Coherent Signal Subspace Method Research Articles

Direction of Arrival Estimation and Highlighting Characteristics of Testing Wideband Echoes from Multiple Autonomous Underwater Vehicles.

Multiple autonomous underwater vehicles (AUVs) have gradually become the trend in underwater operations. Identifying and detecting these new underwater multi-targets is difficult when studying underwater moving targets. A 28-element transducer is used to test the echo of multiple AUVs with different layouts in a lake. The characteristics of the wideband echo signals are studied. Under the condition that the direction of arrival (DOA) is not known, an autofocus coherent signal subspace (ACCSM) method is proposed. The focusing matrix is constructed based on the received data. The spatial spectrum of the array signal of multiple AUVs at different attitudes is calculated. The algorithm estimates the DOA of the echo signals to overcome the shortcomings of traditional wideband DOA estimation and improve its accuracy. The results show that the highlights are not only related to the number of AUVs, but are also modified by scale and attitude. The contribution of the microstructure of the target in the overall echo cannot be ignored. Different parts of the target affect the number of highlights, thus resulting in varying numbers of highlights at different attitude angle intervals. The results have significant implications for underwater multi-target recognition.

Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array.

Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests.

Weighted Frequency Smoothing for Enhanced Speaker Localization

The coherent signal subspace method may be used in order to apply subspace localization methods (e.g. MUSIC) to coherent sources. This method involves a focusing process followed by frequency smoothing, which is intended to decorrelate source signals from coherent sources. In practice, however, only moderate decorrelation is obtained, which may lead to performance degradation. Although decorrelation can be improved by widening the smoothing bandwidth, a wider bandwidth may increase focusing error and the smoothing bandwidth is limited by the bandwidth of the actual signal. In this paper, a weighted frequency smoothing that improves decorrelation for a given bandwidth is proposed. It is shown that better decorrelation is obtained by selecting the weights to be inversely proportional to the source signal power at the given frequency. However, since the power of the source is not known, it is estimated by the trace of the array spatial covariance matrix. An experimental study is presented that investigates the effect of the proposed weighting on DOA estimation of speech sources in a reverberant environment.

High-Performance Implementation of Wideband Coherent Signal-Subspace (CSS)-Based DOA Algorithm on FPGA

Coherent Signal-Subspace (CSS) is a technique to separate the wide frequency band into narrowband components which can be applied in many applications such as smart antennas for wireless communications and radar. However, CSS is computationally intensive and may not achieve the real-time requirement. Therefore, this work aims to propose an efficient implementation of the CSS method on Field-Programmable Gate Array (FPGA) to achieve the desired performance. Different parallelization and optimization techniques such as loop unrolling, loop pipelining, dataflow, and loop flattening are adopted and applied to explore the opportunities of any computation and storage that could be eliminated in order to achieve high efficiency. The results of the proposed optimized implementation achieve the highest performance compared with other related implementations.

Focusing and Frequency Smoothing for Arbitrary Arrays With Application to Speaker Localization

The coherent signal subspace method (CSSM) enables the direction-of-arrival (DoA) estimation of coherent sources with subspace localization methods. The focusing process that aligns the signal subspaces within a frequency band to its central frequency is central to the CSSM. Within current focusing approaches, a direction-independent focusing approach may be more suitable for reverberant environments since no initial estimation of the sources' DoAs is required. However, these methods use integrals over the steering function, and cannot be directly applied to arrays around complex scattering structures, such as robot heads. In this article, current direction-independent focusing methods are extended to arrays for which the steering function is available only for selected directions, typically in a numerical form. Spherical harmonics decomposition of the steering function is then employed to formulate several aspects of the focusing error. A case of two coherent sources is studied and guidelines for the selection of the frequency smoothing bandwidth are suggested. The performance of the proposed methods is then investigated for an array that is mounted on a robot head. The focusing process is integrated within the direct-path dominance (DPD) test method for speaker localization, originally designed for spherical arrays, extending its application to arrays with arbitrary configurations. Finally, experiments with real data verify the feasibility of the proposed method to successfully estimate the DoAs of multiple speakers under real-world conditions.

