# Multi-Antenna Dual-Blind Deconvolution for Joint Radar-Communications via SoMAN Minimization

arXiv: https://arxiv.org/abs/2303.13609 · HTML: https://mlsanity.com/paper/2303.13609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Toward Millimeter Wave Joint Radar-Communications: A Signal Processing Perspective](https://mlsanity.com/paper/1905.00690/) (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)
- [Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization](https://mlsanity.com/paper/1506.02751/) (2015)
- [A New Atomic Norm for DOA Estimation With Gain-Phase Errors](https://mlsanity.com/paper/1910.02207/) (2019)
- [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)
- [Semidefinite representations of gauge functions for structured low-rank matrix decomposition](https://mlsanity.com/paper/1604.02500/) (2016)
- [Estimation of Angles of Arrival Through Superresolution -- A Soft Recovery Approach for General Antenna Geometries](https://mlsanity.com/paper/1711.03996/) (2017)
- [Gridless DOA Estimation with Multiple Frequencies](https://mlsanity.com/paper/2207.06159/) (2022)
- [Beurling-Selberg Extremization for Dual-Blind Deconvolution Recovery in Joint Radar-Communications](https://mlsanity.com/paper/2211.09253/) (2022)

## Abstract (arXiv)

In joint radar-communications (JRC) applications such as secure military receivers, often the radar and communications signals are overlaid in the received signal. In these passive listening outposts, the signals and channels of both radar and communications are unknown to the receiver. The ill-posed problem of recovering all signal and channel parameters from the overlaid signal is termed as textitdual-blind deconvolution (DBD). In this work, we investigate DBD for a multi-antenna receiver. We model the radar and communications channels with a few (sparse) textitcontinuous-valued parameters such as time delays, Doppler velocities, and directions-of-arrival (DoAs). To solve this highly ill-posed DBD, we propose to minimize the sum of multivariate atomic norms (SoMAN) that depend on unknown parameters. To this end, we devise an exact semidefinite program using theories of positive hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples and antennas required for perfect recovery is logarithmically dependent on the maximum of the number of radar targets and communications paths rather than their sum. We show that our approach is easily generalized to include several practical issues such as gain/phase errors and additive noise. Numerical experiments show the exact parameter recovery for different JRC scenarios.