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The Wigner–Ville distribution (WD) and ambiguity function (AF) are serviceable tools for the global analysis of non-stationary signals. However, when dealing with time-varying signals that exhibit changing characteristics and require real-time signal processing, they have high limitations due to the existence of cross-items. In this paper, we propose the short-time Wigner–Ville distribution (STWD) as a novel approach that effectively analyzes time-varying signals with changing characteristics. First, the definition of STWD and short-time ambiguity function (STAF) and their properties are advanced. Next, three uncertainty principles that define the lower bound for the product of signal spread and its bandwidth are derived. Then, the discrete STWD (DSTWD) and the process of computerization are also proposed which can be used more widely in practice. Finally, the optimization of window functions based on Rényi entropy is discussed. Simulation experiments show that the STWD can be effectively applied for the analysis of local change characteristics and real-time processing of signals with valid and accurate results. • The short-time Wigner-Ville distribution (STWD) is proposed. • Three uncertainty principles of the STWD are derived. • Discrete STWD and window function optimization based on Rényi entropy are discussed. [ABSTRACT FROM AUTHOR]

• The proposed scheme is the first work for ambiguity attack of SDM watermarking. • The implementation of the scheme only requires a small cost. • Our method does not need the original training data. • The proposed method is effective to various SDM watermarking. In recent years, the text-to-image diffusion models have achieved excellent performance. Among them, stable diffusion models (SDMs) have become one of the most widely used models because of their excellent performance. Scholars have proposed many model watermarking techniques to protect the copyright of the text-to-image diffusion models. In order to measure the security and potential risks of the existing text-to-image diffusion model watermarking techniques, an ambiguity attack against the text-to-image diffusion model watermarking is proposed for the first time in this paper. Specifically, we take the SDMs as an example, take advantage of the reversibility of the model watermarking and combine the ideas of adversarial examples and discrete prompt optimization to re-embed a forged watermark in the watermarked SDMs, thus confounding the watermark containing copyright information. A large number of experiments show that our ambiguity attack is effective and can make the original watermark lose its uniqueness without changing the watermarked text-to-image diffusion models. [ABSTRACT FROM AUTHOR]

For pulse Doppler radars, targets become undetectable for Doppler frequencies in the detection-blind range occupied by the clutter Doppler spectrum. To overcome this problem, different Pulse Repetition Frequencies (PRFs) are used to search for targets with Doppler ambiguity and estimate their velocity, which is required for target tracking. Owing to the different PRFs used for velocity estimation, many beam dwells are required for illuminating the targets, Doppler compensation cannot be realized in a short time. In this paper, we propose a novel velocity estimation method that uses multicarrier signals in a single dwell. First, we obtain separated subcarrier signals from the echo signal and multiply some separated subcarrier signals by other separated subcarrier signals in a conjugate manner, obtaining Frequency-Converted Subcarrier (FCS) signals. We derive the potential ambiguous and unambiguous Doppler frequencies for the separated subcarrier and FCS signals, respectively, using a slow-time Discrete Fourier Transformation (DFT). Subsequently, the actual Doppler ambiguity number is derived from the results. Finally, the unambiguous Doppler frequency and target velocity are inferred. The effectiveness and superiority of the proposed method are validated by performing simulation studies. • Extending the unambiguous Doppler range. • Simple implementation. • Solving Doppler ambiguity at a PRF. [ABSTRACT FROM AUTHOR]

The coexistence of clutter range ambiguity and range dependence in the airborne forward-looking radar may render the common space–time adaptive processing (STAP) ineffective. To cope with this challenge, a novel vertical element-pulse coding (EPC) radar is proposed in our paper. Note that both the elevation angles and coding factors determine the transmitted spatial frequency of the proposed vertical EPC radar. Therefore, the clutters corresponding to different ambiguous areas can be distinguished in the spatial frequency dimension based on this property. The element-pulse decoding and pre-STAP filtering are devised to separate and extract these clutters corresponding to different ambiguous areas. In the following, the clutter elimination is independently accomplished for each ambiguous area that has been separated. Consequently, the clutter range ambiguity as well as clutter range dependence are addressed simultaneously. The efficacy of the proposed approach is verified with simulation experiments. • A general signal model of vertical EPC array radar is established. • Clutter properties are analyzed in the vertical spatial frequency domain. • Range-ambiguous clutter is separated using element-pulse decoding and pre-filtering. • The design criteria of the element-pulse coding factor are derived. [ABSTRACT FROM AUTHOR]

