The backprojection (BP) algorithm is a precise time-domain technique in synthetic aperture radar (SAR) imaging, known for its robustness in scenarios where frequency-domain algorithms struggle, such as nonlinear flight paths, high-resolution demands, or large imaging swaths. However, the unknown spectral structures of BP images pose significant challenges for frequency-domain autofocus algorithms, including phase gradient autofocus (PGA). This article introduces a novel interpretation of the BP algorithm, and then compares the image spectra between BP and the polar format algorithm (PFA). Our findings indicate that BP image’s spectrum suffers from severe range ambiguity and spectral misalignment, which is the key reason why BP images cannot be directly applied to PGA. To address these issues, we first improve the postprocessing method, and then propose a modified BP algorithm. Both the approaches reconstruct the signal spectrum, thereby facilitating the direct application of PGA. Compared with the postprocessing method, the proposed algorithm is more efficient. Simulation and real data experiments validate the feasibility and efficacy of the proposed method, demonstrating the proposed algorithm’s suitability for autofocusing in the frequency domain.

The separation of multiple transmit waveforms with time and frequency synchronization constitutes a considerable challenge for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems. It is well-known that aliased signal returns may be separable by digital beamforming (DBF) on receive in elevation. However, the current orthogonal-waveform beamforming schemes significantly increase the hardware complexity. Moreover, the direction of arrival (DOA) mismatch issue caused by topographical variations significantly increases the complexity of the DBF process. To alleviate these issues, we here introduce a multiple-subpulse separation and weighting synthesis (MSS-WS) echo separation framework, which is formed using segmented phase coding (SPC) waveforms. The proposed MSS-WS scheme can halve the number of interferences from far arrival angles, allowing for a reduction of the system complexity. In addition, constrained/generalized least absolute shrinkage and selection operator (LASSO) regression is exploited to form the beamformer with relatively high robustness in terms of dealing with the presence of topographical variations. The so-called LASSO-based dynamic beam response (LASSO-DBR) technique introduced here contains two parts: the source localization and the beamforming based on the designed constraint matrices. In this respect, the proposed LASSO-DBR beamformer can produce a distortionless response to the desired signal and still yield wide nulls for the unwanted interferences. Using numerical simulations, we illustrate the feasibility and performance of the proposed MSS-WS framework using the LASSO-DBR beamforming technique.

Phase gratitude algorithm (PGA) is a high-efficient autofocus technique that can estimate and compensate phase errors of SAR (synthetic aperture radar) imagery produced by frequency-domain algorithms. However, from conventional viewpoint, applying PGA on refocusing imagery produced by the time-domain algorithm, i.e., FBP, remains a huge challenge because the spectrum characteristics of FBP imagery are special. In this paper, a modified PGA (MPGA) for spotlight FBP (Filtered Backprojection) imagery is proposed, in which a spectrum correction is performed first to provide advantages for the standard PGA application. Simulations and real data experiments have been carried out to prove the effectiveness and prospect of the proposed approach for refocusing FBP imagery.

The Polar Format Algorithm (PFA) is a popular choice for general bistatic synthetic aperture radar (BiSAR) imaging due to its computational efficiency and adaptability to situations with complicated geometries or arbitrary flight trajectories. However, efficient and accurate compensation of two-dimensional (2-D) residual phase errors induced by the wavefront curvature remains challenging when obtaining high quality BiSAR PFA images. In this paper, an analytical expression for the phase errors in the wavenumber domain is derived. With it, the inherent structural characteristics of the phase errors are formulated, where the 2-D phase errors can be reduced to one-dimensional (1-D) phase errors for an optimal coordinate system. Moreover, the mapping relationship between distorted point targets in the optimal imaging coordinates and their actual point targets in the original imaging coordinates is investigated. By exploiting the structural characteristics and the mapping relationship, a highly efficient BiSAR PFA wavefront curvature compensation method is proposed. This allows a reduced-dimensional space-variant filter to be constructed to mitigate the 2-D defocusing effect without compromising the compensation accuracy, with the distortion correction being performed using interpolation. The proposed method significantly reduces the complexity required for residual 2-D phase error compensation while simplifying the distortion correction, resulting in a notable robustness. The effectiveness of the method is demonstrated using point target and scene target simulations.

