Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

https://vpa.sabanciuniv.edu/vpadb/findfile_get_anonymous_paper.php?f=2011

Sparsity and Compressed Sensing in Radar Imaging

Time delay estimation has been a research topic of significant practical importance in many fields (radar, sonar, seismology, geophysics, ultrasonics, hands-free communications, etc.). It is a first stage that feeds into subsequent processing blocks for identifying, localizing, and tracking radiating sources. This area has made remarkable advances in the past few decades, and is continuing to progress, with an aim to create processors that are tolerant to both noise and reverberation. This paper presents a systematic overview of the state-of-the-art of time-delay-estimation algorithms ranging from the simple cross-correlation method to the advanced blind channel identification based techniques. We discuss the pros and cons of each individual algorithm, and outline their inherent relationships. We also provide experimental results to illustrate their performance differences in room acoustic environments where reverberation and noise are commonly encountered.

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Time delay estimation in room acoustic environments: an overview

In this work, spectral estimation techniques are used to exploit baseline diversity of a multichannel interferometric synthetic aperture radar (SAR) system and overcome the layover problem. This problem arises when different height contributions collapse in the same range-azimuth resolution cell, due to the presence of strong terrain slopes or discontinuities in the sensed scene. We propose a multilook approach to counteract the presence of multiplicative noise, which is due to the extended nature of natural targets; to this purpose we extend the RELAX algorithm to the multilook data scenario (M-RELAX). A thorough performance analysis of nonparametric (beamforming and Capon) and parametric (root MUSIC and M-RELAX) techniques is carried out based on Monte Carlo simulations and Cramer-Rao lower bounds (CRLB) calculation. The results suggest the superiority of parametric methods over nonparametric ones.

Layover solution in multibaseline SAR interferometry

The theory of compressed sampling (CS) indicates that exact recovery of an unknown sparse signal can be achieved from very limited samples. For inversed synthetic aperture radar (ISAR), the image of a target is usually constructed by strong scattering centers whose number is much smaller than that of pixels of an image plane. This sparsity of the ISAR signal intrinsically paves a way to apply CS to the reconstruction of high-resolution ISAR imagery. CS-based high-resolution ISAR imaging with limited pulses is developed, and it performs well in the case of high signal-to-noise ratios. However, strong noise and clutter are usually inevitable in radar imaging, which challenges current high-resolution imaging approaches based on parametric modeling, including the CS-based approach. In this paper, we present an improved version of CS-based high-resolution imaging to overcome strong noise and clutter by combining coherent projectors and weighting with the CS optimization for ISAR image generation. Real data are used to test the robustness of the improved CS imaging compared with other current techniques. Experimental results show that the approach is capable of precise estimation of scattering centers and effective suppression of noise.

Resolution Enhancement for Inversed Synthetic Aperture Radar Imaging Under Low SNR via Improved Compressive Sensing

Recent theory of compressed sampling (CS) suggests that exact recovery of an unknown sparse signal with overwhelming probability can be achieved from very limited number of samples. In this letter, we adapt this idea and present a framework of high-resolution inverse synthetic aperture radar imaging with limited measured data. During the framework, we mathematically convert the imaging into a problem of signal reconstruction with orthogonal basis; hence, a conceptive upper bound of the cross-range resolution is presented based on the CS theory. Real data results show that the CS imaging approach outperforms the conventional range-Doppler one in resolution.

Achieving Higher Resolution ISAR Imaging With Limited Pulses via Compressed Sampling

We consider estimating time delays and amplitudes (real- or complex-valued) from the superposition of very closely spaced signals with known shapes. The well-known high resolution MODE (Method Of Direction Estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with our efficient time delay estimation method WRELAX (Weighted Fourier transform and RELAXation based) algorithm to deal with this problem. The proposed method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreover, it can be used for both complex- and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding Cramer-Rao bound. Efficient implementation of the algorithm is also discussed.

Super resolution time delay estimation via MODE-WRELAX

An inverse synthetic aperture radar (ISAR) can be used to produce high-resolution images of moving targets of interest by utilizing the relative motion between the target and the radar and by transmitting signals with large bandwidth. Most ISAR imaging algorithms are based on the range-Doppler processing, which implies that the Doppler shifts remain constant during the coherent integration time. For maneuvering targets, the Doppler shifts are time varying. In this case, the algorithms will produce blurred images. We present herein an adaptive Capon (1969) spectral estimation algorithm for the complex ISAR image formation of maneuvering targets. It is an efficient recursive implementation of the well-known Capon complex spectral estimation algorithm by using FFT and simple matrix operations.

Complex ISAR imaging of maneuvering targets via the Capon estimator

This correspondence presents a zoom-FFT based RELAX algorithm for estimating sinusoidal parameters in the presence of unknown colored noise. The amount of computations required by this algorithm is much less than the original zero-padding FFT based RELAX. Yet the estimation performance of the new algorithm is only slightly degraded as compared with the original one.

Implementation of the RELAX algorithm

We propose an efficient algorithm for estimating the code timing of direct-sequence code-division multiple-access (DS-CDMA) systems that consist of an arbitrary antenna array at the receiver and work in a flat-fading and near-far environment. The algorithm is an asymptotic (for large number of data samples) maximum-likelihood (ML) estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and the additive noise as unknown colored Gaussian noise. The algorithm does not require the search over a parameter space and the code timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and channel fading. It requires a shorter training sequence than the single-antenna-based estimators.

An efficient code-timing estimator for receiver diversity DS-CDMA systems

We propose an efficient algorithm for estimating the code-timing of DS-CDMA (direct-sequence code-division multiple-access) systems that consist of an arbitrary antenna array at the receiver and work in a flat fading and near-far environment. The algorithm is an asymptotic (for a large number of data samples) maximum likelihood estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and the additive noise as unknown colored Gaussian noise. The algorithm does not require the search over a parameter space and the code-timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and channel fading. It requires a shorter training sequence than the single antenna based estimators.

Zheng-She Liu

Papers

Super resolution time delay estimation via MODE-WRELAX

Complex ISAR imaging of maneuvering targets via the Capon estimator

Implementation of the RELAX algorithm

An efficient code-timing estimator for receiver diversity DS-CDMA systems

An efficient code-timing estimator for receiver diversity DS-CDMA systems