Multiple Signal Classification Algorithm Research Articles

An Efficient MUSIC Algorithm Enhanced by Iteratively Estimating Signal Subspace and Its Applications in Spatial Colored Noise

The classical multiple signal classification (MUSIC) algorithms mainly have two limitations. One is an insufficient number of snapshots, which usually causes an ill-posed sample covariance matrix in many real applications. The other limitation is the intense space-colored and time-white noise, which also breaks the separability between signal and noise subspaces. In the case of the insufficient sample, there are few signal components in the non-zero delay sample covariance matrix (SCM), where the space-colored and time-white noise components are suppressed by the temporal method. A set of non-zero delay sample covariance matrices are constructed, and a nonlinear object function is formulated. Hence, the sufficient non-zero delay SCMs ensure that enough signal components are used for signal subspace estimation. Then, the constrained optimization problem is converted into an unconstrained one by exploiting the Lagrange multiplier method. The nonlinear equation is solved by Newton’s method iteratively. Moreover, a proper initial value of the new algorithm is given, which can improve the convergence of the iterative algorithm. In this paper, the noise subspace is removed by the pre-projection technique in every iteration step. Then, an improved signal subspace is obtained, and a more efficient MUSIC algorithm is proposed. Experimental results show that the proposed algorithm achieves significantly better performance than the existing methods.

A low-complexity two-dimensional DOA estimation algorithm based on an L-shaped sensor array

In this paper, a derivative-based MUSIC (multiple signal classification) algorithm for a mixture of circular and noncircular signals (DB-MUSIC-M) is proposed for two-dimensional (2D) direction of arrival (DOA) estimation employing an L-shaped uniform array. The DB-MUSIC-M transforms the 2D DOA estimation problem into a single one-dimensional (1D) estimation by finding the derivative of the objective function of the 2D improved MUSIC (I-MUSIC) algorithm, which greatly reduces its computational complexity. As it utilizes both the pseudo covariance matrix and the covariance matrix of the array data, the maximum number of signals that can be estimated is much higher than the total number of sensors. As a special case, the derivative-based MUSIC (DB-MUSIC) for circular signals is also proposed. There is no need for angle pairing for the proposed algorithms and they can handle the angle ambiguity problem effectively. As shown by simulation results, the proposed DB-MUSIC-M algorithm outperforms existing algorithms, with significantly reduced complexity compared to a direct 2D search method. Moreover, the proposed approach can be applied to some other array structures such as the uniform planar array.

Gain-Phase Error-Calibrated Piezoelectric Sensor Array-Based Impact Localization on Stiffened Curved Composite Structures.

Stiffened structure-induced gain-phase errors degrade the performance of the high-resolution two-dimensional multiple signal classification (2D-MUSIC) algorithm, which makes it impossible to ensure the high accuracy of impact localization results. To eliminate the localization bias caused by these errors, a calibrated 2D-MUSIC-based impact localization method is first introduced. Firstly, time-frequency characteristics of the non-stationary impact signals are evaluated by experiment to obtain a clear first wave packet or a wave packet that purely corresponds to a single mode through continuous wavelet transform (CWT). Then, the uniform linear array covariance matrix with gain-phase errors is calibrated to be constructed as a Toeplitz structural matrix. By reconstructing covariance matrix R, 2D-MUSIC-based impact localization is calibrated for stiffened curved composite structures. Experimental research on the stiffened curved composite panel is carried out, and these impact localization results demonstrate the validity and effectiveness of the calibrated 2D-MUSIC-based method.

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.

Angle of arrival estimation in a multi-antenna software defined radio system: impact of hardware and radio environment

Contemporary wireless communication transceivers can utilize their multiple antennas to improve positioning abilities. Angle of Arrival (AoA) estimation utilizes shifts in phase between the signal of interest arriving at different receiving antennas. Software Defined Radio (SDR) USRP B210 and GNU Radio implementing the Root Multiple Signal Classification (Root-MUSIC) algorithm are used in this paper. However, this setup requires the consideration of errors caused by hardware and radio environment. The impact of these effects is shown using an analytical model, assessed, mostly by measurements, and relevant solutions are proposed. The hardware distortions are caused mostly by synchronization errors. The intricacies of the most problematic phase synchronization are investigated with the wired setup showing, e.g., changes with frequency or gain. Both synchronizations emitting calibration tone from the same radio front end, resulting in cross-talk, or a separate one are tested. Recommendations enhancing the performance of the system and alleviating hardware imperfections are provided in this paper. The accuracy of AoA estimation is degraded by multipath propagation or radio interference. A signal processing scheme including filtering has been proposed. A set of over-the-air experiments assessed the performance of the system. The presented and publicly available software package, scalable to a higher number of RX antennas, enables straightforward implementation by other researchers.

Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold.

Inspection robots are widely used in the field of smart grid monitoring in substations, and partial discharge (PD) is an important sign of the insulation state of equipment. PD direction of arrival (DOA) algorithms using conventional beam forming and time difference of arrival (TDOA) require large-scale antenna arrays and high computational complexity, making them difficult to implement on inspection robots. To address this problem, a novel directional multiple signal classification (Dir-MUSIC) algorithm for PD direction finding based on signal strength is proposed, and a miniaturized directional spiral antenna circular array is designed in this paper. First, the Dir-MUSIC algorithm is derived based on the array manifold characteristics. This method uses strength intensity information rather than the TDOA information, which could reduce the computational difficulty and the requirement of array size. Second, the effects of signal-to-noise ratio (SNR) and array manifold error on the performance of the algorithm are discussed through simulations in detail. Then, according to the positioning requirements, the antenna array and its arrangement are developed and optimized. Simulation results suggested that the algorithm has reliable direction-finding performance in the form of six elements. Finally, the effectiveness of the algorithm is tested by using the designed spiral circular array in real scenarios. The experimental results show that the PD direction-finding error is , which meets the need for partial discharge DOA estimation using inspection robots in substations.

Localization of Dielectric Anomalies with Multi-Monostatic S11 Using 2D MUSIC Algorithm with Spatial Smoothing.

This article demonstrates that the complex value of S11 of an antenna, acquired in a multi-monostatic configuration, can be used for localization of a dielectric anomaly hidden inside a dielectric background medium when the antenna is placed close (~5 mm) to the geometry. It uses an Inverse Synthetic Aperture Radar (ISAR) imaging framework where data is acquired at multiple frequencies and look-angles. Initially, near-field scattering data are used for simulation to validate this methodology since the basic derivation of the Multiple Signal Classification (MUSIC) algorithm is based on the plain wave assumption. Later on, from an applications perspective, data acquisition is performed using an antipodal Vivaldi antenna that has eight constant-width slots on each arm. This antenna operates in a frequency range of 1 to 8.5 GHz and its S11 is fed to the 2D MUSIC algorithm with spatial smoothing whereas the antenna artifact and background effect are removed by subtracting the average S11 at each antenna location. Measurements reveal that this methodology gives accurate results with both homogeneous and inhomogeneous backgrounds because the size of data sub-arrays trades between the image noise and resolution, hence reducing the effect of inhomogeneity in the background. In addition to near-field ISAR imaging, this study can be used in the ongoing research on breast tumors and brain stroke detection, among others.

DOA estimation algorithm based on spread spectrum sequence in low signal-to-noise ratio

Spread spectrum communication is a common communication method in underwater communication. Based on the space-time processor received by the array, it can filter the signals arriving along each path separately. Combined with the diversity of space-time clusters, it can effectively improve the communication system’s reliability. The core problem of the space-time processor is the direction of arrival (DOA) and signal source number estimation. Based on the good self-coherence of the spread spectrum sequence, this paper proposes a multiple signal classification algorithm (MUSIC) for accurate DOA estimation. However, since the MUSIC algorithm uses the received signal’s covariance matrix for DOA estimation, the number of sources needs to be predicted in advance. Under a low signal-to-noise ratio (SNR), the signal eigenvalues and the noise eigenvalues of the covariance matrix differ slightly, which makes signal source number estimation difficult. To address this issue, a singular value decomposition method using the delay structure information of the array element is proposed to estimate the number of sources of the spreading sequence under a low SNR. The method proposed in this paper can well estimate the DOA of the signal under a low SNR. Meanwhile, there is no need to convert the signal to the individual sub-bands, which effectively reduces the calculation overhead. At the same time, the Hankel matrix is used to solve the problem that the MUSIC algorithm cannot accurately estimate the number of signal sources under the condition of low SNR. Compared with the conventional algorithm, the Hankel matrix can more accurately estimate the number of signal sources in the case of low SNR. Through simulation experiments, the effectiveness of our DOA estimation algorithm is validated under a low SNR.