Range ambiguity is a significant challenge in conventional pulse-Doppler radar systems with medium or high pulse repetition frequencies, greatly impacting radar detection and imaging capabilities. The classic approaches such as waveform diversity and compressed sensing are based on the isolation between pulses. However, these methods encounter issues like residual ambiguity and grid mismatch, resulting in poor range ambiguity suppression performance. In this paper, the multiple signal classification-alternating projection (MUSIC-AP) method is proposed to address these challenges and achieve high-resolution estimation. The proposed method converts the range-velocity estimate into a spectrum estimate, enabling the utilization of the MUSIC algorithm to solve the grid mismatch problem and improve echo reconstruction. Then, to mitigate the effect of ambiguous energy on reconstruction, the MUSIC reconstruction subprocess is embedded into the AP framework. Through iterative approximation, the method gradually suppresses ambiguous and noise energy, thereby further enhancing the echo reconstruction accuracy and range ambiguity suppression performance. Simulations demonstrate the effectiveness of the proposed method. Moreover, algorithm analysis is conducted, considering aspects such as resolution, robustness, and sparsity, which provides a basis for parameter selection and applicability conditions. [Display omitted] • The range-velocity estimation is transformed into spectrum estimation problem. • Unambiguous range-velocity high-resolution estimation via the MUSIC algorithm. • The MUSIC is embedded into AP outer frame to gradually suppress ambiguity and noise. [ABSTRACT FROM AUTHOR]

• Phase ambiguity problem limits the development of broadband direction finding. • Constructing virtual arrays with different aperture sizes can solve the problem. • Multi-layer convolutional operation can construct virtual arrays with different sizes. • Error backpropagation algorithm can optimize the combination of virtual arrays. As the electromagnetic environment becomes more complex, radio direction finding systems need to cover a wide frequency range. However, the phase ambiguity of high frequency limits the development of broadband direction finding technology. The existing methods in solving the phase ambiguity problem heavily rely on designing the precise actual sparse array structure by theoretical derivation, which is expensive and time-consuming. To solve this problem, we propose a broadband direction finding method based on constructing virtual sparse arrays. First, we perform the convolutional operation on the direction feature matrix to achieve the weighted summation of the original baselines, which generates numerous virtual array elements and virtual baselines with different directions. The virtual array elements are combined to form virtual sparse arrays with different aperture sizes. Second, we optimize the parameters through the error backpropagation algorithm and obtain the optimal combination of virtual sparse arrays, which eliminates the phase ambiguity. Meanwhile, the virtual sparse arrays can maintain the advantages of sparse arrays, which can accomplish high-precision broadband direction finding. The experimental results demonstrate that the proposed method can solve the phase ambiguity problem effectively. It has high accuracy and strong robustness in simulation environment. [ABSTRACT FROM AUTHOR]

• A joint calibration method for the sensor positions, omnidirectional sensor gain and directional sensor phase is proposed. • The phase ambiguities due to the large mismatches in sensor positions of the highly deformed arrays are solved and ghost positions are efficively eliminated. • The Cramer–Rao lower bounds of unknown sensor gain/phase and position for wideband signals are derived. • The proposed method achieves high estimation accuracy and the Cramer–Rao lower bounds are well approached. A joint sensor position and gain/phase calibration method for highly deformed arrays is proposed. It applies to the case where the sensor gain is omnidirectional and frequency-invariant, and the sensor phase is directional and frequency-invariant. The method is initialized with the raw estimates of the sensor gains, which are simply obtained from the main diagonal elements of the sample covariance matrix. Then, it alternately updates either the sensor gain estimates or the sensor position and phase estimates while fixing the other. When the sensor gain estimates are available, the steering matrices for all the frequency bins are estimated using the constant modulus method. By combining all these steering matrices, the estimates of the sensor positions and the frequency-invariant sensor phases are straightforwardly derived. Then, the sensor gain estimates are refined for the next iteration by using the orthogonality of the subspaces. To resolve the phase ambiguities due to the large position mismatches of highly deformed arrays, the nominal intersensor distance and the array bending angle are used. The Cramer–Rao lower bounds (CRLBs) for the unknown sensor gain/phase and position are also derived. The performance of the proposed method is evaluated using simulation data and compared with the CRLBs. [ABSTRACT FROM AUTHOR]

