Spatial Spectrum Estimation Research Articles

Beam-space spatial spectrum reconstruction under unknown stationary near-field interference: Algorithm design and experimental verification.

In acoustic array signal processing, spatial spectrum estimation and the corresponding direction-of-arrival estimation are sometimes affected by stationary near-field interferences, presenting a considerable challenge for the target detection. To address the challenge, this paper proposes a beam-space spatial spectrum reconstruction algorithm. The proposed algorithm overcomes the limitations of common spatial spectrum estimation algorithms designed for near-field interference scenarios, which require knowledge of the near-field interference array manifold. The robustness and efficacy of the proposed algorithm under strong stationary near-field interference are confirmed through the analysis of simulated and real-life experimental data.

Virtual Array-Based Signal Detection and Carrier Frequency Offset Estimation in a Multistatic Collaborative Passive Detection System

To tackle the problem of difficult signal detection and carrier frequency synchronization faced by wireless communication among stations of the multistatic passive detection system in interference environments, an adaptive signal detection and carrier frequency offset (CFO) estimation method based on a virtual array is proposed in this paper. This is a data-aided method that utilizes a training sequence composed of three segments of sub-training sequences with different symbols. This method first uses spatial spectrum estimation to obtain the coarse frequency estimations of interference signals and CFO from virtual array signals constructed from the first two sub-training sequences. Then, beamforming is conducted accordingly on the virtual array signals constructed from the third sub-training sequence to suppress the in-band interferences and protrude the expected signal. Finally, improved performance of signal detection and CFO estimation is obtained with the beamformed signals. Simulation experiments show that a missed detection probability as low as 1 × 10−4, with a false detection probability of 1 × 10−3, can be obtained under a signal-to-interference ratio (SIR) of −10 dB and Eb/N0 of 1 dB. Moreover, the proposed method can also simultaneously achieve a CFO estimation error that is lower than 3%, with the condition of Eb/N0 being as low as −5 dB under different SIRs. Simulation results validate the proposed method and demonstrate the promising application prospects of the proposed method in networked passive detection scenarios.

Spatial Spectrum Estimation of Weak Scattering Wave Signal in Range-Doppler Domain

How to enhance the desired signal with low signal-to-noise ratio (SNR) is a difficult problem in the estimation process of the direction-of-arrival (DOA) of the target scattering wave signal. In this paper, the feasibility of spatial spectrum estimation in the Range-Doppler (RD) domain is analyzed in principle, and the SNR gain expression of weak scattering wave signal is derived when constructing multi-snapshots virtual array data. On this basis, the mutual eigenvector singular value decomposition (MESVD) method based on RD domain mode excitation is proposed, which can robustly and effectively estimate the direction of the coherent weak signals. Simulation experiments verify that the RD domain spectral estimation method has the ability to simultaneously obtain the direction of multiple weak target scattering waves, and the direction-finding accuracy can reach the Cramer–Rao bound (CRB) of conventional spectral estimation method. The results of Monte Carlo experiments show that the root-mean-square-error (RMSE) of azimuth estimation of RD domain spatial spectrum estimation method is 5.76° lower than that of a conventional multiple signal classification (MUSIC) method. In addition, the practicability of the proposed method is demonstrated by comparing the DOA estimation results of a set of real data with Automatic Dependent Surveillance-Broadcast (ADS-B) data.

Super-resolution spatial spectrum reconstruction under unknown near-field interferences

In underwater acoustic signal processing, conventional spatial spectrum estimation and the associated direction-of-arrival estimation are often impaired by strong near-field interferences at the same frequency as the far-field target signal, leading to significant performance degradation and even detection failure. In contrast to prevalent near-field interference suppression algorithms that require prior knowledge of near-field interference positions, this paper proposes a super-resolution spatial spectrum reconstruction algorithm designed for more general scenarios where crucial information about the near-field interference, such as positions and magnitudes, is unknown. The proposed algorithm demonstrates its adaptability in mitigating unknown near-field interference and achieves this by leveraging rank constraint-based relaxation and alternating minimization, resulting in an effective spatial spectrum reconstruction strategy. The efficacy of the proposed spatial spectrum reconstruction method in handling strong near-field interference is confirmed through analysis of simulated and synthetic experimental data. It exhibits superiority over traditional competitors in terms of resolution, denoising capabilities, and estimation accuracy. Moreover, it achieves comparable results to algorithms that utilize prior information about near-field interference positions. The enhanced performance remains consistent even in challenging scenarios such as snapshot deficiency and low signal-to-noise ratios.

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

Neural-Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.

