2D-MUSIC Algorithm Research Articles

A novel hybrid algorithm for two-dimensional direction-of-arrival estimation in massive MIMO systems

Massive Multiple-Input Multiple-Output (mMIMO) systems have been significantly exploited to enhance mobile network capacity. Increasing the number of antennas provided higher direction-of-arrival (DOA) estimation accuracy, especially when utilizing a two-dimensional multi-signal classification algorithm (2D-MUSIC). However, this algorithm suffers from the heavy computational complexity imposed by the 2D angle search. This paper proposes a novel hybrid algorithm called the 2D-MM, which combines the strengths of the 2D-MUSIC algorithm with the 2D-Minimum Variance Distortionless Response (2D-MVDR) algorithm to reduce the computational complexity using a fast new DOAs search strategy. To be more precise, the new search strategy involves two stages: the 2D-MVDR stage detects the approximate DOAs within a whole angular field of view using as few antennas as possible and snapshots of received data. Then, the 2D-MUSIC stage accurately determines the number and locations (azimuths and elevations) of those sources within the angular sectors in which they appear. Furthermore, the choice of utilizing a uniform circular array (UCA) configuration for representing mMIMO systems is enhanced by introducing a new geometric structure featuring two concentric rings. The simulation results indicate that confining the spectral peak searching process into octant areas with an angular sector spanning π⁄4 instead of the total angular field of view (0–2π) would avoid searching empty areas and then reduce the computational complexity, where the improvement percentage in the proposed algorithm's running time was approaching 80 % when utilized with mMIMO arrays. In contrast, the proposed algorithm proves effective for mMIMO systems, irrespective of the increased number of antennas utilized.

Low-Complexity Joint Angle of Arrival and Time of Arrival Estimation of Multipath Signal in UWB System.

In an ultra-wideband (UWB) system, the two-dimensional (2D) multiple signal classification (MUSIC) algorithms based on high-precision 2D spectral peak search can jointly estimate the time of arrival (TOA) and angle of arrival (AOA). However, the computational complexity of 2D-MUSIC is very high, and the corresponding data model is only based on the dual antennas. To solve these problems, a low-complexity algorithm for joint AOA and TOA estimation of the multipath ultra-wideband signal is proposed. Firstly, the dual antenna sensing data model is extended to the antenna array case. Then, based on the array-sensing data model, the proposed algorithm transforms the 2D spectral peak search of 2D-MUSIC into a secondary optimization problem to extract the estimation of AOA via only 1D search. Finally, the acquired AOA estimations are brought back, and the TOA estimations are also obtained through a 1D search. Moreover, in the case of an unknown transmitted signal waveform, the proposed method can still distinguish the main path signal based on the time difference of arrival of different paths, which shows wider applications. The simulation results show that the proposed algorithm outperforms the Root-MUSIC algorithm and the estimation of signal parameters using the rotational invariance techniques (ESPRIT) algorithm, and keeps the same estimation accuracy but with greatly reduced computational complexity compared to the 2D-MUSIC algorithm.

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.

FEM simulation based adaptive sensors array error compensation method for impact monitoring on stiffened composite structures

To eliminate the sensor array based impact localization bias on stiffened composite structures, a finite element method (FEM) simulation based adaptive sensors array errors compensation method for impact monitoring is introduced. Firstly, detailed analysis and comparison discussion about Lamb wave propagation errors between the simple and stiffened plate are provided using FEM simulation, and the gain-phase errors obtained are structured as a array error matrix. Secondly, array error matrix is substituted into the steering vector of standard two-dimensional Multiple Signal Classification (2D-MUSIC) algorithm to compensate the stiffener effect. And then initial estimates of impact could be estimated by the compensated 2D-MUSIC algorithm. Finally substituting these initial estimates, the cost function is minimized by adaptive iterative to calculate the reasonable location of the impact source. The experiments on a carbon fiber composite stiffened plate demonstrate the validity and effectiveness of the proposed method.

Recurrent NEAT Assisted 2D-DOA Estimation With Reduced Complexity for Satellite Communication Systems

Direction-of-arrival (DOA) estimation plays a vital role in the field of array signal processing. However, the need for heavy computing tasks in most traditional DOA algorithms, e.g., multiple signal classification (MUSIC), makes their engineering practicality significantly compromised in satellite communication systems. The neuroevolution of augmenting topologies (NEAT) can quickly search for appropriate topologies and weights of neural network functions, but its computational complexity is still too high for satellite systems. This paper proposes a modified NEAT architecture featuring a recurrent structure (RNEAT) that only needs a small number of phase components of the received signal covariance matrix as inputs to reduce the complexity and simplify the neural network architecture. The proposed RNEAT incorporated with multiple signal classification (RNEAT-MUSIC) features low complexity to achieve high resolution and low complexity simultaneously. Validation has been done by applying the proposed method in a two-dimensional direction of arrival estimation (2D-DOA) problem. Results show that the proposed RNEAT-MUSIC efficiently restricts the scanning region before forwarding the covariance matrix to the MUSIC stage. Consequently, the computational workload is reduced by 3/4 compared with the traditional 2D-MUSIC algorithm while maintaining satisfactory DOA resolution.

