Yunhua Zhang

Magnetic field integral equation at very low frequencies

It is known that there is a low-frequency breakdown problem when the method of moments (MOM) with Rao-Wilton-Glisson (RWG) basis is used in the electric field integral equation (EFIE); it can be solved through the loop and tree basis decomposition. The behavior of the magnetic field integral equation (MFIE) at very low frequencies is investigated using MOM, where two approaches are presented based on the RWG basis and loop and tree bases. The study shows that MFIE can be solved by the conventional MOM with the RWG basis at arbitrarily low frequencies, but there exists an accuracy problem in the real part of the electric current. Although the error in the current distribution is small, it results in a large error in the far-field computation. This is because a big cancellation occurs during the far field computation. The source of error in the current distribution is easily detected through the MOM analysis using the loop and tree basis decomposition. To eliminate the error, a perturbation method is proposed, from which a very accurate real part of the tree current has been obtained. Using the perturbation method, the error in the far-field computation is also removed. Numerical examples show that both the current distribution and the far field can be accurately computed at extremely low frequencies by the proposed method.

Fast-forward solvers for the low-frequency detection of buried dielectric objects

It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while it is much more accurate than the Born approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires O(N/sup 2/) computational load, where N is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy Earth. When the buried objects are discretized with uniform rectangular mesh and the Greens functions are extended appropriately, the computational load can be reduced to O(N log N) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the fast ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms.

A Novel Compressive Sensing Algorithm for SAR Imaging

A novel compressive sensing (CS) algorithm for synthetic aperture radar (SAR) imaging is proposed which is called as the two-dimensional double CS algorithm (2-D-DCSA). We first derive the imaging operator for SAR, which is named as the chirp-scaling operator (CSO), from the chirp-scaling algorithm (CSA), then we show its inverse is a linear map, which transforms the SAR image to the received baseband radar signal. We show that the SAR image can be reconstructed simultaneously in the range and azimuth directions from a small number of the raw data. The proposed algorithm can handle large-scale data because both the CSO and its inverse allow fast matrix-vector multiplications. Both the simulated and real data are processed to test the algorithm and the results show that the 2-D-DCSA can be applied to reconstructing the SAR images effectively with much less data than regularly required.

Composite Right/Left-Handed Ridge Substrate Integrated Waveguide Slot Array Antennas

A composite right/left-handed (CRLH) ridge substrate integrated waveguide (RSIW) is proposed and applied to slot array antennas, where the longitudinal slots are etched on the surface of CRLH RSIW, behaving as the radiating elements. Two slot array antennas are designed, fabricated, and measured, one with fixed slot offset, and the other one with varied slot offsets used for achieving low side-lobe level (SLL) of radiation patterns. Compared with the slot array antennas using CRLH rectangular waveguides, the investigated CRLH RSIW ones have the advantages of miniaturized size in transverse direction, relative low cost, low profile, and easy to integrate with other planar circuits. Besides, unlike other proposed planar CRLH leaky wave antennas (LWAs), slots of varied offsets can be adopted on the CRLH RSIW surface to achieve a tapered excitation. Thus the radiation patterns can be optimized for low SLL. In summary, this CRLH RSIW enables a tapered excitation in the beam-steering antenna design while keeps a relative simple structure.

Resolution Threshold Analysis of MUSIC Algorithm in Radar Range Imaging

Super-resolution algorithms used in radar imaging, e.g., MUltiple SIgnal Classification (MUSIC), can help us to get much higher resolution image beyond what is limited by the signals bandwidth. We focus on MUSIC imaging algorithm in the paper and investigate the uniqueness and effectiveness conditions of the MUSIC algorithm when used in 1-D radar range imaging. Unlike conventional radar resolution analysis, we introduced the concept of resolution threshold from Direction of Arrival (DOA) into the MUSIC radar range imaging, we derive an approximate expression of theoretical resolution threshold for 1-D MUSIC imaging algorithm through the approach of asymptotic and statistical analysis to the null spectrum based on the perturbation theory of algebra and matrix theories. Monte Carlo simulations are presented to verify the work.

