Nonlinear Chirp Scaling Research Articles

A Two-Step Nonlinear Chirp Scaling Method for Multichannel GEO Spaceborne–Airborne Bistatic SAR Spectrum Reconstructing and Focusing

Due to the high-altitude illumination and the separation of the receiver and transmitter, geosynchronous (GEO) spaceborne–airborne bistatic synthetic aperture radar (BiSAR) is more flexible and accessible in remote sensing applications. In this paper, the Doppler characteristics of GEO BiSAR with a squint receiver are analyzed. It is found that the Doppler spectrum is generally aliased in GEO BiSAR regarding the low pulse repetition frequency (PRF) adopted by the GEO SAR. In order to suppress the ambiguity without adjusting the PRF of GEO SAR, the azimuth multichannel receiving technique is applied to the receiver and then the multichannel transfer function for GEO BiSAR is derived. However, the whole bandwidth of the imaging scene is much larger than that of the center point, which requires extra receiving channels to suppress the ambiguity and thereby increasing the system complexity. A two-step nonlinear chirp scaling (NLCS) method is proposed to obtain the well-focused image with reduced receiving channels. First, a preprocessing step is conducted to achieve space-variant range cell migration correction. After that, the first-step NLCS processing is applied to equalize the 2-D space-variant Doppler centroid and thereby the Doppler bandwidth is decreased, i.e., the required number of receiving channels for reconstruction is reduced. Then, the unambiguous spectrum is reconstructed based on the proposed multichannel transfer function. Finally, the second-step NLCS processing is carried out to equalize the 2-D space-variant high-order Doppler parameters and obtain the well-focused image. The simulation results validate the effectiveness of the proposed method. With the proposed two-step NLCS method, the well-focused image for GEO BiSAR is obtained and the required number of receiving channels can be decreased, which is beneficial to reducing the system complexity and hardware cost.

Focusing High-Resolution High Forward-Looking Bistatic SAR With Nonequal Platform Velocities Based on Keystone Transform and Modified Nonlinear Chirp Scaling Algorithm

This paper presents a focusing solution for high-resolution high forward-looking bistatic synthetic aperture radar with nonequal platform velocities (NPV-BFSAR). In NPV-BFSAR, due to the high-resolution SAR and high forward-looking angle, range cell migration, and two-dimensional spatial variation are more serious. To solve this problem, a modified imaging algorithm based on second-order keystone transform (KT) and modified nonlinear chirp scaling (NLCS) method are proposed. The second-order KT method can correct the linear range cell migration and reduce the strong coupling between azimuth and range. The proposed modified azimuth NLCS algorithm is more accurate than traditional NLCS algorithm on eliminating the variation of azimuth reference function that can improve the focus quality of edge targets. Finally, some simulation results confirm the efficiency of the proposed algorithm.

Fast nonlinear compressive sensing lithographic source and mask optimization method using Newton-IHTs algorithm.

Source and mask optimization (SMO) is an important method to improve lithography imaging fidelity. However, constrained by the computational inefficiency, the current SMO method can be used only in clip level applications. In this paper, to our best knowledge, the fast nonlinear compressive sensing (CS) theory is for the first time applied to solve the nonlinear inverse reconstruction problem in SMO. The proposed method simultaneously downsamples the layout pattern in the SMO procedure, which can effectively reduce the computation complexity. The space basis and two-dimensional (2D) discrete cosine transform (DCT) basis are selected to sparsely represent the source pattern and mask pattern, respectively. Based on the sparsity assumption of source and mask pattern, the SMO can be formulated as a nonlinear CS reconstruction problem. A Newton-iteration hard thresholding (Newton-IHTs) algorithm, by taking into account the second derivative of the cost function to accelerate convergence, is innovated to realize nonlinear CS-SMO with high imaging fidelity. Simulation results show the proposed method can significantly accelerate the SMO procedure over a traditional gradient-based method and IHTs-based method by a factor of 9.31 and 7.39, respectively.

Imaging for Small UAV-Borne FMCW SAR.

