Multiple Signal Classification Spectrum Research Articles

Mixed-field source localization based on robust matrix propagator and reduced-degree polynomial rooting

This paper develops two new algorithms based on multiple signal classification (MUSIC) and matrix propagator for near-field (NF) and far-field (FF) source localization, which substantially reduce the computational complexities and can be applied no matter whether the source number is known as a priori. In the developed algorithms, two special fourth-order cumulant (FOC) matrices are constructed. Then the noise subspace is obtained by incorporating lower-upper (LU) decomposition into the matrix propagator approach. This avoids the computationally burdensome eigenvalue decomposition (EVD) or singular value decomposition (SVD) as well as the dependence of source number. The direction-of-arrivals (DOAs) of FF and NF sources are distinguished by the oblique projection and then estimated based on the MUSIC spectrum. To further improve the computational efficiency, an alternating root-propagator scheme is proposed to determine DOAs, where the real lower-degree polynomial is formulated, which increases the computational speed by a factor about eight compared to the standard root-MUSIC. Finally, the NF ranges are calculated from the FOC and the DOA estimates via the least square (LS) criterion. The effectiveness and performance of the proposed approach are validated by using numerical simulation.

Coherent Target Direction‐of‐Arrival Estimation for Coprime Arrays: From Spatial Smoothing Perspective

In this paper, we investigate the issue of direction‐of‐arrival (DOA) estimation of multiple signals in coprime arrays. An algorithm based on multiple signal classification (MUSIC) and forward and backward spatial smoothing (FBSS) is used for DOA estimation of this signal caused by multipath and interference. The large distance between adjacent elements of each subarray in the coprime arrays will bring phase ambiguity issues. According to the feature of the coprime number, the ambiguity problem can be eliminated. The correct DOA estimation can be obtained by searching for the common peak of the spatial spectrum and finding the overlapping peaks in the MUSIC spectrum of the two subarrays. For the rank deficit problem caused by the coherent signal, the FBSS algorithm is used for signal preprocessing before the MUSIC algorithm. Theoretical analysis and simulation results show that the algorithm can effectively solve the rank deficiency and phase ambiguity problems caused by coherent signals and sparse arrays in the coprime arrays.

Asymptotic Performance Analysis of the MUSIC Algorithm for Direction-of-Arrival Estimation

We consider the performance analysis of the multiple signal classification (MUSIC) algorithm for multiple incident signals when the uniform linear array (ULA) is adopted for estimation of the azimuth of each incident signal. We derive closed-form expression of the estimation error for each incident signal. After some approximations, we derive closed-form expression of the mean square error (MSE) for each incident signal. In the MUSIC algorithm, the eigenvectors of covariance matrix are used for calculation of the MUSIC spectrum. Our derivation is based on how the eigenvectors of the sample covariance matrix are related to those of the true covariance matrix. The main contribution of this paper is the reduction in computational complexity for the performance analysis of the MUSIC algorithm in comparison with the traditional Monte–Carlo simulation-based performance analysis. The validity of the derived expressions is shown using the numerical results. Future work includes an extension to performance analysis of the MUSIC algorithm for simultaneous estimation of the azimuth and the elevation.

Compressive Joint Angular and Frequency Spectrum Sensing Based on MUSIC Spectrum Reconstruction

