Advances in Array Signal Processing with Errors: Models, Algorithms, and Applications

The utilization of efficient digital self-interference cancellation technology enables the simultaneous transmit and receive (STAR) phased array system to meet most application requirements through STAR capabilities. However, the development of application scenario requirements makes array configuration technology for STAR phased arrays increasingly important. Thus, this paper proposes a sparse shared aperture STAR reconfigurable phased array design based on beam constraints which are achieved by a genetic algorithm. Firstly, a design scheme for transmit and receive arrays with symmetrical shared apertures is adopted to improve the aperture efficiency of both transmit and receive arrays. Then, on the basis of shared aperture, sparse array design is introduced to further reduce system complexity and hardware costs. Finally, the shape of the transmit and receive arrays is determined by constraining the side lobe level (SLL), main lobe gain, and beam width. The simulated results indicate that the SLL of the transmit and receive patterns under beam-constrained design have been reduced by 4.1 dBi and 7.1 dBi, respectively. The cost of SLL improvement is a reduction in transmit gain, receive gain, and EII of 1.9 dBi, 2.1 dBi, and 3.9 dB, respectively. When the sparsity ratio is greater than 0.78, the SLL suppression effect is also significant, and the attenuation of EII, transmit, and receive gains do not exceed 3 dB and 2 dB, respectively. Overall, the results demonstrate the effectiveness of a sparse shared aperture design based on beam constraints in producing high gain, low SLL, and low-cost transmit and receive arrays. Full article

Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples. Full article

In modern applications such as robotics, autonomous vehicles, and speaker localization, the computational power for sound source localization applications can be limited when other functionalities get more complex. In such application fields, there is a need to maintain high localization accuracy for several sound sources while reducing computational complexity. The array manifold interpolation (AMI) method applied with the Multiple Signal Classification (MUSIC) algorithm enables sound source localization of multiple sources with high accuracy. However, the computational complexity has so far been relatively high. This paper presents a modified AMI for uniform circular array (UCA) that offers reduced computational complexity compared to the original AMI. The complexity reduction is based on the proposed UCA-specific focusing matrix which eliminates the calculation of the Bessel function. The simulation comparison is done with the existing methods of iMUSIC, the Weighted Squared Test of Orthogonality of Projected Subspaces (WS-TOPS), and the original AMI. The experiment result under different scenarios shows that the proposed algorithm outperforms the original AMI method in terms of estimation accuracy and up to a 30% reduction in computation time. An advantage offered by this proposed method is the ability to implement wideband array processing on low-end microprocessors. Full article

The epistemic uncertainty in coronavirus disease (COVID-19) model-based predictions using complex noisy data greatly affects the accuracy of pandemic trend and state estimations. Quantifying the uncertainty of COVID-19 trends caused by different unobserved hidden variables is needed to evaluate the accuracy of the predictions for complex compartmental epidemiological models. A new approach for estimating the measurement noise covariance from real COVID-19 pandemic data has been presented based on the marginal likelihood (Bayesian evidence) for Bayesian model selection of the stochastic part of the Extended Kalman filter (EKF), with a sixth-order nonlinear epidemic model, known as the SEIQRD (Susceptible–Exposed–Infected–Quarantined–Recovered–Dead) compartmental model. This study presents a method for testing the noise covariance in cases of dependence or independence between the infected and death errors, to better understand their impact on the predictive accuracy and reliability of EKF statistical models. The proposed approach is able to reduce the error in the quantity of interest compared to the arbitrarily chosen values in the EKF estimation. Full article