Unmanned aerial vehicle borne frequency modulated continuous wave synthetic aperture radars are attracting more and more attention due to their low cost and flexible operation capacity, including the ability to capture images at different elevation angles for precise target identification. However, small unmanned aerial vehicles suffer from large trajectory deviation and severe range-azimuth coupling due to their simple navigational control and susceptibility to air turbulence. In this paper, we utilize the squint minimization technique to reduce this coupling while simultaneously eliminating intra-pulse motion-induced effects with an additional spectrum scaling. After which, the modified range doppler algorithm is derived for second order range compression and block-wise range cell migration correction. Raw data-based motion compensation is carried out with a doppler tracker. Squinted azimuth dependent phase gradient algorithm is employed to deal with azimuth dependent parameters and inexact deramping, with minimum entropy-based autofocusing algorithms. Finally, azimuth nonlinear chirp scaling is used for azimuth compression. Simulation and real data experiment results presented verify the effectiveness of the above signal processing approach.

Focusing forward-looking linear-array synthetic aperture radar with high speed based on keystone transform and modified nonlinear chirp scaling algorithm

For forward-looking linear-array synthetic aperture radar with high speed, the traditional algorithm neglects its high speed, which leads to poor focusing imaging quality. Due to the high speed movement of the platform, range cell migration (RCM) and two-dimensional spatial variation are more serious. To overcome this problem, an equivalent range model is proposed, which takes the platform’s high speed into consideration. Based on this model, linear range walk correction and second-order keystone transform method are used to eliminate the RCM and range-azimuth coupling, and then a modified nonlinear chirp scaling algorithm based on a circle model is used to improve the focus quality of edge targets. Finally, simulation results are presented to confirm the efficiency of the proposed algorithm.

Focusing one-stationary bistatic forward-looking synthetic aperture radar based on squint minimization and modified nonlinear chirp scaling algorithm

ABSTRACTThis article deals with the imaging problem of bistatic forward-looking synthetic aperture radar with a stationary transmitter (one-stationary BFSAR). In one-stationary BFSAR, due to the large forward-looking (or squint) angle, it causes more serious range cell migration and two-dimensional spatial variation. To solve this problem, an imaging algorithm based on squint minimization and modified nonlinear chirp scaling (NLCS) method is proposed. The squint minimization method can decrease the coupling between range and azimuth and correct the linear range cell migration. The modified NLCS can eliminate the variation of azimuth reference function more accurately than traditional NLCS algorithm, which improves the focus quality of marginal targets. Finally, simulation results confirm the efficiency of our proposed algorithm.

An improved ENLCS algorithm based on a quadratic ellipse model for high-resolution one-stationary bistatic SAR

ABSTRACTHigh-resolution one-stationary bistatic synthetic aperture radar (BiSAR) data focusing is a challenging task due to the large range cell migration (RCM) and the azimuth-variant Doppler phases. In this letter, an extended nonlinear chirp scaling (ENLCS) based on a quadratic ellipse model is investigated for the one-stationary BiSAR configuration. An analytical relationship of iso-equivalent-sum-of-bistatic-range (iso-ESBR) of azimuth distributed targets is derived after range cell migration correction (RCMC) which is combined by linear range walk correction (LRWC) and keystone transform (KT). Following which, a new quadratic ellipse model is constructed to analyze the azimuth-variant property of the Doppler phases. Based on the new quadratic ellipse model, an improved ENLCS algorithm with new coefficients is derived to accomplish the azimuth equalization for azimuth compression. Simulation results validate the effectiveness of the proposed algorithm.

High-Resolution Ice-Sounding Radar Measurements of Ice Thickness Over East Antarctic Ice Sheet as a Part of Chinese National Antarctic Research Expedition

This paper presents the ice thickness, fine resolution internal reflecting horizons (IRHs), and distinct bottom topography measurements of Chinese Kunlun Station and Grove Mountains, Antarctica, derived from sounding these glaciers with a high-resolution radar. To enable the development of next-generation ice-sheet models, we need information on IRHs, bottom topography, and basal conditions. To this end, we performed measurements with the progressively improved ice-sounding radar system, currently known as the high-resolution ice-sounding radar developed by the Key Laboratory of Electromagnetic Radiation and Sensing Technology of Institute of Electronics, Chinese Academy of Sciences, Beijing, China. We processed the collected data using focused synthetic aperture radar (SAR) algorithm named the modified range migration algorithm using curvelets and the modified nonlinear chirp scaling algorithm to improve radar sensitivity and reduce along-track surface clutter. Representative results from selected transects indicate that we successfully sounded 3-km-thick ice with a fine resolution of 0.75 m. In this paper, we provide a brief description of the radar system, discuss the focused SAR processing algorithms, and provide sample results to demonstrate the successful sounding of the ice sheet in Antarctica.