A Novel Method for Diagnosis of Broken Bars Based on Optimum Resolution of Prescient Direction Algorithm

Fourier transformation (FT) and Multiple Signal Classification (MUSIC) method suffer the insufficient ability in diagnosing broken rotor bar (BRB) fault using short-time data. Theoretical and simulation analyses show that the Optimum Resolution of Prescient Direction (ORPD) algorithm has the best frequency resolution performance due to a priori knowledge. The main objective of this paper is to detect BRB faults in induction machines using a condition monitoring architecture based on ORPD algorithm. In the proposed application, the ORPD algorithm with the best frequency resolution performance is used to estimate the fault-sensitive frequencies in the stator current signature. The prior information of BRB fault characteristic distribution is used to construct a weighting matrix in the ORPD algorithm, for acquiring the lowest signal-to-noise ratio resolution threshold. Once frequencies are estimated, their corresponding amplitudes are obtained by using the least squares estimator. The proposed methods were tested using experimental induction motors with different fault severity under the effect of several load levels or supply frequencies. Two types of power supply modes are considered: main and inverter. The results show that compared with traditional method which uses FT and MUSIC algorithm for fault diagnosing, the method based on ORPD algorithm has a higher frequency resolution and identification ability with short-time data, and still has good diagnostic performance even under light loading and lower supply frequencies.

Target Sensing With Intelligent Reflecting Surface: Architecture and Performance

Intelligent reflecting surface (IRS) has emerged as a promising technology to reconfigure the radio propagation environment by dynamically controlling wireless signal’s amplitude and/or phase via a large number of reflecting elements. In contrast to the vast literature on studying IRS’s performance gains in wireless communications, we study in this paper a new application of IRS for sensing/localizing targets in wireless networks. Specifically, we propose a new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self-sensing IRS</i> architecture where the IRS controller is capable of transmitting probing signals that are not only directly reflected by the target (referred to as the direct echo link), but also consecutively reflected by the IRS and then the target (referred to as the IRS-reflected echo link). Moreover, dedicated sensors are installed at the IRS for receiving both the direct and IRS-reflected echo signals from the target, such that the IRS can sense the direction of its nearby target by applying a customized multiple signal classification (MUSIC) algorithm. However, since the angle estimation mean square error (MSE) by the MUSIC algorithm is intractable, we propose to optimize the IRS passive reflection for maximizing the average echo signals’ total power at the IRS sensors and derive the resultant Cramer-Rao bound (CRB) of the angle estimation MSE. Last, numerical results are presented to show the effectiveness of the proposed new IRS sensing architecture and algorithm, as compared to other benchmark sensing systems/algorithms.

DNN-Assisted Particle-Based Bayesian Joint Synchronization and Localization

In this work, we propose a Deep neural network-assisted Particle Filter-based (DePF) approach to address the Mobile User (MU) joint synchronization and localization (sync&loc) problem in ultra-dense networks. In particular, DePF deploys an asymmetric time-stamp exchange mechanism between the MUs and the Access Points (APs), which, traditionally, provides us with information about the MUs’ clock offset and skew. However, information about the distance between an AP and an MU is also intrinsic to the propagation delay experienced by the exchanged time-stamps. In addition, to estimate the angle of arrival of the received synchronization packets, DePF draws on the multiple signal classification algorithm that is fed with the Channel Impulse Response (CIR) experienced by the sync packets. The CIR is also leveraged to determine the link condition, i.e. Line-of-Sight (LoS) or Non-LoS. Finally, to perform joint sync&loc, DePF capitalizes on particle Gaussian mixtures that allow for a hybrid particle-based and parametric Bayesian Recursive Filtering (BRF) fusion of the aforementioned pieces of information and, thus, jointly estimates the position and clock parameters of the MUs. The simulation results verify the superiority of the proposed algorithm over the state-of-the-art schemes, especially that of the extended Kalman filter- and linearized BRF-based joint sync&loc. In particular, only drawing on the synchronization time-stamp exchange and CIRs from a single AP, for 90% of the cases, the absolute position and clock offset estimation error remain below 1 meter and 2 nanoseconds, respectively.

Service Antenna Array-Based Parameter Estimation for Decimeter Level Indoor Localization

Since the antenna interval of service antenna array for communication is greater than half a wavelength and does not satisfy the spatial sampling theorem, it is a great challenge to leverage service antenna array for channel state information-based signal parameters estimation, such as time-of-flight (TOF) and angle-of-arrival (AOA) estimation. To overcome this challenge, this letter proposes a diagonal spatial mapping-based multiple signal classification (MUSIC) and matching pursuit (MP) fusion (DSM-MMF) algorithm. First, a new virtual linear array is constructed by mapping the service antenna array on the diagonal of the plane array. Second, a fusion AOA and TOF estimation for the signal mapped on the virtual linear array is realized by utilizing the MUSIC and MP fusion algorithm. Third, through the unique geometric relationship between the virtual linear array and the service antenna array, the AOA and TOF can be obtained. Finally, experimental results show that the DSM-MMF’s median localization error is about four decimeters.