Direction of arrival (DOA) estimation for conformal arrays is challenging due to non-omnidirectional element patterns and shadow effects. Conical conformal array (CCA) can avoid the shadow effect at small elevation angles. So CCA is suitable for DOA estimation on both azimuth and elevation angles at small elevation angles. However, the element pattern in CCA cannot be obtained by conventional directional element coordinate transformation. Its local element pattern also has connection with the cone angle. The paper establishes the CCA radiation pattern in local coordinate system using 2-D coordinate transformation. In addition, in the case of large elevation angle, only half elements of the CCA can receive signal due to the shadow effect. The array degrees of freedom (DOF) are reduced by halves. We introduce the difference coarray method, which increases the DOF. Moreover, we propose a more accurate propagator method for 2-D cases. This method constructs a new propagation matrix and reduces the estimation error. In addition, this method reduces computational complexity by using linear computations instead of eigenvalue decomposition (EVD) and avoids spectral search. Simulation and experiment verify the estimation performance of the CCA. Both demonstrate the CCA model established in this paper is corresponding to the designed CCA antenna, and the proposed algorithms meet the needs of CCA angle detection. When the number of array elements is 12, the estimation accuracy is about 5 degrees. Full article

Height measurement of meter wave radar is a difficult and important problem. This paper studies the height measurement of meter wave polarimetric (MWP)-MIMO array radar under complex terrain. The traditional electrically short dipole has low radiation efficiency, and the collocated dipole vector antenna has strong mutual coupling. This paper proposes to use electrically long dipoles and separated vector antennae to solve the problems of low radiation efficiency and strong mutual coupling. In addition, different from the traditional flat terrain, the research of this paper is based on the conditions of complex undulating terrain. First, the height measurement signal model of the MWP-MIMO radar with separated electrically long dipole under the complex terrain is derived. Then, a preprocessing method of block orthogonal matching pursuit is proposed to obtain the coarse estimation of the target’s elevation. Then, under the guidance of the coarse estimation, the generalized MUSIC algorithm is used to obtain the high-precision elevation estimation of the target, and then the height measurement of the target is obtained according to the geometric relationship. Finally, the effectiveness of the proposed algorithm is proved by computer simulations. Full article

The application of identification techniques using artificial intelligence to the gas turbine (GT), whose nonlinear dynamic behavior is difficult to describe through differential equations and the laws of physics, has begun to gain importance for a little more than a decade. NARX (Nonlinear autoregressive network with exogenous inputs) is one of the models used to identify GT because it provides good results. However, existing studies need to show a systematic method to generate robust NARX models that can identify a GT with satisfactory accuracy. In this sense, a systematic method is proposed to design NARX models for identifying a GT, which consists of nine precise steps that go from identifying GT variables to obtaining the optimized NARX model. To validate the method, it was applied to a case study of a 215 MW SIEMENS TG, model SGT6-5000F, using a set of 2305 real-time series data records, obtaining a NARX model with an MSE of 1.945 × 10⁻⁵, RMSE of 0.4411% and a MAPE of 0.0643. Full article

This paper studies the problem surrounding distributed passive arrays (sensors) locating multiple emitters while performing self-calibration to correct possible errors in the assumed array directions. In our setting, only the angle-of-arrival (AoA) information is available for localization. However, such information may contain bias due to array directional errors. Hence, localization requires self-calibration. To achieve both, the key element behind our approach is that the received signals from the same emitter should be geometrically consistent if sensor arrays are successfully calibrated. This leads to our signal model, which is built on a mapping directly from emitter locations and array directional errors to received signals. Then we formulate an atomic norm minimization and use group sparsity to promote geometric consistency and align ‘ghost’ emitter locations from calibration errors. Simulations verify the effectiveness of the proposed scheme. We derive the Cramér Rao lower bound and numerically compare it to the simulations. Furthermore, we derive a necessary condition as a rule of thumb to decide the feasibility of joint localization and calibration. Full article

This paper investigates the challenging problem of direction-of-arrival (DOA) estimation in impulsive noise and presents a fast iterative shrinkage-thresholding algorithm (FISTA)-based approach to tackle the difficulty. More specifically, the underlying noise is modelled as the superposition of outliers in the white Gaussian noise. Leveraging on the spot-sparse characteristic of the outlier matrix, the FISTA is conducted on each snapshot of the array output. With the estimated outlier matrix and the coarse on-grid DOA estimates, an alternating optimization method is developed to retrieve the final off-grid DOA estimates. Simulation results show that the proposed method outperforms existing methods in terms of resolution capability and estimation accuracy especially in severe noise environments. Full article

