Conventional Multiple Signal Classification Research Articles

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

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

Frequency estimation of multiple complex sinusoids using noise suppressing predictive FIR filter

The paper presents a predictive filter based frequency estimation algorithm (PF-FE) for multiple complex sinusoids corrupted by additive white Gaussian noise. The proposed frequency estimator combines the noise suppression capability of an FIR filter with a least squares approach minimizing the sum of the squared errors of a prediction filter. The FIR filter coefficients are chosen such that the sinusoidal components are predicted with minimum distortion. Computer simulation results are given to contrast the performance of the proposed PF-FE method with six other state-of-the-art frequency-estimators and the Cramer-Rao lower bound. Furthermore, the paper provides a complexity analysis of the PF-FE method and compares it with those of the conventional MUltiple SIgnal Classification algorithm and some selected state-of-the-art methods from the literature. Performance of the proposed PF-FE method is validated with effective mean square error (EMSE) plots for model orders of three and five and under different observation lengths and signal-to-noise ratio values. Finally, the paper demonstrates how EMSE varies for the proposed method when the prediction filter length is increased from 20 to 75. After extensive simulations, it is observed that when filter length is larger than half the observation length the EMSE will start to degrade.

Channel Reconstruction-Aided MUSIC Algorithms for Joint AoA&AoD Estimation in MIMO Systems

This letter discusses the issue of joint angle-of-arrival (AoA) and angle-of-departure (AoD) estimation for multi-input multi-output (MIMO) arrays, so as to conceive a novel one-snapshot multiple signal classification (MUSIC)-derived algorithm based on channel reconstruction therein. Compared to conventional two-dimensional MUSIC (2D-MUSIC), not only does the proposed algorithm avoid the problem of matrix rank deficit, but it also brings a prominent complexity reduction yet achieving satisfactory accuracy. Simulation results verify the utility and advancement of our algorithm, especially in the scheme with high real-time requirements.

DOA Estimation of Indoor Sound Sources Based on Spherical Harmonic Domain Beam-Space MUSIC

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm.

Azimuth Estimation for the Backscatter Device in Ambient Backscatter Communication System

In this letter, we study the azimuth estimation for the backscatter device (BD) in ambient backscatter communication system, where the receiver is equipped with the uniform linear array (ULA). By utilizing the covariance matrices in two symbol periods with different BD symbols, we apply the conventional multiple signal classification (MUSIC) algorithm to estimate the azimuths of both the BD and the ambient radio frequency (RF) source. Then, we propose a novel eigenvector-based algorithm to identify the azimuth of the BD from the two estimated azimuths. Moreover, we qualitatively analyze the impacts of the reflection coefficients on the performance of the proposed azimuth estimation approach. Finally, the simulation results are provided to validate the effectiveness of the proposed method and to justify the qualitative analytical conclusions.

FMCW Radar Estimation Algorithm with High Resolution and Low Complexity Based on Reduced Search Area.

We propose a frequency-modulated continuous wave (FMCW) radar estimation algorithm with high resolution and low complexity. The fast Fourier transform (FFT)-based algorithms and multiple signal classification (MUSIC) algorithms are used as algorithms for estimating target parameters in the FMCW radar systems. FFT-based and MUSIC algorithms have tradeoff characteristics between resolution performance and complexity. While FFT-based algorithms have the advantage of very low complexity, they have the disadvantage of a low-resolution performance; that is, estimating multiple targets with similar parameters as a single target. On the other hand, subspace-based algorithms have the advantage of a high-resolution performance, but have a problem of very high complexity. In this paper, we propose an algorithm with reduced complexity, while achieving the high-resolution performance of the subspace-based algorithm by utilizing the advantages of the two algorithms; namely, the low-complexity advantage of FFT-based algorithms and the high-resolution performance of the MUSIC algorithms. The proposed algorithm first reduces the amount of data used as input to the subspace-based algorithm by using the estimation results obtained by FFT. Secondly, it significantly reduces the range of search regions considered for pseudo-spectrum calculations in the subspace-based algorithm. The simulation and experiment results show that the proposed algorithm achieves a similar performance compared with the conventional and low complexity MUSIC algorithms, despite its considerably lower complexity.

Probability of Resolution of MUSIC and g-MUSIC: An Asymptotic Approach

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in the asymptotic regime.