• The signal model of bistatic FDA-MIMO STAP radar is derived. • The new 3D clutter characteristics of bistatic FDA-MIMO STAP radar are analyzed. • The proposed 3D filter has the advantage on training data selection. • The criteria for designation of Tx array parameters are provided. • Both problems of range dependence and range ambiguity in bistatic STAP are solved. Detection of moving targets under range-dependent clutter background is a challenging task in conventional bistatic space-time adaptive processing (STAP) radar. It is more intractable in the presence of range ambiguity, which also results in parameter estimation ambiguities. To tackle these issues, this paper proposes a novel framework of bistatic multiple-input multiple-output (MIMO) STAP radar with frequency diverse array (FDA) as the transmit array. The FDA employs a micro frequency increment across the array elements. Therefore, it is capable of providing additional degrees-of-freedom (DOFs) in range domain in the transmit end. After combining the DOFs in transmit, receive and pulse dimensions, the clutter or target of bistatic FDA-MIMO radar possesses the following properties: (i) for a particular range region, the clutter ridges of all range bins are located in a common plane of the three-dimensional (3D) space. (ii) By properly designing the frequency increment of FDA, the clutter ridges from different range regions are located in distinct 3D planes and thus are discriminable in 3D space. (iii) As long as the sum of the target radial velocities relative to the transmitter and the receiver is unequal to zero, the target will not be located in these clutter planes. By exploiting these new properties, a 3D localized space-time-range adaptive processing (STRAP) approach is presented to realize clutter suppression. It evidently reduces the computational complexity and the requirement for the amount of training data. Several numerical examples are provided to demonstrate the superiority of the proposed technique over the existing techniques. [ABSTRACT FROM AUTHOR]

• We quantitatively derive the relationship between spatial angle and frequency points. The transmit beampattern design problem can be transformed into the simple spectral shaping issue in coherent FDA. • We devise the piecewise LFM waveform to synthesize the desired beampattern. It enjoys the advantage of constant modulus, reduced computation complexity and low sidelobe level. • We derive the transmit beampattern response and the multi-dimensional ambiguity function to evaluate relevant properties in range and angle domain. 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. [ABSTRACT FROM AUTHOR]

