root-MUSIC Algorithm Research Articles

A Subspace-Based Frequency Synchronization Algorithm for Multicarrier Communication Systems

We present a subspace-based polynomial rooting algorithm to estimate the frequency bias (FB) of generalized frequency division multiplexing (GFDM) systems employing null subcarriers and repetitive sub-symbols. The estimation process is classified into fractional FB (FFB) and integer FB (IFB) estimation. The use of repetitive sub-symbols creates a quasi-periodic structure in the FB-distorted received signal, allowing the proposed algorithm to estimate the FFB using the root-MUSIC algorithm. Based on this, the proposed algorithm compensates for the FFB in the received signal and then estimates the null subcarrier pattern (NSP) in the frequency domain. As a result, the IFB estimate can be obtained in a maximum likelihood (ML) manner. Before the NSP estimation, this study uses a sub-symbol combiner to enhance signal strength of the FFB-aligned signal, ensuring the reliability of the IFB estimate. Computer simulations show that the proposed subspace-based algorithm has several advantages over traditional FB estimation methods: 1. Unlike some existing algorithms that use a training sequence to estimate FB, the proposed approach is a semi-blind algorithm because it can deliver information through repeated sub-symbols while estimating FB; 2. The proposed algorithm demonstrates excellent estimation accuracy compared to most traditional FB estimation algorithms; and 3. The proposed algorithm is computationally efficient, making it applicable to real-time applications in future communication systems.

UNet-rootMUSIC: A high accuracy direction of arrival estimation method under array imperfection

In the practical direction-finding systems, the accuracy and resolution of the direction of arrival (DOA) estimation are affected not only by the Gaussian noise and array size but also by hardware configuration imperfections, such as errors in element manufacturing and mounting. These impairments cause phase and amplitude errors in estimating the DOA of signal sources. To address this issue, this paper proposes to combine a U-shape deep neural network (UNet) with the multiple signal classification via the root of the polynomial (rootMUSIC) algorithm (so-called UNet-rootMUSIC) to improve the DOA estimation accuracy. In this approach, the UNet model plays a role in converting a covariance matrix of received signals containing phase and gain errors into a nearly perfect one of the ideal antenna array. The rootMUSIC algorithm is then employed to estimate the signal DOA based on the converted covariance matrix. The DOA estimation performance of the uniform linear array of eight elements with an inter-element distance of λ/2 is analyzed through experimental simulations. The simulation results demonstrate that our method can significantly reduce the root mean square error of DOA estimation compared to the conventional MUSIC, rootMUSIC, ESPRIT methods and two deep neural network-based angular classification methods.

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.

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.

Transformation of a circular array to a linear array with a Vandermonde structure

We address the transformation of a uniform circular array to a virtual uniform linear array. This phase mode transformation is widely used because many computationally efficient techniques that are not applicable to circular arrays can be implemented after the transformation. However, the transformed array is only approximately linear and its steering vector lacks a crucial property of a uniform linear array: a Vandermonde structure. The performances of the algorithms designed for uniform linear arrays can be substantially improved by removing the error in the transformation, thereby enforcing the Vandermonde structure in the steering vectors. We present an analytical technique to remove errors in the transformation and validate its efficacy by demonstrating an improvement in the root MUSIC algorithm.

Buried gas pipe leak localization using dual-wave spectrum estimation

To accurately locate leaks in buried gas pipes, a three-dimensional (3D) localization method using dual-wave velocity pairing and multi-array fusion localization was developed in this study to locate leak-induced vibroacoustic sources. Two velocities at which the P1 and S waves propagated along soil were estimated when the peaks of the dual-wave spectrum coincided with each other. Root-MUSIC algorithm was introduced to quickly determine the superimposed peak, thereby reducing the computational complexity. To address the issue of 3D localization using the P1 wave that propagated in soil according to a far-field model, least-squares (LS) estimation for the 3D coordinates was performed using the fusion localization method. A numerical model of geometrical dilution of precision (GDOP) was constructed to analyze the performances of multi-array layouts. A uniform circular array of eight accelerometers was utilized to visualize the leak-induced vibroacoustic source, and the imaging showed that the vibroacoustic source coincided with the leak. Accurate direction of arrival (DOA) estimation under multiple soil conditions was achieved, which proved that the velocity near the array was accurately estimated. An equilateral-triangle multi-array layout was selected using GDOP analyzing, and the results of localization experiments revealed that the equilateral-triangle layouts with 1.5-m and 2-m spacings achieved relatively good accuracy. Compared to the 3D localization method using a single array, the fusion localization method showed better accuracy for the remote leak, and the maximum reduction in error is 84.75 %. GDOP of fusion localization was found less than 0.1 m when the internal pipe pressure ≥ 0.4 MPa and the signal-to-noise ratio (SNR) ≥ 0 dB under the conditions of experiments in this study.

