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

TL;DR

This paper introduces a Riemannian gradient descent method for joint blind super-resolution and demixing in ISAC, effectively addressing an ill-posed parameter estimation problem by exploiting low-rank structures, with proven convergence and validated results.

Contribution

The paper proposes a novel Riemannian gradient descent approach for joint super-resolution and demixing in ISAC, with theoretical convergence guarantees and extensive numerical validation.

Findings

Achieves linear convergence to target matrices.

Effectively handles ill-posed parameter estimation in ISAC.

Validated through extensive numerical experiments.

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.