Hardware Acceleration of MUSIC Algorithm for Sparse Arrays and Uniform Linear Arrays

Multiple Signal Classification (MUSIC) is a high-performance Direction of Arrival (DOA) estimation algorithm, which has been widely used. The algorithm needs to calculate the covariance matrix, eigenvalue decomposition and spectral peak search. In the paper, the hardware structure of the existing Jacobi algorithm for Hermitian matrices is proposed. On this basis, a novel hardware acceleration of the MUSIC algorithm for sparse arrays and uniform linear arrays is proposed, and the sparse array is a nested array. There are two designs, Design 1 supports 1~10 nested array elements or 1~32 uniform linear array elements, distinguishes 1~32 sources, configures snapshots 1~2048, and the maximum number of iterations and iteration accuracy of the complex Jacobi algorithm. Design 2 only needs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$101.8~\mu $ </tex-math></inline-formula> s to complete a DOA estimation when the number of array elements is 8, the number of sources is 1, and the snapshots is 128. In more detail, the Root Mean Squared Error (RMSE) of both can reach 0.03°. The logic resources on the Zynq-7000 development board are 14,761 and 28,305 Look-Up Tables (LUTs), respectively.

Three-Dimensional Imaging with Bistatic Vortex Electromagnetic Wave Radar

The vortex electromagnetic wave radar based on monostatic geometry can realize the imaging of a radar target in both range dimension and azimuth dimension by adjusting vortex electromagnetic wave modes, but it has no ability to distinguish the elevation of the radar target. To achieve three-dimensional imaging of the radar target, a three-dimensional imaging method of vortex electromagnetic wave based on bistatic geometry is proposed. The echo model of the target based on vortex electromagnetic wave in bistatic geometry is constructed firstly. The elevation resolution of the target is realized, and then the three-dimensional coordinate of the target is reconstructed. Moreover, the elevation resolution and the computational complexity of the proposed method are also analyzed. Simulation results demonstrate the effectiveness of the proposed method. The results also illustrate that the array element requirements and the computational complexity of presented algorithm are less than Multiple Signal Classification (MUSIC) algorithm.

Joint Estimation Method of DOD and DOA of Bistatic Coprime Array MIMO Radar for Coherent Targets Based on Low-Rank Matrix Reconstruction.

Based on low-rank matrix reconstruction theory, this paper proposes a joint DOD and DOA estimation method for coherent targets with bistatic coprime array MIMO radar. Unlike the conventional vectorization, the proposed method processed the coprime array with virtual sensor interpolation, which obtained a uniform linear array to generate the covariance matrix. Then, we reconstructed the Toeplitz matrix and established a matrix optimization recovery model according to the kernel norm minimization theory. Finally, the reduced dimension multiple signal classification algorithm was applied to estimate the angle of the coherent targets, with which the automatic pairing of DOD and DOA could be realized. With the same number of physical sensors, the proposed method expanded the array aperture effectively, so that the degree of freedom and angular resolution could be improved significantly for coherent signals. However, the effectiveness of the method was largely limited by the signal-to-noise ratio. The superiority and effectiveness of the method were proved using simulation experiments.

Joint 2D‐DOA and polarization estimation for Electromagnetic vector sensors array with compressive measurements

Electromagnetic vector sensors (EMVS) arrays have been employed extensively in the field of array signal processing for their advantage in terms of polarization diversity. However, with the introduction of EMVS, the cost of the hardware equipment and the complexity of the corresponding parameter estimation algorithms increase considerably, as the number of received signal channels and the dimension of the received signal are much larger than the traditional scalar array. In order to effectively reduce hardware cost and algorithm complexity, we propose a scheme that combines an electromagnetic vector sensor array with a compression network. We construct the corresponding signal model and based on this we derive a Compressed Reduced Dimensional MUltiple SIgnal Classification (Compressed To avoid the multi-dimensional search, Reduced Dimension MUSIC) algorithm which can effectively reduce the computational complexity. While selecting the coefficient matrix of the compressed network, random selection can cause information loss, which leads to the performance degradation of the estimation algorithm. To address this problem, we propose an optimization method for coefficient matrix selection based on the maximum signal-to-noise ratio (SNR) criterion. Numerical simulations are conducted in different scenarios to verify the effectiveness of the parameter estimation algorithm and the optimization algorithm.

