Signal Subspace Research Articles

An Efficient 2-D DOA Estimation Method for Unfolded Coprime L-Shaped Array

In this article, a novel two-dimensional direction of arrival (2-D DOA) estimation method using unfolded coprime L-shaped array is presented. First, the signal subspace is divided to establish the relationship between two subarrays. Thus, the 2-D DOA estimation problem is transformed into one-dimensional (1-D) one. Moreover, by introducing the extraction matrix, the nonuniform array can also fit polynomial root finding, from which the initial elevation and azimuth estimates can be obtained. Finally, to further improve the estimation accuracy, we compensate the estimation offsets via least square constructed from the first-order Taylor expansion of the direction matrix. The proposed algorithm outperforms the conventional algorithms in the aspect of computational complexity while achieves preferable estimation performance. Specifically, the complexity of the proposed method is reduced by several orders of magnitude, with RMSE reduced by up to 6 dB.

Downlink channel estimation of intelligent reflective surface aided MU-MIMO system

Obtaining channel status information (CSI) is one of the main problems of the intelligent reflective surface (IRS) assisted communication system. This is because IRS has only a large number of passive reflective components and cannot process signals. In this paper, we aim to estimate downlink channel of IRS assisted multi-user multiple-input multiple-output (MU-MIMO) communication system. In time division duplex (TDD) mode, the downlink channel is estimated according to the uplink pilot by using channel reciprocity. We propose a parallel factor analysis based on projection subspace (PSS-PARAFAC) channel estimation scheme. In the first step, the common sparsity among multiple users is used for signal subspace projection to reduce noise energy and complexity. The second step is to convert each user signal received of base station (BS) into the PARAFAC problem. The iterative method of alternating least squares (ALS) is used to solve this problem. From the analysis of simulation results, the channel estimation performance of the proposed algorithm is better.

Two Rapid Power Iterative DOA Estimators for UAV Emitter Using Massive/Ultra-Massive Receive Array

To provide rapid direction finding (DF) for unmanned aerial vehicle (UAV) emitters in future wireless networks, a low-complexity direction of arrival (DOA) estimation architecture for massive multiple-input multiple-output (MIMO) receiver arrays is constructed. In this paper, we propose two strategies to address the extremely high complexity caused by eigenvalue decomposition of the received signal covariance matrix. Firstly, a rapid power iterative rotational invariance (RPI-RI) method is proposed, which adopts the signal subspace generated by power iteration to obtain the final direction estimation through rotational invariance between subarrays. RPI-RI causes a significant complexity reduction at the cost of a substantial performance loss. In order to further reduce the complexity and provide good directional measurement results, the rapid power iterative polynomial rooting (RPI-PR) method is proposed, which utilizes the noise subspace combined with the polynomial solution method to obtain the optimal direction estimation. In addition, the influence of initial vector selection on convergence in the power iteration is analyzed, especially when the initial vector is orthogonal to the incident wave. Simulation results show that the two proposed methods outperform the conventional DOA estimation methods in terms of computational complexity. In particular, the RPI-PR method achieves more than two orders of magnitude lower complexity than conventional methods and achieves performance close to the Cramér–Rao Lower Bound (CRLB). Moreover, it is verified that the initial vector and the relative error have a significant impact on the performance with respect to the computational complexity.

A constraint optimization problem for model order estimation

In this paper, we present a new method for estimating the number of terms in a sum of exponentially damped sinusoids embedded in noise. In particular, we propose to combine the shift-invariance property of the Hankel matrix associated with the signal with a constraint over its singular values to penalize small-order estimations. With this new methodology, the algebraic structure of the Hankel matrix and the statistical properties of the noise are considered. The new order estimation technique shows significant improvements over subspace-based methods. In particular, when a good separation between the noise and the signal subspaces is not possible, the new methodology outperforms known techniques. We evaluate the performance of our method using numerical experiments and compare its performance with previous results found in the literature.