Optimized Sonar Broadband Focused Beamforming Algorithm

Biases of initial direction estimation and focusing frequency selection affect the final focusing effect and may even cause algorithm failure in determining the focusing matrix in the coherent signal–subspace method. An optimized sonar broadband focused beamforming algorithm is proposed to address these defects. Initially, the robust Capon beamforming algorithm was used to correct the focusing matrix, and the broadband signals were then focused on the optimal focusing frequency by the corrected focusing matrix such that the wideband beamforming was transformed into a narrowband problem. Finally, the focused narrowband signals were beamformed by the second-order cone programming algorithm. Computer simulation results and water pool experiments verified that the proposed algorithm provides a good performance.

Estimation of Direction of Arrival by Time Reversal for Low-Angle Targets

In a low-angle target parameter estimation scenario, the backscattered signals from targets are often distorted due to clutter and multipath, which significantly degrades the performance of direction-of-arrival (DOA) estimation. In general, the backscattered multipaths are modeled as coherent signals with respect to the direct path. Decorrelation algorithms such as spatial smoothing and matrix reconstruction can mitigate the effect of multipath. However, most of these methods will perform poorly or even fail for solving parameter estimation problem of low-angle targets in complex terrain where there are rich multipath scatterings. This paper presents a novel method that combines time reversal (TR) technique, coherent signal-subspace method (CSM), and multiple signal classification algorithm to perform DOA estimation in a low-angle target scenario. The TR technique takes advantage of multipath echoes recorded by a sensor array and adaptively adjusts TR probing waveforms to increase the signal-to-noise ratio in a rich scattering environment. Moreover, the CSM method compresses the energy of a signal into a predefined subspace to exploit the full time-bandwidth product of signal sources and cope with coherent wavefronts. As a result, the proposed new DOA estimation algorithm outperforms significantly the conventional methods. The Cramer–Rao bounds analysis and numerical simulations commendably validate the accuracy and robustness of the proposed method.

DOA estimation for wideband signals based on weighted Squared TOPS

This paper introduces a new direction-of-arrival (DOA) estimation method for wideband signal sources. The new method estimates the DOA of wideband signal sources based on squared test of orthogonality of projected subspaces (Squared TOPS) which is an improved method of TOPS. TOPS and Squared TOPS use the signal and noise subspaces of multiple frequency components of wideband signal sources. Although coherent wideband method, such as coherent signal subspace method (CSSM), performs high DOA estimation accuracy, it requires the initial estimate of signal source directions. On the other hand, TOPS and Squared TOPS can provide good performance of DOA estimation without the initial value of signal sources; however, some false peaks appear in spatial spectrum based on these methods. The proposed method, called weighted Squared TOPS (WS-TOPS), uses the modified squared matrix and selective weighted averaging process to improve DOA estimation performance. The performance of WS-TOPS is compared with those of TOPS, Squared TOPS, incoherent MUSIC, and test of orthogonality of frequency spaces (TOFS) through computer simulations. The simulation results show that WS-TOPS can suppress all false peaks in spatial spectrum and improve DOA estimation accuracy and also keep the same resolution performance as Squared TOPS.

A Coherent PMI Estimation Scheme for Double Codebook

The double codebook structures are proposed and applied in LTE-advanced, which can track both long-term and short-term channel state information. In traditional incoherent estimation, precoding matrix indicators (PMI) estimation is performed on each individual subcarrier and some form of averaging procedure then follows to combine the results from individual narrow-band processing. As a result, if there is a large deviation in any estimates of a subcarrier, it will lead to a larger deviation in the final result. Thus incoherent PMI estimation has a poor performance in low signal to noise ratio. This paper introduces a new PMI feedback scheme for wideband sources with coherent signal subspace method. This new technique estimates PMI based on an approximately coherent combination of each subcarrier by a focusing matrix. Simulation results show that the coherent estimation scheme has a better throughput performance than the traditional incoherent estimation.

Simulation on locating Partial Discharge source occurring on distribution line by estimating the DOA of emitted EM waves

AbstractA new method for locating the position of partial discharge (PD), which occurs on distribution line, is presented. The method uses the direction‐of‐arrival (DOA) of electromagnetic (EM) waves emitted from PD source. The DOAs of EM waves in azimuth and elevation angles are estimated by using the two‐dimensional improved coherent signal subspace method (2D I‐CSM). The position of PD can be located as the intersection of DOAs estimated at two points. In this paper, the finite difference time domain (FDTD) method is applied to simulate the propagation of EM waves emitted from PD, which occurs on distribution line. The proposed method is applied to locate the position of PD based on the simulation results. The method is shown to be useful for locating the position of PD in multipath environment. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Improvement on coherent signal-subspace method using several reference frequencies

An improved coherent signal-subspace method is proposed using several reference frequencies for wideband direction-of-arrival (DOA) estimation. In this proposed method, the whole bandwidth of the received signal is divided into several parts, then a reference frequency is selected from each part for the coherent signal-subspace method to estimate the DOAs of wideband sources separately, and the results from all frequency parts are averaged to obtain a final estimate. Compared with the conventional coherent signal-subspace method, the proposed method achieves higher resolution and smaller root mean square error, especially when the bandwidth of the source is large. The performance of the proposed method is demonstrated and analyzed through the computer simulations.