Distributed Two-Dimensional MUSIC for Joint Range and Angle Estimation with Distributed FMCW MIMO Radars.

To estimate range and angle information of multiple targets, FMCW MIMO radars have been exploited with 2D MUSIC algorithms. To improve estimation accuracy, received signals from multiple FMCW MIMO radars are collected at the data fusion center and processed coherently, which increases data communication overhead and implementation complexity. To resolve them, we propose the distributed 2D MUSIC algorithm with coordinate transformation, in which 2D MUSIC algorithm is operated with respect to the reference radar’s coordinate at each radar in a distributed way. Rather than forwarding the raw data of received signal to the fusion center, each radar performs 2D MUSIC with its own received signal in the transformed coordinates. Accordingly, the distributed radars do not need to report all their measured signals to the data fusion center, but they forward their local cost function values of 2D MUSIC for the radar image region of interest. The data fusion center can then estimate the range and angle information of targets jointly from the aggregated cost function. By applying the proposed scheme to the experimentally measured data, its performance is verified in the real environment test.

Environmental Effects on Piezoelectric Sensors Array Signals and a Compensated Damage Imaging Method.

Piezoelectric sensors array based damage imaging method as a high resolution source localization algorithm is becoming a promising method in structural health monitoring (SHM) technology. However, the environmental variations could affect the gain-phase of array signal. This paper experimentally evaluates the environmental effects on piezoelectric sensors array, and presents a compensated 2D-MUSIC based damage imaging method for composite structures. Firstly, detailed analysis and comparison discussion about the gain-phase difference of array signal when the environmental parameters change, and the gain-phase changes respect to the environmental parameters could be obtained. Secondly, array error matrix is structured and substituted into the steering vector of the original 2D-MUSIC algorithm to compensate. Finally, the compensated 2D-MUSIC algorithm is applied for estimating the initial estimates of damage. After substituting these initial estimates, the cost function is minimized by adaptive iterative calculating the reasonable location of the damage source. The experiments on an epoxy laminate plate demonstrate the validity and effectiveness of the proposed method.

A Reduced-Dimension MUSIC Algorithm for Monostatic FDA-MIMO Radar

This letter proposes a one-dimensional multiple signal classification (MUSIC) algorithm for the joint angle and range estimation in monostatic multi-input multi-output (MIMO) radar with frequency diverse array (FDA). The proposed algorithm can reduce the computational complexity greatly compared to the two-dimensional MUSIC (2D-MUSIC) algorithm but have the same performance as the 2D-MUSIC algorithm. Simulation results verify the performance of the proposed algorithm.

Adaptive Sensor Array Error Calibration Based Impact Localization on Composite Structure

Gains and phases delay induced by sensor position error would significantly degrade the performance of high-resolution two-dimensional multiple signal classification (2D-MUSIC) algorithm, which resulting in low positioning estimation accuracy and poor imaging. In this study, adaptive piezoelectric sensor array calibration based method is proposed for impact localization on composite structure. First, observed signal vector from the sensor array is represented by error calibration matrix with unknown gains and phases, and then it used to construct the cost function including sensor array parameters. Second, a 2D-MUSIC algorithm based on linear attenuation calibration is applied for estimating the initial estimate of impact location. Finally, substituting the initial estimate, the cost function is minimized by adaptive iterative to calculate the sensor array error parameters and the exact location of the impact source. Both finite element method (FEM) simulation and experimental results on carbon-fiber composite panel demonstrate the validity and effectiveness of the proposed method.

A Novel High-Resolution Imaging Method Using Reduced-Dimension Beamspace Unitary MUSIC for OFDM-MIMO Radar

Imaging of maneuvering targets has become a challenging topic recently. This study proposes an improved MUSIC-based single-snapshot imaging method for OFDM-MIMO radar. At the transmitter part, for orthogonal waveform generation, the interleaved OFDM structure is developed that each transmitter only radiates at an equidistant set of OFDM subcarriers unique to itself. At the receiver part, a novel preprocessing scheme is presented to separate multiple transmit/receive paths and compensate the reference point. Preprocessed echo matrix can fit the model of two-Dimensional (2D) MUSIC algorithm, except for the coupling between radial/cross-range in the virtual antenna array. Correspondingly, we modify the 2D ElementSpace (ES)-MUSIC. In the meantime, a 2D Reduced-Dimension BeamSpace Unitary-MUSIC (RD-BS-UMUSIC) algorithm is proposed for computational complexity reduction and estimation performance enhancement. Numerical results of a simulated target consists of limited number of scatterers and a complex target (a Boeing 737-800 plane) verify that the proposed algorithm can improve the imaging quality and reduce computational complexity effectively compared with the traditional method.

