Sub-Nyquist Radar: Principles and Prototypes

In the past few years, new approaches to radar signal processing have been introduced which allow the radar to perform signal detection and parameter estimation from much fewer measurements than that required by Nyquist sampling. These systems - referred to as sub-Nyquist radars - model the received signal as having finite rate of innovation and employ the Xampling framework to obtain low-rate samples of the signal. Sub-Nyquist radars exploit the fact that the target scene is sparse facilitating the use of compressed sensing (CS) methods in signal recovery. In this chapter, we review several pulse-Doppler radar systems based on these principles. Contrary to other CS-based designs, our formulations directly address the reduced-rate analog sampling in space and time, avoid a prohibitive dictionary size, and are robust to noise and clutter. We begin by introducing temporal sub-Nyquist processing for estimating the target locations using less bandwidth than conventional systems. This paves the way to cognitive radars which share their transmit spectrum with other communication services, thereby providing a robust solution for coexistence in spectrally crowded environments. Next, without impairing Doppler resolution, we reduce the dwell time by transmitting interleaved radar pulses in a scarce manner within a coherent processing interval or "slow time". Then, we consider multiple-input-multiple-output array radars and demonstrate spatial sub-Nyquist processing which allows the use of few antenna elements without degradation in angular resolution. Finally, we demonstrate application of sub-Nyquist and cognitive radars to imaging systems such as synthetic aperture radar. For each setting, we present a state-of-the-art hardware prototype designed to demonstrate the real-time feasibility of sub-Nyquist radars.Comment: 51 pages, 26 figures, 2 tables, Book chapter. arXiv admin note: text overlap with arXiv:1611.0644

Power Allocation and Measurement Matrix Design for Block CS-Based Distributed MIMO Radars

Multiple-input multiple-output (MIMO) radars offer higher resolution, better target detection, and more accurate target parameter estimation. Due to the sparsity of the targets in space-velocity domain, we can exploit Compressive Sensing (CS) to improve the performance of MIMO radars when the sampling rate is much less than the Nyquist rate. In distributed MIMO radars, block CS methods can be used instead of classical CS ones for more performance improvement, because the received signal in this group of MIMO radars is a block sparse signal in a basis. In this paper, two new methods are proposed to improve the performance of the block CS-based distributed MIMO radars. The first one is a new method for optimal energy allocation to the transmitters, and the other one is a new method for optimal design of the measurement matrix. These methods are based on the minimization of an upper bound of the sensing matrix block-coherence. Simulation results show an increase in the accuracy of multiple targets parameters estimation for both proposed methods.Comment: The paper is accepted in Elseveir Aerospace Science and Technolog

A Coherent Integration Method Based on Radon Non-uniform FRFT for Random Pulse Repetition Interval (RPRI) Radar

To solve the range cell migration (RCM) and spectrum spread during the integration time induced by the motion of a target, this paper proposes a new coherent integration method based on Radon non-uniform FRFT (NUFRFT) for random pulse repetition interval (RPRI) radar. In this method, RCM is eliminated via searching in the motion parameters space and the spectrum spread is resolved by using NUFRFT. Comparisons with other popular methods, moving target detection (MTD), Radon-Fourier transform (RFT), and Radon-Fractional Fourier Transform (RFRFT) are performed. The simulation results demonstrate that the proposed method can detect the moving target even in low SNR scenario and is superior to the other two methods.Comment: 7 pages, 3 figure

CSSF MIMO RADAR: Low-Complexity Compressive Sensing Based MIMO Radar That Uses Step Frequency

A new approach is proposed, namely CSSF MIMO radar, which applies the technique of step frequency (SF) to compressive sensing (CS) based multi-input multi-output (MIMO) radar. The proposed approach enables high resolution range, angle and Doppler estimation, while transmitting narrowband pulses. The problem of joint angle-Doppler-range estimation is first formulated to fit the CS framework, i.e., as an L1 optimization problem. Direct solution of this problem entails high complexity as it employs a basis matrix whose construction requires discretization of the angle-Doppler-range space. Since high resolution requires fine space discretization, the complexity of joint range, angle and Doppler estimation can be prohibitively high. For the case of slowly moving targets, a technique is proposed that achieves significant complexity reduction by successively estimating angle-range and Doppler in a decoupled fashion and by employing initial estimates obtained via matched filtering to further reduce the space that needs to be digitized. Numerical results show that the combination of CS and SF results in a MIMO radar system that has superior resolution and requires far less data as compared to a system that uses a matched filter with SF

