Xiaoli Zhou

Sparse Auto-Calibration for Radar Coincidence Imaging with Gain-Phase Errors

Radar coincidence imaging (RCI) is a high-resolution staring imaging technique without the limitation of relative motion between target and radar. The sparsity-driven approaches are commonly used in RCI, while the prior knowledge of imaging models needs to be known accurately. However, as one of the major model errors, the gain-phase error exists generally, and may cause inaccuracies of the model and defocus the image. In the present report, the sparse auto-calibration method is proposed to compensate the gain-phase error in RCI. The method can determine the gain-phase error as part of the imaging process. It uses an iterative algorithm, which cycles through steps of target reconstruction and gain-phase error estimation, where orthogonal matching pursuit (OMP) and Newton’s method are used, respectively. Simulation results show that the proposed method can improve the imaging quality significantly and estimate the gain-phase error accurately.

Radar coincidence imaging with phase error using Bayesian hierarchical prior modeling

Abstract. Radar coincidence imaging (RCI) is a high-resolution imaging technique without the limitation of relative motion between target and radar. In sparsity-driven RCI, the prior knowledge of imaging model requires to be known accurately. However, the phase error generally exists as a model error, which may cause inaccuracies of the model and defocus the image. The problem is formulated using Bayesian hierarchical prior modeling, and the self-calibration variational message passing (SC-VMP) algorithm is proposed to improve the performance of RCI with phase error. The algorithm determines the phase error as part of the imaging process. The scattering coefficient and phase error are iteratively estimated using VMP and Newton’s method, respectively. Simulation results show that the proposed algorithm can estimate the phase error accurately and improve the imaging quality significantly.

Radar Coincidence Imaging for Off-Grid Target Using Frequency-Hopping Waveforms

Radar coincidence imaging (RCI) is a high-resolution staring imaging technique without the limitation of the target relative motion. To achieve better imaging performance, sparse reconstruction is commonly used. While its performance is based on the assumption that the scatterers are located at the prediscretized grid-cell centers, otherwise, off-grid emerges and the performance of RCI degrades significantly. In this paper, RCI using frequency-hopping (FH) waveforms is considered. The off-grid effects are analyzed, and the corresponding constrained Cramer-Rao bound (CCRB) is derived based on the mean square error (MSE) of the “oracle” estimator. For off-grid RCI, the process is composed of two stages: grid matching and off-grid error (OGE) calibration, where two-dimension (2D) band-excluded locally optimized orthogonal matching pursuit (BLOOMP) and alternating iteration minimization (AIM) algorithms are proposed, respectively. Unlike traditional sparse recovery methods, BLOOMP realizes the recovery in the refinement grids by overwhelming the shortages of coherent dictionary and is robust to noise and OGE. AIM calibration algorithm adaptively adjusts the OGE and, meanwhile, seeks the optimal target reconstruction result.

Off-Grid Radar Coincidence Imaging Based on Variational Sparse Bayesian Learning

Radar coincidence imaging (RCI) is a high-resolution staring imaging technique motivated by classical optical coincidence imaging. In RCI, sparse reconstruction methods are commonly used to achieve better imaging result, while the performance guarantee is based on the general assumption that the scatterers are located at the prediscretized grid-cell centers. However, the widely existing off-grid problem degrades the RCI performance considerably. In this paper, an algorithm based on variational sparse Bayesian learning (VSBL) is developed to solve the off-grid RCI. Applying Taylor expansion, the unknown true dictionary is approximated accurately to a linear model. Then target reconstruction is reformulated as a joint sparse recovery problem that recovers three groups of sparse coefficients over three known dictionaries with the constraint of the common support shared by the groups. VSBL is then applied to solve the problem by assigning appropriate priors to the three groups of coefficients. Results of numerical experiments demonstrate that the algorithm can achieve outstanding reconstruction performance and yield superior performance both in suppressing noise and in adapting to off-grid error.

Radar coincidence imaging with array position error

As a novel staring imaging technique, radar coincidence imaging (RCI) shows great potentials in various applications. However, the array position error, exists in array radar generally, has a bad influence on RCI and impairs the imaging performance extremely. In this paper, the mathematical model of RCI in the presence of array position error is established and to obtain the analytic result, the nonlinear relationship between the received signal and array position error is approximated linearly by the first-order Taylor expansion. Thus, the alternating iterative imaging algorithm is designed to compensate the array position error based on basis pursuit. Simulation results are presented to show the effectiveness of the proposed algorithm.

