Estimation Of Signal Parameters Via Rotational Invariance Techniques Research Articles

Extrapolation-RELAX Estimator Based on Spectrum Partitioning for DOA Estimation of FMCW Radar

This paper proposes an extrapolation-RELAX estimator based on spectrum partitioning (SP) for the direction of arrival (DOA) estimation of frequency-modulated continuous-wave (FMCW) radar. The FMCW radar employs fast Fourier transform (FFT)-based digital beamforming (DBF) for the DOA estimation owing to its low complexity and easy implementation. However, the DBF algorithm has a disadvantage of low angle resolution. To improve the angle resolution, super-resolution algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) are proposed. However, these algorithms require the high signal-to-noise ratio (SNR) to meet the required performance. To overcome this drawback of super-resolution algorithms, the SP-based extrapolation method has been proposed. However, this algorithm still has the problem that the resolution performance degrades owing to the insufficient number of actual antenna arrays. To solve this problem, we propose the SP-based extrapolation-RELAX algorithm for DOA estimation of FMCW radar. Through extrapolation, the proposed structure solves the problem of insufficient number of arrays, resulting in high reliability of SP results. When the extrapolation algorithm is used to generate the input signal of the RELAX algorithm, the RELAX method improves the performance of the DOA estimation. To confirm the effectiveness of the proposed estimation, we compare the Monte Carlo simulation and root-mean-square error results of the proposed and conventional algorithms. To verify the performance of the proposed algorithm in practical conditions, experiments were performed using the FMCW radar module within a chamber and in an indoor environment.

Multi-Cell Multi-User Massive FD-MIMO: Downlink Precoding and Throughput Analysis

In this paper, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive Full-Dimension MIMO (FD-MIMO) network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically characterized and the characterized DoA estimation error is incorporated into the corresponding DL precoding and power allocation strategy. Simulation results verify the accuracy of our analytical characterization of the DoA estimation and demonstrate that the introduced multi-user MIMO precoding and power allocation strategy outperforms existing zero-forcing based massive MIMO strategies.

Wi-Fi Signal Processing for Automotive Doppler Radar: Feasibility and Implementation

In recent years, there has been growing research into the field of Wi-Fi radar signal processing for dual radar-communication purposes. Combining these two features enables cost savings to vehicle manufacturers by lowering the design complexity, while also saving precious radio frequency spectrum. This work presents a feasibility study and a hardware implementation of a Doppler radar that operates on the IEEE 802.11p Wi-Fi packets. A 5-MHz OFDM modem that adheres closely to the 802.11p PHY was implemented on two Universal Software Defined Peripherals (USRP) via MATLAB's USRP toolbox. By applying the estimation of signal parameters via rotational invariance technique (ESPRIT) to a collection of received Wi-Fi symbols, the real-time Doppler radar was achieved, which demonstrated an average accuracy of sub-0.64 m/s in measuring a vehicle's velocity.

Time Reversal ESPRIT Imaging with Frequency-domain Sampling of Single Target

A time-reversal imaging method, based on frequency-domain data sampling and the estimation of signal parameters via rotational invariance techniques (ESPRIT), is proposed to obtain imaging with higher resolution in this paper. The proposed algorithm is obtained, which firstly applies the coarse and fine frequencies sampling to all received scatter signal, thus forming the plurality of frequency-frequency multistatic data matrices (FF-MDM); subsequently, the signal subspace is obtained through the application of singular value decomposition (SVD) to the FF-MDM; finally, the imaging pseudo-spectrum can be acquired by processing to the signal subspace with ESPRIT. The simulation results show that the proposed method has better resolution for imaging as compared with conventional imaging methods.

Successive DSPE-based coherently distributed sources parameters estimation for unmanned aerial vehicle equipped with antennas array

In electronic countermeasures and reconnaissance, unmanned aerial vehicle (UAV) has played a more and more significant role. Usually when UAV conducts low altitude reconnaissance, due to the complicated environment, the reflected signals of the same source through different propagation paths will produce multipath signals. In this paper, we construct the received multipath signals of UAV with antennas array as coherently distributed (CD) sources model and propose a successive distributed signal parameter estimation (S-DSPE) algorithm to estimate its nominal direction of arrival (DOA) and angular spread. The proposed algorithm simplifies two-dimensional (2D) spectral peak searching within the conventional DSPE algorithm to one-dimensional spectral peak searching, which remarkably reduces the computational complexity of conventional DSPE algorithm. Furthermore, the parameters estimation performance of the proposed algorithm is close to the conventional DSPE algorithm, and outperforms the estimation of signal parameters via rotational invariance technique (ESPIRT) algorithm and propagator method (PM). The simulations results verify the usefulness of the proposed algorithm.