• Combining the advantages of the phase-coded signal and LFM signal, a waveform with good Doppler tolerance and low sidelobe levels is designed. • The shape of the ambiguity function is designed directly without similarity constraints to obtain better degrees of freedom. • A fractional programming problem is constructed to minimize the ratio of the peak sidelobe level to the minimum mainlobe level in order to obtain good Doppler tolerance and low peak sidelobe levels. • Experimental results demonstrate that the designed waveform is applicable for high-speed moving target detection. Although the thumbtack-type ambiguity functions (AF) of the existing phase-coded signals are of good range-Doppler resolutions, they are not suitable for detection of high-speed targets due to their poor Doppler tolerance. In this paper, we address the design of waveform with good Doppler tolerance, which is expected to be of both diagonal-ridge-type AF and also local low peak sidelobe level (PSL). First we formulate the design model of Doppler tolerant waveform via minimizing the ratio of PSL to the minimum mainlobe level. Then, we solve the resulting fractional programming problem via quartic polynomial transfer and high-order polynomial optimization. Numerical results demonstrate the excellent Doppler tolerance and low PSL performance of our design. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional (2-D) direction-of-arrival (DOA) estimation method for a mixture of circular and strictly noncircular signals is presented based on a uniform rectangular array (URA). We first formulate a new 2-D array model for such a mixture of signals, and then utilize the observed data coupled with its conjugate counterparts to construct a new data vector and its associated covariance matrix for DOA estimation. By exploiting the second-order non-circularity of incoming signals, a computationally effective ESPRIT-like method is adopted to estimate the 2-D DOAs of mixed sources which are automatically paired by joint diagonalization of two direction matrices. One particular advantage of the proposed method is that it can solve the angle ambiguity problem when multiple incoming signals have the same angle θ or β . Furthermore, the theoretical error performance of the proposed method is analyzed and a closed-form expression for the deterministic Cramer-Rao bound (CRB) for the considered signal scenario is derived. Simulation results are provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• The proposed method can simultaneously correct the complex DFBs with a one-step process of matrix multiplication, thereby simplifying the corrections of different order DFBs. • The improved time-scaled transform is proposed to correct the linear RCM without searching the Doppler ambiguity number. • The proposed method achieves well-focused result without searching and estimating the target's unknown parameters. • The proposed method is simple to implement and computationally efficient. Maneuvering target presents a great threat for radar detection applications. The complex unknown motions between radar and maneuvering target seriously affect the performance of target coherent integration. Existing methods utilizing parameter search or estimation are limited by the high computational burden and the propagation errors of different parameter estimations. In this study, a fast nonparametric estimation method is proposed for coherent integration of maneuvering target. Firstly, the second-order Keystone transform is adopted to eliminate the quadratic range cell migration (RCM). Secondly, the modified range frequency reversal process is proposed to simultaneously remove the complex low- and high-order Doppler frequency broadenings (DFBs) by a one-step matrix multiplication operation. Subsequently, the residual RCM is corrected by the proposed improved time-scaled transform without searching for the Doppler ambiguity number, and then a well-focused result can be obtained. The proposed method is simple to implement and computationally efficient given that searching and estimation of parameters are avoided. It also addresses the high-order DFB and blind speed sidelobe. The processing results of simulated and real data are presented to verify the performance of the presented approach. [ABSTRACT FROM AUTHOR]

• A generalized ambiguity function (GAF) signal model of FDA radar based on transmitting beamspace is established. • Based on the proposed FDA radar GAF signal model, its range resolution, angular resolution, and Doppler resolution are analyzed. • A method to improve the performance of FDA radar GAF by optimizing the transmitting beamspace is proposed, and its correctness is verified by simulation. • The transmitting beamspace optimization problem is modeled as a quasi-convex optimization problem, which can be efficiently solved using Matlab's CVX toolbox. The ambiguity function is a conventional method to evaluate the performance of radar waveform. Currently, the existing letter only evaluation the Frequency Diversity Array (FDA) radar generalized ambiguity function (GAF) that transmits coherent or orthogonal waveforms. No literature discusses the GAF performance of FDA radar transmission arbitrary waveforms. We implement a general GAF performance evaluation with the transmitting beamspace-based FDA radar. Then, we improve the performance of the GAF through beamspace optimization by semidefinite programming (SDP), essentially the waveform design of the FDA radar. The theoretical analysis and numerical calculation results show that the FDA radar can improve its range and angular resolution by optimizing the emission waveform. [ABSTRACT FROM AUTHOR]

• A novel coupling KF problem of model uncertainty and non-Gaussian noise is solved. • A novel MEE criterion minimax Wasserstein distribution Kalman Filter is proposed. • The proposed algorithm is proven to be convergent. • The proposed algorithm is effectiveness verified in typical simulation scenarios. Recently, the divergence-based minimax approach was proposed and introduced to robust Kalman filtering under model uncertainty and Gaussian noise, and it significantly outperformed the standard Kalman filter. In this study, we consider a new Wasserstein-distribution based Kalman filter in which model uncertainty and non-Gaussian noise exist simultaneously. First, we construct a joint Gaussian distribution of states and observations in state space. Then, we set the equivalent estimator joint Gaussian distribution as a Wasserstein ambiguity set allowable neighborhood centered on the true distribution. Thus, the estimator distribution problem is transformed into a minimax problem, and the model uncertainty is tolerated accordingly. Subsequently, we introduce minimum error entropy to optimize the minimax problem based on Wasserstein ambiguity sets, so as to handle the influence of non-Gaussian noise. The minimax problem constrained by the minimum error entropy is transformed into a semi-positive definite convex optimization problem. By constructing two iterative sub-problems that are mutually conditional, the nonlinear semi-definite program finite convex optimization problem is solved. Finally, the minimum error entropy Wasserstein distribution Kalman filter algorithm is proposed. Additionally, the convergence of the proposed algorithm is clarified, and its effectiveness verified by comparing a series of algorithms in typical simulation scenarios. [ABSTRACT FROM AUTHOR]