Estimation of DOAs of EM Waves Emitted from Multiple Partial Discharge Sources in Free Space by Using Wideband Signal Subspace Methods

AbstractDetecting partial discharge (PD) caused by the degradation of insulating materials is needed to prevent the electric breakdown. We have studied radio remote sensing to detect PD. Therefore, it is necessary to remove the electromagnetic (EM) waves reflected on the power equipment when PD source is localized. In this paper, we consider to estimate the direction-of-arrival (DOA) of EM waves emitted from PD in a free space. The signal subspace method, which uses an eigenstructure of the correlation matrix obtained from the received signals, is approved useful to estimate DOA. The finite difference time domain (FDTD) method is used to simulate the propagation of EM waves emitted from PD sources. The wideband signal subspace methods, e.g. coherent signal subspace method (CSSM), test of orthogonality of projected subspace (TOPS), test of orthogonality of frequency (TOFS), and improved CSSM (I-CSSM) are applied to estimate the DOA of EM waves.

Improved TOPS about Direction of Arrival Estimation for Wideband Signals

The study about the direction-of-arrival (DOA) estimation for wideband signals is a basic topic of Signal Processing. The method called test of orthogonality of projected subspaces (TOPS) does not require initial values to form focusing matrix compared with the coherent signal subspace method (CSSM), but it has poor performance for coherent wideband signals at low signal-to-noise ratio (SNR). Based on the lack of the conventional TOPS, this paper reconstructs a set of new matrices with the narrowband correlated matrices coming from the DFT decomposition of the array output and modifies the method frame of the conventional TOPS. So we get a set of reconstructed matrices with full rank corresponding to each frequency bin, and which have no array aperture loss. The improved TOPS can estimate the DOA for coherent wideband sources at low SNR, and enhances the performance of the conventional TOPS. Simulation results show that the improved TOPS is effective, and the total performance of which is similar to the rotational signal-subspace (RSS) method.

A novel wideband DOA estimator based on Khatri–Rao subspace approach

A novel DOA estimation method for uncorrelated wideband sources named focusing Khatri–Rao subspace method (FKR) is proposed based on coherent signal-subspace method (CSM) and Khatri–Rao (KR) subspace. Compared with the conventional CSM that simply averages the covariance matrices of different frequency bins after focusing, FKR transforms the covariance matrices into a higher dimensional matrix through KR product. This method has three major advantages: (1) it achieves a higher resolution than CSM, (2) the root mean square error of DOA estimation from FKR is smaller than that of CSM when the initial angles are inaccurate and (3) it performs well even when the number of sensors is reduced to about half of the sources. The performance of the FKR method is demonstrated and analyzed through the computer simulations.

Pruned Multiangle Resolution Fast Beamforming

Delay-and-sum (DS) beamforming is a simple processing method that can estimate the direction-of-arrival from multiple signal sources. The major advantage of DS beamforming is that it can handle wideband as well as narrowband signals. However, DS beamforming exhibits high computational complexity. The multiangle resolution fast beamformer was proposed as a computationally efficient approximation of DS beamforming, reducing the computational order of complexity from to . In this paper, we introduce the pruned multiangle resolution fast beamformer to further reduce the computational complexity. The new algorithm includes an energy detector at intermediate stages of the fast beamformer to prune sectors that do not exhibit increasing energy consistent with coherent integration. Simulations are provided to assess the performance of the pruned fast beamformer. One use for the estimates from the pruned fast beamformer is to initialize high-resolution direction-of-arrival (DOA) estimators such as coherent signal subspace methods.

TOPS: new DOA estimator for wideband signals

This paper introduces a new direction-of-arrival (DOA) estimation algorithm for wideband sources called test of orthogonality of projected subspaces (TOPS). This new technique estimates DOAs by measuring the orthogonal relation between the signal and the noise subspaces of multiple frequency components of the sources. TOPS can be used with arbitrary shaped one-dimensional (1-D) or two-dimensional (2-D) arrays. Unlike other coherent wideband methods, such as the coherent signal subspace method (CSSM) and WAVES, the new method does not require any preprocessing for initial values. The performance of those wideband techniques and incoherent MUSIC is compared with that of the new method through computer simulations. The simulations show that this new technique performs better than others in mid signal-to-noise ratio (SNR) ranges, while coherent methods work best in low SNR and incoherent methods work best in high SNR. Thus, TOPS fills a gap between coherent and incoherent methods.

Robust auto-focusing wideband DOA estimation

Within the last decade there has been a growing interest in developing techniques for the estimation of the direction of arrival (DOA) of wavefronts carrying wideband signals in order to locate the emitting sources. The coherent signal-subspace method (CSM) is one of the most largely adopted iterative technique based upon the concept of signal-subspace, due to its ability in handling coherent sources, while showing very good detection and resolution thresholds, low bias and high accuracy. Central to CSM is the use of the so-called focusing matrices, whose characteristics strongly influence its overall performance. In the literature, several focusing matrices have been proposed and the most effective of them often require initial estimation of the DOAs, which could be a drawback for the overall estimation procedure. Furthermore classical focusing design techniques do not take into account the fact that at each iteration of the algorithm estimated DOAs may differ from the actual ones on which the manifold should be focused. In this paper we propose a novel focusing matrices design technique aimed at counteracting some of the main disadvantages of other classical focusing matrices. It is shown that the classes of Rotational Signal Subspace and Signal Subspace Transformation focusing matrices leave room for further optimization of the available degrees of freedom, that are exploited here to create a CSM robust against DOA estimation errors. For this reason, the proposed method is referred to as robust coherent signal-subspace method (R-CSM). Thanks to the peculiarities of these novel focusing matrices, the initial preprocessing stage of the classical CSM is no longer required. Furthermore, the convergence speed is improved, because at each iteration the degrees of freedom are used to concentrate the focusing closer and closer about the estimated DOAs.

Application Of Fast Predictive Bearing Algorithm In 3D Wideband Signal Tracking

Many conventional algorithms for direction-of-arrival (DOA) tracking suffer high computational complexity because of the eigendecomposition of the sample covariance matrix. In this paper, we propose a new DOA tracking algorithm that uses the Kalman filter, named the Fast Predictive Angle Tracking (FPAT) algorithm. Because the FPAT algorithm is based on a single snapshot, it requires low computational complexity and is able to track fast-moving targets. A weighting matrix which restrain the angle variation is used to overcome DOA misjudgement caused by abnormally large angular variation when the targets are at or nearby the crossing points. It also applies the prediction characteristic of Kalman filter to prevent the problem of data association. Combining the coherent signal-subspace (CSS) method, the narrowband FPAT algorithm is extended to track the DOA of wideband signals. We also extend the narrowband FPAT algorithm to track the range, azimuth, and elevation of narrowband sources in 3-D space.

Localization of wideband signals using least-squares and total least-squares approaches

In this paper, we introduce a new focusing technique for localization of wideband signals. Relaxing the unitary assumption for the focusing matrices, we formulate the least-square (LS) and the total least-square (TLS) coherent signal-subspace methods. The TLS is an alternative to the conventional LS and uses the fact that errors can exist both in the focusing location matrix as well as in the estimated location matrix at a given frequency bin. To prevent the focusing loss, we use a class of focusing matrices that are constant under multiplication by their Hermitian transpose. The class of unitary matrices comports with this property. We then develop a new focusing technique based on a modification to the TLS (MTLS). It is shown that the computational complexity of the new technique is significantly lower than that for the rotational signal subspace method (RSS). The focusing gain of the new technique is also larger than the focusing gain of the RSS algorithm. The simulation study shows that, compared with the RSS, the new algorithm has a smaller resolution signal to-noise ratio (SNR).

Broadband DOA estimation using frequency invariant beamforming

A new method of direction-of-arrival (DOA) estimation for multiple broadband farfield signals is presented. The technique uses a beamspace preprocessing structure based on frequency invariant beamforming. Specifically, a set of beam-shaping filters focus the received array data in the time domain, thereby avoiding the need for frequency decomposition. Hence, the proposed method is conceptually different from most other broadband DOA estimators, which require frequency decomposition. Numerical results are presented to demonstrate the use of the new method and compare it with conventional coherent signal subspace methods.