Super-Resolution Radar

In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed and Doppler shifted versions of the input. This problem arises in a multitude of applications such as wireless communications and radar imaging. Due to practical constraints, the input signal has finite bandwidth B, and the received signal is observed over a finite time interval of length T only. This gives rise to a delay and Doppler resolution of 1/B and 1/T. We show that this resolution limit can be overcome, i.e., we can exactly recover the continuous delay-Doppler pairs and the corresponding attenuation factors, by solving a convex optimization problem. This result holds provided that the distance between the delay-Doppler pairs is at least 2.37/B in time or 2.37/T in frequency. Furthermore, this result allows the total number of delay-Doppler pairs to be linear up to a log-factor in BT, the dimensionality of the response of the system, and thereby the limit for identifiability. Stated differently, we show that we can estimate the time-frequency components of a signal that is S-sparse in the continuous dictionary of time-frequency shifts of a random window function, from a number of measurements, that is linear up to a log-factor in S.Comment: Revised versio

Identification of Parametric Underspread Linear Systems and Super-Resolution Radar

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of underspread linear systems (ULSs), whose responses lie within a unit-area region in the delay Doppler space, by probing them with a known input signal. It is shown that sufficiently-underspread parametric linear systems, described by a finite set of delays and Doppler-shifts, are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay Doppler pairs in the system. In addition, an algorithm is developed that enables identification of parametric ULSs from an input train of pulses in polynomial time by exploiting recent results on sub-Nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials. Finally, application of these results to super-resolution target detection using radar is discussed. Specifically, it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay Doppler space, resulting in a resolution that substantially exceeds that of standard matched-filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing-based radar methods.Comment: Revised version of a journal paper submitted to IEEE Trans. Signal Processing: 30 pages, 17 figure

Generating a Super-resolution Radar Angular Spectrum Using Physiological Component Analysis

In this study, we propose a method for generating an angular spectrum using array radar and physiological component analysis. We develop physiological component analysis to separate radar echoes from multiple body positions, where echoes are phase-modulated by propagating pulse waves. Assuming that the pulse wave displacements at multiple body positions are constant multiples of a time-shifted waveform, the method estimates echoes using a simplified mathematical model. We exploit the mainlobe and nulls of the directional patterns of the physiological component analysis to form an angular spectrum. We applied the proposed method to simulated data to demonstrate that it can generate a super-resolution angular spectrum

Density Criteria for the Identification of Linear Time-Varying Systems

This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform Beurling density of the delay-Doppler support set is strictly smaller than 1/2 and stable identifiability is impossible for densities strictly larger than 1/2. The proof of this density theorem reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Finally, we introduce a subspace method for solving the system identification problem at hand.Comment: IEEE International Symposium on Information Theory (ISIT), Hong Kong, China, June 201

Super-Resolution Radar Imaging with Sparse Arrays Using a Deep Neural Network Trained with Enhanced Virtual Data

This paper introduces a method based on a deep neural network (DNN) that is perfectly capable of processing radar data from extremely thinned radar apertures. The proposed DNN processing can provide both aliasing-free radar imaging and super-resolution. The results are validated by measuring the detection performance on realistic simulation data and by evaluating the Point-Spread-function (PSF) and the target-separation performance on measured point-like targets. Also, a qualitative evaluation of a typical automotive scene is conducted. It is shown that this approach can outperform state-of-the-art subspace algorithms and also other existing machine learning solutions. The presented results suggest that machine learning approaches trained with sufficiently sophisticated virtual input data are a very promising alternative to compressed sensing and subspace approaches in radar signal processing. The key to this performance is that the DNN is trained using realistic simulation data that perfectly mimic a given sparse antenna radar array hardware as the input. As ground truth, ultra-high resolution data from an enhanced virtual radar are simulated. Contrary to other work, the DNN utilizes the complete radar cube and not only the antenna channel information at certain range-Doppler detections. After training, the proposed DNN is capable of sidelobe- and ambiguity-free imaging. It simultaneously delivers nearly the same resolution and image quality as would be achieved with a fully occupied array.Comment: 15 pages, 12 figures, Accepted to IEEE Journal of Microwave

Development and Demonstration of a TDOA-Based GNSS Interference Signal Localization System

Background theory, a reference design, and demonstration results are given for a Global Navigation Satellite System (GNSS) interference localization system comprising a distributed radio-frequency sensor network that simultaneously locates multiple interference sources by measuring their signals’ time difference of arrival (TDOA) between pairs of nodes in the network. The end-to-end solution offered here draws from previous work in single-emitter group delay estimation, very long baseline interferometry, subspace-based estimation, radar, and passive geolocation. Synchronization and automatic localization of sensor nodes is achieved through a tightly-coupled receiver architecture that enables phase-coherent and synchronous sampling of the interference signals and so-called reference signals which carry timing and positioning information. Signal and crosscorrelation models are developed and implemented in a simulator. Multiple-emitter subspace-based TDOA estimation techniques are developed as well as emitter identification and localization algorithms. Simulator performance is compared to the CramérRao lower bound for single-emitter TDOA precision. Results are given for a test exercise in which the system accurately locates emitters broadcasting in the amateur radio band in Austin, TX.Aerospace Engineering and Engineering Mechanic

Cost-effective photonic super-resolution millimeter-wave joint radar-communication system using self-coherent detection

A cost-effective millimeter-wave (MMW) joint radar-communication (JRC) system with super resolution is proposed and experimentally demonstrated, using optical heterodyne up-conversion and self-coherent detection down-conversion techniques. The point lies in the designed coherent dual-band constant envelope linear frequency modulation-orthogonal frequency division multiplexing (LFM-OFDM) signal with opposite phase modulation indexes for the JRC system. Then the self-coherent detection, as a simple and low-cost means, is accordingly facilitated for both de-chirping of MMW radar and frequency down-conversion reception of MMW communication, which circumvents the costly high-speed mixers along with MMW local oscillators and more significantly achieves the real-time decomposition of radar and communication information. Furthermore, a super resolution radar range profile is realized through the coherent fusion processing of dual-band JRC signal. In experiments, a dual-band LFM-OFDM JRC signal centered at 54-GHz and 61-GHz is generated. The dual bands are featured with an identical instantaneous bandwidth of 2 GHz and carry an OFDM signal of 1 GBaud, which help to achieve a 6-Gbit/s data rate for communication and a 1.76-cm range resolution for radar