This paper aims to introduce a new tool for wideband spectrum sensing in cognitive radio applications based on the multiple signal classification (MUSIC) two-dimensional (2D)-pseudospectrum, which is able to locate the active sources [licenced users (LUs)] or other secondary users in both the angular and frequency domains. The proposed tool consists of two-stages compression and reconstruction procedures. The spatial-domain compression is introduced by activating only some of the antennas in the underlying uniform linear array (ULA) leading to a non-ULA of active antennas. The time-domain compression is introduced by allowing the receivers connected to every active antenna to sample the analog signals below the Nyquist rate. This compression aims to alleviate the burden on the analog-to-digital converter especially when a broad frequency band has to be sensed. The simulation study shows that the constructed MUSIC 2D-pseudospectrum can be used to locate the direction-of-arrival (DoA) and the frequency band of the LUs with a much better resolution than the one that can be afforded by the already proposed 2D power spectrum. Note that the number of sources is beyond that of active antennas and the sampling rate in each receiver is only 17 / 42 times the Nyquist rate. Moreover, the evaluation on the root mean square error in terms of DoA estimation indicates that the proposed MUSIC 2D-pseudospectrum construction approach outperforms the already proposed 2D power spectrum reconstruction method. In fact, the performance of the proposed approach based on the sub-Nyquist-rate samples is only slightly below the approach that is based on the pseudospectrum constructed from Nyquist-rate samples. Furthermore, the evaluation on the detection performance of the spectrum sensing tool based on the MUSIC 2D-pseudospectrum underlines the promising benefits of the proposed approach.

MUSIC-based Non-contact Heart Rate Estimation with Adaptive Window Size Setting.

Continuous HR (Heart Rate) monitoring enables the stress estimation in daily life. A Doppler sensor could be a key device to facilitate the non-contact HR estimation. As one of the Doppler sensor-based HR estimation methods, we have previously proposed a MUSIC (MUltiple SIgnal Classification)-based HR estimation method. MUSIC is the algorithm widely used as a tool to estimate DOA (Direction of Arrival). In our previous method, MUSIC spectrum is calculated in each sliding window, and then HR is estimated by the maximum peak detection over the MUSIC spectrum. However, when HR changes largely within the window, several peaks due to heartbeats appear over the MUSIC spectrum, which might cause the incorrect peak detection. Hence, an adaptive window is required so that only one peak appears. In this paper, we propose a MUSIC-based HR estimation method with an adaptive window size setting. When several peaks due to heartbeats appear over the MUSIC spectrum, our proposed method shortens the time window and re-calculates the MUSIC spectrum, which is repeated until only one peak appears. The experimental results showed that our method outperformed not only our previous one but also the other existing MUSIC-based HR estimation one in terms of the estimation accuracy of the HR, the stress indexes CVI (Cardiac Vagal Index) and CSI (Cardiac Sympathetic Index).

Hilbert-Transform-Based Accurate Determination of Ultrashort-Time Delays in Terahertz Time-Domain Spectroscopy

Accurate determination of time delays is crucial for distinguishing a sample's different interfaces in terahertz time-domain spectroscopy (THz-TDS), especially for ultrathin samples or interfacial gaps. In this paper, Hilbert transform (HT) is invoked, along with posttransform signal spectral estimation of several varieties, including the conventional, that based on multiple-signal classification spectrum estimation (HT-MUSIC), and that based on autoregressive spectrum estimation using Yule–Walker law (HT-AR), to determine the sample's different interfaces. The results are compared with the traditional method of obtaining time delays in THz-TDS, along with analysis of the resolution and accuracy, as well as advantages and deficiencies of the various approaches. It is demonstrated that HT is an effective method for determining different interfaces of an ultrathin sample by simulation and experiments. The simulation results show that MUSIC-HT has the best resolution, at about 0.35 ps and AR-HT has the best accuracy, whose error is less than 0.075 ps. Experimental results for ultrathin air gaps and polymer films confirmed that MUSIC-HT can distinguish time delays as short as 0.44 ps from the THz time-domain spectra.

Millimeter-Wave Channel Estimation Based on 2-D Beamspace MUSIC Method

Due to the spatial sparsity caused by severe propagation loss, mm-wave channel estimation can be performed by estimating the directions and gains of the paths that have significant power. In this paper, we apply the beamspace 2-D multiple signal classification (MUSIC) method to estimate the path directions (the angles of departure and arrival) and use the least-squares method to estimate the path gains. Different from its element-space counterpart, the beamspace MUSIC method may exhibit spectrum ambiguity caused by the beamformers. In this paper, we therefore analyze the sufficient conditions on the beamformers under which the MUSIC spectrum has no ambiguity which also leads to the maximum number of resolvable path directions. Moreover, based on the uniform linear array with half-wavelength spacing, we show that the discrete Fourier transform beamformers, which are naturally analog and often employed in the mm-wave communication systems with hybrid precoding structure, can avoid the spectrum ambiguity and maximize the number of resolvable path directions. Simulation results demonstrate that the proposed 2-D beamspace MUSIC mm-wave channel estimator significantly outperforms existing estimators that are based on beam training and sparse recovery; and in the meantime, it requires much less training slots than these existing methods.