OFDM Synthetic Aperture Radar Imaging with Sufficient Cyclic Prefix

The existing linear frequency modulated (LFM) (or step frequency) and random noise synthetic aperture radar (SAR) systems may correspond to the frequency hopping (FH) and direct sequence (DS) spread spectrum systems in the past second and third generation wireless communications. Similar to the current and future wireless communications generations, in this paper, we propose OFDM SAR imaging, where a sufficient cyclic prefix (CP) is added to each OFDM pulse. The sufficient CP insertion converts an inter-symbol interference (ISI) channel from multipaths into multiple ISI-free subchannels as the key in a wireless communications system, and analogously, it provides an inter-range-cell interference (IRCI) free (high range resolution) SAR image in a SAR system. The sufficient CP insertion along with our newly proposed SAR imaging algorithm particularly for the OFDM signals also differentiates this paper from all the existing studies in the literature on OFDM radar signal processing. Simulation results are presented to illustrate the high range resolution performance of our proposed CP based OFDM SAR imaging algorithm.Comment: This version has been accepted by IEEE Transactions on Geoscience and Remote Sensing. IEEE Transactions on Geoscience and Remote Sensing 201

A Sub-Nyquist Radar Prototype: Hardware and Algorithms

Traditional radar sensing typically involves matched filtering between the received signal and the shape of the transmitted pulse. Under the confinement of classic sampling theorem this requires that the received signals must first be sampled at twice the baseband bandwidth, in order to avoid aliasing. The growing demands for target distinction capability and spatial resolution imply significant growth in the bandwidth of the transmitted pulse. Thus, correlation based radar systems require high sampling rates, and with the large amounts of data sampled also necessitate vast memory capacity. In addition, real-time processing of the data typically results in high power consumption. Recently, new approaches for radar sensing and detection were introduced, based on the Finite Rate of Innovation and Xampling frameworks. These techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's detection capabilities at high enough SNR. Here we present for the first time a design and implementation of a Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demostrate by real-time analog experiments that our system is able to maintain reasonable detection capabilities, while sampling radar signals that require sampling at a rate of about 30MHz at a total rate of 1Mhz

Complexity Analysis of Heuristic Pulse Interleaving Algorithms for Multi-Target Tracking with Multiple Simultaneous Receive Beams

This paper presents heuristic algorithms for interleaved pulse scheduling problems on multi-target tracking in pulse Doppler phased array radars that can process multiple simultaneous received beams. The interleaved pulse scheduling problems for element and subarray level digital beamforming architectures are formulated as the same integer program and the asymptotic time complexities of the algorithms are analyzed.Comment: 29 pages, 6 figure

Non-Linear Signal Processing methods for UAV detections from a Multi-function X-band Radar

This article develops the applicability of non-linear processing techniques such as Compressed Sensing (CS), Principal Component Analysis (PCA), Iterative Adaptive Approach (IAA) and Multiple-input-multiple-output (MIMO) for the purpose of enhanced UAV detections using portable radar systems. The combined scheme has many advantages and the potential for better detection and classification accuracy. Some of the benefits are discussed here with a phased array platform in mind, the novel portable phased array Radar (PWR) by Agile RF Systems (ARS), which offers quadrant outputs. CS and IAA both show promising results when applied to micro-Doppler processing of radar returns owing to the sparse nature of the target Doppler frequencies. This shows promise in reducing the dwell time and increase the rate at which a volume can be interrogated. Real-time processing of target information with iterative and non-linear solutions is possible now with the advent of GPU-based graphics processing hardware. Simulations show promising results

Gridless Parameter Estimation for One-Bit MIMO Radar with Time-Varying Thresholds

We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varying threshold in the temporal domain and employs compressive sensing in the spatial and Doppler domains. The goals are to significantly reduce the hardware cost, energy consumption, and amount of stored data. The joint angle and Doppler frequency estimations from noisy one-bit data are studied. By showing that the effect of noise on one-bit sampling is equivalent to that of sparse impulsive perturbations, we formulate the one-bit $\ell_1$-regularized atomic-norm minimization (1b-ANM-L1) problem to achieve gridless parameter estimation with high accuracy. We also develop an iterative method for solving the 1b-ANM-L1 problem via the alternating direction method of multipliers. The Cram$\acute{\text{e}}$r-Rao bound (CRB) of the 1b-MIMO radar is analyzed, and the analytical performance of one-bit sampling with two different threshold strategies is discussed. Numerical experiments are presented to show that the 1b-MIMO radar can achieve high-resolution parameter estimation with a largely reduced amount of data.Comment: 31 pages, 12 figure