This study proposes broadband direction (DOA) estimation through discrete Fourier transform (DFT) extrapolation. We used DFT extrapolation in the lower band and extended the sampled data to reduce the beam width in the spectral domain and improved the accuracy of the estimated DOA. The sampled data with a length of 12 were extrapolated to 36 by the addition of 12-element virtual arrays to 12 real arrays on both sides. The average RMSEs of the estimated DOAs were measured throughout the wide frequency band. To verify the validity of the proposed algorithm, we demonstrated that the RMSE obtained from the broadband DOA estimation for multiple signals of interest (SOIs) was reduced in the extrapolated array. It was demonstrated that the proposed algorithm can broaden the frequency band at which a fixed number of array can estimate the DOA accurately. Full article

Frequency modulated continuous wave (FMCW) multiple-input multiple-output (MIMO) radars are widely applied in target localization. However, during the process, the estimation accuracy decreases sharply without considerable signal-to-noise ratio (SNR) and sufficient snapshot number. It is therefore necessary to consider estimation schemes that are valid under low signal-to-noise ratio (SNR) and snapshot. In this paper, a fast target localization framework based on multiple deep neural networks named Multi-DeepNet is proposed. In the scheme, multiple interoperating deep networks are employed to achieve accurate target localization in harsh environments. Firstly, we designed a coarse estimate using deep learning to determine the interval where the angle is located. Then, multiple neural networks are designed to realize accurate estimation. After that, the range estimation is determined. Finally, angles and ranges are matched by comparing the Frobenius norm. Simulations and experiments are conducted to verify the efficiency and accuracy of the proposed framework. Full article

Calibration of the unknown direction-dependent (DD) sensor phase and aliasing-free directions of arrival (DOA) estimation for sparse linear arrays are difficult tasks. In this work, we deploy an individual standard sensor with a known sensor phase response along the axis of the uncalibrated sparse linear array, a self-calibration method is proposed, in which the unknown DD sensor phase and the aliasing-free DOAs are both estimated. The proposed method is realized with a two-step scheme. In the first step, the sensor phase is eliminated by the Kronecker product of the covariance matrices in two different frequency bins, and the frequency difference satisfies the spatial Nyquist sampling theorem. Then, the DOAs can be robustly estimated without the influences of grating lobes and unknown sensor phase parameters. In the second step, the steering matrix is estimated with the known phase parameters of the deployed standard sensor. Then, the DD sensor phase is extracted from the steering matrix using the DOAs obtained in the first step. Hence, the disadvantages of iteration-based strategies in conventional calibration algorithms (e.g., local minima convergence) can be avoided. The performance of the proposed method is evaluated using simulation data and compared with that of Cramer–Rao bounds. Full article

Deep unfolded networks have recently been regarded as an essential way to direction of arrival (DOA) estimation due to the fast convergence speed and high interpretability. However, few consider gridless DOA estimation. This paper proposes two deep unfolded gridless DOA estimation networks to resolve the above problem. We first consider the atomic norm-based 1D and decoupled atomic norm-based 2D gridless DOA models solved by the alternating iterative minimization of variables, respectively. Then, the corresponding deep networks are trained offline after constructing the corresponding complete training datasets. At last, the trained networks are applied to realize the 1D DOA and 2D estimation, respectively. Simulation results reveal that the proposed networks can secure higher 1D and 2D DOA estimation performances while maintaining a lower computational expenditure than typical methods. Full article