Multi-Source DoA Estimation of EM Waves Impinging Spherical Antenna Array With Unknown Mutual Coupling Using Relative Signal Pressure Based Multiple Signal Classification Approach

Spherical antenna array (SAA) is a configuration that scans almost all the radiation sphere with constant directivity. It finds applications in spacecraft and satellite communication. Multiple signal classification (MUSIC) is a widely used multiple source direction-of-arrival (DoA) estimation method because of its low complexity implementation in practical applications. Conversely, it is susceptible to noise, which consequently affects its accuracy of localization. In this paper, MUSIC-based methods that operate at low signal-to-noise ratio (SNR) are developed via relative electromagnetic (EM) wave pressure measurements of a SAA. The proposed methods are the relative pressure MUSIC (RP-MUSIC), and in spherical domain (SH-RP-MUSIC). The developed SH-RP-MUSIC algorithm is in spherical domain thereby allows frequency-smoothing approach for the de-correlation of the coherent source signals towards an enhanced accuracy of localization. Both RP-MUSIC and SH-RP-MUSIC algorithms developed have the ability to estimate the number of active sources that is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the conventional MUSIC algorithm. Numerical experiments were used to demonstrate the adequacy of the developed algorithms. In addition, measured data from experiment, which is the practically acceptable way to examine any procedure is employed to demonstrate the merits of the developed algorithms against the conventional MUSIC algorithm and other recent multiple source localization method in literature. Finally, in order to achieve DoA estimations with adequate localization accuracy at low SNR using SAA, SH-RP-MUSIC algorithm is a better choice.

Computationally Efficient Direction-of-Arrival Estimation Algorithms for a Cubic Coprime Array.

In this paper, we investigate the problem of direction-of-arrival (DOA) estimation for massive multi-input multi-output (MIMO) radar, and propose a total array-based multiple signals classification (TA-MUSIC) algorithm for two-dimensional direction-of-arrival (DOA) estimation with a coprime cubic array (CCA). Unlike the conventional multiple signal classification (MUSIC) algorithm, the TA-MUSIC algorithm employs not only the auto-covariance matrix but also the mutual covariance matrix by stacking the received signals of two sub cubic arrays so that full degrees of freedom (DOFs) can be utilized. We verified that the phase ambiguity problem can be eliminated by employing the coprime property. Moreover, to achieve lower complexity, we explored the estimation of signal parameters via the rotational invariance technique (ESPRIT)-based multiple signal classification (E-MUSIC) algorithm, which uses a successive scheme to be computationally efficient. The Cramer–Rao bound (CRB) was taken as a theoretical benchmark for the lower boundary of the unbiased estimate. Finally, numerical simulations were conducted in order to demonstrate the effectiveness and superiority of the proposed algorithms.

Ameliorated-multiple signal classification (Am-MUSIC) for damage imaging using a sparse sensor network

Multiple Signal Classification (MUSIC) – a directional scanning and searching algorithm, has gained its prominence in phased array-facilitated nondestructive evaluation. Nevertheless, prevailing MUSIC algorithms are largely bound up with the use of a dense linear array, which fail to access the full planar area of an inspected sample, leaving blind zones to which an array fails to scan, along with the incapability of differentiating multiple damage sites that are close one from another. To break above limitations, conventional MUSIC algorithm is ameliorated in this study, by manipulating the signal representation matrix at each pixel using the excitation signal series, instead of the scattered signal series, which enables the use of a sparse sensor network with arbitrarily positioned transducers. In the ameliorated MUSIC (Am-MUSIC), the orthogonal attributes between the signal subspace and noise subspace inherent in the signal representation matrix is quantified, in terms of which the Am-MUSIC yields a full spatial spectrum of the inspected sample, and damage, if any, can be visualized in the spectrum. Am-MUSIC is validated, in both simulation and experiment, by evaluating single and multiple sites of damage in plate-like waveguides with a sparse sensor network. Results verify that i) detectability of Am-MUSIC-driven damage imaging is not limited by damage quantity; ii) Am-MUSIC has full access to a sample, eliminating blind zones; and iii) the amelioration expands conventional MUSIC from phased array-facilitated nondestructive evaluation to health monitoring using built-in sparse sensor networks.

High-Efficiency Super-Resolution FMCW Radar Algorithm Based on FFT Estimation.

This paper proposes a high-efficiency super-resolution frequency-modulated continuous-wave (FMCW) radar algorithm based on estimation by fast Fourier transform (FFT). In FMCW radar systems, the maximum number of samples is generally determined by the maximum detectable distance. However, targets are often closer than the maximum detectable distance. In this case, even if the number of samples is reduced, the ranges of targets can be estimated without degrading the performance. Based on this property, the proposed algorithm adaptively selects the number of samples used as input to the super-resolution algorithm depends on the coarsely estimated ranges of targets using the FFT. The proposed algorithm employs the reduced samples by the estimated distance by FFT as input to the super resolution algorithm instead of the maximum number of samples set by the maximum detectable distance. By doing so, the proposed algorithm achieves the similar performance of the conventional multiple signal classification algorithm (MUSIC), which is a representative of the super resolution algorithms while the performance does not degrade. Simulation results demonstrate the feasibility and performance improvement provided by the proposed algorithm; that is, the proposed algorithm achieves average complexity reduction of compared to the conventional MUSIC algorithm while achieving its similar performance. Moreover, the improvement provided by the proposed algorithm was verified in practical conditions, as evidenced by our experimental results.

