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The perfectly partly calibrated antenna array is a frequently assumption in most of the existing array gain/phase calibration methods. In practice, however, the partly calibrated array is usually not available. In this letter, a tail optimization method for direction finding with unknown gains and phases in the presence of spatially non-uniform noise is proposed. Specifically, the unknown gain/phase entry is firstly merged into the signal power by using the sparse representation. Subsequently, a tail optimization method that can significantly suppress the occurrence of pseudo-peaks is designed to determine the signal DOAs without a priori information of unknown sensor gain and phase errors. In addition, the spatially non-uniform noise can be removed by a linear transformation to improve the robustness against the noise. Numerical simulations examples are presented to demonstrate the effectiveness and superior performance of the proposed approach over the other existing counterparts.

Coherent frequency diverse array (FDA) can provide the full spatial illumination with a stable transmit gain by employing a single frequency-shifted waveform. However, the authors find that the range resolution is scaled linearly with the number of elements. In this work, the problem is first quantitatively analysed through mathematical derivation. To solve the issue, a subarray-based coherent FDA transmitting pulsed linear frequency modulation signals is proposed. The essence of the subaperture technique is to partition the transmit antenna array into multiple regular or irregular subarrays, wherein an identical carrier frequency is utilised in each subarray. Meanwhile, distinct carrier frequencies are adopted between subarrays. Moreover, the multi-dimensional ambiguity function is studied to assess the properties including the range resolution, spatial coverage and sidelobe level. Simulation results demonstrate that the proposed approach has superiorities in range resolution enhancement and range sidelobe reduction.

By transmitting a single frequency-shifted waveform, coherent frequency diverse array (FDA) can provide a simple way to realize full spatial coverages with stable gains. Owing to the range-angle dependency in coherent FDA, the authors implement a two-dimensional angle-time matched filter to perform equivalent transmit beamforming and matched filtering simultaneously. However, such filter structures merely control main-lobes of equivalent transmit beams towards target directions. It fails to form nulls at interference directions. Moreover, traditional adaptive beamforming by designing adaptive weight vectors are no longer applicable. Additionally, they find that the range resolution scales linearly with the element number. To tackle these issues, a space-time matched filter (STMF) in combination with the hybrid coding technique is proposed. Aiming at mitigating interferences, the STMF is designed with a formulation of quadratically constrained quadratic programing. By relaxation of quadratic constraints, the hard non-convex problem can be turned into the second-order cone programing to obtain optimal filter parameters. Furthermore, the hybrid coding technique is devised to jointly improve the range resolution. Numerical experiments of both two-dimensional range-angle outputs and one-dimensional range profiles via filtering are provided, which demonstrate that the STMF with hybrid coding can effectively suppress sidelobe interferences with a range resolution enhancement.

In this article, we propose a novel phase unwrapping method termed the square-root cubature Kalman filter phase unwrapping (SCKFPU) method. Specifically, as the system model of the interferometric synthetic aperture (InSAR) phase unwrapping can be formulated as the discrete Markovian jump system for tracking a maneuvering target, a phase unwrapping method is proposed by combining the SCKF algorithm with a phase gradient estimator. Moreover, we design a phase quality estimate function, and present an optimal path-following strategy. The strategy ensures that the SCKFPU method simultaneously performs noise suppression and unwraps InSAR images along the pixels with high-reliance to the pixels with low-reliance. Simulation results based on synthetic data, true InSAR data, and measured (real) InSAR data show that the proposed InSAR phase unwrapping method can achieve better performance compared with other existing phase unwrapping methods.