Compressive Sampling Framework for 2D-DOA and Polarization Estimation in mmWave Polarized Massive MIMO Systems

The polarized massive multiple-input multiple-output (MIMO) technique has been regarded as a promising solution to millimeter wave (mmWave) communication systems, because it experiences more degrees-of-freedom than the scalar configuration, and it represents a significant opportunity for secure communication. To deliver smart service to terminals, it is essential to provide base stations (BS) with the capability of terminal’s direction-of-arrival (DOA) awareness. In this paper, a compressive sampling (CS) framework is proposed for two-dimensional (2D) DOA and polarization estimation in mmWave polarized massive MIMO systems. The proposed approach first reduces the data volume via a reduced-dimension matrix. Then it computes the signal subspace via the eigendecomposition of the compressed array measurement. Thereafter, the rotational invariance characteristic is utilized to form a normalized polarization steering vector. Finally, 2D-DOA and polarization are estimated by incorporating the Poynting vector and the least squares (LS) techniques. The proposed architecture is computationally much more economical than existing algorithms. Besides, it allows a mmWave BS to provide comparable estimation performance with arbitrary sensor geometry, which is more flexible than most of the existing architectures. Furthermore, it is robust to the sensor position error. Numerical simulations verify the advantages of the proposed framework.

Semi-Blind structured subspace method for signal estimation in nonlinear convoluted mixture

This work proposes a novel semi-blind structured subspace signal estimation approach for nonlinear single-input multiple-output (SIMO) systems. Here, in this work, a quadratic nonlinearity is considered in the analysis. The proposed approach exploits the Toeplitz structure present in a convolutive communication model together with pilot signals in a semi-blind scheme. It directly estimates the signal with no channel estimation step, which saves the extra computational cost needed when considering a two steps approach (i.e., channel identification then equalization). The simulation findings show that the proposed method is resilient to channel order overestimation errors and allows achieving good signal restoral quality with only few pilot symbols, outperforming the pilot-based approach in such a context.

Low-rank approximation of Hankel matrices in denoising applications for statistical damage diagnosis of wind turbine blades

Model order selection is a fundamental task in subspace identification for estimation of modal parameters, uncertainty propagation and damage diagnosis. However, the true model order and the related low-rank structure of the dynamic system are generally unknown. In this paper, a statistical methodology to actively select the dynamic signal subspace in covariance-driven subspace identification is developed on the basis of statistical analysis of the eigenvalue condition numbers of the output covariance Hankel matrix. It is shown that the condition numbers highly sensitive to random perturbations characterize the noise subspace. The signal subspace is separated from the noise subspace by analyzing two statistical parameters associated with the condition number sensitivity, whose thresholds are user-defined. A practical algorithm to retrieve the system dynamics is designed and demonstrated on a running example of a simulated wind turbine blade benchmark. The resultant framework is then applied in the context of damage detection on a medium-size wind turbine blade. It is demonstrated that the detectability of small damage is enhanced compared to the classic approaches and robustness of damage diagnosis is increased by reducing the number of false alarms.

An efficient damage imaging method for composite structure based on self-correcting phase error compensation MUSIC algorithm

The increasing use of composite materials on aircraft structures, most of which are plate-like, has attracted much attention for damage monitoring based on guided wave as a kind of structural health monitoring (SHM) method. The multiple signal classification (MUSIC) algorithm is a directional scanning and searching method to unbiasedly estimate the signal features in terms of the orthogonal attributes between signal subspace and noise subspace. The MUSIC algorithm is gradually shifted into the field of SHM used for damage localization. However, the anisotropy of the composites and the sensor position errors cause the phase errors of the array response signal, resulting in a decrease in the accuracy of the MUSIC method. In addition, the complexity of the array monitoring network causes a significant increase in the amount of operations for signal information processing, making online real-time monitoring challenging. In order to reduce the impact of multiple forms of array errors on the MUSIC algorithm and to improve the efficiency of it, this paper proposes an efficient damage imaging method for composite structure based on self-correcting phase error compensation MUSIC algorithm, which compensates for the array phase errors caused by structural anisotropy and sensor position errors, and achieves high efficiency. The method has been verified on a stiffened composite structure, and the results show its superiority and effectiveness.

