In recent years, iterative adaptive approach (IAA) has been proposed for super-resolution imaging in scanning radar, providing improved azimuth resolution. Traditional IAA involves computing the correlation matrix R for target scattering in each range cell, leading to iterative row-by-row solving and matrix inversion operations, causing high computational complexity. To this end, this paper proposes a Fast Batch-Based Iterative Adaptive Approach (FBB-IAA) that enables parallel and synchronized super-resolution processing of each range cell in the echo matrix. Additionally, it utilizes the two-dimensional conjugate gradient (2D-CG) method to avoid matrix inversion operation, significantly reducing the computational complexity compared to traditional IAA. Simulation results validate the superiority of the proposed method.

High-squint super-resolution imaging for airborne scanning radar is crucial in remote sensing and earth information observation. Various methods have been proposed to enhance the azimuth resolution of imaging. However traditional methods are often limited by the requirement for manual adjustment of hyperparameters. In this paper, we propose a hyperparameter-free high-squint super-resolution method for airborne scanning radar based on likelihood based estimation of sparse parameters (LIKES). Compared to traditional sparse imaging methods, our presented approach ensures super-resolution while addressing the issue of manual hyperparameter adjustment. Simulation results demonstrate the effectiveness of the proposed method.

Forward-looking radar (FLR) has been widely discussed because of its super-resolution capability. However, for the high-speed radar platform, the super-resolution performance of FLR degrades significantly due to the limited signal model accuracy. In this article, to observe the azimuth–elevation information of multiple targets based on a high-speed radar platform, a sparse Doppler phase convolution (SDPC) model is proposed by randomly and sparsely scanning the radar beam to reduce the coherent processing interval (CPI) and limit the signal model errors. On the one hand, the Doppler phase is introduced to characterize the vector superposition relations of the echo in each azimuth–elevation direction, thus limiting the error of the conventional convolution model (CM). On the other hand, an azimuth–elevation sparse scanning scheme is proposed to reduce the CPI, allowing for accurate second-order approximation of the range history and further limiting the reconstructed errors for high-speed radar platforms. In addition, the velocity application boundary and the sparsity boundary of the SDPC model are quantitatively analyzed. Simulations compare and validate the performance of the proposed SDPC model with the conventional CM using three classical super-resolution algorithms. Based on the proposed model, azimuth–elevation information of multiple targets can be accurately reconstructed on high-speed radar platforms.

Deconvolution methods can be applied in airborne scanning radar to enhance its angular resolution for improving the collision avoidance ability in the forward-looking direction. However, as the movement speed of the airborne platform increases, the traditional convolution signal model cannot be applied because of the model errors in the amplitude profile and Doppler phase. In this article, an accurate profile-phase deconvolution method is proposed to achieve scanning radar forward-looking super-resolution imaging, particularly for high-speed platforms. On one hand, a profile-phase convolution (PPC) model is established by analyzing the influence of high-speed platform on echo amplitude profile and Doppler phase. The proposed model accurately captures the variation of beam dwell time caused by the coupling of platform motion and beam scanning, which directly affects the echo amplitude profile. On the other hand, relying on the proposed PPC model, an adaptive regularization (AR) deconvolution method is derived to avoid hyperparameter selection. Point-target and surface-target results demonstrate that the proposed PPC model and the AR deconvolution method are competent for super-resolution imaging on high-speed platforms.

Constrained by the coarse angular resolution, the real aperture radar (RAR) typically suffers from low location accuracy. Superresolution methods have been proposed to improve its location performance by an enhanced radar image. However, the limit of angular location has not been fully investigated. In this paper, an angular deterministic (conditional) Cramer-Rao bound (CRB) of the RAR is deduced to describe the angular location error bound. First, a virtual array projection model is analyzed in spatial frequency domain, which normalize the signal model of different antenna types. Then, a general form CRB based on complex signal is deduced. Last, the result for a single target is illustrated to verify the deduced CRB. The bound is significant to the design of radar system parameters and superresolution methods.

Recently, the iterative adaptive approach (IAA) has been widely applied to enhance the azimuth resolution of real beam mapping (RBM) imagery. However, the IAA suffers from extremely high computational complexity in practice. This paper proposes a Split IAA for sparse scene to reduce the complexity. First, the IAA cost function is decomposed. Then the echo data is split into blocks, and the iterative model is redefined according to the target block and its corresponding cost function. Consequently, the high-dimensional data inversion problem is decomposed into multiple low-dimensional sub-problems to achieve fast super-resolution imaging. The measured results show that the proposed Split IAA significantly reduces the computational complexity without affecting super-resolution performance.

