division multiplexing signals to be less than or equal to 3 dB.

Reliable Majority Vote Computation with Complementary Sequences for UAV Waypoint Flight Control

TL;DR

This work tackles reliable MV computation over fading wireless channels without CSI at transmitters by introducing a non-coherent OAC scheme based on Golay complementary sequences. The method encodes MV votes into a length- CS, preserves PMEPR with a bound of dB, and uses non-coherent energy detection at the UAV via and to recover the MV even under time-varying channels. The authors derive average energy expressions and a CER framework, provide convergence analysis for MV-driven UAV control, and validate performance through extensive simulations, showing CER improvements over Goldenbaum’s approach and robust UAV trajectories under MV-based updates. The results indicate substantial reductions in computation error rate while maintaining hardware-friendly PMEPR, enabling scalable, CSI-free distributed MV computation for UAV guidance and similar control tasks. Overall, the paper advances practical over-the-air MV computation with bounded PMEPR and provable stability, highlighting its potential for real-time wireless control and distributed decision-making.

Abstract

In this study, we propose a non-coherent over-the-air computation scheme to calculate the majority vote (MV) reliably in fading channels. The proposed approach relies on modulating the amplitude of the elements of complementary sequences based on the sign of the parameters to be aggregated. Since it does not use channel state information at the nodes, it is compatible with time-varying channels. To demonstrate the efficacy of our method, we employ it in a scenario where an unmanned aerial vehicle is guided by distributed sensors, relying on the MV computed using our proposed scheme. We show that the proposed scheme notably reduces the computation error rate with a longer sequence length in fading channels while maintaining the peak-to-mean-envelope power ratio of the transmitted orthogonal frequency division multiplexing signals to be less than or equal to 3 dB.
Paper Structure (21 sections, 8 theorems, 43 equations, 3 figures, 2 tables)

This paper contains 21 sections, 8 theorems, 43 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work and Challenges
  3. Over-the-air computation
  4. Wireless Control Systems
  5. Contributions
  6. System Model
  7. Complementary Sequences
  8. Signal Model and Wireless Channel
  9. Problem Statement
  10. Proposed Scheme
  11. Performance Analysis
  12. Average Performance
  13. Computation Error Rate
  14. Computation Rate and Resource Utilization Ratio
  15. Complexity Analysis
  16. ...and 6 more sections

Key Result

Theorem 1

Let $\bm{\pi}=({\pi_{n}})_{n=1}^{m}$ be a permutation of $\{1,2,\dots,m\}$. For any $H,m\in\mathbb{Z}^{+}$, $a_{n},a_{0}\in\mathbb{R}$, and $b_{n},b_{0} \in \mathbb{Z}_H$ for $n\in\{1,2,\hbox{...},m\}$, let where $y_{{\pi_{n}}}$ is $(x_{{\pi_{n}}} +x_{{\pi_{n+1}}})_2$ and $x_{{\pi_{m}}}$ for $n<m$ and $n=m$, respectively. Then, the sequence $\textit{t}_{}=({t}_{0},\hbox{...},{t}_{L-1})$, where it

Figures (3)

  • Figure 1: Transmitter and receiver diagrams for the proposed OAC scheme.
  • Figure 2: PMEPR distribution.
  • Figure 3: CER for flat and frequency-selective channels ($K=50$ sensors).

Theorems & Definitions (12)

  • Theorem 1: sahin_2020gm
  • Lemma 1
  • Corollary 1
  • Lemma 2
  • Corollary 2
  • proof
  • Corollary 3
  • Definition 1: lv2023sliding
  • Theorem 2
  • proof
  • ...and 2 more