Enhanced Root-MUSIC Algorithm Based on Matrix Reconstruction for Frequency Estimation.

In recent years, frequency-modulated continuous wave (FMCW) radar has been widely used in automatic driving, settlement monitoring and other fields. The range accuracy is determined by the estimation of the signal beat frequency. The existing algorithms are unable to distinguish between signal components with similar frequencies. To address this problem, this study proposed an enhanced root-MUSIC algorithm based on matrix reconstruction. Firstly, based on the sparsity of a singular value vector, a convex optimization problem was formulated to identify a singular value vector. Two algorithms were proposed to solve the convex optimization problem according to whether the standard deviation of noise needed to be estimated, from which an optimized singular value vector was obtained. Then, a signal matrix was reconstructed using an optimized singular value vector, and the Hankel structure of the signal matrix was restored by utilizing the properties of the Hankel matrix. Finally, the conventional root-MUSIC algorithm was utilized to estimate the signal beat frequency. The simulation results showed that the proposed algorithm improved the frequency resolution of multi-frequency signals in a noisy environment, which is beneficial to improve the multi-target range accuracy and resolution capabilities of FMCW radar.

Multi-Target Parameter Estimation of the FMCW-MIMO Radar Based on the Pseudo-Noise Resampling Method.

Subspace methods are widely used in FMCW-MIMO radars for target parameter estimations. However, the performances of the existing algorithms degrade rapidly in non-ideal situations. For example, a small number of snapshots may result in the distortion of the covariance matrix estimation and a low signal-to-noise ratio (SNR) can lead to subspace leakage problems, which affects the parameter estimation accuracy. In this paper, a joint DOA-range estimation algorithm is proposed to solve the above issues. Firstly, the improved unitary root-MUSIC algorithm is applied to reduce the influence of non-ideal terms in building the covariance matrix. Subsequently, the least squares method is employed to process the data and obtain paired range estimation. However, in a small number of snapshots and low SNR scenarios, even if the impact of non-ideal terms is reduced, there will still be cases where the estimators sometimes deviate from the true target. The estimators that deviate greatly from targets are regarded as outliers. Therefore, threshold detection is applied to determine whether outliers exist. After that, a pseudo-noise resampling (PR) technology is proposed to form a new data observation matrix, which further alleviates the error of the estimators. The proposed method overcomes performance degradation in a small number of snapshots or low SNRs simultaneously. Theoretical analyses and simulation results demonstrate the effectiveness and superiority.

A MOBA-Root-MUSIC-Based Demodulation Method for Surface Acoustic Wave Torque Sensor

To improve the measurement accuracy of surface acoustic wave (SAW) torque sensor, an ultrahigh precision SAW torque sensor demodulation method based on multi-objective bat algorithm (MOBA) and root-MUSIC algorithm was proposed. The root-MUSIC algorithm was adopted to construct the polynomial equation of SAW echo signals. The construction of the objective function was based on two principles: the least distance to unit circle and least phase angle to the mean roots. MOBA was used to optimize the objective function to improve the accuracy of the roots. The numerical simulation and actual interrogating experiments were carried out and comparisons with other methods were conducted. The demodulation results verified that the proposed method had a minimum estimation error with standard deviation of 1 Hz. The designed demodulation method was used to the SAW torque measurement system. The torque sensing SAW resonator (SAWR) was designed using an FEM software and manufactured with a frequency of 433.945 MHz and an unload <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> factor of 13 370. The SAWR was glued on a bearing to measure applied torque. The torque loading and unloading experiments demonstrated that the nonlinearity of the proposed method was 0.1402%, which is the minimum when compared to other methods. The hysteresis was 1.1791%, and the sensitivity was 1.3570 kHz/Nm. Numerical simulation and experimental results demonstrated the effectiveness and accuracy of the designed algorithm in SAW torque sensor demodulation system.

An algebraic geometry perspective for the estimation of the directions of arrival

Directions of Arrival for Uniform Linear Arrays represent a widely studied topic in many fields of signal processing, with large attention on computational complexity, estimation accuracy and noise rejection. In this article we study the mathematical model behind Directions of Arrival from the point of view of algebraic geometry, focusing on its relation with the rational normal curve. On this basis, we give a novel interpretation for the root-MUSIC algorithm, that is a widely adopted estimation approach in signal processing. Furthermore, we propose some novel estimation techniques. The first one is based on the computation of the points on the rational normal curve that minimize the distance from the linear subspace defined by the measured Directions of Arrival. The others require the study of the secant varieties of the rational normal curve and the minimization of the distance between the point of the Grassmannian defined by the signal subspace and a certain secant variety. The results obtained from simulations in a noisy scenario show that our estimators are statistically consistent. One algorithm outperforms root-MUSIC over a wide range of scenarios, especially in presence of few snapshots and low Signal to Noise Ratio.