The target detection of the passive multiple-input multiple-output (MIMO) radar that is comprised of multiple illuminators of opportunity and multiple receivers is investigated in this paper. In the passive MIMO radar, the transmitted signals of illuminators of opportunity are totally unknown, and the received signals are contaminated by the colored Gaussian noise with an unknown covariance matrix. The generalized likelihood ratio test (GLRT) is explored for the passive MIMO radar when the channel coefficients are also unknown, and the closed-form GLRT is derived. Compared with the GLRT with unknown transmitted signals and channel coefficients but a known covariance matrix, the proposed method is applicable for a more practical case whenthe covariance matrix of colored noise is unknown, although it has higher computational complexity. Moreover, the proposed GLRT can achieve similar performance as the GLRT with the known covariance matrix when the number of training samples is large enough. Finally, the effectiveness of the proposed GLRT is verified by several numerical examples.

Spatial spectrum estimation, also known as direction of arrival (DOA) detection, is a popular issue in many fields, including remote sensing, radar, communication, sonar, seismic exploration, radio astronomy, and biomedical engineering. MUltiple SIgnal Classification (MUSIC) and Estimation Signal Parameter via Rotational Invariance Technique (ESPRIT), which are well-known for their high-resolution capability for detecting DOA, are two examples of an eigen-subspace algorithm. However, missed detection and estimation accuracy reduction often occur due to the low signal-to-noise ratio (SNR) and snapshot deficiency (small time-domain samples of the observed signal), especially for sources with different SNRs. To avoid the above problems, in this study, we develop a DOA detection approach through signal subspace reconstruction using Quantum-Behaved Particle Swarm Optimization (QPSO). In the developed scheme, according to received data, a noise subspace is established through performing an eigen-decomposition operation on a sampling covariance matrix. Then, a collection of angles randomly selected from the observation space are used to build a potential signal subspace on the basis of the steering matrix of the array. Afterwards, making use of the fact that the signal space is orthogonal to the noise subspace, a cost function, which contains the desired DOA information, is designed. Thus, the problem of capturing the DOA information can be transformed into the optimization of the already constructed cost function. In this respect, the DOA finding of multiple signal sources—that is, the multi-objective optimization problem—can be regarded as a single objective optimization problem, which can effectively reduce the probability of missed detection of the signals. Subsequently, the QPSO is employed to determine an optimal signal subspace by minimizing the orthogonality error so as to obtain the DOA. Ultimately, the performance of DOA detection is improved. An explicit analysis and derivation of the developed scheme are provided. The results of computer simulation show that the proposed scheme has superior estimation performance when detecting signals with very different SNR levels and small snapshots.

In transmit beampattern design, it is desirable to maximize the power around locations of interest. Multiple-input multiple-output (MIMO) radar transmits orthogonal waveforms, which is hardly achievable in practical applications. Moreover, the constant modulus constraint and the computational burden limit the system performance. In this paper, we propose an effective piecewise linear frequency modulation (PLFM) waveform for coherent frequency diverse array (FDA) radar to synthesize the desired transmit beampattern. By deriving the relationship between the beam direction and the transmit signal frequency, we find that different sub-band of transmitted signal corresponds to different angular sector. With the relationship between frequency band and mainlobe of beampattern, the beampattern synthesis is transformed into the design of waveform spectrum which is realized by designing the PLFM waveform in this paper. Compared with the state-of-the-art technique, the proposed PLFM waveform in coherent FDA enjoys the advantage of the constant modulus, low sidelobe level and reduced computation complexity. In addition, the multi-dimensional ambiguity function and the transmit beampattern response are derived to examine the properties. Numerical results are presented to validate the effectiveness of the proposed method.