DOA Estimation Using Second-Order Differential of Invariant Noise MUSIC (SODIN-MUSIC)

Sensor arrays are widely used to locate the radiating sources by estimating the direction of arrival (DOA) of their incident signals. Among the most well-known methods employed for DOA estimation is the multiple signal classification (MUSIC). MUSIC provides outstanding performance in estimating DOAs in good propagation environments; however, it fails to estimate the DOAs in severe environments like low signal-to-noise ratio, small number of snapshots, when the incident waves are coming from close angles or when the sources are highly correlated. In this paper, we propose a new approach for DOA estimation with super-resolution capabilities and high accuracy even in the severe environments. The proposed approach is based on computing the second-order differential of invariant noise MUSIC (SODIN-MUSIC) spectrum. SODIN-MUSIC benefits from extracting useful information provided by the second-order differential of MUSIC spectrum and also utilizing the invariance property of noise subspace with respect to changing the power of the emitted signals. In this paper, the proposed SODIN-MUSIC method is developed to estimate both one-dimensional and two-dimensional DOA with any arbitrary array configurations. The simulation results show that SODIN-MUSIC yields superior performance in all distinct environments if compared to both conventional MUSIC and other newly developed MUSIC-based methods.

High-performance MIMO imaging radar with hybrid transmit and receive arrays

In this study, a sparse multiple-input multiple-output radar system with difference co-array processing is presented. It consists of two non-uniform transmitter arrays in split configuration and a symmetrical hybrid receiver array. A combination of a periodically thinned array and two non-uniform sub-arrays is used to construct the receiver structure. A low-cost three-step optimization procedure is proposed to synthesize the array arrangement with system constraints. In addition, a combination of fast Fourier transform (FFT) and MUltiple SIgnal Classification (MUSIC) techniques is applied for a range/direction-of-arrival estimation with low computational effort. High angular resolution is achieved in the MUSIC spectrum by implementing a difference co-array concept together with spatial smoothing. A thinning rate in excess of 95% is demonstrated. Lastly, the performance of the proposed system is validated by measurements of point scatterers and extended objects.

MUSICに基づくパーティクルフィルタによる２音源追尾の高速化

In this paper, MUSIC (multiple signal classification) algorithm is applied for a sound source tracking using particle filters. MUSIC algorithm is a high-resolution sound source localization method but has high computational costs. Therefore, a reduction of computational cost is attempted by using the MUSIC spectrum function as a likelihood function of particle filters. When there are two sound sources, however, a particle intensification problem arises simultaneously. Therefore, a method to overcome this problem is also proposed. Several experimental results in a reverberant environment show that the proposed method can track two sound sources in real time.

A fast computation method for MUSIC spectrum function based on circular arrays

The large computation amount of multiple signal classification (MUSIC) spectrum function seriously affects the timeliness of direction finding system using MUSIC algorithm, especially in the two-dimensional directions of arrival (DOA) estimation of azimuth and elevation with a large antenna array. This paper proposes a fast computation method for MUSIC spectrum. It is suitable for any circular array. First, the circular array is transformed into a virtual uniform circular array, in the process of calculating MUSIC spectrum, for the cyclic characteristics of steering vector, the inner product in the calculation of spatial spectrum is realised by cyclic convolution. The computational amount of MUSIC spectrum is obviously less than that of the conventional method. It is a very practical way for MUSIC spectrum computation in circular arrays.

