Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Riemannian Gradient Descent Method to Joint Blind Super-Resolution and Demixing in ISAC

Zeyu Xiang, Haifeng Wang, Jiayi Lv, Yujie Wang, Yuxue Wang, Yuxuan Ma, Jinchi Chen

TL;DR

This work tackles an ill-posed parameter estimation problem within ISAC as a joint blind super-resolution and demixing problem, and proposes a Riemannian gradient descent (RGD) method that achieves linear convergence to the target matrices.

Abstract

Integrated Sensing and Communication (ISAC) has emerged as a promising technology for next-generation wireless networks. In this work, we tackle an ill-posed parameter estimation problem within ISAC, formulating it as a joint blind super-resolution and demixing problem. Leveraging the low-rank structures of the vectorized Hankel matrices associated with the unknown parameters, we propose a Riemannian gradient descent (RGD) method. Our theoretical analysis demonstrates that the proposed method achieves linear convergence to the target matrices under standard assumptions. Additionally, extensive numerical experiments validate the effectiveness of the proposed approach.

Riemannian Gradient Descent Method to Joint Blind Super-Resolution and Demixing in ISAC

TL;DR

This work tackles an ill-posed parameter estimation problem within ISAC as a joint blind super-resolution and demixing problem, and proposes a Riemannian gradient descent (RGD) method that achieves linear convergence to the target matrices.

Abstract

Integrated Sensing and Communication (ISAC) has emerged as a promising technology for next-generation wireless networks. In this work, we tackle an ill-posed parameter estimation problem within ISAC, formulating it as a joint blind super-resolution and demixing problem. Leveraging the low-rank structures of the vectorized Hankel matrices associated with the unknown parameters, we propose a Riemannian gradient descent (RGD) method. Our theoretical analysis demonstrates that the proposed method achieves linear convergence to the target matrices under standard assumptions. Additionally, extensive numerical experiments validate the effectiveness of the proposed approach.

Paper Structure

This paper contains 8 sections, 3 theorems, 34 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Algorithms
  4. Theoretical Results
  5. Numerical Experiments
  6. Proof of Main Result
  7. Useful Lemmas
  8. Conclusion

Key Result

Theorem 4.1

Assume that Assumptions assumption 0 and assumption 1 hold. If the number of measurements satisfies $n\geq C_{\gamma} K^2s^2r^2 \kappa^2\mu_0^2\mu_1 \log^2(sn)$, then with probability at least $1-(sn)^{-\gamma}$, the iterations produced by Algorithm alg: SGD satisfy for $t=0,1,\cdots, T$, where $\sigma_0^2 = \sum_{k=1}^{K}\sigma_r^2(\bm{Z}_{k, \natural})$ and $\kappa =\frac{\max_k \sigma_1(\bm{Z}

Figures (3)

  • Figure 1: The Empirical probability of successful recovery for RGD, GD and Scaled-GD (a) with frequency separation (b) without frequency separation.
  • Figure 2: The CPU running time for RGD, GD and Scaled-GD.
  • Figure 3: Convergence rate (a) $n=160, s=r=K=2$, (b) $n=256, s=r=4, K=2$

Theorems & Definitions (5)

  • Theorem 4.1
  • Remark 4.1
  • Lemma 6.1
  • Lemma 6.2
  • proof