Toeplitz Matrix Reconstruction Algorithm for Rectangular Hollow Array

Among the directional angle calculation models of Bluetooth 5.1, the rectangular hollow array offers the advantage of shorter sampling time due to its fewer elements compared to traditional planar arrays. However, the antimultipath algorithms suitable for traditional planar arrays cannot be applied to rectangular hollow arrays. Therefore, this study proposes a virtual array filling algorithm, wherein four virtual matrices are inserted into the hollow matrix to transform the array into a uniform rectangular array. This algorithm ensures translation invariance of the rectangular array, enabling the application of the antimultipath coherent source algorithm to a rectangular hollow array. An algorithm for reconstructing Toeplitz matrices in two‐dimensional uniform planar arrays is also proposed. Through the analysis of the spatial spectrum and angle estimation results of various algorithms, the effectiveness of the signal angle of arrival estimation theory is verified.

Altitude measurement method of VHF radar based on spatial smoothing of correlation matrix

For very high frequency (VHF) phased array radar, the key problem to be solved in altitude measurement is the super-resolution spatial spectrum estimation under the condition of coherent sources. The spatial smoothing algorithm is a kind of decorrelation algorithm with excellent properties, but the decorrelation process is at the expense of the effective array aperture. Because it only uses the autocorrelation information of the subspace, its performance is significantly reduced, when the positions of the coherent sources are very close. In order to solve the above problems, this paper proposes an altitude measurement method of VHF radar based on the space smoothing of autocorrelation and cross-correlation matrix, which is used to realize the correlation and super-resolution processing of echo signals and multipath signals. The proposed method does not need to construct a weighting matrix, and can make full use of the received data, enhance the signal components in the equivalent spatial smoothing matrix, reduce the impact of noise, and improve the resolution of coherent sources. The simulation results show that the weighted spatial smoothing method proposed in this paper is correct and effective.

Fast and accurate wideband sparse spatial spectrum estimation in an underwater strong interference environment.

Wideband sparse spatial spectrum estimation is an important direction-of-arrival (DOA) estimation method that can obtain a high resolution with few snapshots and a low signal-to-noise ratio. However, in an underwater strong interference environment, the accuracy of DOA estimation may be seriously affected, and even the weak targets could be completely masked. In this paper, we propose a fast matrix filter design method based on truncated nuclear norm regularization to attenuate strong interferences while passing weak targets. The matrix filter operator and the exact covariance matrix after filtering can be obtained simultaneously by solving a convex optimization problem that contains the output power term and non-Toeplitz error propagation control term. Then the modified sparse spectrum fitting algorithm based on the matrix filter is used to estimate spatial spectrum over closely spaced wideband signals. Compared with existing methods, the proposed method achieves higher DOA estimation accuracy and lower computational time for matrix filter design. Meanwhile, the estimation accuracy of the proposed method is verified with the experimental results.

Enhanced approach to fusing automatic characteristic frequency extraction and adaptive array signals weighting for abnormal machine sound localization

In this paper, an enhanced approach for sound localization is proposed, which fuses automatic extraction of array signal characteristic frequencies and adaptive weighting. The method refines the autoregressive power spectral estimation algorithm and improves density-based spatial clustering of applications with noise algorithm for characteristic frequency extraction. Adaptive weighting technique is introduced to alleviate the problem of frequency mismatch in the localization process. The initial weight of narrowband signals is calculated and normalized using the frequency domain amplitude integration of narrowband signals, followed by adaptive threshold correction to eliminate invalid narrowband signal weights. The adaptive weight vector improves the localization method’s accuracy and interference suppression. The effectiveness and universality of the proposed method are demonstrated with test data from dry transformers and pumps, and its applicability is shown to extend to various spatial spectrum estimation algorithms and deep learning-based sound source localization techniques.

A Separation Method for Electromagnetic Radiation Sources of the Same Frequency

To separate electromagnetic interference sources with an unknown source number, a new separation method is proposed, which includes five key steps: spatial spectrum estimation, source number and direction-of-arrival estimation, mixed matrix estimation, separation matrix estimation, and source signal recovery. A pseudospatial spectrum estimation network based on a convolutional neural network is proposed to estimate the number of electromagnetic radiation sources, their direction of arrival, and the mixing matrix. A new loss function is designed as an optimization criterion for estimating the separation matrix. To ensure generalization, both simulated and measured datasets are used to train the proposed network. Experimental results demonstrate that the proposed separation method outperforms existing source separation techniques in terms of correlation coefficient, root mean square error, and running time. Importantly, it exhibits strong performance in underdetermined cases, as well as in overdetermined or determined cases.