Weighted sparse Bayesian method for direction of arrival estimation based on grid fission

AbstractAn off‐grid weighted sparse Bayesian learning algorithm based on grid fission for direction of arrival estimation is proposed. The existing grid fission algorithms can use fewer grid points with variant intervals to estimate the true DOAs. However, their learning processes are based on the traditional sparse Bayesian algorithm, which only assigns the same prior distribution assumption to the signals on all grids, but ignores the difference of signal distribution of different grid points. It will result in inaccurate fission location and fission direction because of the insufficient resolution of the spatial spectrum, reducing the estimation accuracy. Moreover, the fission strategy will cost much computation time due to the increase of grid points. To solve these problems, the proposed algorithm utilises the orthogonality of signal subspace and noise subspace to design the weights for prior signal distribution assumption, making the peaks of spatial spectrum more pronounced and easy to distinguish, using more accurate estimated DOAs and off‐grid parameter to determine the fission location and direction. In addition, the fission process deletes redundant grid points to simplify calculations. Compared with the existing grid fission algorithms, the proposed method has superior performance in estimation accuracy and computational time.

Joint range, angle and polarization estimation in polarimetric FDA-MIMO radar based on Tucker tensor decomposition

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

Forward-propagation-free focusing MUSIC algorithm for Lamb waves

The multiple signal classification (MUSIC) algorithm is originally used for direction of arrival estimation and frequency identification. MUSIC-like algorithms have gained their popularity in structural health monitoring (SHM) owing to their super-resolution characteristic and the virtue of baseline independence. MUSIC essentially is a searching algorithm to find the best phase difference matching between the eigenvector from signal subspace and the presupposed steering vector. However, in the guided-wave-based SHM (in plate-like structure, the guided wave is Lamb wave), the dispersion effect will definitely lead to phase distortion. Therefore, Xu et al. presented a focusing MUSIC algorithm where the time reversal technique is adopted to eliminate the dispersion in the way of back propagation. Seeing that the phase difference information, which is necessary for MUSIC, disappears after back propagation, the damage scattered wave packet, obtained by window truncation, is forward propagated again at the constant group velocity to recover the time of flight information. Nevertheless, the forward propagation process is superfluous from the view of phase matching. In the presented forward-propagation-free focusing MUSIC (FPF-F MUSIC) algorithm (the simplified version of Xu’s work), by revising the steering vector in the form of phase coincidence, the matching relation for MUSIC is modified from phase difference matching to phase alignment matching, so that the forward propagation and the steering vector traversal setting for every inspection point are all omitted. The damage localization performance of FPF-F MUSIC is verified on the aluminum plate with double through-hole and surface defects under uniform linear and circular arrays.

Surface Biology and Geology imaging spectrometer: A case study to optimize the mission design using intrinsic dimensionality

The information content that can be derived from spectroscopic imagery tends to increase with finer ground sampling distance, finer spectral sampling, more frequent revisit, and higher signal-to-noise ratios (SNRs). However, these parameters are not independent, and it is thus impossible to design a space-borne imaging spectrometer to maximize all of them simultaneously. We present an instrument model and simulation environment that enable us to find the optimal combination of these four mission design parameters, using intrinsic dimensionality (ID) as the metric. ID is the size of the signal subspace – the maximum degrees of freedom when noise can be disregarded – and is a metric that is independent of any one particular algorithm or application area. This study is important for upcoming missions such as NASA's Earth System Observatory mission to study the Earth's Surface Biology and Geology (SBG), which will comprise a visible to shortwave infrared spectrometer in addition to a multi-channel thermal radiometer on a separate platform. When evaluating a desert site and a tropical forested site, we find that spectral resolution drives information content, with a significant drop in normalized ID (15–45% decrease) when simulating 15 nm spectral sampling as opposed to 10 nm spectral sampling. However, there was some variation between sites, with the forested site benefiting from 5 nm spectral sampling, whereas the desert site had poorer results at this resolution, due to the impact on noise. At 10 nm spectral sampling, ground sampling distances in the range 30–50 m provided the optimal balance between spatial resolution and SNR, although more frequent revisit, potentially by combining data from multiple missions, would maximize total information content.