In modern electronic warfare, artificial repeat jamming from hostile jammers and range-Doppler sidelobe interference from strong scatterers seriously affect target detection performance. Most of the existing anti-jamming methods are proposed for one of them. In this paper, we propose a pulse diversity phase coded (PDPC) waveform design scheme based on periodic ambiguity function (PAF) shaping. This method can minimize the jamming energy in the target detection area and has significant applications in the radar anti-jamming field. We first define the PDPC waveform and analyze its characteristics. On this basis, the principle of jamming suppression based on PDPC waveform PAF shaping is discussed. Further, a closed-loop confrontation method including jamming cognition and suppression is proposed. Simulation examples demonstrate that the proposed method can comprehensively call waveform optimization resources to suppress two kinds of jamming simultaneously and possess better jamming suppression performance. [ABSTRACT FROM AUTHOR]

• Critical survey of existing performance indices. • Introduce an index, called CorrIndex, whose reliability is proved theoretically. • Provides interpretable upper and lower bounds, with a low computational cost. • Possible applications include Blind Source Separation or Tensor Decompositions. Permutation and scaling ambiguities are relevant issues in tensor decomposition and source separation algorithms. Although these ambiguities are inevitable when working on real data sets, it is preferred to eliminate these uncertainties for evaluating algorithms on synthetic data sets. As shown in the paper, the existing performance indices for this purpose are either greedy and unreliable or computationally costly. In this paper, we propose a new performance index, called CorrIndex, whose reliability can be proved theoretically. Moreover, compared to previous performance indices, it has a low computational cost. Theoretical results and computer experiments demonstrate these advantages of CorrIndex compared to other indices. [ABSTRACT FROM AUTHOR]

• Nonlinear distortions are important issues in many communications systems. This work proposes original blind and semi-blind solutions for the identification of nonlinear, finite alphabet, multichannel systems. • The proposed solutions rely on the maximum likelihood approach and are based on the EM-algorithm. The blind one is initialized by a subspace method combined with an original ambiguity removal technique. They lead to a significant performance gain as compared to the state-of-the-art. • We provide theoretical performance bounds and identifiability results for the considered problem and show how our solutions can be extended to a large class of nonlinear models. • Our methods, not only outperform the existing solutions in the literature but also, allow to achieve channel estimation and data detection simultaneously. Nonlinear distortions are important issues in many communications systems. Therefore, this paper deals with the blind and semi-blind identification of nonlinear SIMO/MIMO channels. Quadratic and cubic nonlinearities are considered for the system model as well as a discussion on how the developed work can be extended to more general nonlinear models. The proposed blind solution is initialized by using a subspace approach, which is followed by an appropriate ambiguity removal method, then refined by a Maximum Likelihood (ML) based processing using the Expectation-Maximization (EM) algorithm. The proposed semi-bind solution, involving both data and pilots, is fully based on the EM algorithm. These solutions are supported by some identifiability results and performance bounds analysis related to the considered models (blind and semi-blind). Finally, simulation results essentially show that the proposed algorithms exhibit very attractive channel estimation performance, with interesting convergence speed for the EM-based iterative processing. [ABSTRACT FROM AUTHOR]

Abstract: Sparse linear arrays provide better performance than the filled linear arrays in terms of direction estimation and resolution with reduced size and low cost. However, they are subject to manifold ambiguity. A method based on the Multiple Signal Classification (MUSIC) algorithm to solve the manifold ambiguity of uncorrelated sources for sparse array is proposed in this paper. The method consists of two steps. The first step is to obtain all the directions of arrivals (DOAs), including true and spurious DOAs, using traditional MUSIC. The second step is to estimate the power values of the all DOAs by substituting all the DOAs to a cost function. The well-known Davidson Fletcher Powell (DFP) and Broyden Fletcher Goldfarb Shanno (BFGS) algorithms are used to estimate the power values. The power values of spurious DOAs are very small or tend to zero compared with the values of the true DOAs. The true DOAs are then discriminated easily from the spurious DOAs with the power values. Simulation results demonstrate the effectiveness and the feasibility of the method. [Copyright &y& Elsevier]