Retracted: A Spatial Spectrum Estimation Method for Optimization and Improvement of Resource Allocation and Management of Public Sport and Health Facilities.

[This retracts the article DOI: 10.1155/2022/3800237.].

A survey of GNSS interference monitoring technologies

With the increasing economic and strategic significance of the global navigation satellite systems (GNSS), interference events also occur frequently. Interference monitoring technologies aim to monitor the interference that may affect the regular operation of the GNSS. Interference monitoring technologies can be divided into three parts: interference detection and recognition, interference source direction finding, and interference source location and tracking. Interference detection aims to determine whether interference exists. This paper introduces the classification of interference and the corresponding detection methods. The purpose of interference recognition is to recognize and classify interference. It is often combined with pattern recognition and machine learning algorithms. Interference source direction finding aims to estimate the direction of the interference signal. There are three kinds of methods: amplitude, phase, and spatial spectrum estimation. Interference source location aims to estimate the position of the interference signal. It is usually based on the received signal strength (RSS), time difference of arrival (TDOA), frequency difference of arrival (FDOA), angle of arrival (AOA) or direction of arrival (DOA). Interference source tracking aims to track moving interference sources, and it is generally based on Kalman filter theory. This paper summarizes the interference monitoring technologies and their latest progress. Finally, prospects for interference monitoring technologies are offered.

Improved Coprime Array Designs Based on Moving Platform for Direction of Arrival Estimation

In this article, we mainly propose two improved coprime arrays (CAs) on array motion, ImCAAM1 and ImCAAM2, for direction of arrival (DOA) estimation, which can generate a longer consecutive difference co-array. Both the designs can solve the problem that part of lags, not surrounded by holes in difference co-array, have invalid use, when considering moving sparse array. The first scheme primarily implements two operations: compressing the interelement spacing of one subarray and staggering a certain distance between two subarrays. Two operations make contributions to increasing consecutive degrees of freedom (cDOF). Whereas the second one is able to further fill the remaining holes located at both the ends of virtual array. With the interelement spacing compress factor, equal to the number of elements of another subarray, and re-staggering the distance between subarrays, we can eventually obtain a longer full-populated virtual array. Finally, numerical simulations are presented to verify the efficacy of the proposed sparse array geometries using the subspace-based DOA estimation algorithm in terms of cDOF, spatial spectrum, and DOA estimation accuracy.

Broadband Spatial Spectrum Estimation Based on Space-Time Minimum Variance Distortionless Response and Frequency Derivative Constraints

The two-dimensional optimization capability of the space-time minimum variance distortionless response (STMVDR) can improve the spatial spectrum estimation performance of the broadband beamformer with limited samples, but its high sensitivity to frequency errors may lead to the suppression of some narrowband signals not at the grid point of the frequency response calculation. In order to reduce the sensitivity of STMVDR to frequency errors, a broadband spatial spectrum estimation method based on STMVDR and frequency derivative constraints is proposed in this paper. First, based on the beam response of the STMVDR beamformer, an arbitrary order frequency derivative constraint is derived. Second, combining the gain constraint and frequency derivative constraint, the linear constrained minimum variance problem is established to solve the optimal weight of the beamformer. Finally, the calculation method of the broadband spatial spectrum is derived. Numerical simulations show that the proposed method not only solves the problem of frequency mismatch caused by the insufficient number of points for calculating frequency response, but also does not cause the spatial response related peaks to deviate from the true direction due to the broadening of the main lobe of frequency response. In addition, the proposed method can reduce the computational complexity of the algorithm by more than half by increasing the interval of the frequency calculation grid points, and does not significantly loss in the angular resolution capability and estimation accuracy of the algorithm.

Spatial Spectrum Estimation of Co-Channel Direct Signal in Passive Radar Based on Coprime Array

The received signal of passive radar based on mobile communication signals contains direct and multipath interference (DMI) signals from multiple co-channel base stations (CCBS). The direct signal spatial spectrum of each CCBS should be obtained first to eliminate the co-channel interference. The performance of the traditional spatial spectrum estimation algorithms based on uniform linear array (ULA) is related to the number of array elements. In the complex co-channel interference environment, the array requires an ultra-large number of array elements and the spatial spectrum estimation resolution is poor. This paper proposes a method for estimating the direct signal spatial spectrum of the CCBS by fusing coprime array and compressive sensing. Firstly, an augmented virtual array signal is constructed by using the second-order statistics of the received signals of the coprime array and then the compressive sensing algorithm is used to estimate the spatial spectrum of the direct signal of the CCBS. The proposed method can achieve higher resolution and higher-degrees-of-freedom (DOFs) performance than traditional ULA by using the same number of array elements. The effectiveness of the proposed method is verified by numerical simulation analysis and experimental data.