The image of ground maneuvering targets may be defocused due to the Doppler ambiguity, high-order range migration (RM), and Doppler frequency migration (DFM) caused by the target’s complex motions in a synthetic aperture radar (SAR) system. To settle these problems, an efficient algorithm based on discrete polynomial-phase transform (DPT), keystone transform (KT), and matched filtering processing (MFP) is presented for ground maneuvering target refocusing and motion parameter estimation in this paper. Firstly, the DPT is applied to transform the cubic phase into the quadratic phase and simultaneously eliminate the quadratic RM, cubic RM, and quadratic DFM. Furthermore, the Doppler ambiguity containing Doppler center blur and Doppler spectrum ambiguity is also dealt with effectively by introducing a very small fixed lay time after DPT operation. Then, the KT is performed to correct the linear RM. After that, the matched filtering function related to the target’s equivalent third-order coefficient is constructed to compensate for the residual linear DFM in the range-time and slow-time domain. Lastly, a well-refocused image of the maneuvering target can be acquired, and the target’s motion parameters can be estimated effectively. The proposed algorithm has high computational efficiency and possesses favorable refocusing performance and motion parameter estimation precision. Simulation and real data processing results prove the effectiveness of the presented algorithm.

Ground maneuvering targets may be smeared in a synthetic aperture radar (SAR) image due to the Doppler ambiguity, high-order range migration (RM) and Doppler frequency migration (DFM) caused by unknown motion parameters. To address these problems, an efficient method based on discrete polynomial-phase transform (DPT) and matched filtering process (MFP) is developed to refocus the ground maneuvering targets in this paper. Firstly, the DPT is applied to eliminate the quadratic RM, cubic RM and quadratic DFM simultaneously. Then, the matched filtering functions are constructed to remove the residual linear RM and linear DFM. At last, the target energy is well focused by performing the azimuth fast Fourier transform (FFT). The proposed algorithm has high computational efficiency and superior performance of target detection and motion parameters estimation under high signal to noise (SNR) environment. The numerical results prove the effectiveness of the proposed method.

In microwave staring imaging, spatial-resolution of real aperture imaging is limited by actual antenna array aperture. In order to achieve high-resolution imaging of targets with sparse feature, this paper proposes a high-resolution imaging method based on temporal-spatial stochastic radiation field combining compressive sensing (CS) theory. Firstly, the formation and property of temporal-spatial stochastic radiation field are discussed. Then, signal model based on random radiation field is deduced in detail, and on this basis, high-resolution imaging method based on CS is discussed. The proposed method can distinguish targets within the beam coverage and higher quality image is achieved. Finally, numerical simulations and experiments in microwave chamber are performed to validate the method and its analysis.

In this paper, a beampattern design method is proposed for the multi-input-multi-output (MIMO) dual-function radar-communication (DFRC) system with an interleaved array. To make full use of the whole aperture, first, the transmit array is partitioned into two interleaved subarrays, one is for radar and the other is for downlink communications. Then, both the radar waveform and communication beamformers are optimized by combining the null-space projection (NSP) method and cyclic approach (CA) to perform the coexistence of MIMO radar and downlink communications. Besides, the communication beampattern can be utilized to improve the detection performance. Finally, several numerical results are given to show the effectiveness of the proposed method.

For the coexistent radar and communications system, the radar can receive the communications-path signal, i.e., the target return due to the transmission from the communications. The communications-path signal can be exploited to improve the radar detection performance when it has high signal to noise ratio (SNR). To show this, the statistical signal model at the radar receiver is developed, and then the generalized likelihood ratio test (GLRT) for the coexistent radar and communications system is derived in this paper. The derived GLRT has constant false alarm rate (CFAR). Finally, several numerical examples are presented to verify the performance gain by exploiting the communications-path signal with high SNR.

Many efforts have been recently devoted to adaptive beamformers using one uncertainty set to achieve robustness against steering vector mismatch. However, these robust adaptive beamformers based on worst-case performance optimization suffer from difficulty in selecting an appropriate size of the uncertainty set. Besides, their performances degrade dramatically if large steering vector mismatch occurs. This motivates us to develop a robust beamforming approach to handle the large uncertainty set problem. In this paper, we utilize multiple small uncertainty sets, instead of using a single large set, to cover the whole large uncertainty region. Two efficient algorithms, iterative semidefinite programming-based robust adaptive beamforming (ISDP-RAB) and iterative linearization-based robust beamforming (IL-RAB), are developed to solve the nonconvex problem. Simulation results indicate that the proposed method offers a significant performance improvement in case of large steering vector mismatch.

