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Joint Time-Phase Synchronization for Distributed Sensing Networks via Feature-Level Hyper-Plane Regression

Kailun Tian, Kaili Jiang, Dechang Wang, Yuxin Zhao, Yuxin Shang, Hancong Feng, Bin Tang

Abstract

Achieving coherent integration in distributed Internet of Things (IoT) sensing networks requires precise synchronization to jointly compensate clock offsets and radio-frequency (RF) phase errors. Conventional two-step protocols suffer from time-phase coupling, where residual timing offsets degrade phase coherence. This paper proposes a generalized hyper-plane regression (GHR) framework for joint calibration by transforming coupled spatiotemporal phase evolution into a unified regression model, enabling effective parameter decoupling. To support resource-constrained IoT edge nodes, a feature-level distributed architecture is developed. By adopting a linear frequency-modulated (LFM) waveform, the model order is reduced, yielding linear computational complexity. In addition, a unidirectional feature transmission mechanism eliminates the communication overhead of bidirectional timestamp exchange, making the approach suitable for resource-constrained IoT networks. Simulation results demonstrate reliable picosecond-level synchronization accuracy under severe noise across kilometer-scale distributed IoT sensing networks.

Joint Time-Phase Synchronization for Distributed Sensing Networks via Feature-Level Hyper-Plane Regression

Abstract

Achieving coherent integration in distributed Internet of Things (IoT) sensing networks requires precise synchronization to jointly compensate clock offsets and radio-frequency (RF) phase errors. Conventional two-step protocols suffer from time-phase coupling, where residual timing offsets degrade phase coherence. This paper proposes a generalized hyper-plane regression (GHR) framework for joint calibration by transforming coupled spatiotemporal phase evolution into a unified regression model, enabling effective parameter decoupling. To support resource-constrained IoT edge nodes, a feature-level distributed architecture is developed. By adopting a linear frequency-modulated (LFM) waveform, the model order is reduced, yielding linear computational complexity. In addition, a unidirectional feature transmission mechanism eliminates the communication overhead of bidirectional timestamp exchange, making the approach suitable for resource-constrained IoT networks. Simulation results demonstrate reliable picosecond-level synchronization accuracy under severe noise across kilometer-scale distributed IoT sensing networks.

Paper Structure

This paper contains 19 sections, 25 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Distributed Signal Model and Small-Aperture Hyper-line Geometry
  3. Distributed Observation Model and Time-Phase Coupling Dilemma
  4. Dynamic Manifold and Small-Aperture Hyper-line Geometry
  5. Generalized Dynamic Geometry and Hyper-plane Regression Algorithm
  6. The Dynamic Hyper-plane
  7. Generalized Hyper-plane Regression Algorithm
  8. Distributed GHR Calibration Framework and Performance Boundaries
  9. Distributed Feature-Level Interaction Architecture
  10. Algorithmic Complexity and Dimensionality Reduction
  11. Theoretical Operating Boundaries
  12. Experimental Results
  13. Experiment 1: High-Order Manifold Topology and Multidimensional Hyper-plane Validation
  14. Experiment 2: The GHR Algorithm Under LFM Signal
  15. Experiment 3: Validation of Effective Distance for Distributed Nodes
  16. ...and 4 more sections

Figures (11)

  • Figure 1: Architecture of the proposed feature-level cooperative calibration framework in a distributed IoT sensing network.
  • Figure 2: High-order manifold topology of far-field transmitting node signal.
  • Figure 3: Multidimensional Hyper-plane of QFM signal.
  • Figure 4: 3D Hyper-line Geometry.
  • Figure 5: A visual comparison of multi-antenna node's noise-canceling capabilities.
  • ...and 6 more figures