A sequential MUSIC algorithm for scatterers detection in SAR tomography enhanced by a robust covariance estimator

Synthetic aperture radar (SAR) tomography (TomoSAR) is an appealing tool for the extraction of height information of urban infrastructures. Due to the widespread applications of the multiple signal classification (MUSIC) algorithm in source localization, it is a suitable solution in TomoSAR when multiple snapshots (looks) are available. While the classical MUSIC algorithm aims to estimate the whole reflectivity profile of scatterers, sequential MUSIC algorithms are suited for the detection of sparse point-like scatterers. In this class of methods, successive cancellation is performed through orthogonal complement projections on the MUSIC power spectrum. In this work, a new sequential MUSIC algorithm named recursive covariance cancelled MUSIC (RCC-MUSIC), is proposed. This method brings higher accuracy in comparison with the previous sequential methods at the cost of a negligible increase in computational cost. Furthermore, to improve the performance of RCC-MUSIC, it is combined with the recent method of covariance matrix estimation called correlation subspace. Utilizing the correlation subspace method results in a denoised covariance matrix which in turn, increases the accuracy of subspace-based methods. Several numerical examples are presented to compare the performance of the proposed method with the relevant state-of-the-art methods. As a subspace method, simulation results demonstrate the efficiency of the proposed method in terms of estimation accuracy and computational load.

DOA Estimation Method for Ultra-Wide-Band Insect Radar Based on Variable Conical Conformal Array: Adjustable MUSIC Algorithm

Insect radar is an important tool for studying the ecological behaviors of insects. Due to the harsh environment, radar is susceptible to interference from ground echoes, which makes it difficult to monitor insects in low altitude. To study the flying insects at low altitude in radar entomology, the research of ultra-wideband (UWB) insect radar based on log-periodic antenna array was proposed. This method uses a conical conformal array to receive signals and an improved multiple signal classification (MUSIC) algorithm to process the signals. This array is capable of monitoring insects of different sizes in the ultra-wideband range, adjusting the angle of the cone tip to change the position and polarization information, and obtaining information on various insects flying at low altitude. The problem of two-dimensional angle of arrival estimation of insect cone conformal array was analyzed by computer simulation, which are low-altitude flying targets with different cone apex angles. In addition, a modified multiple signal classification algorithm was implemented to make the radar search and catch multiple targets faster and more accurate. The algorithm greatly reduces computational complexity while maintaining the accuracy of estimation. There is a linear relationship between the time calculation and the accuracy with the modified algorithm, compared with the relationship between exponential growth and the generalized MUSIC algorithm. Finally, the experimental simulation has proved the superiority of the proposed algorithm.

Direction of arrival and target scale estimation based on split beamforming algorithm

Based on the theory of split beamforming algorithm and the experimental data collected by circular array, this paper analyzes the characteristics of DOA and target size estimation. In this paper, the signal receiving model of planar circular array and the split beamforming algorithm are studied. Then, based on the data collected from the lake experiment, the DOA estimation results of conventional beamforming algorithm, multiple signal classification algorithm and split beamforming algorithm are analyzed, and the target scale estimation results of split beamforming algorithm is analyzed. The experimental data analysis shows that the split beamforming algorithm has good direction finding stability, and the target scale estimation error based on the split beamforming algorithm is small.

Energy Efficiency of Angle of Arrival Estimation in Massive MIMO Systems

In the next generation of wireless systems, massive Multiple Input Multiple Output (MIMO) offers high angular resolution for localization. By virtue of large number of antennas, Angle of Arrival (AoA) of User Terminals (UTs) can be estimated accurately. Measurements of Dense Multipath Channel (DMC) indicate multipath signals contribute up to 95% of total link power. This fact urges the necessity of studying the contribution of multipath signals accompanying dominant path in AoA estimation. We obtain a deterministic form for Cramer-Rao Lower Bound ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CRLB$ </tex-math></inline-formula> ) in multi-user scenario when contribution of multipath signals is considered. We do this when the multipath signals are independent and identically distributed (i.i.d) with arbitrary distribution. Then, we redefine a localization efficiency function for multi-user scenario and optimize it with respect to (w.r.t) the number of antennas. When only a subset of available antennas is used, we prove that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CRLB$ </tex-math></inline-formula> can be minimized w.r.t which set is used. An antenna selection strategy that minimizes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CRLB$ </tex-math></inline-formula> is proposed. As a benchmark, we apply the proposed antenna selection to MUltiple SIgnal Classification (MUSIC) algorithm and study its efficiency. Numerical results validate the accuracy of our analysis and show significant improvement in efficiency when the proposed antenna selection is employed.