The problem of echo separation using digital beamforming (DBF) on receive for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is of notable importance to allow for practical systems. Regrettably, current DBF-MIMO-SAR schemes, such as the short-term shift-orthogonal (STSO) scheme, are computationally cumbersome, increasing the required hardware complexity. To alleviate this problem, we here propose an improved echo separation solution for realizing a low-cost MIMO-SAR system. We detail a generic waveform design scheme as well as optimized monostatic radar waveforms (e.g., nonlinear frequency modulation (NLFM) signal) showing how these can be directly adopted in the proposed scheme to improve the imaging performance. The proposed scheme enables the number of the interference segments generated by unmatched waveforms to be halved by the use of the fast time spectrum preprocessing and segment synthesis, dramatically simplifying the array configuration and reduces the system complexity. By exploiting inter-pulse phase coding techniques, the proposed method can provide a reconfigurable waveform transmitting scheme, allowing the system resources in range frequency, elevation space, and Doppler domains to be jointly exploited for the separation of aliased signal returns. The proposed scheme is evaluated using extensive numerical and measured data sets, demonstrating the feasibility and potential of the proposed method for resource-limited spaceborne/airborne MIMO-SAR systems.

The phase gratitude algorithm (PGA) is a robust autofocusing approach that can efficiently refocus defocused SAR imagery produced by frequency-domain algorithms. However, from a conventional viewpoint, PGA cannot be extended to refocus SAR imagery produced by time-domain algorithms, such as the Filtered Back Projection (FBP), as the spectrum of the FBP imagery is range ambiguous and azimuth space-variant. In this letter, a novel interpretation of FBP is presented, in which the spectrum structure of the FBP imagery is analyzed in detail. By incorporating the derived spectral information, an efficient spectrum preprocessing is proposed for spectrum restructuring. After this preprocessing, PGA is shown to be able to refocus defocused FBP imagery. The validity and feasibility of the proposed autofocusing approach are demonstrated using both simulated and experimental data.

The filtered backprojection (FBP) algorithm is viewed as a preferred candidate for general bistatic synthetic aperture radar (BiSAR) imaging since it does not pose any restrictions on SAR configurations or flight paths. However, high-efficient autofocus methods such as phase gradient autofocus (PGA) or Mapdrift (MD) cannot be effectively integrated with the FBP algorithm due to the unknown properties of the BiSAR FBP imagery spectrum. In this article, a novel Fourier-based interpretation of the BiSAR FBP algorithm is presented. Based on the new viewpoint, spectral characteristics of the BiSAR FBP imagery in the wavenumber domain, including range spectral ambiguity, space-variant spectral support, and the structural 2-D phase error, are derived in detail. Using these characteristics, a computationally efficient 2-D autofocus approach is proposed. First, a preprocessing is performed to eliminate the range spectral ambiguity and to align the skewed spectrum support, which facilitates the following phase error estimation and correction. Then, an estimation of the 1-D azimuth phase error (APE) is applied by combining multiple estimation results from different subband data. Finally, the 2-D phase error is computed directly from the estimated APE by exploiting the derived analytical structure of the 2-D phase error, which is then applied to restore the BiSAR FBP image. The simulation results are presented to show the effectiveness of the proposed approach.

In this article, a new interpretation of the polar format algorithm (PFA) for general bistatic spotlight synthetic aperture radar (SAR) imaging is presented. From the viewpoint of 2-D decoupling, we examine the commonly adopted implementation of the PFA, i.e., the separable 1-D range and azimuth resampling procedures for their roles in range cell migration (RCM) correction, respectively. Utilizing this new formulation, we analyze the effect of range and azimuth resampling on the residual 2-D phase error and reveal the inherent structure characteristics of the residual 2-D phase error in the wavenumber domain. By exploiting the available a priori knowledge on the phase error structure, a structure-aided 2-D autofocus approach to refocus the defocused PFA imagery is proposed. The proposed approach fully exploits the potentiality of the available data and the a priori knowledge about the phase error that need to estimate, so the accuracy of the residual 2-D phase error estimation and correction can be greatly improved. Finally, experimental results are presented to show the effectiveness of the proposed approach.