A novel single-carrier-based space-time code construction scheme to exploit the advantages of a frequency-selective fading channel is investigated in this paper. The proposed construction scheme is based on multiplexing independent streams of phase-rotated space-time codes in a time-interleaved fashion. The advantage of such design is that it guarantees full space-time-multipath diversity by using traditional space-time codes or MIMO signaling schemes originally designed for flat fading channels as the constituent codes. Another advantage is that this approach incurs no loss in bandwidth efficiency and it alleviates the problem of high PAPR in OFDM-based space-time codes. By employing random or algebraic rotations, the design is potentially suitable for any number of transmit antennas or multipaths. The simulation results indicate that full space-time-multipath diversity is attained using this new approach, and comparisons with some existing space-time codes designed for frequency-selective channels are made to show its performance advantage. Full article

The biaxial velocity sensor comprises two nominally perpendicular particle velocity sensors and a collocated pressure sensor. Due to real-world imperfections in manufacturing or setup errors, the two axes may suffer from perpendicularity losses. To analytically study how skewness affects its direction-finding performance, the hybrid Cramér-Rao bound (HCRB) of the directions-of-arrival for the polar angle, azimuth angle and the skew angle of a biaxial velocity sensor that suffers from stochastic loss of perpendicularity were derived in closed form. The skew angle was modeled as a zero-mean Gaussian random variable of a known variance, which was assumed to be very small, to capture the uncertainty in the orthogonality of the biaxial velocity sensor. The analysis shows that for the polar and azimuth angle, the loss of perpendicularity introduces the variation of the HCRB along the azimuth angle axis, which is independent of the skew angle, but on its variance. The dynamic range of this variation increases as the variance of the skew angle increases. For the estimation of the skew angle, the HCRB of the skew angle is bounded upwards by the variance of the skew angle and varies with the azimuth angle. The hybrid maximum likelihood- maximum a posterior (hybrid ML/MAP) estimator was used to verify the derived bounds. Full article

Without the estimation of the intermediate parameters, the direct position determination (DPD) method can achieve higher localization accuracy than conventional two-step methods. However, multipath environments are still a key problem, and complex high-dimensional matrix operations are required in most DPD methods. In this paper, a time-difference-of-arrival-based (TDOA-based) DPD method is proposed based on the subspace orthogonality in the cross-spectra between the different sensors. Firstly, the cross-spectrum between the segmented received signal and reference signal is calculated and eigenvalue decomposition is performed to obtain the subspaces. Then, the cost functions are constructed by using the orthogonality of subspace. Finally, the location of the radiation source is obtained by searching the superposition of these cost functions in the target area. Compared with other DPD methods, our proposed DPD method leads to better localization accuracy with less complexity. The superiority of this method is verified by both simulated and real measured data when compared to other TDOA and DPD algorithms. Full article

Recently, the joint estimation for time delay (TD) and direction of arrival (DOA) has suffered from the high complexity of processing multi-dimensional signal models and the ineffectiveness of correlated/coherent signals. In order to improve this situation, a joint estimation method using orthogonal frequency division multiplexing (OFDM) and a uniform planar array composed of reconfigurable intelligent surface (RIS) is proposed. First, the time-domain coding function of the RIS is combined with the multi-carrier characteristic of the OFDM signal to construct the coded channel frequency response in tensor form. Then, the coded channel frequency response covariance matrix is decomposed by CANDECOMP/PARAFAC (CPD) to separate the signal subspaces of TD and DOA. Finally, we perform a one-dimensional (1D) spectral search for TD values and a two-dimensional (2D) spectral search for DOA values. Compared to previous efforts, this algorithm not only enhances the adaptability of coherent signals, but also greatly decreases the complexity. Simulation results indicate the robustness and effectiveness for the proposed algorithm in independent, coherent, and mixed multipath environments and low signal-to-noise ratio (SNR) conditions. Full article

In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method. Full article

Virtual reality, driverless cars, and robotics all make extensive use of 3D shape classification. One of the most popular ways to represent 3D data is with polygonal meshes. In particular, triangular mesh is frequently employed. A triangular mesh has more features than 3D data formats such as voxels, multi-views, and point clouds. The current challenge is to fully utilize and extract useful information from mesh data. In this paper, a 3D shape classification network based on triangular mesh and graph convolutional neural networks was suggested. The triangular face of this model was viewed as a unit. By obtaining an adjacency matrix from mesh data, graph convolutional neural networks can be utilized to process mesh data. The studies were performed on the ModelNet40 dataset with an accuracy of 91.0%, demonstrating that the classification network in this research may produce effective results. Full article