Abstract: In this letter, we discuss the problem of unfolding the frequency spectrum for undersampled wideband data. The problem is of relevance to state-of-the-art radio frequency measurement systems, which capture repetitive waveform based on a sampling rate that violates the Nyquist constraint. The problem is presented in a compact form by the inclusion of a complex operator called the CN operator. The ease-of-use problem formulation eliminates the ambiguity caused by folded frequency spectra, in particular those with lines standing on multiples of the Nyquist frequency that are captured with erroneous amplitude and phase values. [Copyright &y& Elsevier]

• The data model with the bistatic FDA-MIMO radar based on the subarray scheme is presented. • The real-valued subspace method for parameter estimation is provided. • The problem of false range estimation caused by phase ambiguity is analyzed and solved. • An original method is proposed to match the 3D parameter for multi-objective case. The frequency diverse array (FDA) is mainly applied to achieving target localization under the complicated electromagnetic jamming condition. The bistatic multiple-input-multiple-output (MIMO) radar with FDA has gained comprehensive attention in recent years. An innovative method covering the transmitting subarray scheme and the unitary estimation of signal parameters via rotational invariance technology (ESPRIT) is proposed for joint direction of departure (DOD), direction of arrival (DOA), and range estimation. First, a non-overlapping subarray scheme is designed for the transmitting array to decouple DOD and range. For the purpose of enhancing the estimation accuracy and reducing the computational complexity, the real-valued rotational invariance matrix is obtained via applying the unitary transformation to the extended data. The removal method is proposed to avoid the periodic phase ambiguity. The pairing method is put forward to achieving the match of three-dimensional parameter (DOD, DOA and range) for multiple targets. The computational complexity of the proposed algorithm and conventional ESPRIT algorithm are also provided. Finally, extensive experiment results indicate that the proposed algorithm shows the superior performance than the ESPRIT algorithm. [ABSTRACT FROM AUTHOR]

In this paper, ambiguities associated with the geometry of star arrays are studied. The angles between the various axes of a star array are very crucial, in the sense that, if not chosen properly, they give rise to inherent ambiguities. Such inherent ambiguities pose serious problems—they exist regardless of the number of sensors and inter-sensor separations. Fortunately, such ambiguities can be removed by suitable choices of the angles between the axes. The inherent ambiguities associated with uniform circular arrays are also studied. [Copyright &y& Elsevier]

• We describe and analyze a new statistical model, termed Wrapped Ambiguity Gaussian Mixed Model, and show its potential applications in undersampling multiple parameter reconstruction. • We present two efficient algorithms to address the estimation problem in the proposed model, where one is based on clustering and the other is in an iterative searching manner to approximate the maximum a posteriori estimation. • We further show how error correcting coding can further improve the robustness. Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our knowledge, it is the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation. Two novel approaches are established to deal with the problems of ambiguity resolution in parameter estimation. One is to directly calculate a conditional maximum a posteriori probability (MAP) estimation of the residue clustering, and the other is based on a generalized wrapped Gaussian mixture model to iteratively search for MAP of both estimands and clustering. Furthermore, residue error correcting codes are introduced to improve the robustness further. The experimental results show that the statistical schemes achieve much stronger robustness compared to state-of-the-art deterministic schemes, especially in heavy-noise scenarios. [ABSTRACT FROM AUTHOR]

• We demonstrate that the ambiguity of a dictionary cannot be resolved, even when the true sparse vector and sensing matrix are obtained. • We demonstrate that the relative accuracy of sparse vector and signal estimation is proportional to the relative perturbation of dictionary. • Our analysis revealed that there is no trade-off in the precision of simultaneous estimates of the true sparse vector, signal, or dictionary (i.e., no need to reduce the precision of one to increase the precision of others); and. • We numerically verify the tightness of our analytical bounds. An imprecise dictionary is commonly used in compressed sensing in cases where the dictionary is derived via a learning process or is based on incomplete prior knowledge. This paper investigates the issue of ambiguity in dictionary estimation and the sensitivity of a true sparse vector and signal (i.e., signals represented by true sparse vectors with respect to the true dictionary) to dictionary perturbations in compressed sensing. We first demonstrate that the inherent ambiguity in dictionary estimation cannot be resolved, even when the desired sparse vector can be obtained. By imposing conditions on the perturbation of the true dictionary, we then demonstrate that the sparse vector and signal can both be stably estimated within the bounds of the dictionary perturbation. Our analysis results are based on the condition that AD holds the restricted isometry property (RIP), where A is a precise sensing matrix and D is a dictionary mismatch. The RIP of AD cannot be efficiently determined for a general over-complete dictionary; therefore, we numerically verified our analytical results by conducting experiments under the specific but commonly encountered situation in which D (an orthonormal matrix) and A (a Gaussian sensing matrix), in which the RIP of AD holds with a high degree of probability. [ABSTRACT FROM AUTHOR]