Fast optical proximity correction method based on nonlinear compressive sensing.

Optical proximity correction (OPC) is an extensively used resolution enhancement technique (RET) in optical lithography. To date, the computational efficiency has become a big issue for pixelated OPC techniques due to the increasing complexity of lithographic masks in modern integrated circuits. This paper is the first to apply nonlinear compressive sensing (CS) theory to break through the computational efficiency of gradient-based pixelated OPC methods. The proposed method reduces the dimensionality of the OPC problem by downsampling the layout pattern. Then, a nonlinear cost function is established to guarantee the lithography imaging performance on the downsampled layout. Under the sparsity assumption of the mask, the OPC problem is formulated as an inverse nonlinear CS reconstruction problem. The iterative hard thresholding (IHT) algorithm is then used to solve for the OPC problem. The proposed method proves to improve the computational efficiency of traditional gradient-based OPC methods, while improving the process windows of the lithography systems. Benefiting from the sparse property of the mask patterns, the mask manufacturability can also be improved compared to traditional methods.

Focus High-Resolution Highly Squint SAR Data Using Azimuth-Variant Residual RCMC and Extended Nonlinear Chirp Scaling Based on a New Circle Model

The combination of linear range walk correction and keystone transform is a good choice to focus high-resolution highly squint synthetic aperture radar (SAR) data because it is an effective way to remove linear range cell migration (RCM) completely and mitigate range–azimuth coupling. However, the results of this kind of imaging algorithm produce 2-D-variant residual RCM and variant-dependence Doppler phases. To obtain high-quality SAR image, an improved imaging algorithm using an azimuth-variant residual RCM correction (RCMC) and an extended nonlinear chirp scaling (ENLCS) is proposed in this letter. A new circle model is constructed to analyze the azimuth-variant properties of the residual high-order RCM and the Doppler phases. Based on this circle model, an azimuth-variant residual RCMC is implemented by multiplying a fourth-order phase function, and an improved ENLCS is derived to accomplish the azimuth equalization for azimuth compression. Simulation results validate the excellent performance of the proposed algorithm.

A Nonlinear Chirp Scaling Algorithm for Processing Multi-Receiver SAS Data with Small Squint Angle

Squint multi-receiver synthetic aperture sonar (SAS) data is more challenging to process than data about its common side-looking counterpart because the geometry is complicated. While traditional multi-receiver algorithms mainly handle general side-looking cases, they do not work well for squint cases. Up to now, no multi-receiver algorithm for handling squint multi- receiver SAS data has been reported. This paper focuses on an imaging algorithm for the squint multi-receiver SAS. Firstly, the “non-stop-go-stop” signal model is established for squint multi- receiver SAS. Then a squint multi-receiver nonlinear chirp scaling algorithm (SMANLCSA) is proposed that is suited to process multi-receiver SAS data with small squint angle and SMANLCSA involves three key steps. The first step is to turn squint multi-receiver data into squint single-receiver data. The second step is a Doppler centroid frequency shift. The third step is range cell migration correction using nonlinear chirp scaling. Simulations have shown that SMANLCSA can handle squint multi-receiver data more accurately and effectively than the previous algorithm..

