Efficient Multi-Antenna Dual-Blind Deconvolution for Joint Radar-Communications Signal Recovery

Core Concepts

The core message of this paper is to propose an efficient multi-antenna dual-blind deconvolution (M-DBD) framework that can jointly recover the unknown radar and communications signals and their corresponding channel parameters from the overlaid received signal.

Abstract

The paper investigates the problem of dual-blind deconvolution (DBD) in a multi-antenna joint radar-communications (JRC) receiver, where both the radar and communications signals and their respective channels are unknown. The authors model the radar and communications channels using sparse continuous-valued parameters such as time delays, Doppler velocities, and directions-of-arrival (DoAs).
To solve this highly ill-posed DBD problem, the authors propose to minimize the sum of multivariate atomic norms (SoMAN) that depend on the unknown parameters. They devise an exact semidefinite program (SDP) using the theories of positive hyperoctant trigonometric polynomials (PhTP). The theoretical analysis shows that the minimum number of samples and antennas required for perfect recovery scales logarithmically with the maximum of the number of radar targets and communications paths, rather than their sum.
The authors also generalize their approach to handle practical issues such as gain/phase errors and additive noise, and provide the optimal regularization parameters. Extensive numerical experiments demonstrate the exact parameter recovery for different JRC scenarios.

Stats

[𝐲]̃
𝑚=
𝐿
∑
𝓁=1
[𝜶𝑟]𝓁𝐭𝐻
𝑛𝐯𝑒−j2𝜋(𝑛[𝝉𝑟]𝓁+𝑝[𝝂𝑟]𝓁+𝑚[𝜷𝑟]𝓁) +
𝑄
∑
𝑞=1
[𝜶𝑐]𝑞𝐝𝐻
𝑣𝐯𝑒−j2𝜋(𝑛[𝝉𝑐]𝑞+𝑝[𝝂𝑐]𝑞+𝑚[𝜷𝑐]𝑞)

Quotes

The minimum number of overall samples for perfect recovery scale logarithmically with the maximum of the radar targets and communications paths rather than their sum.
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.

Key Insights Distilled From

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

by Roman Jacome... at arxiv.org 04-01-2024

https://arxiv.org/pdf/2303.13609.pdf

Deeper Inquiries

How can the proposed M-DBD framework be extended to handle time-varying or non-stationary radar and communications channels

The proposed M-DBD framework can be extended to handle time-varying or non-stationary radar and communications channels by incorporating adaptive algorithms and techniques. One approach is to introduce time-varying parameters in the channel models, such as varying Doppler frequencies or changing delay profiles. This can be achieved by updating the channel parameters over time using adaptive estimation algorithms like Kalman filters or particle filters. By dynamically adjusting the channel parameters based on the evolving channel conditions, the M-DBD framework can adapt to changes in the environment and effectively track the time-varying channels.

What are the potential applications of the M-DBD approach beyond the joint radar-communications scenario, such as in biomedical imaging or seismic exploration

The potential applications of the M-DBD approach extend beyond the joint radar-communications scenario to various other fields such as biomedical imaging or seismic exploration. In biomedical imaging, M-DBD can be utilized for simultaneous radar-based imaging and communication in medical devices, enabling real-time monitoring and data transmission without interference. For seismic exploration, M-DBD can be applied to extract information from overlapping seismic signals and communication signals, enhancing the efficiency and accuracy of seismic data analysis in geophysical surveys. The flexibility and robustness of the M-DBD framework make it suitable for diverse applications where multiple signals need to be separated and analyzed simultaneously.

Can the SoMAN minimization be further optimized to reduce the computational complexity for real-time implementation of the M-DBD algorithm

To optimize the SoMAN minimization for reducing computational complexity in real-time implementation of the M-DBD algorithm, several strategies can be employed. One approach is to utilize parallel processing and distributed computing techniques to speed up the optimization process. By leveraging the computational power of multiple processors or GPUs, the optimization iterations can be performed in parallel, reducing the overall computation time. Additionally, implementing efficient algorithms for sparse signal recovery and matrix factorization can help streamline the optimization process and improve the algorithm's runtime performance. Furthermore, optimizing the formulation of the SDP and exploring approximation methods can also contribute to reducing the computational complexity while maintaining the accuracy of the M-DBD algorithm.