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Windowing Optimization for Fingerprint-Spectrum-Based Passive Sensing in Perceptive Mobile Networks

Xiao-Yang Wang, Shaoshi Yang, Hou-Yu Zhai, Christos Masouros, J. Andrew Zhang

TL;DR

A near-optimal window is derived, and the theoretical synchronization mean square error (MSE) when utilizing this window is not practically achievable, and a practical “window function” is tested by utilizing the multiple signal classification (MUSIC) algorithm, which may lead to excellent synchronization performance.

Abstract

Perceptive mobile networks (PMN) have been widely recognized as a pivotal pillar for the sixth generation (6G) mobile communication systems. However, the asynchronicity between transmitters and receivers results in velocity and range ambiguity, which seriously degrades the sensing performance. To mitigate the ambiguity, carrier frequency offset (CFO) and time offset (TO) synchronizations have been studied in the literature. However, their performance can be significantly affected by the specific choice of the window functions harnessed. Hence, we set out to find superior window functions capable of improving the performance of CFO and TO estimation algorithms. We firstly derive a near-optimal window, and the theoretical synchronization mean square error (MSE) when utilizing this window. However, since this window is not practically achievable, we then test a practical "window function" by utilizing the multiple signal classification (MUSIC) algorithm, which may lead to excellent synchronization performance.

Windowing Optimization for Fingerprint-Spectrum-Based Passive Sensing in Perceptive Mobile Networks

TL;DR

A near-optimal window is derived, and the theoretical synchronization mean square error (MSE) when utilizing this window is not practically achievable, and a practical “window function” is tested by utilizing the multiple signal classification (MUSIC) algorithm, which may lead to excellent synchronization performance.

Abstract

Perceptive mobile networks (PMN) have been widely recognized as a pivotal pillar for the sixth generation (6G) mobile communication systems. However, the asynchronicity between transmitters and receivers results in velocity and range ambiguity, which seriously degrades the sensing performance. To mitigate the ambiguity, carrier frequency offset (CFO) and time offset (TO) synchronizations have been studied in the literature. However, their performance can be significantly affected by the specific choice of the window functions harnessed. Hence, we set out to find superior window functions capable of improving the performance of CFO and TO estimation algorithms. We firstly derive a near-optimal window, and the theoretical synchronization mean square error (MSE) when utilizing this window. However, since this window is not practically achievable, we then test a practical "window function" by utilizing the multiple signal classification (MUSIC) algorithm, which may lead to excellent synchronization performance.
Paper Structure (11 sections, 3 theorems, 68 equations, 11 figures, 1 table)

This paper contains 11 sections, 3 theorems, 68 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Syetem Model
  3. Windowing for Synchronization and Formulation of Our Optimization Problem
  4. Asymptotically Optimized Ideal Window Function
  5. Practical Window Design based on Super Resolution Estimation Algorithm
  6. Numerical Simulations
  7. Conclusions
  8. Proof of proposition 1
  9. Proof of the noise $\bar{\sigma}^2$
  10. Proof of proposition 2
  11. Proof of the proposition 3

Key Result

Proposition 1

If $\frac{\Delta\delta^\tau}{T_{\rm R}}$ is an integer, $f_{\rm MSE}(\boldsymbol{\psi}_{N_c})$ is asymptotically minimized when the SNR tends to infinity and ${\bf s}$ satisfies and the corresponding MSE is $f_{\rm MSE}(\boldsymbol{\psi}_{N_c})=\sum_{\substack{q=1, q\neq {\Delta\delta^\tau}/{T_{\rm R}}}}^{KN_c}$$\left[ q_{\rm r}- \frac{\Delta\delta^\tau}{T_{\rm R}}\right]^2\int_{-\infty}^{\infty}

Figures (11)

  • Figure 1: System model.
  • Figure 2: Data processing flow at receivers in PMN systems.
  • Figure 3: Demonstration of the sliding window cross-correlation in (\ref{['unsimplified']}).
  • Figure 4: ${\bf u}_1$ and ${\bf u}_2$ are two implementations of ${\bf s}$. ${\bf u}_1$ has a sharper mainlobe than ${\bf u}_2$.
  • Figure 5: Frequency smoothing schemes. The matrix shown in this figure is $\boldsymbol{\Gamma}_m$. The smoothing vectors in the same color, such as $\bar{\bf y}_{1,1}^{\rm s}$ and $\bar{\bf y}_{G_s,1}^{\rm s}$, will be stacked into the same vector, $\bar{\bf y}_{1,1}$.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Proposition 2
  • Proposition 3