We consider the problem of detecting a distributed target in compound-Gaussian sea clutter with Gamma distributed texture components. We design the Rao, Wald, and generalized likelihood ratio test (GLRT) detectors according to the two-step method: the first step is to obtain the Rao, Wald tests and GLRT on the assumption that the texture or/and covariance matrix structure are known; then the maximum a posteriori probability estimate of the clutter texture and the fixed point estimate of covariance matrix exploiting persymmetry are employed to replace the known texture and covariance matrix in the tests derived in the first step. Remarkably these proposed detectors ensure constant false alarm rate with respect to the covariance matrix structure. The effectiveness of the proposed detectors is verified by using simulated and real sea clutter data.

A space-time coding array (STCA) system transmits an identical waveform with a small time offset across the array elements. It shares the characteristics of high angular resolution and instant wide angular coverage, leading to the low probability of interception as seen in the traditional multiple-input and multiple-output radar. Angle-time two-dimensional matched filter is required in the STCA. However, the sidelobe level (SLL) of the multi-dimensional ambiguity function in the range and angle domains is not as low as that desired in practical applications and the range resolution decreases as the number of elements increases. Here, two kinds of subarray-based time-delay methods are proposed to improve the resolution and reduce the SLL of the ambiguity function for STCA. Both the regular and irregular subarrays are considered, which increase the degrees of freedom and thus enhance the range resolution. Moreover, the SLL of the ambiguity function is reduced. Simulation results are provided to demonstrate the effectiveness of the proposed methods.

Ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler ambiguity and azimuth spectrum split caused by target unknown motion parameters. To handle these problems, we propose a fast non-searching method for maneuvering target refocusing and motion parameters estimation in this paper. First, the azimuth-deramp is conducted, which is capable of eliminating the azimuth spectrum splitting. In the sequel, the second-order keystone transform (SOKT) based on the scaling principle is applied to further correct the residual range curvature. Then, the phase difference (PD) is performed to eliminate the range walk and estimate the motion parameters, which does not require the prior knowledge of Doppler ambiguity number. Finally, the moving target can be well focused with the estimated parameters. This method has high computational efficiency and improved parameter estimation accuracy. Both simulated and real data are processed to demonstrate the effectiveness of the proposed method.

In the presence of range ambiguity, the synthetic aperture radar (SAR) systems suffer from image aliasing, which dramatically degrades the quality of SAR images. In this article, an easy-to-implement technique for range ambiguity suppression is investigated, which is based on phase coding in the transmit pulse dimension, referred to as pulse phase coding (PPC). By properly designing the PPC series, it is possible to discriminate the range ambiguous echoes from different range areas in the Doppler frequency domain. To further suppress the range ambiguous echo, a two-pulse cancellation (TPC)-based SAR imaging method is proposed, which improves the quality of SAR images in the presence of range ambiguity. The proposed two-pulse cancellation is performed followed by the azimuth compression. The simulation results demonstrate the effectiveness of the proposed method.

This paper investigates a new and special imaging mode, bistatic forward-looking high-speed maneuvering platform synthetic aperture radar, in which both platforms travel curvilinear trajectories with high velocities and accelerations. A thorough understanding of its new properties of motion, 2-D resolution, and echo signal coupling is given. Applicability of gradient method neglecting time dependence of gradient to this special configuration is addressed. Moreover, 2-D coupling characteristic of echo signal at different imaging distances is investigated.

Multiple clusters of particles characterized in terms of fixed-position and fixed-distribution are utilized for target capture, target state estimation, and track maintenance in traditional particle filters. It is often unsustainable in target acquisition and track maintenance since the prior information of target is hard to acquire. In addition, the obtained measurement information may be fuzzy (interval measurement) in practical engineering applications. This is also a challenge in traditional particle filters. In view of these two problems, a novel measurement-driven AParticle-δ-GLMB-IM filter is proposed. The AParticle-δ-GLMB-IM filter uses RLF to determine the affiliation between the survival targets and the interval measurements. A newborn label or a survival label will be given to the newborn particles driven by the same single interval measurement. Furthermore, this paper presents a new box particle application named ABox-δ-GLMB filter. Numerical experiments verify the effectiveness and superiority of the proposed methods.

