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Holographic & Channel-Aware Distributed Detection of a Non-cooperative Target

Domenico Ciuonzo, Alessio Zappone, Marco Di Renzo, Ciro D'Elia

TL;DR

This paper tackles distributed detection in wireless sensor networks with a non-cooperative, spatially uncertain target by integrating a reconfigurable holographic surface (RHS) at the fusion center. It derives a GLR fusion baseline for fixed RHS but reframes the problem via deflection-based, channel-aware designs that pair analog RHS optimization with WL fusion. Two complementary strategies, eFuC and bFuC, are proposed and solved efficiently using Alternating Optimization and Majorization–Minimization, yielding four sub-approaches (eFuC-0, eFuC-1, bFuC-0, bFuC-1). Simulations show substantial performance gains over baseline RIS/RHS methods and IS designs, with bFuC achieving near-ideal performance under uncertainty while maintaining manageable complexity; results demonstrate favorable scaling with the number of sensors and RHS aperture, highlighting practical applicability for IoT-scale deployments.

Abstract

This work investigates Distributed Detection (DD) in Wireless Sensor Networks (WSNs), where spatially distributed sensors transmit binary decisions over a shared flat-fading channel. To enhance fusion efficiency, a reconfigurable metasurface is positioned in the near-field of a few receive antennas, enabling a holographic architecture that harnesses large-aperture gains with minimal RF hardware. A generalized likelihood ratio test is derived for fixed metasurface settings, and two low-complexity joint design strategies are proposed to optimize both fusion and metasurface configuration. These suboptimal schemes achieve a balance between performance, complexity, and system knowledge. The goal is to ensure reliable detection of a localized phenomenon at the fusion center, under energy-efficient constraints aligned with IoT requirements. Simulation results validate the effectiveness of the proposed holographic fusion, even under simplified designs.

Holographic & Channel-Aware Distributed Detection of a Non-cooperative Target

TL;DR

This paper tackles distributed detection in wireless sensor networks with a non-cooperative, spatially uncertain target by integrating a reconfigurable holographic surface (RHS) at the fusion center. It derives a GLR fusion baseline for fixed RHS but reframes the problem via deflection-based, channel-aware designs that pair analog RHS optimization with WL fusion. Two complementary strategies, eFuC and bFuC, are proposed and solved efficiently using Alternating Optimization and Majorization–Minimization, yielding four sub-approaches (eFuC-0, eFuC-1, bFuC-0, bFuC-1). Simulations show substantial performance gains over baseline RIS/RHS methods and IS designs, with bFuC achieving near-ideal performance under uncertainty while maintaining manageable complexity; results demonstrate favorable scaling with the number of sensors and RHS aperture, highlighting practical applicability for IoT-scale deployments.

Abstract

This work investigates Distributed Detection (DD) in Wireless Sensor Networks (WSNs), where spatially distributed sensors transmit binary decisions over a shared flat-fading channel. To enhance fusion efficiency, a reconfigurable metasurface is positioned in the near-field of a few receive antennas, enabling a holographic architecture that harnesses large-aperture gains with minimal RF hardware. A generalized likelihood ratio test is derived for fixed metasurface settings, and two low-complexity joint design strategies are proposed to optimize both fusion and metasurface configuration. These suboptimal schemes achieve a balance between performance, complexity, and system knowledge. The goal is to ensure reliable detection of a localized phenomenon at the fusion center, under energy-efficient constraints aligned with IoT requirements. Simulation results validate the effectiveness of the proposed holographic fusion, even under simplified designs.
Paper Structure (23 sections, 1 theorem, 52 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 23 sections, 1 theorem, 52 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation and Background
  3. Related Works
  4. Summary of Contributions and Paper Organization
  5. System Model
  6. Sensing Model & Modulation Format
  7. Channel Model
  8. Statistical Characterization
  9. Joint Fusion Rule and RHS design Problem Formulation
  10. Optimal fusion rule
  11. Deflection-based Design of RHS Matrix & WL Fusion Rule
  12. Proposed AO-based Solution
  13. AO Designed Steps
  14. Summary and Complexity Overview
  15. Simulation Results
  16. ...and 8 more sections

Key Result

Lemma 1

The optimization problems $\breve{\mathcal{P}}{}_{\mathrm{eFuC,}i}^{(\mathrm{B)}}$ and $\breve{\mathcal{P}}{}_{\mathrm{bFuC,}i}^{(\mathrm{B)}}$ admit closed-form solutions, which can be compactly expressed as follows. For the bFuC-based design, the optimal phase vector at iteration $(\ell+1)$ is giv In the case of eFuC-based design, the same expression applies with the substitutions $N_{\mathrm{t}

Figures (7)

  • Figure 1: The RHS-assisted DF system model considered in the case of a non-cooperative target (unknown location $\bm{p}^t$).
  • Figure 2: Assessing the gaps of existing joint design in holographic DF via ROCs ($P_{D_{0}}$ vs $P_{F_{0}}$). WSN with $K=15$ sensors and target emission strength set to $\mathrm{SNR_{sen}}=15\,\mathrm{dB}$. Holographic DF is implemented with an RHS made of $M=64$ elements and $N=1$ receive feed; channel noise variance is set to $\sigma_{w}^{2}=-50$ dBm.
  • Figure 3: Assessing the gains of eFuC/bFuC joint design in holographic DF via ROCs ($P_{D_{0}}$ vs $P_{F_{0}}$). WSN with $K=15$ sensors and target emission strength set to $\mathrm{SNR_{sen}}=15\,\mathrm{dB}$. Holographic DF is implemented with an RHS made of $M=64$ elements and $N=1$ receive feed; channel noise variance is set to $\sigma_{w}^{2}=-50$ dBm.
  • Figure 4: Assessing the sensitivity of bFuC joint design w.r.t. the grid size $N_t$ via $P_{D_{0}}$, where the false-alarm rate is set to $P_{F_{0}}=10^{-2}$. WSN with $K=15$ sensors and target emission strength set to $\mathrm{SNR_{sen}}=15\,\mathrm{dB}$. Holographic DF is implemented with an RHS made of $M=64$ elements and $N=1$ receive feed; channel noise variance is set to $\sigma_{w}^{2}=-50$ dBm.
  • Figure 5: Impact of WSN size ($K$) on joint design in holographic DF via $P_{D_{0}}$ [%], where the false-alarm rate is set to $P_{F_{0}}=10^{-2}$. A WSN with $K\in\{10,15,30,50\}$ sensors is considered. Target strength is set to $\mathrm{SNR_{sen}}=15\,\mathrm{dB}$. Holographic DF is implemented with an RHS made of $M=64$ elements and $N=1$ receive feed; channel noise variance is $\sigma_{w}^{2}=-50$ dBm. "N/A" indicates that GLR performance could not be computed due to prohibitive computational requirements.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof