Sub-Nyquist Radar via Doppler Focusing (1211.0722v3)

Abstract: We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets, sparsely populated in the radar's unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a sub-Nyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys an SNR increase which scales linearly with P, obtaining good detection performance even at SNRs as low as -25dB. The recovery is based on the Xampling framework, which allows reducing the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling prototype.

• The paper introduces Doppler focusing, a method combining sub-Nyquist sampling and compressed sensing for efficient radar target detection and estimation.
• The method employs Xampling and compressed sensing to reconstruct target parameters from low-rate samples, significantly outperforming classic techniques at sub-Nyquist rates.
• The practical implementation offers significant implications for radar systems, including reduced power consumption, lower cost, and increased viability in high bandwidth scenarios.

Sub-Nyquist Radar via Doppler Focusing

"Sub-Nyquist Radar via Doppler Focusing" by Omer Bar-Ilan and Yonina C. Eldar presents a sophisticated approach to radar signal processing focused on overcoming traditional limitations associated with Nyquist sampling rates. The key innovation introduced in this work is the concept of Doppler focusing, which leverages sub-Nyquist sampling along with compressed sensing (CS) techniques to deliver high efficacy in target detection and parameter estimation in pulse-Doppler radar systems.

Overview

The radar signal environment involves detecting sparsely populated targets within the radar's unambiguous time-frequency region, relying traditionally on Nyquist-compliant sampling rates. These conventional methods often enforce impractical constraints on operational bandwidth, sample rates, and handle noise inadequately. By addressing these constraints, Doppler focusing contributes an efficient mechanism to handle target signals even as low as -25dB SNR, boasting improvements proportional to the number of pulses received, $P$, thus maintaining robustness in noise.

Methodology

Central to their method is utilizing the Xampling framework, which optimizes the analog-to-digital conversion by performing analog prefiltering to produce compressed samples, or "Xamples," retaining crucial signal information at sub-Nyquist rates. Doppler focusing operates by aligning signals based on Doppler frequency, thereby enhancing coherence across pulses, improving SNR linearly by a factor of $P$. This is achieved without significant restrictions on the transmitter structure or needing to revert to higher Nyquist rates for digital processing.

The paper further proposes CS solutions to reconstruct each target's delay and Doppler profile from the low-rate Xamples, using a dictionary independent of the pulse count. This approach circumvents the scalability issues surrounding existing CS recovery techniques that require extensive dictionary sizes, rendering them impractical in real-time applications.

Simulation and Results

Simulation results indicate that this approach significantly outperforms existing methods, including classic matched filter processing and the two-stage CS recovery techniques, especially when operated at a mere tenth of Nyquist rates. This demonstrates the ability to maintain high detection accuracy and parameter estimation while significantly reducing sampling rates and storage requirements.

Implications and Future Directions

The practical implementation of Doppler focusing harbors notable implications for radar systems, promising reduced power consumption, cost, and increased viability in high bandwidth scenarios. The technology aligns with future trends in radar systems requiring increasingly precise measurement and processing capabilities while managing real-world constraints, such as dynamic range and clutter interference.

Future developments of this framework could address limitations such as estimation when the number of targets is unknown and further enhancements in dealing with broader target dynamic ranges and clutter, enabling enhanced detection in complex environments.

In summary, "Sub-Nyquist Radar via Doppler Focusing" contributes a scalable and efficient radar processing methodology, potentially transforming approaches to target detection, signal processing, and system design in radar research and development. This paper adds valuable insight into practical solutions overcoming intrinsic limitations imposed by Nyquist theory in modern radar systems.