Mainlobe deceptive jammer suppression is a critical issue for radar systems. To address this problem, the element-pulse coding (EPC) scheme is proposed in multiple-input multiple-output (MIMO) radar. In EPC-MIMO radar, a novel phase modulation is performed in the joint transmit element and pulse domain, resulting in an equivalent spatial frequency offset corresponding to different pulses. In such a way, the true target and mainlobe deceptive jammers, which are generated after a relatively large time delay, are distinguishable because they have different equivalent spatial distributions in the joint transmit-receive spatial frequency domain. In this respect, by selecting an appropriate coding coefficient, the mainlobe deceptive jammers can be suppressed by nulling at the equivalent transmit beampattern of the true target. Moreover, a preset beampattern synthesis (PBPS) method is proposed to enhance the robustness of jammer suppression against direction mismatches by broadening nulls around the jammers and generating a flat-top mainlobe. At the analysis stage, both simulated and measured results are provided to corroborate the effectiveness of the mainlobe deceptive jammer suppression with the developed methods.

In a multiple-input multiple-output (MIMO) radar, it is desired to maximize the power radiation in an angular region of interest, which, however, is hardly achievable because a set of orthogonal waveforms is employed at the engineering. Different from traditional colocated MIMO radar, space-time coding array (STCA) transmits an identical waveform with a tiny time delay circulating across array elements. It can provide a simple way to achieve the full angular coverage with a stable gain. In this paper, a new scheme referred to as chirp-STCA is proposed to synthesize the desired beampattern flexibly. With the quantitative relationship between the time delay and the span of beam spreading, the transmit beampattern synthesis issue is converted to the design of time delay value which can be readily realized based on the framework of chirp-STCA. As a result, the desired angular sector coverage of the radiation power can be realized by setting a proper time delay. The proposed chirp-STCA can provide many desired features including low range sidelobe level, low computational complexity, and constant modulus. In addition, the range-angle properties are examined by analyzing the transmit beampattern response and the ambiguity function. Numerical results are presented to demonstrate the effectiveness and simplicity of the chirp-STCA scheme for the transmit beampattern synthesis.

In practical application, the time when the maneuvering targets enter and leave the radar coverage observation is usually unknown, which will seriously deteriorate the performance of coherent integration and target detection. To solve this problem, we propose a method based on the symmetric autocorrelation function and the proposed window Lv's transform (SAF-WLVT) for coherent integration and motion parameters estimation of maneuvering target, involving the range migration (RM) and Doppler frequency migration (DFM). Firstly, the SAF is utilized to correct the linear RM induced by target's radial velocity and range curvature caused by target's radial acceleration simultaneously. Then, the proposed WLVT is applied to eliminate the residual DFM caused by the target's radial acceleration, accumulate the target energy without introducing excess noise energy, and obtain the baseband velocity and acceleration estimations. Finally, the Doppler ambiguity number is estimated by matched filtering and 1-D parameter searching, and then the target's radial velocity is obtained. The proposed method has low computational complexity, and possesses favorable performance of target detection and parameter estimation in the high signal to noise (SNR) environment. The mathematical analysis and simulation results demonstrate the effectiveness of the proposed method.