• A two-level sparse nested array configuration is proposed for aperture extension to realize the highly accurate angle estimation. • By exploiting the proposed SNA, an ESPRIT-based algorithm is developed to extract two sets of angle estimates: a set of coarse estimates and a set of fine but ambiguous estimates. Fine and unique angle estimates are then obtained by a simple refine step. • The SNA concept herein proposed may also be applied to other types of nonuniform arrays for highly accurate angle estimation with increased degrees-of-freedom. Sparse nested arrays (SNAs) are presented for highly accurate angle estimation. A nested array is sparse if its sensor-spacing of the first level is extended beyond a half-wavelength. Each array grid is equipped with an identical two-component subarray, such as a half-wavelength spaced doublet, a spatially-colocated p-u probe and a spatially-orthogonal dipole/loop pair, to solve angle ambiguities caused by aperture extension. [ABSTRACT FROM AUTHOR]

• Statistical approach for radar ambiguity function optimization is proposed. • A code defining the waveform and resulting from a random variable with an appropriate distribution allows a good ambiguity function. • The chaotic codes generated by the skew tent map have almost the desired statistical properties. • The ambiguity function allowed by theses chaotic codes still present high side lobe peaks for time delays close to zero. • This drawback is avoided by down-sampling the considered chaotic sequences. In this paper we adopt a statistical approach to optimize the ambiguity function of a radar system. By considering the codes defining the transmitted waveform as realizations of a random variable we firstly show that a suitable distribution of the random variable allows to obtain good codes. Secondly we show that using the chaotic skew tent map it is possible to generate deterministic codes having the desired statistical properties. This allows to obtain an optimized global ambiguity function of the radar system. The advantage of using chaos-based sequences is that they can be easily generated in any length and number. We further improve their performance by introducing down sampling. It appears that the proposed sequences have performance quite similar to those of the sequences of the literature computationally optimized. [ABSTRACT FROM AUTHOR]

• Doppler ambiguity and acceleration reduce the integration gain of conventional coherent detection methods. • The frequency scope of DFT is extended by reintroducing its redundant period to estimate the under-sampled Doppler frequency. • The scaling and product operations are used to eliminate the couplings and suppress the grating lobes. • A good balance is achieved between computational complexity and detection performance. This paper considers the coherent integration problem for Doppler-ambiguous maneuvering target. A novel method based on the product scaled periodic Lv's distribution (PSPLVD) is proposed. To be specific, the acceleration could be accurately estimated via Lv's distribution (LVD). Then, the periodic discrete Fourier transform (DFT), which periodically extends the frequency scope of DFT, is introduced to modify the LVD to estimate the unambiguous centroid frequency. Thereafter, scaling and product operations are respectively employed to eliminate the coupling and suppress the grating lobes. Finally, coherent integration is achieved after compensating off the range migration and Doppler frequency migration. Cross term analysis indicates the applicability in the scenario of multiple targets. Efficient implementation based on chirp-z transform is also presented to alleviate the computational burden and eliminate the brute force searching procedure. Detailed comparisons with several representative methods lead us to conclude that the proposed method could strike a good balance between computational cost and detection probability. Extensive simulations and real data processing results are provided to verify the proposed method. [ABSTRACT FROM AUTHOR]