In order to solve the problem of severely decreased performance under the situation of rapid moving sources and unstable array platforms, a null broadening robust adaptive beamforming algorithm based on power estimation is proposed in this paper. First of all, we estimate the interference signal power according to the characteristic subspace theory. Then, the correspondence between the signal power and steering vector (SV) is obtained based on the orthogonal property, and the interference covariance matrix (ICM) is reconstructed. Finally, with the aim of setting virtual interference sources, null broadening can be carried out. The proposed algorithm results in a deeper null, lower side lobes and higher tolerance of the desired signal steering vector mismatch under the condition of low complexity. The simulation results show that the algorithm also has stronger robustness. Full article

With the increasingly obvious trend of satellite communication and network integration, especially the emergence of inter satellite links, the interconnection between space nodes has become the development trend and inevitable requirement of future space communication. However, problems, such as long communication distance, large transmission delay and loss, limited network resources and frequent switching of transmission links, limit the ability of spatial information transmission. Firstly, based on the idea of ring planning and design, this paper uses the joint design of beamforming between nodes to design the physical layer network coding in the relay to realize the reliable transmission of information. Secondly, according to the diversity of relay signal space resources and network node information exchange, a joint design method of relay compression matrix and node precoding vector is studied, which breaks through the existing configuration constraints. In this scheme, the computational complexity is reduced by compressing and precoding the matrix to ensure reliable decoding while obtaining spatial alignment gain and degrees of freedom. Simulated and real data results demonstrate the superiority and effectiveness of the proposed method. Full article

To improve the accuracy of the maximum correntropy Kalman filter (MCKF) in wireless sensors networks (WSNs) positioning, a dynamic self-tuning maximum correntropy Kalman filter (DSTMCKF) is proposed, where innovation and the sensors information of the WSNs are used to adjust the noise covariance matrices, and the maximum correntropy criterion is the criterion for the filter’s optimality. By dynamically adjusting the noise covariance matrices, the DSTMCKF ensures that the correntropy distribution is accurate in the presence of non-Gaussian noise (NGN), thus improving its ability to handle the NGN. In simulation and real environment positioning experiments, the DSTMCKF is used to compare with the MCKF, variable kernel width–maximum correntropy Kalman filter (VKW-MCKF) and robust minimum error entropy Kalman filter (R-MEEKF). Among the four filters, the DSTMCKF has the highest accuracy, and the error of the DSTMCKF is reduced by 34.5, 42.9 and 40.0%, respectively, compared with the MCKF, VKW-MCKF and R-MEEKF in the real-world environment positioning experiment. The application of the DSTMCKF in WSNs positioning systems improves the stability of the control systems because of the rising positioning accuracy, which makes WSNs positioning systems more widely used in scenarios requiring high stability, such as automatic parking. Full article

As an emerging technique for detection, electromagnetic vector sensor multiple-input multiple-output (EVS-MIMO) radar has attracted extensive interest recently. This paper focuses on the coherent targets issue in EVS-MIMO radar, and a spatial smoothing estimator is developed to estimate the multiple parameters. It first recovers the rank of the array data via forward spatial smoothing. Then, it estimates the elevation angles via the rotational invariance technique. Combined with the vector cross-product method, the azimuth angles are obtained. Thereafter, with the previously achieved direction angles, the polarized parameters are acquired by using the least squares technique. Unlike the existing polarization smoothing techniques, the proposed estimator is able to estimate the two-dimensional direction parameter. Furthermore, it can provide a polarized parameter of the target. In addition, the proposed estimator is computationally efficient, since it offers closed-form and automatically paired solutions to all the parameters. Numerical experiments are carried out to show its superiority and effectiveness. Full article