New Compact Antenna Array for MIMO Internet of Things Applications.

A communication system is proposed for the Internet of Things (IoT) applications in desert areas with extended coverage of regional area network requirements. The system implements a developed six-element array that operates at a 2.45 GHz frequency band and is optimized to reduce the size and limit element coupling to less than −20 dB. Analysis of the proposed system involves a multiple-input multiple-output (MIMO) operation to obtain the diversity gain and spectral efficiency. In addition, the radiation efficiency of the proposed antenna is greater than 65% in the operation bandwidth (more than 30 MHz) with a peak of 73% at 2.45 GHz. Moreover, an adaptive beamforming system is presented based on monitoring the direction of arrival (DOA) of various signals using the root MUSIC algorithm and utilizing the DOA data in a minimum variance distortionless response (MVDR) technique beamformer. The developed array is found to have an envelope correlation coefficient (ECC) value of less than 0.013, mean effective gain (MEG) of more than 1 dB, diversity gain of more than 9.9 dB, and channel capacity loss (CCL) of less than 0.4 bits/s/Hz over the operation bandwidth. Adaptive beamforming is used to suppress interference and enhance the signal-to-interference noise ratio (SINR) and is found to achieve a data rate of more than 50 kbps for a coverage distance of up to 100 km with limited power signals.

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC.

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

Gridless Underdetermined Direction of Arrival Estimation in Sparse Circular Array Using Inverse Beamspace Transformation.

Underdetermined DOA estimation, which means estimating more sources than sensors, is a challenging problem in the array signal processing community. This paper proposes a novel algorithm that extends the underdetermined DOA estimation in a Sparse Circular Array (SCA). We formulate this problem as a matrix completion problem. Meanwhile, we propose an inverse beamspace transformation combined with the Gridless SPICE (GLS) algorithm to complete the covariance matrix sampled by SCA. The DOAs are then obtained by solving a polynomial equation with using the Root-MUSIC algorithm. The proposed algorithm is named GSCA. Monte-Carlo simulations are performed to evaluate the GSCA algorithm, the spatial spectrum plots and RMSE curves demonstrated that the GSCA algorithm can give reasonable results of underdetermined DOA estimation in SCA. Meanwhile, the performance of the algorithm under various configurations of SCA is also evaluated. Numerical results indicated that the GSCA algorithm can provide access to solve the DOA estimation problem in Uniform Circular Array (UCA) when random sensor failures occur.

Design of efficient single target real-time beam tracking system

This paper builds a system for real-time tracking of a single target Radio Frequency (RF) signal source, in which the transmitter uses a low-cost HackRF One software radio transceiver platform, and the receiving antenna array uses two monopole antennas to form a 1×2 receiving array. The receiver uses Xilinx 7-Series development board Zedboard and AD9361 RF transceiver to build a wireless receiving platform to process the received signal. In this RF beam tracking system, it needs to perform Direction of Arrival (DOA) estimation on the calibrated signal, the DOA algorithm plays a crucial role in the accuracy of beam pointing and system running time, the MUSIC algorithm takes some time to conduct spectrum peak search, so the Root-Music algorithm is used here to avoid the spectrum peak search problem. To enable the Root-MUSIC algorithm to be better executed on this two-element receiving platform, this work simplifies the entire calculation process, requiring only a small amount of calculation and running time to complete the DOA estimation step, which effectively save FPGA processing time and computing resources. It provides a guarantee for the real-time performance of the system.

Fast DoA estimation of the signal received by textile wearable antenna array based on ANN model

MLP_DoA module, being an integral part of the smart TWAA DoA subsystem, intended for fast DoA estimation is proposed. Multilayer perceptron network is used to create the MLP_DoA module that provides a radio gateway location in azimuthal plane at its output when a spatial correlation matrix, found by receiving the radio gateway signal using two-element textile wearable antenna array, is on its input. MLP_DoA network training with monitoring the generalization capabilities on the validation set of samples is applied. The accuracy of the proposed modeling approach is compared to the classical approach in MLP_DoA module training previously developed by the authors. Comparison of the presented ANN model with the root MUSIC algorithm in terms of accuracy and program execution time is also done.