Recently, a two-dimensional (2-D) scanning radar super-resolution model has been proposed to simultaneously achieve azimuth-pitch super-resolution imaging. However, due to the addition of the pitch dimension, the complexity of the state-of-art methods becomes extremely high. In this paper, based on the sparse learning via iterative minimization (SLIM), we propose a low-complexity 2-D sparse scanning radar super-resolution method. First, the signal model of 2-D scanning radar is established. Then, base on the traditional SLIM method, the 2-D scattering estimation of the target can be iteratively solved by exploiting the conjugate gradient (CG) algorithm and the Kronecker product property. Compared with the existing methods, the proposed method has lower computational complexity and stronger adaptive ability without losing resolution performance. The simulation verifies the effectiveness of the proposed method.

To design configuration parameters for coherent multistatic synthetic aperture radar (C-MuSAR), a wavenumber spectra projection (WSP) approach is proposed in this paper based on the relationship between the wavenumber support regions (WSRs) and configuration parameters, including synthetic aperture time, positions and flight directions of receivers. First, the projected pattern of multiple WSRs is deduced, and the relationship between multiple WSRs and the point spread function (PSF) is analyzed. Second, the primary WSR is designed based on the relationship between the transmitter and the leading receiver. A WSP method is proposed to quickly deduce the configuration parameters of the following receivers. Finally, based on the designed configuration parameters of C-MuSAR, an adaptive WSP method is adopted to reconstruct the targets. Simulations are carried out to testify the proposed method.

Recently, deep learning has gained increasing popularity in array signal processing. In this paper, we estimate the direction of arrival (DOA) for the multiple-input and multiple-output (MIMO) radar system based on deep learning. First, we convert DOA estimation into a linear inverse problem with spatial sparsity, and construct a neural network based on the iterative shrinkage thresholding algorithm (ISTA) to improve the interpretability of the network. Then, a stacked denoising autoencoder (DAE) is employed to achieve data-driven denoising, which improves the anti-jamming ability of DOA estimation. Finally, a new deep unfolded network named denoising learned ISTA (Denoising-LISTA) is proposed for DOA estimation. Simulation results illustrate that the proposed method improves the robustness of DOA estimation with single snapshot sampling and keeps significant predominance in beam sharpening and sidelobe suppression.

Ground-to-air real aperture radar scans the airspace to acquire range-azimuth-pitch 3D echoes for imaging. In real situations, the echo data may be corrupted by interference, making it difficult to reconstruct the original scene using echoes with missing data. To overcome this problem, a fast superresolution imaging method under the non-uniform sampling model is proposed in this paper. Firstly, a non-uniform sampling model is proposed to well model the echoes with missing data, which makes it possible to reconstruct the real target distribution from the echoes with missing data. Secondly, we use the sparse regularization (SR) super-resolution imaging method to reconstruct the real target distribution. Since the high dimension of the dictionary matrix leads to the expensive computational cost of the SR method, we propose a fast superresolution imaging algorithm based on low-rank approximation to reconstruct the targets quickly. Simulation results show that the original scene can be effectively reconstructed from the echoes with missing data based on our proposed model, and the proposed algorithm greatly improves the computational efficiency compared with the traditional methods while not leading to a loss of imaging performance.

Ground-based two-dimensional (2D) array radar suffers from low angular resolution, including azimuth and pitch directions because of the limited size of antenna aperture. In this paper, to improve the two-dimensional angular resolution for a ground-based 2D array radar, a 2D low-rank Truncated Singular Value Decomposition (2D-LRTSVD) superresolution algorithm is proposed by transforming the 2D deconvolution problem into several low-rank inversion problem. First, the traditional 2D convolution signal model is transformed as a low-dimensional signal model by dividing the Kronecker product matrix into several low-dimensional steering matrices. Second, a 2D-LRTSVD method is proposed by compressing the data dimensions of the low-rank steering matrices. Based on the proposed method, the operational complexity can be reduced by avoiding direct high-dimensional matrix inversion. Finally, the 2D angular resolution of array radar can be enhanced without performance loss in a low computational complexity. Simulations are carried out to verify the proposed method.

Recently, a split sparse iterative covariance-based estimation (Split SPICE) method has been proposed for synthetic aperture radar (SAR) imaging to enhance the azimuth resolution. However, this method suffers the significant high computational complexity, which is caused by the high-dimensional matrix inversion. To this end, a fast Split SPICE approach is proposed to reduce the tricky complexity of the traditional ones for airborne scanning radar super-resolution imaging. It takes advantage of the low displacement rank feature of the Toeplitz matrix to solve the matrix inversion by Gohberg–Semencul (GS) representation efficiently. Compared with traditional methods, the proposed method offers higher computational efficiency for scanning radar super-resolution imaging with marginal resolution loss. The simulation results verify the effectiveness of the proposed method.

