A Fast High-Resolution Imaging Algorithm for Helicopter-Borne Rotating Array SAR Based on 2-D Chirp-Z Transform

Introduction. Range Cell Migration (RCM) is a source of image blurring in synthetic aperture radars (SAR). There are two groups of signal processing algorithms used to compensate for migration effects. The first group includes algorithms that recalculate the SAR signal from the "along–track range – slant range" coordinate system into the "along-track range – cross-track range" coordinates using the method of interpolation. The disadvantage of these algorithms is their considerable computational cost. Algorithms of the second group do not rely on interpolation thus being more attractive in terms of practical application.Aim. To synthesize a simple algorithm for compensating for RCM without using interpolation.Materials and methods. The synthesis was performed using a simplified version of the Chirp Scaling algorithm.Results. A simple algorithm, which presents a modification of the Keystone Transform algorithm, was synthesized. The synthesized algorithm based on Fast Fourier Transforms and the Hadamard matrix products does not require interpolation.Conclusion. A verification of the algorithm quality via mathematical simulation confirmed its high efficiency. Implementation of the algorithm permits the number of computational operations to be reduced. The final radar image produced using the proposed algorithm is built in the true Cartesian coordinates. The algorithm can be applied for SAR imaging of moving targets. The conducted analysis showed that the algorithm yields the image of a moving target provided that the coherent processing interval is sufficiently large. The image lies along a line, which angle of inclination is proportional to the projection of the target relative velocity on the line-of-sight. Estimation of the image parameters permits the target movement parameters to be determined.

The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm was adopted to compensate for the azimuth FM rate. First, the geometric configuration and echo signal model of the spaceborne missile bistatic synthetic aperture radar (SAR) were built, and then the Doppler frequency correction was performed, and the 2-D spectrum of the signal was derived by the method of series reversion. Next, range migration correction and range compression were finished in the 2-D frequency domain. Following this, a modified NLCS algorithm was proposed to solve the space variance of Doppler phase problem. After compensating for the azimuth FM rate, the azimuth compression focusing was completed and the imaging result was obtained. Finally, by comparing the calculation amount, imaging effect, and performance index with the traditional NLCS algorithm, it can be concluded that the algorithm reduced the calculation amount by 1.0128 × 108 floating point operations per second (FLOPs) compared with the traditional NLCS algorithm, and the azimuth focusing effect of the edge point was greatly improved. Its resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) were improved by 0.87 m, 3.32 dB, and 1.79 dB, respectively, which proved the effectiveness and feasibility of this method.

A novel autofocus method for synthetic aperture radar (SAR) image is studied. Based on a quadratic model for the phase error within each sub-area (narrow strip × sub-aperture) after a wide range swath is subdivided into narrow range strips and long azimuth aperture into sub-apertures, an objective function for estimation of the error is derived through the principle of minimum entropy. There is only one unknown variable in the function. With the Chebyshev approximation, the function is approximated as a polynomial, and the unknown is then solved using the method of series reversion. Curve-fitting methods are applied to estimate phase error for an entire scene of the full-swath by full-aperture. Through simulations, the proposed method is applied to restore the defocused SAR imagery that is well focused. The restored and original images are almost identical qualitatively and quantitatively. Next, the method is implemented into an existing SAR data processor. Two sets of SAR raw data at X- and Ku-bands are processed and two images are formed. Well-focused and high-resolution images from plain and rugged terrain are obtained even without the use of ancillary attitude data of the airborne SAR platform. Thus, the studied method is verified.