Joint Interference Mitigation and Data Recovery for Massive Carrier Aggregation via Non-Linear Compressive Sensing

Due to the demand for higher throughput, there is need for aggregating more carriers to serve one user equipment. Massive carrier aggregation (MCA) may help as it aggregates a large number of potentially non-contiguous carriers spanning a wide bandwidth. However, implementing MCA brings challenges to the design of the receiver and corresponding data recovery algorithms. For example, if we assign a separate receiver chain for each carrier, the number of receiver chains will be large, which imposes a huge cost. If we use a single receiver chain for all non-contiguous carriers, an expensive high rate analog-to-digital converter (ADC) is required to sample the entire span of the carriers. To reduce the cost, we propose a receiver architecture that employs only one receiver chain with a non-uniform ADC, whose sampling rate is much smaller than the Nyquist rate, and a low cost power amplifier with small dynamic range. Under such architecture, the received signal suffers from non-linear distortion and interference, and the resulting data recovery is a challenging non-linear compressive sensing problem. We propose an algorithm to jointly mitigate the interference and recover the data, which is proved to have theoretical performance guarantees and verified advantageous over baselines in simulations.

Wide Nonlinear Chirp Scaling Algorithm for Spaceborne Stripmap Range Sweep SAR Imaging

The spaceborne stripmap range sweep synthetic aperture radar (SS-RSSAR) is a new concept spaceborne SAR system that images the region of interest (ROI) with ROI-orientated strips, which, unlike the traditional spaceborne SAR, are allowed to be not parallel with the satellite orbit. The SS-RSSAR imaging is a challenging problem because echoes of a wide region have strong spatial varieties, especially in high-squint geometries, and are hard to be focused by a single swath. The traditional imaging algorithms could solve this problem by cost-ineffectively dividing an ROI into many subswaths for separate processing. In this paper, a new wide nonlinear chirp scaling (W-NLCS) algorithm is proposed to efficiently image the SS-RSSAR data in a single swath. Comparing with the traditional nonlinear chirp scaling algorithm, the W-NLCS algorithm is superior in three major aspects: the nonlinear bulk range migration compensation (RMC), the interpolation-based residual RMC, and the modified azimuth frequency perturbation. Specifically, the interpolation for the residual RMC, the most significant step in achieving the wide-swath imaging performance, is made innovatively in the time domain. The derivation of the W-NLCS algorithm, as well as the performance analyses of the W-NLCS algorithm in aspects of the azimuth resolution, accuracy, and complexity, are all provided. The presented approach is evaluated by the point target simulations.

A New Nonlinear Chirp Scaling Algorithm for High-Squint High-Resolution SAR Imaging

Among high-squint high-resolution (HSHR) synthetic aperture radar imaging algorithms, nonlinear chirp scaling algorithm (NLCSA) and its extensions, such as extended NLCSA (ENLCSA), have a common drawback in that they all neglect the spatial variations of linear range migration (LRM) and Doppler centroid, and thus, only targets in a specific central slant range plane can be strictly focused. In this letter, we show that by using a new NLCSA, targets can be focused in the ground plane under HSHR conditions. Based on a more accurate 2-D spectrum, the new NLCSA outperforms the ENLCSA by introducing a new range–Doppler domain interpolation to correct residual range migration and a new perturbation function to remove the dependence of Doppler phase on azimuth. The coefficients of the new perturbation function are numerically calculated and then smoothed by polynomial fitting. Though the outputs of the numerical calculation are somewhat unstable at the current stage, it has been demonstrated to perform better than the algorithms neglecting the spatial variations of LRM and Doppler centroid, such as the ENLCSA, by point target simulations.

Focusing Nonparallel-Track Bistatic SAR Data Using Extended Nonlinear Chirp Scaling Algorithm Based on a Quadratic Ellipse Model

Image formation for bistatic synthetic aperture radar data with nonparallel tracks is a challenging task due to the existence of the spatial variance of range cell migration (RCM) and azimuth frequency modulation (FM) rate. In this letter, an extended nonlinear chirp scaling (ENLCS) algorithm based on a quadratic ellipse model with two motion platform parameters is proposed for this configuration. For range processing, a method combining linear range walk correction and keystone transform is adopted to remove linear RCM completely and mitigate range–azimuth cross coupling. For azimuth focusing, a quadratic ellipse model using the two motion platform parameters is established to depict the azimuth-variant properties of the azimuth FM rate, and its accurate high-order approximation is derived as well. Investigations of the quadratic phase error show that great improvement can be made by this model. Following which, coefficients of the ENLCS are derived to accomplish the azimuth equalization. Simulation results validate the effectiveness of the algorithm proposed by this letter.