Terahertz reflection imaging using virtual arrays and MUSIC in a synthetic aperture array

Terahertz imaging using synthetic aperture arrays (SAAs) is an attractive nondestructive measurement method, as it can increase the spatial resolution while reducing the restrictions on target placement. MUltiple SIgnal Classification (MUSIC), which is a high-resolution direction of arrival estimation method, is also attractive because it increases the resolution of terahertz imaging. However, the resolution of the MUSIC spatial spectrum deteriorates when correlated signals are received. Spatial smoothing (SS) can reduce the correlation of incoming waves; however, this technique is only applicable to equispaced linear arrays in plane wave reception environments. This paper introduces MUSIC with SS to THz imaging using an arcuate SAA by applying array interpolation using virtual arrays. The imaging results and position estimation accuracy using simulated or measured arcuate synthetic array responses of two metal wire targets demonstrate the effectiveness of the method compared with the conventional beamformer and MUSIC methods.

Joint Channel and AoA Estimation in OFDM Systems: One Channel Tap With Multiple AoAs Problem

Recently, a joint channel and angle-of-arrival (AoA) estimation scheme for pilot-assisted multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with digital arrays has been proposed; in that scheme, compressive sensing-based time-domain channel estimation is applied. In the scheme, it is assumed that each channel tap has only one AoA. However, in reality, one channel tap may contain responses from multiple paths with different AoAs. In this letter, we propose an improved approach to solve the aforementioned problem. The underlying concept is to transmit multiple OFDM symbols with different beamforming vectors, rendering the time-invariant channel equivalently time-variant. Subsequently, the correlation matrix, imbedded with AoA information, can be estimated. Finally, subspace-based algorithms, such as multiple signal classification (MUSIC), can be used for AoA estimation. The advantage of the proposed method is that the number of detectable AoAs is much larger than that in conventional MUSIC. The performance of the proposed method was also theoretically analyzed. Simulation results demonstrated that with a small number of OFDM symbols, both channel gains and AoAs could be satisfactorily estimated and the theoretical analysis results were accurate.

One-Dimensional MUSIC-Type Algorithm for Spherical Microphone Arrays

Spherical microphone arrays have been widely used in direction-of-arrival (DOA) estimation in recent years. The conventional multiple signal classification method formulated in spherical harmonic domain (SHMUSIC) is computationally expensive, particularly in the application of joint estimation of the azimuth and elevation. In this paper, one-dimensional MUSIC-type approach (ODMUSIC) is proposed to estimate the elevation and azimuth. We construct a mapping matrix between the spherical harmonic function and Fourier series, then utilize the Vandermonde structure of Fourier series to develop the polynomial rooting method. The mapping matrix only depends on the array configuration and can be calculated prior to DOA estimation. The two-dimensional angle search can be transformed into two one-dimensional angle findings based on the mapping matrix. By using the characteristic of Fourier series, we can construct two root polynomials to estimate the azimuth and elevation, respectively. The proposed method can avoid the two-dimensional spectral search and the angles are automatically paired. Computer simulations validate the effectiveness of the proposed method.

Off-Grid Direction-of-Arrival Estimation Based on Steering Vector Approximation

In this paper, a novel off-grid direction-of-arrival (DOA) estimation algorithm is proposed based on steering vector approximation. The conventional multiple signal classification (MUSIC) technique estimates the DOA with a uniformly discretized grid by assuming that the true DOAs lie on the grids. In practice, this assumption is rarely satisfied. In order to improve the estimation accuracy, a dense sampling grid is required for the MUSIC technique. Besides the higher computational complexity, it is still not guaranteed that the dense sampling grids will cover the true DOAs. In order to address the off-grid problem with a lower computational complexity, we use the Taylor series expansion to approximate the steering vectors. We first construct a two-dimensional spectrum searching method to simultaneously estimate the nearest on-grid DOA and the corresponding off-grid error. To further improve the estimation accuracy, we then solve an optimization problem to obtain the accurate DOA estimation, which is formulated by the fact that the signal and noise subspaces are orthogonal to each other. Simulation results demonstrate the effectiveness of the proposed off-grid DOA estimation algorithm.