Resolving Manifold Ambiguities for Sparse Array Using Planar Substrates

Aiming to resolve the manifold ambiguities for sparse arrays, a method based on the multiple signal classification (MUSIC) algorithm using planar substrate is proposed. The main reason for spurious MUSIC spectrum is that the steering vector of spurious direction of arrival (DOA) is a linear combination of the steering vectors of true DOAs. The main idea of the proposed method is to add some planar substrates at the front-ends of the elements of an array. The refractive indices and thicknesses of the substrates can be different from each other. This treatment breaks down the linearity which induces the ambiguity of a sparse array. Because the equivalent positions of the elements change for different DOAs after adding the substrates on the array, the spurious peaks will disappear or not overlap on the old peaks. Nevertheless the peaks of the true directions will remain. The spurious peaks can be discriminated according to this feature. Simulation results demonstrate the effectiveness and the feasibility of the method. Meanwhile the simulation results also show that the proposed method can partially resolve the trivial ambiguities even if the true DOA and the spurious DOA are confined to (0°, 180°).

Radar target classification method with high accuracy and decision speed performance using MUSIC spectrum vectors and PCA projection

This paper introduces the performance of an electromagnetic target recognition method in resonance scattering region, which includes pseudo spectrum Multiple Signal Classification (MUSIC) algorithm and principal component analysis (PCA) technique. The aim of this method is to classify an “unknown” target as one of the “known” targets in an aspect‐independent manner. The suggested method initially collects the late‐time portion of noise‐free time‐scattered signals obtained from different reference aspect angles of known targets. Afterward, these signals are used to obtain MUSIC spectrums in real frequency domain having super‐resolution ability and noise resistant feature. In the final step, PCA technique is applied to these spectrums in order to reduce dimensionality and obtain only one feature vector per known target. In the decision stage, noise‐free or noisy scattered signal of an unknown (test) target from an unknown aspect angle is initially obtained. Subsequently, MUSIC algorithm is processed for this test signal and resulting test vector is compared with feature vectors of known targets one by one. Finally, the highest correlation gives the type of test target. The method is applied to wire models of airplane targets, and it is shown that it can tolerate considerable noise levels although it has a few different reference aspect angles. Besides, the runtime of the method for a test target is sufficiently low, which makes the method suitable for real‐time applications.

Radar target classification method with reduced aspect dependency and improved noise performance using multiple signal classification algorithm

This study introduces a novel aspect and polarisation invariant radar target classification method based on the use of multiple signal classification (MUSIC) algorithm for feature extraction. In the suggested method, for each candidate target at each designated reference aspect, feature matrices called ‘MUSIC spectrum matrices (MSMs)’ are constructed using the target's scattered data at different late-time intervals. An individual MSM corresponds to a map of a target's natural resonance-related power distribution over the complex frequency plane under the chosen aspect angle/late-time interval conditions. The collection of these feature matrices is used first to determine the best late-time interval for optimal feature extraction. Then, the MSM of a target, which are computed over the optimal time interval at all reference aspects, are superposed to obtain the ‘fused MUSIC spectrum matrix (FMSM)’. The FMSM of a target is its main classifier feature in the proposed method as the aspect dependency of an FMSM is highly reduced because of its multi-aspect construction process. The suggested method is demonstrated for both simple and complex target geometries such as conducting spheres, dielectric spheres and small-scale aircraft targets with high accuracy rates even for low SNR values using feature fusion at only a few different reference aspects.

Fast music spectrum peak search VIA Metropolis-Hastings sampler

A fast MUltiple SIgnal Classification (MUSIC) spectrum peak search algorithm is devised, which regards the power of the MUSIC spectrum function as target distribution up to a constant of proportionality, and uses Metropolis-Hastings (MH) sampler, one of the most popular Markov Chain Monte Carlo (MCMC) techniques, to sample from it. The proposed method reduces greatly the tremendous computation and storage costs in conventional MUSIC techniques i.e., about two and four orders of magnitude in computation and storage costs under the conditions of the experiment in the paper respectively.