A novel joint satellite-transmitter and ground-receiver (JSG) digital pre-distortion (DPD) (JSG-DPD) technique is proposed to improve the linearity and power efficiency of the space-borne active phased arrays (APAs) in low Earth orbit (LEO) satellite communications. Different from the conventional DPD technique that requires a complex RF feedback loop, the DPD coefficients based on a generalized memory polynomial (GMP) model are extracted at the ground-receiver and then transmitted to the digital baseband front-end of the LEO satellite-transmitter via a satellite–ground bi-directional transmission link. The issue of the additive white Gaussian noise (AWGN) of the satellite–ground channel affecting the extraction of DPD coefficients is tackled using a superimposing training sequences (STS) method. The proposed technique has been experimentally verified using a 28 GHz phased array. The performance improvements in terms of error vector amplitude (EVM) and adjacent channel power ratio (ACPR) are 7.5% and 3.6 dB, respectively. Requiring limited space-borne resources, this technique offers a promising solution to achieve APA DPD for LEO satellite communications. Full article

Combining the advantages of diversity provided by polarization MIMO radar and good decoherence ability of matrix reconstruction technology, a method for height measurements based on matrix reconstruction after real valued processing is developed. To solve height measurement problem in meter wave polarization MIMO radar, we first derive the corresponding flat ground signal model; then, the received data matrix is reconstructed to eliminate the influence of multipath coherent signal on height measurements. Then, the reconstructed data matrix is transformed into a real valued matrix using a unitary matrix. In order to reduce the influence of noise on the signal subspace and reduce the data dimension, singular value decomposition technology is applied to receive the signal data. Finally, the elevation and height of the target are estimated according to the principle that the signal subspace is orthogonal to the noise subspace. The proposed method does not require prior knowledge, such as the reflection coefficient, wave path difference and polarization information. Simulation experiments show that the proposed algorithm has better estimation performance and less computational complexity than conventional algorithms. Full article

In this work, the parameter identifiability of sensor position perturbations in a distributed network is analyzed through establishing the link between rank of the Jacobian matrix and parameter identifiability under Gaussian noise. Here, the calibration is classified as either external or internal, dependent on whether auxiliary sources are exploited. It states that, in the case of internal calibration, sensor position perturbations can be precisely calibrated when the position of a sensor and orientation to a second sensor along with the coordinate of a third sensor along some axis, are known. In the case of external calibration where auxiliary sources are introduced to support the process, the identifiability condition for configuration calibration is to have at least three noncollinear auxiliary sources with the distributed sensor network avoiding the collinear and coplanar geometries. As the assumption of small perturbations is considered, the parameter identifiability is capable of being measured by virtue of the Bayesian Cramer–Rao lower bound (BCRLB), after asymptotical tightness of the BCRLB is verified. Simulations corroborate well with the theoretical development. Full article

Multiscale PCA (MSPCA) is a well-established fault-detection and isolation (FDI) technique. It utilizes wavelet analysis and PCA to extract important features from process data. This study demonstrates limitations in the conventional MSPCA fault detection algorithm, thereby proposing an enhanced MSPCA (EMSPCA) FDI algorithm that uses a new wavelet thresholding criterion. As such, it improves the projection of faults in the residual space and the threshold estimation of the fault detection statistic. When tested with a synthetic model, EMSPCA resulted in a 30% improvement in detection rate with equal false alarm rates. The EMSPCA algorithm also relies on the novel application of reconstruction-based fault isolation at multiple scales. The proposed algorithm reduces fault smearing and consequently improves fault isolation performance. The paper will further investigate the use of soft vs. hard wavelet thresholding, decimated vs. undecimated wavelet transforms, the choice of wavelet decomposition depth, and their implications on FDI performance.The FDI performance of the developed EMSPCA method was illustrated for sensor faults. This undertaking considered synthetic data, the simulated data of a continuously stirred reactor (CSTR), and experimental data from a packed-bed pilot plant. The results of these examples show the advantages of EMSPCA over existing techniques. Full article