Multiple Signal Classification-Based Impact Localization in Composite Structures Using Optimized Ensemble Empirical Mode Decomposition

Multiple signal classification (MUSIC) algorithm-based structural health monitoring technology is a promising method because of its directional scanning ability and easy arrangement of the sensor array. However, in previous MUSIC-based impact location methods, the narrowband signals at a particular central frequency had to be extracted from the wideband Lamb waves induced by each impact using a wavelet transform. Additionally, the specific center frequency had to be obtained after carefully analyzing the impact signal, which is time consuming. Aiming at solving this problem, this paper presents an improved approach that combines the optimized ensemble empirical mode decomposition (EEMD) and two-dimensional multiple signal classification (2D-MUSIC) algorithm for real-time impact localization on composite structures. Firstly, the impact signal at an unknown position is obtained using a unified linear sensor array. Secondly, the fast Hilbert Huang transform (HHT) with an optimized EEMD algorithm is introduced to extract intrinsic mode functions (IMFs) from impact signals. Then, all IMFs in the whole frequency domain are directly used as the input vector of the 2D-MUSIC model separately to locate the impact source. Experimental data collected from a cross-ply glass fiber reinforced composite plate are used to validate the proposed approach. The results show that the use of optimized EEMD and 2D-MUSIC is suitable for real-time impact localization of composite structures.

Initial Phase Effect on DOA Estimation in MMIMO Using Separated Steering Matrix

Providing simple and low complexity algorithms for estimating the direction of arrival in large systems using Massive MIMO is considered an important issue. In this paper a method with reduced complexity was proposed to estimate the direction of arrival in FD- MMIMO. The Separated Steering Matrix (SSM) algorithm uses two separated equations for estimating elevation and azimuth angles of Multi-users. This method reduces the complexity of calculating the covariance matrix by decreasing the size of this matrix. This technique is tested using 2D-MUSIC algorithm. Since the mobility of devices affects the accuracy of direction estimation, thus the effect of the initial phase of transmitted signal from mobile device is tested.

Fast Estimation Method of Space-Time Two-Dimensional Positioning Parameters Based on Hadamard Product

The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA) and direction of arrival (DOA) parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC) algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM) system, and the Cramer-Rao bound (CRB) is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and 2D matrix pencil (MP) algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.

A Fast Algorithm for 2D DOA Estimation Using an Omnidirectional Sensor Array.

The traditional 2D MUSIC algorithm fixes the azimuth or the elevation, and searches for the other without considering the directions of sources. A spectrum peak diffusion effect phenomenon is observed and may be utilized to detect the approximate directions of sources. Accordingly, a fast 2D MUSIC algorithm, which performs azimuth and elevation simultaneous searches (henceforth referred to as AESS) based on only three rounds of search is proposed. Firstly, AESS searches along a circle to detect the approximate source directions. Then, a subsequent search is launched along several straight lines based on these approximate directions. Finally, the 2D Direction of Arrival (DOA) of each source is derived by searching on several small concentric circles. Unlike the 2D MUSIC algorithm, AESS does not fix any azimuth and elevation parameters. Instead, the adjacent point of each search possesses different azimuth and elevation, i.e., azimuth and elevation are simultaneously searched to ensure that the search path is minimized, and hence the total spectral search over the angular field of view is avoided. Simulation results demonstrate the performance characters of the proposed AESS over some existing algorithms.

Two-Dimensional DOA Estimation Using Arbitrary Arrays for Massive MIMO Systems

With the quick advancement of wireless communication networks, the need for massive multiple-input-multiple-output (MIMO) to offer adequate network capacity has turned out to be apparent. As a portion of array signal processing, direction-of-arrival (DOA) estimation is of indispensable significance to acquire directional data of sources and to empower the 3D beamforming. In this paper, the performance of DOA estimation for massive MIMO systems is analyzed and compared using a low-complexity algorithm. To be exact, the 2D Fourier domain line search (FDLS) MUSIC algorithm is studied to mutually estimate elevation and azimuth angle, and arbitrary array geometry is utilized to represent massive MIMO systems. To avoid the computational burden in estimating the data covariance matrix and its eigenvalue decomposition (EVD) due to the large-scale sensors involved in massive MIMO systems, the reduced-dimension data matrix is applied on the signals received by the array. The performance is examined and contrasted with the 2D MUSIC algorithm for different types of antenna configuration. Finally, the array resolution is selected to investigate the performance of elevation and azimuth estimation. The effectiveness and advantage of the proposed technique have been proven by detailed simulations for different types of MIMO array configuration.