Vector Set Classification by Signal Subspace Matching

We present a powerful solution to the problem of vector set classification, based on a novel goodness-of-fit metric, referred to as signal subspace matching (SSM). Unlike the existing solutions based on principal component analysis (PCA), this solution is eigendecomposition-free and dimension-selection-free, i.e., it does not require PCA nor the election of the subspace dimension, which is done implicitly. More importantly, it copes effectively with the challenging cases wherein the subspaces characterizing the classes are partially or fully overlapping. The SSM metric matches the subspaces characterizing the vector sets of the test and the classes by minimizing the distance between respective soft-projection matrices constructed from the vector sets. We prove the consistency of the solution for the high signal-to-noise-ratio limit, and also for the large-sample limit, conditioned on the noise being white. Experimental results, demonstrating the superiority of the SSM solution over the existing PCA-based solutions, especially in the challenging cases of overlapping subspaces, are included.

On BT-limited Signals

In this paper, we introduce and characterize a subspace of bandlimited signals. The subspace consists of all bandlimited signals such that the non-zero parts of their Fourier transforms are pieces of some T bandlimited signals. The signals in the subspace are called BT-limited signals and the subspace is named as BT-limited signal space. For BT-limited signals, a signal extrapolation with an analytic error estimate exists outside the interval [−T, T ] of given signal values with errors. Some new properties about and applying BT-limited signals are also presented.

Target Parameter Estimation Algorithm Based on Real-Valued HOSVD for Bistatic FDA-MIMO Radar

Since there is a frequency offset between each adjacent antenna of FDA radar, there exists angle-range two-dimensional dependence in the transmitter. For bistatic FDA-multiple input multiple output (MIMO) radar, range-direction of departure (DOD)-direction of arrival (DOA) information is coupled in transmitting the steering vector. How to decouple the three information has become the focus of research. Aiming at the issue of target parameter estimation of bistatic FDA-MIMO radar, a real-valued parameter estimation algorithm based on high-order-singular value decomposition (HOSVD) is developed. Firstly, for decoupling DOD and range in transmitter, it is necessary to divide the transmitter into subarrays. Then, the forward–backward averaging and unitary transformation techniques are utilized to convert complex-valued data into real-valued data. The signal subspace is obtained by HOSVD, and the two-dimensional spatial spectral function is constructed. Secondly, the dimension of spatial spectrum is reduced by the Lagrange algorithm, so that it is only related to DOA, and the DOA estimation is obtained. Then the frequency increment between subarrays is used to decouple the DOD and range information, and eliminate the phase ambiguity at the same time. Finally, the DOD and range estimation automatically matched with DOA estimation are obtained. The proposed algorithm uses the multidimensional structure of high-dimensional data to promote performance. Meanwhile, the proposed real-valued tensor-based method can effectively cut down the computing time. Simulation results verify the high efficiency of the developed method.

Blind Estimation of Spreading Code Sequence of QPSK-DSSS Signal Based on Fast-ICA

Most of the existing estimation methods of spreading code sequence are not suitable for the QPSK-DSSS. We propose a spreading code sequence estimation method based on fast independent component analysis (Fast-ICA). It mainly includes signal preprocessing, calculations of separation matrix, and spreading code sequence. Firstly, the received signal is segmented according to the period of the spreading code sequence, and the covariance matrix can be calculated. Then, the signal subspace and corresponding eigenvalues are obtained by eigenvalue decomposition of the covariance matrix. Subsequently, the received signal matrix needs to be whitened. Finally, the Fast-ICA algorithm is used to find the separation matrix to estimate the in-phase and orthogonal spreading code sequence. The experiment result shows that the estimation of the spreading code sequence can be carried out based on Fast-ICA under a low SNR of −12 dB. Compared with the constant modulus algorithm (CMA) and the decomposition method for the real part of the self-covariance matrix (EVD-R), this method has a better performance.

