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

arXiv: https://arxiv.org/abs/2211.09253 · HTML: https://mlsanity.com/paper/2211.09253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Toward Millimeter Wave Joint Radar-Communications: A Signal Processing Perspective](https://mlsanity.com/paper/1905.00690/) (2019)
- [Doppler-Resilient 802.11ad-Based Ultra-Short Range Automotive Joint Radar-Communications System](https://mlsanity.com/paper/1902.01306/) (2019)
- [Terahertz-Band Joint Ultra-Massive MIMO Radar-Communications: Model-Based and Model-Free Hybrid Beamforming](https://mlsanity.com/paper/2103.00328/) (2021)
- [Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional (d≥ 2) Off-the-Grid Frequencies](https://mlsanity.com/paper/1312.0485/) (2013)
- [Co-Designing Statistical MIMO Radar and In-band Full-Duplex Multi-User MIMO Communications -- Part I: Signal Processing](https://mlsanity.com/paper/2006.14774/) (2020)
- [Localization with One-Bit Passive Radars in Narrowband Internet-of-Things using Multivariate Polynomial Optimization](https://mlsanity.com/paper/2007.15108/) (2020)
- [The Rise of Intelligent Reflecting Surfaces in Integrated Sensing and Communications Paradigms](https://mlsanity.com/paper/2204.07265/) (2022)
- [An Overview of Advances in Signal Processing Techniques for Classical and Quantum Wideband Synthetic Apertures](https://mlsanity.com/paper/2205.05602/) (2022)
- [Resource Allocation in Heterogeneously-Distributed Joint Radar-Communications under Asynchronous Bayesian Tracking Framework](https://mlsanity.com/paper/2108.10432/) (2021)
- [Joint Radar-Communications Processing from a Dual-Blind Deconvolution Perspective](https://mlsanity.com/paper/2111.06304/) (2021)
- [Multi-dimensional dual-blind deconvolution approach toward joint radar-communications](https://mlsanity.com/paper/2206.05166/) (2022)

## Built on by (most cited first, 1 of 1)

- [Multi-Antenna Dual-Blind Deconvolution for Joint Radar-Communications via SoMAN Minimization](https://mlsanity.com/paper/2303.13609/) (2023)

## Abstract (arXiv)

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.