Two-Dimensional Direction-of-Arrivals Estimation Based on One-Dimensional Search Using Rank Deficiency Principle

A novel efficient method for two-dimensional (2D) direction-of-arrivals (DOAs) estimation is proposed to reduce the computational complexity of conventional 2D multiple signal classification (2D-MUSIC) algorithm with uniform rectangular arrays (URAs). By introducing two electrical DOAs, the formula of 2D-MUSIC is transformed into a new one-dimensional (1D) quadratic optimal problem. This 1D quadratic optimal problem is further proved equivalent to finding the conditions of noise subspace rank deficiency (NSRD), which can be solved by an efficient 1D spectral search, leading to a novel NSRD-MUSIC estimator accordingly. Unlike 2D-MUSIC with exhaustive 2D search, the proposed technique requires only an efficient 1D one. Compared with the estimation of signal parameter via rotation invariance techniques (ESPRIT), NSRD-MUSIC has a significantly improved accuracy. Moreover, the new algorithm requires no pair matching. Numerical simulations are conducted to verify the efficiency of the new estimator.

Interference Localization via Direction of Arrival Estimation for Satellite with Planar Array

This paper presents the model of satellite planar array, and interference localization via direction of arrival (DOA) estimation. We derive a dimension reduction DOA estimaton algorithm therein. The proposed algorithm, which only requires a one-dimensional local searching, can avoid the high computational cost within two-dimensional multiple signal classification (2D-MUSIC) algorithm. We illustrate that the proposed algorithm has better angle estimation performance than estimation method of signal parameters via rotational invariance technique (ESPRIT) algorithm, and has very close angle estimation performance to 2D-MUSIC algorithm. Furthermore, our algorithm requires no extra pairing. Simulation results present the usefulness of our algorithm.

SS-BMUSIC Algorithm for Space-Time 2D Signal Model

This paper presents a beamforming matrix with spatial smoothing effect, and extends it to the space-time 2D signal model, which not only reduces the computational complexity of the space-time 2D MUSIC algorithm and improves the coherence resolution capacity, simulation results show that this algorithm has better performance and effectiveness than MUSIC itself.

Joint Estimation of TOA and DOA in IR-UWB System Using a Successive MUSIC Algorithm

Time-of-arrival (TOA) and direction-of-arrival (DOA) are key parameters in the impulse radio ultra wideband (IR-UWB) positioning system with a two-antennas receiver. A two-dimensional (2D) multiple signal classification (MUSIC) algorithm, which requires the 2D spectral peak search, can be used to estimate the parameters, but it has much higher computational complexity. This paper proposes a successive MUSIC algorithm for joint TOA and DOA estimation in IR-UWB system to avoid 2D spectral peak search. The proposed algorithm obtains the initial estimate of TOA corresponding to the first antenna via Root-MUSIC, and simplifies the 2D global search into successive one-dimensional searches to achieve the estimation of TOAs in the two antennas. It then estimates the DOA parameters via the difference of the TOAs between the two antennas. The proposed algorithm can get the parameters paired automatically, and has a much lower complexity than 2D-MUSIC algorithm. In addition, we have derived the mean square error of TOA and DOA estimation of the proposed algorithm and the Cramer---Rao bound of TOA and DOA estimation in the paper. The simulation results show that the parameter estimation performance of the proposed algorithm is better than that of Root-MUSIC, and is almost the same as that of 2D-MUSIC algorithm. Moreover, it has much better performance than matrix pencil algorithm, propagator method and estimation of signal parameters via rotational invariance techniques algorithm.

Information Estimation of Civil Airplane in Interference Localization Background

The ground-air communication of civil aviation is interfered by radios, which has seriously endangered the normal flight of civil airplanes. This paper proposes an airplane information estimation algorithm based on the study of the problem of interference localization. Firstly, a novel signal model to accurately estimate parameters of the airplane is proposed. A method of Doppler estimation based on peak searching is proposed, and the 2D-MUSIC algorithm is applied to estimate the azimuth angle and elevation angle. Furthermore, the velocity and location of the airplane are estimated by employing array geometry. As a result, the airplane localization is achieved in bistatic radar, laying the foundations for interference localization. The correctness and effectiveness of the proposed method are verified with the computer simulation.