Simplified Spatial Smoothing for DOA Estimation of Coherent Signals

In coherent direction of arrival (DOA) estimation, subspace-based methods suffer from performance deterioration because of the rank loss of the signal covariance matrix. A variety of spatial smoothing preprocessing techniques have been proposed for decorrelation, among which the enhanced spatial smoothing preprocessing (ESS) technique shows outstanding performance by exploiting the signal subspace. However, ESS is applied by squaring the matrix whose columns span the signal subspace (called signal matrix), which involves unnecessary computational loads. Besides, the smoothed covariance matrix after ESS is a linear combination of the sub-matrices of signal matrix, where the coefficients of the combination may undermine the decorrelation performance. In this context, a simplified spatial smoothing (SSS) technique is proposed for decorrelation by averaging the sub-matrices of the signal matrix directly, and avoids redundant operations in squared signal matrix. The proposed method is tested numerically in terms of the signal-to-noise ratio (SNR), the number of snapshots, angle separation, and the execution time. Simulation results show the improvement of the decorrelation performance, efficiency, and robustness with the proposed method in coherent scenarios, compared with the other spatial smoothing preprocessing based methods.

Joint DOD and DOA detection for MIMO radar based on signal subspace reconstruction and matching

In this study, the Direction Of Departure (DOD) and Direction Of Arrival (DOA) of signals detection for Multi-Input Multi-Output (MIMO) radar is discussed. A novel signal subspace reconstruction model to match the signal subspace obtained based on the covariance matrix of the array output is developed to enhance the performance of the DOD and DOA detection. In the developed scheme, the technology of beamforming is first introduced to define an objective space in mathematics for the targets to be detected. By considering the orthogonality between the signal subspace and the noise subspace and defining a reconstruction index of the signal subspace, a multi-dimensional objective function of the DOD and DOA is established. Therefore, the problem of DOD and DOA detection is transformed into an optimization of the multi-dimensional objective function. Subsequently, the Quantum-Behaved Particle Swarm Optimization (QPSO) is employed to optimize the multi-dimensional objective function and to determine an optimal signal subspace. At the same time the DOD and DOA can be fast captured. A series of simulations demonstrate that the proposed method provides significant accuracy improvements in DOD and DOA detection, especially for low signal-to-noise ratio thresholds and small snapshots.

High-Accuracy DOA Estimation Based on an Improved Sample Correlation Matrix

In a direction-finding process, high-resolution subspace-based algorithms are the most popular ones. It is well-known that their performance of direction of arrival estimation mainly depends on the accuracy of the signal subspace. However, the traditional methods of capturing the signal subspace do not mine the information hidden in the array output in depth, which may restrict their application to some extent. In this study, we elaborate on a novel scheme to extract the signal subspace through refinement of the correlation matrix of the array output. In the developed scheme, a collection of spatial temporal correlation matrices is firstly established. Then, we define a weighting vector for the correlation matrices, and take the weighted average of the correlation matrices as the covariance matrix of the array output. It is clear that this covariance matrix is more general than the traditional covariance matrix, and the signal subspace can be optimized through adjustment of the weighting vector. In this study, we present an optimal weighting vector by adopting the particle swarm optimization. Simulation results demonstrate that the proposed approach has better performance in root mean square error compared to the existing schemes.

Pressure vessel leakage detection method based on online acoustic emission signals

Pressure vessel leakages cannot initially be visited directly and will gradually cause deterioration, which can result in catastrophic damage. Acoustic emission (AE) signals generated by leakage have the potential of being used for online monitoring. Unfortunately, AE signals have the characteristics of being non-stationary, wide-band and with strong noise interference, which causes the monitoring results to have low reliability. To address the poor robustness of traditional time-domain and time-frequency domain-based monitoring methods, an online monitoring method based on adaptive singular value decomposition (ASVD) is proposed in this paper. Firstly, singular value decomposition (SVD) is used to divide the signal space into a signal subspace and a noise subspace. Experiments indicate that SVD can distinguish leakages under conditions of different pressures and variable temperature, which means that SVD is sensitive to changes in signal. Subsequently, update iteration-based ASVD algorithms are proposed for long-term online health monitoring and ASVD is shown to be successful in distinguishing the different statuses of intact, leakage and repaired. To improve the robustness of ASVD, a novel energy indicator is proposed, which can identify the status change more effectively. With the proposed methodology, an online monitoring application for pressure vessel leakage detection is expected to be achievable.