Beurling-Selberg Extremization for Dual-Blind Deconvolution Recovery in Joint Radar-Communications

TL;DR

This paper introduces a novel approach for dual-blind deconvolution in joint radar-communications, leveraging Beurling-Selberg extremization and low-rank matrix techniques to recover unknown signals and channels under optimal separation conditions.

Contribution

It establishes an optimal joint separation condition using extremal functions and formulates the problem as low-rank matrix recovery, advancing beyond prior methods that required separate separation conditions.

Findings

The joint separation condition guarantees well-conditioned Vandermonde matrices for MUSIC.

The proposed method accurately recovers signals and channels in numerical experiments.

The approach outperforms previous atomic norm minimization techniques in dual-blind deconvolution.

Abstract

Recent interest in integrated sensing and communications has led to the design of novel signal processing techniques to recover information from an overlaid radar-communications signal. Here, we focus on a spectral coexistence scenario, wherein the channels and transmit signals of both radar and communications systems are unknown to the common receiver. In this dual-blind deconvolution (DBD) problem, the receiver admits a multi-carrier wireless communications signal that is overlaid with the radar signal reflected off multiple targets. The communications and radar channels are represented by continuous-valued range-times or delays corresponding to multiple transmission paths and targets, respectively. Prior works addressed recovery of unknown channels and signals in this ill-posed DBD problem through atomic norm minimization but contingent on individual minimum separation conditions for radar and communications channels. In this paper, we provide an optimal joint separation condition using extremal functions from the Beurling-Selberg interpolation theory. Thereafter, we formulate DBD as a low-rank modified Hankel matrix retrieval and solve it via nuclear norm minimization. We estimate the unknown target and communications parameters from the recovered low-rank matrix using multiple signal classification (MUSIC) method. We show that the joint separation condition also guarantees that the underlying Vandermonde matrix for MUSIC is well-conditioned. Numerical experiments validate our theoretical findings.