In this paper, we consider the problem of space-time adaptive processing (STAP) for airborne radar in the presence of direction-of-arrival (DOA) and Doppler frequency uncertainties, either of which would result in steering vector mismatch. A robust STAP method is devised by introducing an accurate steering vector estimator. In particular, by considering the mismatched DOA and Doppler frequency, a spatial-temporal integral covariance matrix including the actual steering vector component is first constructed. The subspace corresponding to the clutter-plus-noise is then extracted from the so-obtained matrix and used to impose an appropriate constraint to estimate the actual steering vector. The resultant problem is a non-convex quadratically constrained quadratic program (QCQP), which is solved using the semidefinite programming (SDP) relaxation technique. Numerical examples are presented to demonstrate the performance of the proposed approach in different hypothetical scenarios. HighlightsA spatial-temporal integral covariance matrix is constructed by considering the mismatched DOA and Doppler frequency.The subspace corresponding to the clutter-plus-noise is extracted from the spatial-temporal integral covariance matrix.Clutter-plus-noise subspace is used for impose an appropriate constraint to estimate the actual steering vector.

As a typical problem of sparse frame representations or compressed sensing with frames, direction of arrival (DOA) estimations, via sparse recovery methodologies such as nonlinear optimizations or various greedy algorithms, suffer seriously under severe noisy measurement without proper treatment. In this article, a crucial and effective correlation operation is outlined to mitigate the severe noise effect from the sparse representation point of view. A fast and super resolution method for DOA estimations is therefore established under very low signal-to-noise ratio, and by a sparse recovery technique of null space tuning in the context of compressed sensing and sparse representations. Improvement to the technique using the thresholding difference and alternating grid refinements are also outlined to estimate the source/target numbers dynamically and to improve the precision. Another characteristic is that only a very small number of snapshots are needed in comparison with other techniques. Simulation results demonstrate apparent advantages of the proposed technique over known approaches. The proposed method has the effectiveness at simultaneous high resolution, robustness to noise, and source number estimations. The algorithm is also computationally efficient, which is critical for large array systems and/or mission critical real-time applications.

In passive multiple input multiple output (MIMO) radar, the transmit signals of the noncooperative illuminators of opportunity are usually not completely known. However, they are often standard communication signals with some specific signal structure. Exploiting such information, the detection performance of passive MIMO radar can be improved. In this paper we derive a generalized likelihood ratio test (GLRT) for passive MIMO radar detection when the covariance matrix of the colored Gaussian noise is unknown and the structure of the transmit signal is known but it contains some unknown information bits. Moreover, a model which employs a reasonable approximation for some practical scenarios while requiring only a limited number of training samples is also considered, and a GLRT for this model is also derived. Our tests are shown to be constant false alarm rate (CFAR), and their performance approaches the optimum performance with known signal structure and known covariance matrix when the number of training samples is increased. Finally, several numerical examples are presented to demonstrate the effectiveness of the proposed method.

The range ambiguity degrades the clutter suppression performance and incurs parameters estimation ambiguities in application of ground moving target indication (GMTI). Thus, in this paper, an adaptive clutter suppression approach based on extended azimuth phase coding (EAPC) for multiple-input multiple-output (MIMO) radar system is presented. The EAPC array encode the transmit pulses for each transmit element, which can introduce additional controllable degrees-of-freedom (DOFs) in coding dimension at the transmit elements. Then, with the DOFs in transmit, receive and pulse dimensions, the coding-angle-Doppler processing can be performed. The echoes from different range-ambiguous regions can be well separated in joint transmit-receive spatial frequency domain by properly designing the EAPC shift factor. In the sequel, the three-dimensional localization (3DL) technique is employed to suppress the range ambiguous clutters, which can evidently reduce the dimensions of the processor. Finally, the results of the experiments based on simulated data demonstrate that the proposed framework can effectively alleviate the space-time adaptive processing (STAP) performance degradation resulting from the range ambiguity.