Recently, a sparse super-resolution method relying on L1iterative reweighted norm (IRN) has been proposed to improve the imaging resolution of scanning radar. However, the method has poor adaptability due to the noise-sensitive user-parameter. To this end, an adaptive L1iterative reweighted sparse super-resolution method with no user-parameter is derived. Firstly, the scanning radar super-resolution model is established. Secondly, the user-parameter selection in the L1-IRN method is analyzed. Finally, the adaptive iteration weights are derived by transforming the sparse estimation problem into a maximum posterior (MAP) estimation problem. Compared with the existing L1-IRN method, the proposed method does not have any user-parameter, so it has adaptability to different signal-to-noise ratios (SNR) and is more robust. Simulation verifies the superiority of the proposed method.

Recently, the sparse ℓ1-alternating direction method of multipliers (ADMM) based estimation algorithm was introduced for scanning radar, resulting in significant enhancements of the azimuth-pitch angular resolution. Regrettably, not only this method selects the hyperparameters manually, but also its time and space complexity increases rapidly with the data size, which restricts the capacity for applying in hardware system. To this end, a 2D weighted sparse iterative algorithm is derived in this paper, allowing for the hyperparameter-free and efficient sparse reconstruction result of scanning radar for the simultaneously azimuth-pitch resolution enhancement. The proposed method is a fast 2D extension of the current weighted Sparse Iterative Covariance-based Estimation (WSPICE) algorithm, which not only offers much less computational and storage cost, but also enjoys the adaptability with no hyperparameter and finer resolution. Experimental results of simulation and measured data demonstrate the advantage of the proposed method in azimuth-pitch resolution enhancement for scanning radar.

Scale information is a significant index for target measurement by real aperture radar (RAR). However, the measured target scale information by RAR is inaccurate because of the limited angular resolution. In this paper, to enhance the scale measurement ability of RAR, a generalized hybrid regularization (GHR) approach is proposed by combining the generalized sparse (GS) regularization norm and the generalized total variation (GTV) regularization norm. On the one hand, the GHR approach is proposed to simultaneously enhance the angular resolution and the scale information of targets by combing the generalized regularization norms. The GS regularization norm can improve the reconstructed angular resolution due to its sparsity over the L1 norm. The GTV regularization norm can preserve the steep target contour because of its edge enhancement ability over the total variation (TV) norm. On the other hand, based on the GHR optimization function, an adaptive iterative reweighted (AIR) solver is proposed to reduce the number of manually selected regularization parameters, allowing for accurate scale information reconstruction. Simulations and experiments verify the performance of the proposed method. Based on the proposed approach and solver, the target scale information can be accurately observed.

The sparse iterative covariance estimation (SPICE) algorithm is promising for hyperparameter-free sparse source location for time-division-multiplexing multiple-input multiple-output (TDM-MIMO) radar systems, with well-documented merits in resolution enhancement and sidelobe suppression. Regrettably, the method typically requires a large number of iterations to converge, each requiring high-dimensional matrix operations, rendering the existing batch SPICE method impractical and expensive to implement in hardware when dealing with massive TDM-MIMO observations. In order to enable real-time processing, this paper presents a sub-aperture-recursive (SAR) SPICE method, allowing for recursively refining the location parameters for each received (RX) block observation that becomes available sequentially in time. The proposed method not only offers the same benefits as the batch SPICE method, but also allows for a computationally efficient online processing, without the need for high-dimensional matrix operations, notably reducing the required hardware resources as well as processing time. We further present a high-throughput architecture for the resulting method on a XCZU15EG-FFVB1156 field-programmable gate array (FPGA). In combination with simulation results, we demonstrate the effectiveness through experimental data measured by a cascaded MIMO radar system with 12 transmit (Tx) and 16 Rx antennas, demonstrating that the computational time of resolving closely spaced sources on 256 predefined grid points can be processed in merely 12 ms.

Recently, the iterative adaptive approach (IAA) method has been adopted to allow for high-resolution direction of arrival (DOA) estimation of MIMO radar. In this paper, the computational complexity caused by traditional rough convergence criterion is reduced by following a selective-coordinate iterative strategy. First, we analyze the iterative termination criterion of the current IAA. Then, considering a novel criterion that defined by the absolute value of the adjacent iterative points of each coordinate, those coordinates that are not converged can be selectively iterated. In this way, unnecessary iterative calculations can be greatly reduced. Finally, the complexity of IAA and the proposed method are compared and analyzed in detail. Simulation and measured data illustrate that the proposed method offers a computational complexity reduction without loss of performance.