A Fast Offset Estimation Approach for InSAR Image Subpixel Registration

A fast offset estimation approach for interferometric synthetic aperture radar (InSAR) image pair subpixel registration is proposed for cases of relatively gentle topography and/or short baseline. A coarse-to-fine registration strategy is taken. The pixel-level offset is estimated in the coarse registration step by a fast feature-based estimation, which uses the speeded up robust feature operator and fast least trimmed squares (Fast-LTS) estimator to accelerate the feature extraction and parameter estimation. A fine registration is performed subsequently. The conventional normalized cross-correlation algorithm (NCCA) searches for the optimal subpixel offset by oversampling either the coarse cross correlation or the InSAR image patch pair. The offset estimation accuracy is restricted by the oversampling rate, and the computational burden is heavy when high accuracy is demanded. In this letter, we transform the oversampling and correlation searching process of NCCA into a nonlinear optimization problem, which takes the maximization of the coherent cross correlation as the objective function; by solving it, the subpixel offset can be fast and exactly obtained without any image oversampling. The final registration parameters are inverted by Fast-LTS fitting of a series of subpixel tie point correspondences which can be constructed after applying the approach to several image patch pairs. RadarSat-2 data are used to test the approach, and the results show that it performs very well not only on the speed but also on the accuracy.

An Airborne SAR Moving Target Imaging and Motion Parameters Estimation Algorithm With Azimuth-Dechirping and the Second-Order Keystone Transform Applied

In this paper, we propose an algorithm for airborne SAR moving target imaging and motion parameters estimation in Doppler ambiguity situation with azimuth-dechirping and the second-order keystone transform (SOKT) applied. In this algorithm, we use a third-order phase model for the echo signal, and after the compensation of third-order phase, the moving target can be symmetrically focused in azimuth. This algorithm has five major steps. The azimuth-dechirping is conducted to eliminate the Doppler ambiguity. The SOKT is conducted to correct the range curvature. The Radon transform is applied to estimate the trajectory slope for range walk correction and the across-track velocity estimation. The fractional Fourier transform (FrFT) is utilized to estimate the Doppler rate for estimating the along-track velocity. The moving target is focused after azimuth compression and third-order phase compensation. Both simulation and real SAR data are processed to validate the proposed algorithm.

A 3D TARGET IMAGING ALGORITHM BASED ON TWO-PASS CIRCULAR SAR OBSERVATIONS

In circular synthetic aperture radar (CSAR), the radar collects data over a circular not a linear trajectory. The two-dimensional (2D) CSAR image also contains three-dimensional (3D) information about the target. In this paper, we propose an imaging algorithm for 3D target reconstruction with two-pass CSAR observations so as to overcome the problem of limited azimuthal persistence for real anisotropic targets, and avoid the assumption that target falls into the same resolution cell for each elevation pass when multi-pass observations are used. In the algorithm, the first step is to divide both of the two full-aperture CSAR data into subapertures in the same way; the second step is to obtain, for each subaperture, the height of target according to the established relationship between the pixel displacements in the image pair of two observations on the same focal plane and the pixel displacements in the image pair of one observation on two different focal planes; the third step is to obtain the 3D target coordinates based on the retrieved height information and the 2D image coordinates; the last step is to get the final 3D image by combining the obtained 3D images of all subapertures. The results of point target simulation indicate that the 3D information (both amplitudes and positions) are well reconstructed. At the same time, the processing results of backhoe data simulated by the Xpatch software show that the outline of the 3D structure is also well reconstructed although the available data corresponding to the depressing angles are not as good as expected.

Cancellations of surface loop basis functions

To capture the fine details of integrated circuits and small antennas, the mesh size is usually much smaller than the wavelength. When the traditional RWG-type bases are used, the electric field integral equation suffers from low-frequency breakdown. This problem can be solved by using the loop-star/tree basis. We have developed a code which uses the loop-tree basis and the low-frequency multi-level fast multipole algorithm to solve a large linear system with small size mesh. The fine details are simulated accurately and efficiently from very low frequencies to very high frequencies. To validate the code, some canonical problems which have closed form solutions are simulated. One of the canonical problems is the scattering from a conducting sphere. We found that the cancellation exists in not only for the excitation on a loop basis function, but also the calculation of the far electric field. We discuss how the cancellation is removed analytically in calculating the far field from a loop basis function. The cancellation also exists in the interaction associated with a loop basis function when it is far away from the other basis function.

A MAP Approach for 1-Bit Compressive Sensing in Synthetic Aperture Radar Imaging

In this letter, we propose a compressive sensing approach for synthetic aperture radar (SAR) imaging of sparse scenes with 1-bit-quantized data. Within the framework of maximum a posteriori estimation, we formulate the SAR image reconstruction problem as a sparse optimization problem and then solve it using a first-order primal-dual algorithm. The processing results of both simulated and real radar data show that our approach can eliminate the ghost target caused by 1-bit quantization in high signal-to-noise ratio situations and suppress the noisy background very well.