It is well known that classic direction-of-arrival (DOA) estimation methods yield poor accuracy and low resolution in the presence of mutual coupling and non-uniform noise. To tackle this problem, a DOA estimation method for jointly optimizing noise-free covariance matrix and mutual coupling coefficient is proposed in this paper. Based on the least squares (LS) criterion, the signal subspace and noise-free covariance matrix under mutual coupling can be obtained in an iterative manner. With the determined signal/noise subspace, the mutual coupling matrix can be reconstructed and the covariance one is estimated after mutual coupling compensation. Finally, the noise-free covariance matrix is preprocessed by spatial smoothing strategy and then used to determine the DOAs with the help of traditional DOA estimators. Compared to the conventional DOA estimation methods, simulation results demonstrate that, the proposed method can suppress the non-uniform noise significantly, alleviate the effect of mutual coupling on spatial smoothing technique obviously, as well as improve the DOA estimation performance in the case of coherent signals considerably.

The conventional robust beamformers based on worst-case performance optimization suffer from difficulty in selecting an appropriate size of the uncertainty set. Besides, their performances degrade dramatically if large steering vector mismatch occurs. In this paper, we propose a semidefinite programming (SDP) based robust beamformer using multiple small uncertainty sets where these sets are used to describe the desired steering vector in the possible large uncertainty region. To solve the nonconvex original problem, we relax the constraints and then recast it in high dimension. By using multiple constraints relaxation, we obtain the optimal solution of the beamformer. Simulation results indicate that the proposed method offers a significant performance improvement in case of large steering vector mismatch.

For the purpose of target parameter estimation of the orthogonal frequency-division multiplexing (OFDM) radar, a high-resolution method of joint estimation on range and direction of arrival (DOA) based on OFDM array radar is proposed in this paper. It begins with the design and analysis of an echo model of OFDM array radar. Since there is no coupling between range and angle parameter estimation for a narrow-band signal, a method which exploits the data of one snapshot to estimate the range and angle of the target by means of multiple signal classification (MUSIC) based on virtual two-dimensional spatial smoothing in range and angle dimensions is devised. The proposed method is capable of joint estimating the range and DOA of the target in a high resolution under a single snapshot circumstance. Simulation experiments demonstrate the validity of the proposal.

Bi-static circular synthetic aperture radar (BCSAR) can realize high resolution imaging of the complex scenario and avoid sheltering due to the straight line propagation of wave. However, it still encounters ring effect and high sidelobe problem due to the discontinuity of Fourier sampling space and limited signal bandwidth, which causes severe performance degradation in practical applications. In this paper, a new BCSAR, referred to as geometric diversity based BCSAR (GD-BCSAR) is presented, then its Fourier sampling space and image resolution are studied. GD-BCSAR breaks through the limitation of signal bandwidth, it can obtain a greater area in Fourier sampling space even with narrow bandwidth, and decrease the discontinuity of Fourier sampling space, thus, eliminating the ring effect and resulting in an improvement in sidelobe reduction. The simulated results are presented to verify the effectiveness and superiority of the proposed GD-BCSAR framework and the corresponding imaging algorithm.

As a special type of coherent collocated Multiple-Input Multiple-Output (MIMO) radar, a circulating space-time coding array (CSTCA) transmits an identical waveform with a tiny time shift. It provides a simple way to achieve a full angular coverage with a stable gain and a low sidelobe level (SLL) in the range domain. In this paper, we address the problem of direction-of-arrival (DOA) estimation in CSTCA. Firstly, we design a novel two-dimensional space-time matched filter on receiver. It jointly performs equivalent transmit beamforming in the angle domain and waveform matching in the fast time domain. Multi-beams can be formed to acquire controllable transmit freedoms. Then, we propose a beamspace multiple signal classification (MUSIC) algorithm applicable in case of small training samples. Next, since targets at the same range cell show characteristics of coherence, we devise a transformation matrix to restore the rotational invariance property (RIP) of the receive array. Afterwards, we perform spatial smoothing in element domain based on the transformation. In addition, the closed-form expression of Cramer-Rao lower bound (CRLB) for angle estimation is derived. Theoretical performance analysis and numerical simulations are presented to demonstrate the effectiveness of proposed approaches.