A 2-D Nonlinear Chirp Scaling Algorithm for High Squint GEO SAR Imaging Based on Optimal Azimuth Polynomial Compensation

GEO SAR can achieve better revisit time and observation performances when using high squint mode. However, high squint mode also causes huge range walk and severe range-azimuth coupling problems as well as severe 2-D spatial variance of the focusing parameters and range cell migration (RCM), which restrict the available scene size and increase the difficulty of GEO SAR imaging. To achieve high squint mode GEO SAR imaging, the effects of squint mode on imaging processing—especially the azimuth-variant RCM—are first analyzed in detail, and the relationship between the azimuth-variant RCM and the azimuth-variant focus parameters is discussed. Then, in this paper, a 2-D nonlinear chirp scaling algorithm (2-D NCSA) based on optimal azimuth polynomial compensation is proposed to realize high squint GEO SAR imaging. In the proposed algorithm, the optimal azimuth polynomial compensation which consists of a time-domain compensation and a frequency compensation removes the range walk, weakens the azimuth-variant RCM, and simplifies the imaging processing, while the 2-D NCSA which consists of a range NCSA and a higher order azimuth NCSA solves the 2-D spatial variance of focusing parameters and achieves high squint GEO SAR imaging. Computer simulations for different orbital positions validate the effectiveness of the proposed algorithm under high squint conditions.

Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging.

This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data.

An efficient NLCS algorithm for maneuvering forward-looking linear array SAR with constant acceleration

Forward-looking linear-array synthetic aperture radar (FLLA-SAR), which can overcome the deficiency of the traditional SAR on forward-looking imaging, continues to gain in significance due to the various applications, such as unmanned aerial vehicle (UAV) reconnaissance. To compensate the space-variant characteristic of along-track frequency modulation (FM) rate caused by the high speed maneuvering UAV, an efficient nonlinear chirp scaling (NLCS) algorithm is proposed in this paper. Based on the analysis of novel geometric configuration and the introduction of NLCS operation, the linear-array UAV SAR can reconstruct the 2-D image of the scout area. Finally, the validation of the proposed algorithm is done by exploiting the simulated data based on 3 × 3 array point targets and an airplane scattering model.

Focusing high-squint and large-baseline one-stationary bistatic SAR data using keystone transform and enhanced nonlinear chirp scaling based on an ellipse model

This paper deals with the imaging problem for one-stationary bistatic synthetic aperture radar (BiSAR) with high-squint, large-baseline configuration. In this bistatic configuration, accurate focusing of BiSAR data is a difficult issue due to the relatively large range cell migration (RCM), severe range-azimuth coupling, and inherent azimuth-geometric variance. To circumvent these issues, an enhanced azimuth nonlinear chirp scaling (NLCS) algorithm based on an ellipse model is investigated in this paper. In the range processing, a method combining deramp operation and keystone transform (KT) is adopted to remove linear RCM completely and mitigate range-azimuth cross-coupling. In the azimuth focusing, an ellipse model is established to analyze and depict the characteristic of azimuth-variant Doppler phase. Based on the new model, an enhanced azimuth NLCS algorithm is derived to focus one-stationary BiSAR data. Simulating results exhibited at the end of this paper validate the effectiveness of the proposed algorithm.

An Azimuth-Variant Autofocus Scheme of Bistatic Forward-Looking Synthetic Aperture Radar

In bistatic forward-looking synthetic aperture radar (BFSAR), conventional autofocus algorithms cannot estimate the phase errors accurately when the range walk is compensated in the azimuthal time domain. This problem stems from the influence of the azimuth-variant Doppler coefficients after linear range cell migration correction in azimuthal time domain. In principle, nonlinear chirp scaling processing can be carried out to remove the azimuth variance. Nevertheless, Doppler azimuth variations of the Doppler parameters induced by the motion errors are not taken into consideration and serious defocus would emerge in the final image. To cope with such a problem, an estimation–evaluation–equalization scheme is proposed before conventional autofocus for BFSAR. Different from the conventional autofocus method, the azimuth-variant Doppler coefficients are additionally estimated and equalized before autofocus, and as a consequence, phase errors can be precisely estimated. The BFSAR data processing results demonstrate the validity of the proposed method on the improvement of autofocus in BFSAR.