An effective focusing approach for azimuth invariant bistatic SAR processing

In the processing of high-resolution wide-swath spaceborne synthetic aperture radar data, the slant range history is difficult to formulate with a high accuracy over a long data-acquisition interval, and the variation of the imaging parameters over the illuminated scene makes it necessary to implement 2-D space-variant processing. To deal with these issues, first, a slant range expression is derived based on a geometry model using a circular arc to approximate the curved trajectory in this paper, which is composed of a hyperbolic term, a cubic term, and a quartic term. Then, the imaging flow based on the slant range model is proposed: a cubic filtering in range is employed to normalize the range-variant secondary range compression; the nonuniform fast Fourier transform (NUFFT) is used to correct the additional range displacement introduced by the cubic filtering and the nonlinear range cell migration (RCM) caused by the range dependence of the velocity; necessary modifications are made on the matched filter for azimuth compression to accommodate the cubic filtering in range and to deal with the high-order terms of the slant range model. The simulation results show that the proposed slant range model has a relatively high accuracy; the range processing procedure that involves an NUFFT following a cubic filtering can apply to the case where the nonlinear chirp scaling algorithm is adopted, and it has the advantage of being capable of dealing with the nonlinear RCM; the azimuth processing procedure can provide satisfactory focusing qualities over a rather large azimuth extent.

In this paper, an omega-K imaging algorithm to focus the raw data of translational invariant (TI) bistatic synthetic aperture radar (BSAR) is proposed. The method utilizes a point target reference spectrum of generalized Loffeld's bistatic formula (GLBF). Without the bistatic deformation term, GLBF is the latest development of Loffeld's bistatic formula. It is comparable in precision with the method of series reversion (MSR), but it has a much simpler form than MSR and a similar form to a monostatic case. Based on the spatial linearization of GLBF, the Stolt transformation relationship is derived. The method can consider the linear spatial variation of Doppler parameters, which is always ignored in previous publications about bistatic omega-K algorithms. This method can handle the cases of TI BSAR with high squint angles and large bistatic degrees. In addition, a compensation method for the phase error caused by the linearization is discussed. Numerical simulations and experimental data processing verify the effectiveness of the proposed method.

Focusing bistatic synthetic aperture radar (SAR) data in frequency domain requires two-dimensional (2D) point target reference spectrum (PTRS). Lofield's bistatic formula (LBF) and the Method of Series Reversion (MSR) have been introduced recently to compute PTRS of bistatic SAR. In this paper, flrstly we generalize the original LBF (OLBF) by introducing the Doppler contribution functions of transmitter and receiver. Thus, OLBF and its derivatives (e.g., extended LBF) can be viewed as special forms of the generalized LBF with constant Doppler contributions. Based on this, secondly the ideal LBF (ILBF) with no computing error, except the error resulting from the principle of stationary phase, is also presented. The ILBF reveals that the theoretical PTRS of bistatic SAR consists of only two monostatic terms, but it does not include bistatic deformation term in comparison with OLBF. It supplies us with a target when we deduce the PTRS for bistatic SAR. Finally, to get the precise analytical PTRS for general bistatic SAR, an approximated ILBF (AILBF) is proposed. It expresses the Doppler contributions of the transmitter and receiver as power series and can approach the ILBF very well. AILBF can keep the precision as MSR and inherit a simple form from LBF. In addition, error limit for the validity of bistatic PTRS is also given. The results in this paper can be used to develop imaging algorithms for extreme bistatic (e.g., spaceborne/airborne) and high squint (e.g., bistatic forward-looking) cases.

Long-time coherent integration works to significantly increase the detection probability for maneuvering targets. However, during the observation time, the problems that often tend to occur are range cell migration (RCM) and Doppler frequency cell migration (DFCM), due to the high velocity and acceleration of the maneuvering target, which can reduce the detection of the maneuvering targets. In this regard, we propose a new coherent integration approach, based on the product scale zoom discrete chirp Fourier transform (PSZDCFT). Specifically, by introducing the zoom operation into the modified discrete chirp Fourier transform (MDCFT), the zoom discrete chirp Fourier transform (ZDCFT) can correctly estimate the centroid frequency and chirp rate of the linear frequency-modulated signal (LFM), regardless of whether the parameters of the LFM signal are outside the estimation scopes. Then, the scale operation, combined with ZDCFT, is performed on the radar echo signal in the range frequency slow time domain, to remove the coupling. Thereafter, a product operation is executed along the range frequency to inhibit spurious peaks and reinforce the true peak. Finally, the velocity and acceleration of the target estimated from the true peak position, are used to construct a phase compensation function to eliminate the RCM and DFCM, thus achieving coherent integration. The method is a linear transform without energy loss, and is suitable for low signal-to-noise (SNR) environments. Moreover, the method can be effectively fulfilled based on the chirp-z transform (CZT), which prevents the brute-force search. Thus, the method reaches a favorable tradeoff between anti-noise performance and computational load. Intensive simulations demonstrate the effectiveness of the proposed method.