Radar Coincidence Imaging with Stochastic Frequency Modulated Array

In radar sensing and imaging, the azimuth resolution is a main concern, which is limited by the antenna aperture, and as a result the targets within the beam cannot be distinguished. By enhancing the diversity of radiation, radar can obtain additional information for resolution. In this paper, a high-resolution staring imaging technique named radar coincidence imaging (RCI) is investigated. Originated from the classical optical coincidence imaging, the RCI captures super-resolution in azimuth, which breaks through the Rayleigh resolution limitation of antenna array by modulating the wavefront of transmissions. The spatial resolution of RCI is defined by the spatial correlation function of the stochastic radiation field. A scheme of RCI with a stochastic frequency modulated array using frequency-hopping waveforms is proposed, while the imaging model is established. Three image reconstruction algorithms, i.e. the pseudo-inverse algorithm, Tikhonov regularization method, and sparse reconstruction algorithm, are investigated and compared with respect to targets of different complexity. Performance analysis of these reconstruction methods in the presence of noise is presented by the relative imaging error. Finally, a typical RCI system based on the digital transmitter/receiver array is established. Outfield experiment results verify the effectiveness of the RCI.

Off-grid radar coincidence imaging based on block sparse Bayesian learning

Radar coincidence imaging (RCI) is a high-resolution and instantaneous imaging technique without the limitation of relative motion between target and radar. In sparse-based RCI, the assumption that the scatterers are located at the pre-discretized grid-cell centers is commonly used. However, the generally existent off-grid degrades the imaging performance considerably. In this paper, the algorithm based on block sparse Bayesian learning (BSBL) framework is developed to solve the off-grid RCI in the range-azimuth space. Applying the Taylor expansion, the unknown true dictionary is approximated to a linear model. Then target reconstruction is reformulated as a block sparse recovery problem. BSBL is then applied to solve the problem by assigning appropriate priors to the coefficients and exploiting the block structure and intra-block correlation. Results of numerical experiments demonstrate that the algorithm can yield superior imaging performance, compared with other block sparse recovery algorithms.

Improved focal underdetermined system solver method for radar coincidence imaging with model mismatch

Abstract. Radar coincidence imaging (RCI) is a staring imaging technique that originated from optical coincidence imaging. In RCI, the reference matrix needs to be computed precisely to reconstruct the image. However, it is difficult to exactly calculate the reference matrix as model mismatch existing in most applications. The signal model of RCI with model mismatch is derived. Based on a Bayesian framework and regularization method, an algorithm called regularization-focal underdetermined system solver (R-FOCUSS) is proposed to solve the RCI problem with model mismatch. In the proposed method, the scattering coefficients and the perturbation matrix can be calculated during the iterations, so the image can be reconstructed. A norm-ratio method is also proposed to determine the regularization parameters in the objective function, which makes the algorithm suitable for the situation, where the distributions of noise, model error, and target’s sparsity are unknown. The constrained Cramér–Rao bound for scatterer estimation is derived. Compared with some existing sparse reconstruction methods, R-FOCUSS is more robust, with a lower computation complexity. Results of numerical experiments demonstrate that the algorithm can achieve outstanding imaging performance and yields superior performance both in suppressing noise and in adapting to model mismatch.

Expansion–compression variance-component-based autofocusing method for joint radar coincidence imaging and gain–phase error calibration

Abstract. Radar coincidence imaging (RCI) is a super-resolution staring technique based on the innovative idea of random radiation and wavefront random modulation. To reconstruct the target, sparsity-driven methods are commonly used in RCI, while the prior knowledge of the imaging model requires to be known accurately. However, model error generally exists, which induces the inaccuracy of the model and defocuses the image. We focus on sparsity-driven RCI in the presence of gain–phase error and propose an autocalibration expansion–compression variance-component (AC-ExCoV)-based autofocusing method in a sparse Bayesian learning framework. The algorithm determines the gain–phase error as a part of the RCI process by reconstructing the target and compensating the gain–phase error iteratively. To probabilistically formulate the target reconstruction problem, a probabilistic model is utilized to fully exploit the sparse prior, and then solved using ExCoV. Meanwhile, the gain–phase error is estimated and calibrated to obtain a high-resolution focused image. The AC-ExCoV algorithm demands no prior knowledge about the sparsity or measurement-noise level with significant superiority in computational complexity. Simulation results show that the proposed algorithm obtains a well-focused target image with high reconstruction accuracy.

Statistical spatial resolution limit for ultrawideband MIMO noise radar

In this paper, the spatial resolution limit for ultrawideband (UWB) MIMO noise radar is presented based on the statistical resolution theory. The signal model of UWB MIMO noise radar is established, and the resolution of two closely spaced targets is modeled as a binary hypothesis test. The statistical spatial resolution limit (SSRL) for UWB MIMO noise radar is derived based on the generalized likelihood ratio test (GLRT) with the constraints on the probabilities of false alarm and detection. The effects of detection parameters, transmit waveforms, array geometry, signal-to-noise ratio (SNR) and parameters of target on the SSRL are analyzed. Compared with the conventional resolution defined by ambiguity function, the SSRL reflects the practical resolution ability of radar and can provide an optimization criterion for radar system design.