In very-high-frequency (VHF) radar, the direction-of-arrival (DOA) estimation performance of low-angle targets tracking is strongly affected by the multipath phenomenon. Especially in the complex terrain conditions, the multipath echo comes from a region where the different scattering media make the multipath echo show the characteristics of multi-channel and uneven energy distribution. In this case, the received signal mismatches with the signal model, which leads to performance degradation and even failure of the traditional DOA algorithm. To deal with this problem, the authors propose a new signal model based on multiple scattering center. A multipath signal equivalent model is deduced and analyzed using multipath vector synthesis. Subsequently, the fitness function is established based on the equivalent model, and the target elevation angle is estimated by particle swarm optimization (PSO) algorithm. Simulation results and real data analysis show that the proposed model and algorithm can effectively improve the DOA estimation accuracy of low elevation target under complex terrain and less snapshot condition. Full article

Direction-of-arrival (DOA) estimation is the preliminary stage of communication, localization, and sensing. Hence, it is a canonical task for next-generation wireless communications, namely beyond 5G (B5G) or 6G communication networks. Both massive multiple-input multiple-output (MIMO) and millimeter wave (mmW) bands are emerging technologies that can be implemented to increase the spectral efficiency of an area, and a number of expectations have been placed on them for future-generation wireless communications. Meanwhile, they also create new challenges for DOA estimation, for instance, through extremely large-scale array data, the coexistence of far-field and near-field sources, mutual coupling effects, and complicated spatial-temporal signal sampling. This article discusses various open issues related to DOA estimation for B5G/6G communication networks. Moreover, some insights on current advances, including arrays, models, sampling, and algorithms, are provided. Finally, directions for future work on the development of DOA estimation are addressed. Full article

This paper investigates the direction-of-arrival (DOA) estimation-based target localization problem using an array radar under complex multipath propagation scenarios. Prevalent methods may suffer from performance degradation due to the deterministic signal model mismatch, especially when the exact knowledge of a propagation environment is unavailable. To cope with this problem, we first establish an improved signal model of multipath propagation for low-angle target localization scenarios, where the dynamic nature of convoluted interferences induced by complex terrain reflections is taken into account. Subsequently, an iterative implementation-based target localization algorithm with the improved propagation model is proposed to eliminate the detrimental effect of coherent interferences on target localization performance. Compared to existing works, the proposed algorithm can maintain satisfactory estimation performance in terms of target location parameters, even in severe multipath interference conditions, where the decorrelation preprocessing and accurate knowledge about the multipath propagation environment are not required. Both simulation and experimental results demonstrate the effectiveness of the proposed propagation model and localization algorithm. Full article

This paper studies the joint range and angle estimation of monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) radar and proposes a joint estimation algorithm. First, the transmit direction matrix is converted into real values by unitary transformation, and the Vandermonde-like matrix structure is used to construct an augmented output that doubles the aperture of the receive array. Then the augmented output is combined into a third-order tensor. Next, the factor matrices are initially estimated. Finally, the direction matrices are estimated utilizing parallel factor (PARAFAC) decomposition, and the range and angle are calculated by employing least square fitting. As contrasted with the classic PARAFAC method, the proposed method can estimate more targets and provide better estimation performance, and requires less computational complexity. The availability and excellence of the proposed method are reflected by numerical simulations and complexity analysis. Full article

Most subspace-based algorithms need exact array manifold for direction of arrival (DOA) estimation, while, in practical applications, the gain-phases of different array elements are usually inconsistent, degrading their estimation performance. In this paper, a novel low-complexity 2D DOA and gain-phase error estimation algorithm is proposed by adding auxiliary array elements in a uniform rectangular array (URA). Firstly, the URA is modeled as the Kronecker product of two uniform linear arrays (ULAs) to decouple the 2D DOA estimation. Then, several well-calibrated auxiliary array elements are added in the two ULAs, based on which the rotation invariant factor of the URA destroyed by the gain-phase error is reconstructed by solving constrained optimization problems. Lastly, ESPRIT is used to estimate the 2-D DOA and the gain-phase error coefficients. The closed-form expressions of the estimation CRBs are also derived, providing insight into the impact of gain-phase error on DOA estimation. Simulation results are used to validate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis. Full article