• The analytical expression of the null spectrum that reveals the relationship among ambiguity, frequency pattern and target relative location is derived. • Three types of target relative locations and two exceptional cases that may cause ambiguity are introduced via the null spectrum analysis. • A series of criteria for identifying unambiguous frequency patterns for two-target localization is proposed. Frequency diverse arrays (FDAs) with random frequency patterns can decouple range and angle with high probability only when the number of elements is sufficiently large. For small-scale arrays, some approaches are developed to identify unambiguous random frequency patterns for a single target. However, for two or more targets, the ambiguity depends not only on the frequency pattern but also the relative location of the targets. Identification is challenging because of the complicated relationship among ambiguity, frequency pattern and target relative location. In this paper, a series of criteria for identifying unambiguous frequency patterns for two-target localization is proposed. The analytical expression of the null spectrum that reveals the relationship among ambiguity, frequency pattern and target relative location is derived. Three types of target relative locations and two exceptional cases that may cause ambiguity are introduced via the null spectrum analysis. Each of the ambiguity conditions leads to a corresponding criterion, which results in the series of criteria proposed. These criteria can provide guide for frequency pattern design in practical application. Numerical simulations illustrate the effectiveness of the proposed unambiguity identification criteria. [ABSTRACT FROM AUTHOR]

Frequency diverse array (FDA) has received much attention in recent years. Different from classic phased-array (PA) that uses the same carrier frequency for all array elements, FDA adopts a small frequency increment across its array elements to produce angle, range and even time dependent transmit beampattern, which provides many promising applications, but it may result in time- and spatial-variant clutter characteristics. Since the impacts of FDA on radar clutter structures and characteristics still have not been systematically investigated, this paper studies range-ambiguous clutter characteristics for airborne FDA radar including FDA multiple-input multiple-output (FDA-MIMO) radar and coherent FDA radar systems. The corresponding receiver filtered signal models are formulated, and the clutter rank in different scenarios are analyzed. Moreover, by exploiting FDA range-dependent beampattern, we propose a method to distinguish range-ambiguous clutter in airborne FDA radar. Both theoretical analysis and simulation results validate the superiority of FDA radar over traditional PA and MIMO radars in suppressing range-ambiguous clutter and FDA-MIMO radar achieves better suppression performance than coherent FDA radar. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

High-resolution and wide-swath (HRWS) imaging is highly desired in future synthetic aperture radar (SAR) systems. However, it is a contradictory requirement between high azimuth resolution and wide unambiguous swath coverage in a traditional SAR system. This paper proposes a novel solution to realize HRWS imaging by resolving the range ambiguity through a phase coding technique. The phase coding is employed in both spatial channels and slow time pulses. By properly designing the coding scheme, it is possible to separate the echoes from multiple ambiguous range regions from each other in the spatial domain. For each particular range region, the corresponding optimized receive beampattern can be used to extract the desired echoes from the presumed range region and suppress the undesired echoes from other range-ambiguous regions. The residual range-ambiguous echoes are also addressed. Specifically, it is capable of further mitigating the residual range-ambiguous echoes by optimally designing the coding scheme and the transmit beampattern. In the final, a bank of imaging processors can be implemented to obtain the high-resolution images of these range regions, which can be synthesized into a whole HRWS SAR image of the scene of interest. Simulation results have demonstrated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Broadband signal design formulation to minimize maximum sidelobe level with Doppler. • Biconvex optimization based solution to solve the signal design problem. • Computationally efficient version of the method to speed up method by 100x. • Study of tuning of free parameters tuning for good performance. • Demonstration of the method for a continuous active sonar application. Constant-modulus signals such as m-sequences are known to have good autocorrelation properties, as well as good peak-to-average power ratio that allows for full utilization of the transmitter's power. However, the broadband ambiguity surface for such signals exhibit high sidelobe levels that are undesirable in applications where the signal is subject to broadband Doppler. We formulate an optimization problem to minimize the maximum sidelobe levels of such signals over a set of delay-Doppler values. This problem is non-convex and difficult to solve. We explore a convex regularization of the problem that can readily be solved using semi-definite programming, and show that optimal or near-optimal signals can be designed using this method. We further explore some heuristic methods to reduce computational and memory complexity of the solution, to enable us to design longer signals. We demonstrate the advantage of our signal design over conventional unimodular signals for target detection in strong clutter in a continuous active sonar application. [ABSTRACT FROM AUTHOR]