The generalized sparse iterative covariance-based estimation ($q$-SPICE) algorithm was recently introduced for scanning radar applications, resulting in substantial improvements in the angular resolution and quality of the processed images. Regrettably, the computational complexity and storage cost are high and quickly increase with growing data size, limiting the applicability of the estimator. In this letter, we strive to alleviate this problem, deriving a beam-updating$q$-SPICE algorithm, allowing for efficiently updating of the sparse reconstruction result for each online radar measurement along the scanned beam. The resulting method is a regularized extension of the current online$q$-SPICE implementation, which not only offers constant computational and storage cost, independent of the data size, but also provides enhanced robustness over the current online$q$-SPICE. Our experimental assessment, conducted using both simulated and real data, demonstrates the advantage of the beam-updating$q$-SPICE method in the task of sparse reconstruction for scanning radar.

Superresolution methods can be applied to real aperture radar (RAR) to improve its angular resolution by solving an inverse problem. However, traditional superresolution methods are achieved after batch data collection, which requires extensive operational complexity and storage space. To solve this problem for RAR, an online detect-before-reconstruct (DBR) framework is proposed in this article based on the sparse property of targets. First, along the range direction, each sample of the echo data is detected to reduce the computational complexity by reducing the dimension of the effective data. Second, along the azimuth direction, a data-adaptive online processing structure is proposed to reduce the storage requirement for the angular superresolution problem. Finally, within the online processing structure, a target data-adaptive updating strategy is proposed to reduce the number of iterations for each target grid. The online DBR-based framework can effectively reduce the operational complexity caused by the noise values of the echo data. Based on the proposed online processing structure, the storage requirement and the operational complexity of the angular superresolution for an RAR system can be greatly reduced without significant reconstruction performance loss. The results of simulations and experimental data verify the proposed framework.

Cross-resolution enhancement for airborne high-squint radar (AHSR) imagery is mathematically equivalent to the ill-conditioned problem of inverse-scattering reconstruction. Although a variety of inversion methods with regularization can be introduced to advance the field of AHSR imagery, they turn out to be computationally intensive when extended to 2-D (range and cross-range dimension) image formulation due to the range-by-range calculation for the space-variant inversion operators over the full range swath. To tackle the problem of efficiency, this article presents a low-complexity inverse-scattering strategy. Our underlying idea is to equalize the space-variant Doppler centroid embedded in an inversion operator for a reference range cell using Doppler centroid compensation. With the proposed strategy, the necessary computational complexity required for 2-D AHSR inverse-scattering reconstruction can be significantly reduced by requiring only the calculation of the inversion operator, independently of the number of range cells. Our experimental assessment, conducted using both the simulation and real data, demonstrates that our proposed inverse-scattering strategy offers preferable computational reduction in the task of inverse-scattering reconstruction for 2-D AHSR imagery without resolution loss.

Recently, a variety of super-resolution (SR) methods have been devoted to enhancing the angular resolution of real beam mapping (RBM) imagery in modern microwave remote sensing applications. When addressing large-scale datasets, however, they suffer from notably high computational complexity due to high-dimensional matrix inversion, multiplication, or singular value decomposition (SVD). To overcome this limitation, this article presents a low-complexity SR strategy based on adaptive low-rank approximation (LRA). Our underlying idea is first to construct a random matrix sketching to sample the raw echo measurements and restore the surface map of reflectivity in a low-dimensional linear space. The resulting low-complexity strategy enables substantial computational complexity reduction for a group of SR methods, at the cost of introducing a manually adjusted LRA parameter. Using the Fourier transform-based antenna analysis method, we further reveal that the LRA parameter that ensures support resolution improvement can be determined by a closed-form function of the aperture length, the wavelength, and the field of view, allowing for adaptively and efficiently selecting the optimal LRA parameter that well balances the tradeoff between LRA error and computational efficiency. We use both simulated and real datasets to demonstrate that the proposed LRA-based SR strategy can provide significant speedup without performance loss.

Airborne radar high-squint looking imaging is an important research for remote sensing. The traditional Doppler beam sharpening based on fast Fourier transform (FFT) has good real-time performance but low cross-range resolution. Many super-resolution methods have been proposed to enhance the cross-range resolution for airborne radar. However, these methods generally adopt the batch processing mode with high computational complexity and high memory usage, which lead to poor real-time performance. This paper proposes an online super-resolution imaging approach for airborne scanning radar based on sliding window recursive least square (SWRLS) algorithm. The current scattering estimation can be derived recursively through downdating and updating. The proposed method effectively improves the cross-range resolution as well as the real-time performance and memory occupancy, which is beneficial to high-quint continuous realtime imaging for airborne radar. Simulation results are given to demonstrate the effectiveness of the proposed method.