Conventional energy detection is a robust method that is usually applied to underwater broadband acoustic signal processing for towed arrays. Due to its low resolution, the weak target detection performance of conventional energy detection is severely degraded in shallow sea environments with strong acoustical reverberation. Subband peak energy detection is an effective method to improve the display resolution of conventional energy detection. However, subband peak energy detection produces false alarms due to the presence of high sidelobe levels. In order to improve the underwater target detection performance, a deconvolved subband peak energy detection method for towed arrays is proposed in this paper. Compared with conventional beamforming, minimum-variance distortionless response with forward–backward averaging and diagonal loading algorithm and subband peak energy detection, the proposed method could robustly provide higher-resolution results and suppress the fake peaks induced by subband peak energy detection. The performance of the proposed method was evaluated with simulation results, and the sea experimental data processing results show that the proposed method is effective in engineering applications. Full article

With the development of Internet of Things (IoT) and edge computing technology, gas sensor arrays based on Micro-Electro-Mechanical System (MEMS) fabrication technique have broad application prospects in intelligent integrated systems, portable devices, and other fields. In such complex scenarios, the normal operation of a gas sensing system depends heavily on the accuracy of the sensor output. Therefore, a lightweight Self-Detection and Self-Calibration strategy for MEMS gas sensor arrays is proposed in this paper to monitor the working status of sensor arrays and correct the abnormal data in real time. Evaluations on real-world datasets indicate that the strategy has high performance of fault detection, isolation, and data recovery. Furthermore, our method has low computation complexity and low storage resource occupation. The board-level verification on CC1350 shows that the average calculation time and running power consumption of the algorithm are 0.28 ms and 9.884 mW. The proposed strategy can be deployed on most resource-limited IoT devices to improve the reliability of gas sensing systems. Full article

Due to clutter inhomogeneity, the clutter suppression ability of space–time adaptive processing (STAP) is usually constrained by the insufficient number of independent and identically distributed (IID) clutter training samples and, as a result, is sacrificed to achieve the demanded sample reduction. Moreover, since clutter heterogeneity is exacerbated in the real environment, the IID training sample size can be heavily reduced, leading to the deterioration in clutter suppression. To solve this problem, a novel robust space–time joint sparse processing method with airborne active array is proposed. This method has several outstanding advantages: (1) only the single snapshot cell under test (CUT) data is used for the superior clutter suppression performance; and (2) the proposed method completely removes the dependence of the system processing ability on IID training samples. In this paper, the signal model of uniform transmitting subarray diversity is first established to obtain the single snapshot echo observed CUT data. Then, with the matched reconstruction, the single snapshot data are equivalently converted into multi-frame echo data. Finally, a fast multi-frame echo data joint sparse Bayesian algorithm is used to achieve heterogeneous clutter suppression. Numerous experiments were performed to verify the advantages of the proposed method. Full article

The development of unmanned aerial vehicles (UAVs) opens up a lot of opportunities but also brings some threats. Dealing with these threats is not easy and requires some good techniques. Knowing the location of the threat is essential to deal with an UAV that is displaying disturbing behavior. Many methods exist but can be very limited due to the size of UAVs or due to technological improvements over the years. However, the noise produced by the UAVs is still predominant, so it gives a good opening for the development of acoustic methods. The method presented here takes advantage of a microphone array with a processing based on time domain Delay and Sum Beamforming. In order to obtain a better signal to noise ratio, the UAV’s acoustic signature is taken into account in the processing by using a time-frequency representation of the beamformer’s output. Then, only the content related to this signature is considered to calculate the energy in one direction. This method enables to have a good robustness to noise and to localize an UAV with a poor spectral content or to separate two UAVs with different spectral contents. Simulation results and those of a real flight experiment are reported. Full article