PUMA Applied to Time Delay Estimation for Processing GPR Data over Debonded Pavement Structures

In this paper, principal-singular-vector utilization for modal analysis (PUMA) was adapted to perform time delay estimation on ground-penetrating radar (GPR) data by taking into account the shape of the transmitted GPR signal. The super-resolution capability of PUMA was used to separate overlapping backscattered echoes from a layered pavement structure with some embedded debondings. The well-known root-MUSIC algorithm was selected as a benchmark for performance assessment. The simulation results showed that the proposed PUMA performs very well, especially in the case where the sources are totally coherent, and it requires much less computational time than the root-MUSIC algorithm.

3D Imaging Algorithm of Directional Borehole Radar Based on Root-MUSIC

A directional borehole radar consists of one transmitting antenna in the borehole and four receiving antennas distributed at equal angles in a ring. The receiving antennas can determine the depth and orientation of targets beside the borehole. However, the problem of target orientation determination and 3D imaging algorithms remains a technological challenge. The MUSIC (multiple signal classification) algorithm requires a peak search, so the accuracy of the operation is limited by the angle interval. Based on the MUSIC algorithm, the Root-MUSIC algorithm is proposed and implemented. By replacing the spectral peak search with calculating the roots of the polynomials greatly improves the orientation recognition accuracy. Finally, the results obtained using the above algorithm are verified with synthetic data and compared with the results of the MUSIC algorithm. The results show that both the MUSIC algorithm and the Root-MUSIC algorithm can achieve very good orientation determination and 3D imaging results. In terms of accuracy, the Root-MUSIC algorithm has an obvious improvement compared with the MUSIC algorithm.

Optimizing the performance of beamforming methods with high-resolution accuracy in a four-element array

As we know, the basis of some beamforming methods is the initial estimation of the input angle, so before applying these techniques, it is necessary to determine the angle of entry of signals into the array. As a result, estimating the input angle of the received waves is very important. In this paper, using the data of a four-element array as well as the data obtained from the electromagnetic simulation software of wired antennas, the performance of MUSIC, ROOT-MUSIC and ESPRIT algorithms is evaluated in real arrays and compared with the performance of this algorithms are discussed in the ideal array. The results show a decrease in the performance of these algorithms in real arrays compared to ideal arrays. This problem is due to the mutual coupling effect between the array elements in actual conditions, so it is necessary to compensate for the mutual coupling effect in practice.

Gridless DOA Estimation and Root-MUSIC for Non-Uniform Linear Arrays

The problem of gridless direction of arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and root-MUSIC are only applicable for measurements from a uniform linear array (ULA). This is because the sample covariance matrix of ULA measurements has Toeplitz structure, and both algorithms are based on the Vandermonde decomposition of a Toeplitz matrix. The Vandermonde decomposition breaks a Toeplitz matrix into its harmonic components, from which the DOAs are estimated. First, we present the `irregular' Toeplitz matrix and irregular Vandermonde decomposition (IVD), which generalizes the Vandermonde decomposition to apply to a more general set of matrices. It is shown that the IVD is related to the MUSIC and root-MUSIC algorithms. Next, gridless DOA is generalized to the NUA case using IVD. The resulting non-convex optimization problem is solved using alternating projections (AP). A numerical analysis is performed on the AP based solution which shows that the generalization to NUAs has similar performance to traditional gridless DOA.

Joint Angle and Range Estimation in the Fda-Mimo Radar: The Reduced-Dimension Root Music Algorithm

The frequency diverse array (FDA) multiple-input multiple-output (MIMO) radar is capable of producing the angle-range-dependent beampattern by utilizing a small frequency increment across the transmit elements, which enables to jointly calculate the angle and range estimates of the targets. However, the methods with tremendous computational burden, e.g., two-dimensional (2D) spectrum peak search (SPS), are involved due to the coupling of parameters, i.e., angle and range. In this study, We propose a reduced-dimension root MUSIC (RD-root-MUSIC) algorithm to detect the angle and range of targets in the FDA-MIMO radar. Specifically, we firstly decompose the angle and range by reconstructing the 2D-MUSIC spatial spectrum, where, resultantly, the range component is dismissed and the angle-dependent spatial spectrum function can be achieved. Moreover, to circumvent the SPS, the polynomial root finding is employed to obtain the angle estimates. Furthermore, we derive the closed-form solution to the range estimates which can be directly calculated based on the angle estimates. The proposed algorithm remarkably reduces the computational complexity without estimation performance degradation. In addition, the Cramer-Rao bounds (CRBs) are presented and the simulation results are provided to demonstrated the effectiveness of the proposed algorithm.