Imaging approach based on range-Doppler algorithm for monostatic SAR is extended to bistatic case. Because of that the transmitter and receiver are located separately, the range cell migration phenomena of bistatic SAR is more complicated than that of monostatic case. In this paper, a simple method of range cell migration correction is used instead of interpolation operation in traditional range-Doppler algorithm for monostatic SAR. Point scatter response, range and azimuth resolutions are also discussed. The simulation results are presented.

Inverse synthetic aperture radar (ISAR) imaging is one of the important high- resolution radar applications for moving target detection and identification. The radial velocity, radial acceleration, and acceleration rate of maneuvering targets can cause range cell migration and Doppler variation in the received signals, which will degrade the imaging quality. Therefore, these parameters should be estimated and compensated before imaging. In low signal-to-noise ratio (SNR) conditions, the conventional motion parameter estimation and compensation algorithms for maneuvering targets do not work properly. To effectively detect and identify the maneuvering targets in low SNR conditions, a new radar imaging algorithm is proposed. The major contributions are as follows: 1) a novel algorithm for envelope migration correction is proposed with adjacent cross correlation function; 2) the target's motion parameters are estimated with the operations of Keystone transform and time-frequency transform to the adjacent cross correlation; 3) a theoretical analysis of the impact of motion parameters on the envelope migration is made, then cross-range phase estimation with the adjacent cross function is presented; 4) based on the estimated motion parameters of targets, a new algorithm for high-resolution ISAR imaging is developed.

A CA-NCS algorithm in curve trajectory for smart global village

Because of the long integration time of geosynchronous earth orbit synthetic aperture radar (GEO SAR), the imaging model and algorithm of low earth orbit (LEO) SAR are not suitable for GEO SAR. Thus, this paper establishes the echo model of the GEO SAR by using the high order range model based on the characters of the GEO SAR movements. Then, the two-dimensional (2-D) spectrum is derived by the method of series reversion (MSR), based on which a new imaging algorithm used for GEO SAR is presented. Finally, simulation results of point targets prove the accuracy and validity of the proposed algorithm.

In geosynchronous (GEO) synthetic aperture radar (SAR), the high orbit height and the long integration time would lead to the significant round-trip delay time and the curved flight path, thus the traditional range model with ‘stop-go’ assumption will be ineffective. In this Paper, based on the analysis of instantaneous Doppler frequency of GEO SAR, an equivalent midpoint mathematical model is proposed to accurately describe the range history, which takes the effect of ‘stop-go’ assumption into account and is more applicable to SAR processing. Based on the equivalent model, the two dimensional (2-D) spectrum of the GEO SAR can be obtained easily by the method of series reversion (MSR). The simulations show the validity of the presented method.

Exploring high-performance speech recognition in noisy environments using high-order taylor series expansion

Synthetic aperture radar imaging at high resolution and highly squint angle is confronted with several difficulties, such as the spatial variance of range cell migration (RCM) and the azimuth-dependent property of high-order terms. In order to address the above-mentioned problems, an improved non-linear chirp scaling algorithm based on keystone transform (KT) and linear range walk correction (LRWC) is proposed. First, KT is applied to correct the second-order RCM in range frequency and azimuth time domain. Then the spatial variance of linear RCM (LRCM) is analysed, and range–azimuth coupling is alleviated through LRWC, in this way, azimuth-variant RCM can be removed by phase multiplication, which avoids the approximate error of RCMC in two-dimensional frequency domain. Taking both the spatial variance of LRCM and the difference of the minimum bistatic slant range caused by LRWC into consideration, high-precision approximation of azimuth-dependent coefficients for azimuth signal are deduced, based on which the Doppler centroid, azimuth FM rate and cubic phase can be equalised by selecting proper perturbation coefficients. The proposed algorithm leads to a large depth of focusing in both range direction and azimuth direction. Simulation results prove the effectiveness of the proposed method.