Damage identification for plate-like structures using ultrasonic guided wave based on improved MUSIC method

The ultrasonic guided wave has emerged as one of the most prominent and promising tools for metal and composite structures in the fields of structural health monitoring (SHM) and nondestructive testing (NDT). This paper presents a novel model-based 2D multiple signal classification (MUSIC) damage identification algorithm for plate-like structures. Unlike the conventional MUSIC algorithm, the proposed model-based 2D MUSIC damage identification algorithm is deduced based on the assumption of near-field according to the propagation model of guided waves. Since scattered signals contain the location information of damage, the cross-correlation function of residual signals received by experiment and scattered signals received by damage scattering model are developed for spatial spectrum estimation MUSIC algorithm. Due to the uncorrelation of signal and noise, the damage can be successfully identified by searching the peak point of spatial spectrum in the monitored area employing the orthogonality of signal subspace and noise subspace. The accuracy and effectiveness of the proposed method are firstly validated by numerical simulation on aluminum plate, and the general applicability is further verified by experiments for the damage identification of laminated composite plate. The numerical and experimental results demonstrate the proposed damage identification algorithm is appropriate for damage identification of plate-like structures with high estimation accuracy and resolution.

Joint Estimation of Azimuth and Elevation via Manifold Separation for Arbitrary Array Structures

Direction-of-arrival estimation is a ubiquitous task in array processing. The conventional MUltiple SIgnal Classification (MUSIC) method is often computationally expensive, particularly in the application of joint azimuth and elevation estimation. In this paper, we propose an efficient way to compute the two-dimentional (2D) spatial spectrum. By using the manifold separation technique, we find that the 2-D null-spectrum has the form of discrete Fourier transform (DFT). Moreover, the coefficients of the DFT form can be truncated and computed in parallel. Then by exploiting the fact that the nonzero coefficients are concentrated only at the top-left corner, we present a partial 2-D DFT to compute the 2-D spatial spectrum, which can reduce the latency significantly. In order to improve the estimation performance, we formulate an iterative multidimensional-subspace-fitting estimator in which we apply the first-order Taylor expansion to expand the projection operator. At each iteration, the estimation errors can be computed by solving a set of linear equations. Numerical results demonstrate that the proposed estimator offers better estimation performance compared with the classical 2-D MUSIC.

Efficient implementation of the ML estimator for high‐resolution angle estimation in an unmanned ground vehicle

Using a maximum-likelihood (ML) estimator for high-resolution angle estimation is well-suited for automotive radars. It is superior to other estimators in cases of small antenna aperture, small samples, and correlated signals. However, the computing power it requires prevents its widespread implementation. In this study, the authors propose a novel implementation method of the ML estimator that achieves appropriate memory requirements and computational costs by defining new variables. The proposed method is appropriate for practical implementation because calculation of the objective function is based only on independent multiply-add operations and can be easily parallelised. Real measured data from their radar of an unmanned ground vehicle system demonstrates the performance of the proposed method. Experimental results show that the proposed ML estimator is more robust than the conventional MUltiple SIgnal Classification method under conditions of low signal-to-noise ratio and a small number of snapshots.

Two‐dimensional direction of arrival estimation for coprime planar arrays via a computationally efficient one‐dimensional partial spectral search approach

The authors investigate the problem of two-dimensional (2D) direction of arrival (DOA) estimation of multiple signals for coprime planar arrays (CPAs) in this study and they propose a computationally efficient 1D partial spectral search approach based on multiple signal classification (MUSIC) algorithm. The conventional 2D MUSIC algorithm for CPAs has a great DOA estimation performance, but suffers from a tremendously expensive computational complexity due to the 2D spectral search. To this end, the proposed approach first decreases the dimension of the spectrum function to one dimension and then utilises the linear relationship between the true and ambiguous DOA estimates to form a 1D partial spectral search over a small sector. Finally, the true DOA estimates can be achieved based on the coprime property. The proposed approach can have an impressively good DOA estimation performance, but with a low computational cost. Simulation results validate the effectiveness and superiority of the proposed approach.

A bias-compensated MUSIC for small number of samples

The multiple signal classification (MUSIC) method is known to be asymptotically efficient, yet with a small number of snapshots its performance degrades due to bias in MUSIC localization function. In this communication, starting from G-MUSIC which improves over MUSIC in low sample support, a high signal to noise ratio approximation of the G-MUSIC localization function is derived. This approximation results in closed-form expressions of the weights applied to each eigenvector of the sample covariance matrix. A new method which consists in minimizing this simplified G-MUSIC localization function is thus introduced, and referred to as sG-MUSIC. Interestingly enough, this sG-MUSIC criterion can be interpreted as a bias correction of the conventional MUSIC localization function. Numerical simulations indicate that sG-MUSIC incur only a marginal loss in terms of mean square error of the direction of arrival estimates, as compared to G-MUSIC, and performs better than MUSIC.