Sparse Bayesian learning-based spatial spectrum estimation for mobile sonar platforms during turning

Mobile sonar platforms usually experience turning in the course of travel. During turning, due to the change of heading, the steering vector of the sonar array is not constant, which will cause the widening of the spatial-spectral peaks or even fail to estimate target bearings. To deal with this problem, this paper first establishes a multi-snapshot fusion equation for observed data from different heading angles. Then, a sparse Bayesian learning-based method is utilized to solve the fusion equation and provides the estimate of the spatial spectrum. The simulation results exhibit that the proposed method can resolve the port and starboard ambiguity problem and provide high estimation accuracy with enough heading change information. The sea trial results validate its feasibility and stability for estimating far-field target bearings in practical applications.

Radar echo simulation of wind turbines array based on scattering center

PurposeThis paper aims to propose a method for accurate radar echo simulation of wind turbines (WTs) array. It can solve the problem of passive interference from wind farms to neighboring radar stations.Design/methodology/approachFirst of all, the equivalent model of scattering centers of a single WT is obtained by using the spatial spectrum estimation method, and the accuracy of this model is verified by the scaled model experiment; then scattering centers model of WTs array was established by using the spatial coordinate transformation method. According to the position relationship between the model and the radar, and combined with the multipath scattering theory, the radar echo equation of WTs array was deduced. Finally, the simulation analysis is carried out with the four GoldWind 77/1500 WTs as an example and compared with the traditional methods.FindingsThis paper verifies the accuracy of the equivalent model of scattering centers through the WT scaled model experiment, and through simulation analysis, it is found that the result of this method is more consistent with the multipath scattering of radar echo between WTs array in practical engineering than the traditional method.Originality/valueBased on the theory of high-frequency scattering, this paper introduces scattering centers into the solution of radar echo and considers the multipath scattering of radar echo, then a method for solving the radar echo of WTs array based on scattering centers is proposed.

Robust Beamforming Based on Covariance Matrix Reconstruction in FDA-MIMO Radar to Suppress Deceptive Jamming.

Frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radars can generate a range-angle two-dimensional transmit steering vector (SV), which is capable of suppressing mainbeam deceptive jamming in the transmit–receive frequency domain by utilizing additional degrees of freedom (DOFs) in the range dimension. However, when there are target SV mismatch, covariance matrix estimation error and target contamination, the jamming suppression performance degrades severely. In this paper, a robust adaptive beamforming algorithm for anti-jammer application based on covariance matrix reconstruction is proposed in FDA-MIMO radar. In this method, the residual noise is further determined by using the spatial power spectrum estimation approach, which results in improved estimation accuracy of the signal covariance matrix and the desired target SV. The jamming SV is obtained from vectors in the intersection of two subspaces (namely, the signal-jamming subspace derived from the sample covariance matrix (SCM) and the jamming subspace generated from the jamming covariance matrix) by an alternating projection algorithm. Furthermore, the jamming power is obtained by exploiting the orthogonality between the different SVs. With the obtained parameters of target and jamming, the optimal adaptive beamformer weight vector is calculated. Simulation results demonstrate that the proposed algorithm can cope with the mainbeam deceptive jamming suppression under various model mismatches and has excellent performance over a wide range of signal-to-noise ratios (SNRs).

Deviated Direction of Arrival Method for Radial Velocity Measurement based on Spatial Spectrum Estimation

In this paper, a new scheme to measure radial velocity based on direction of arrival (DOA) estimation with multiple signal classification (MUSIC) algorithm is proposed. The MUSIC algorithm usual applications in Uniforms Linear Arrays (ULA) don’t enable velocity estimation because the array signals in one snapshot are synchronous and the radial motion does not affect the steering vector. In the proposed scheme, signal snapshot is rearranged so that each vector now contains a sequence of signals from adjacent elements delayed in time, this way the steering vector input to the MUSIC algorithm includes both information of the DOA and radial velocity. An equation describing the relationship of the deviated DOA (dDOA) from the rearranged snapshot with the radial velocity and the DOA is presented. For multi-source situation, pairing problem of DOAs and dDOAs is solved by extracting the combination factors of the steering vectors and the eigenvectors in comparison between the two MUSIC implementations. Comparison with the traditional FFT method shows that a higher accuracy of velocity can be achieved by the proposed method.