An Improved Method for Discerning Broken Rotor Bar Fault and Load Oscillation in Induction Motors

A few methods for discerning broken rotor bar (BRB) fault and load oscillation in induction motors have been reported in the literature. However, they all perhaps inevitably fail in adverse cases in which these two phenomena are simultaneously present. To tackle this problem, an improved method for discerning BRB fault and load oscillation is proposed in this paper based on the following work. On the one hand, the theoretical basis is analytically extended to include such an adverse case, yielding some important findings on the spectra of the instantaneous reactive and active powers. A novel strategy is thus outlined to correctly discern BRB fault and load oscillation even when simultaneously present. On the other hand, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) is adopted as the spectral analysis technique to deal with the instantaneous reactive and active powers, yielding a certain improvement compared to the existing methods, adopting Fast Fourier Transform (FFT). Simulation and experimental results demonstrate that the proposed method can correctly discern BRB fault and load oscillation even when simultaneously present.

Two-Dimensional DOA Estimation for Incoherently Distributed Sources with Uniform Rectangular Arrays.

Aiming at the two-dimensional (2D) incoherently distributed (ID) sources, we explore a direction-of-arrival (DOA) estimation algorithm based on uniform rectangular arrays (URA). By means of Taylor series expansion of steering vector, rotational invariance relations with regard to nominal azimuth and nominal elevation between subarrays are deduced under the assumption of small angular spreads and small sensors distance firstly; then received signal vectors can be described by generalized steering matrices and generalized signal vectors; thus, an estimation of signal parameters via rotational invariance techniques (ESPRIT) like algorithm is proposed to estimate nominal elevation and nominal azimuth respectively using covariance matrices of constructed subarrays. Angle matching method is proposed by virtue of Capon principle lastly. The proposed method can estimate multiple 2D ID sources without spectral searching and without information of angular power distribution function of sources. Investigating different SNR, sources with different angular power density functions, sources in boundary region, distance between sensors and number of sources, simulations are conducted to investigate the effectiveness of the proposed method.

Two-Step Spherical Harmonics ESPRIT-Type Algorithms and Performance Analysis

Spherical arrays have been widely used in direction-of-arrival (DOA) estimation in recent years, and the high-resolution estimation of signal parameter via rotational invariance technique (ESPRIT) was developed in the spherical harmonics domain. However, the spherical harmonics ESPRIT (SHESPRIT) cannot estimate the DOA when the elevation approaches 90°. To solve this problem, we present a two-step SHESPRIT (TS-SHESPRIT) based on two new recurrence relations of complex spherical harmonics. Furthermore, we develop a real-valued two-step SHESPRIT (RTS-SHESPRIT) that exploits a unitary matrix to obtain a real-valued relation between the signal subspace and the steering matrix to further reduce the computational complexity. However, the number of sources that are estimated by RTS-SHESPRIT is limited. Therefore, we propose the semi-RTS-SHESPRIT method, which reduces the computational complexity associated with eigenvalue decomposition (EVD) and avoids the limitations of RTS-SHESPRIT. Relative to SHESPRIT and TS-SHESPRIT, RTS-SHESPRIT and semi-RTS-SHESPRIT reduce the computational burden by 75% during EVD. Furthermore, we derive the mean square errors (MSEs) of the above algorithms and significantly simplify the MSE expressions. Different expressions for the MSEs are due to different recurrence relations used by different SHESPRIT-type algorithms. All proposed two-step SHESPRIT-type algorithms have higher accuracy than traditional SHESPRIT. The simulation results demonstrate the satisfactory performance of our methods.

Doppler Frequency Estimation of Point Targets in the Single-Channel SAR Image by Linear Least Squares

This paper presents a method and results for the estimation of residual Doppler frequency, and consequently the range velocity component of point targets in single-channel synthetic aperture radar (SAR) focused single-look complex (SLC) data. It is still a challenging task to precisely retrieve the radial velocity of small and slow-moving objects, which requires an approach providing precise estimates from only a limited number of samples within a few range bins. The proposed method utilizes linear least squares, along with the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, to provide optimum estimates from sets of azimuth subsamples that have different azimuth temporal distances. The ratio of estimated Doppler frequency to root-mean square error (RMSE) is suggested for determining a critical threshold, optimally selecting a number of azimuth subsample sets to be involved in the estimation. The proposed method was applied to TerraSAR-X and KOMPSAT-5 X-band SAR SLC data for on-land and coastal sea estimation, with speed-controlled, truck-mounted corner reflectors and ships, respectively. The results demonstrate its performance of the method, with percent errors of less than 5%, in retrieved range velocity for both on-land and in the sea. It is also robust, even for weak targets with low peak-to-sidelobe ratios (PSLRs) and signal-to-clutter ratios (RCSs). Since the characteristics of targets and clutter on land and in the sea are different, it is recommended that the method is applied separately with different thresholds. The limitations of the approach are also discussed.

High-resolution bottom detection algorithm for a multibeam echo-sounder system with a U-shaped array

High-resolution approaches such as multiple signal classification and estimation of signal parameters via rotational invariance techniques (ESPRIT) are currently employed widely in multibeam echo-sounder (MBES) systems for sea floor bathymetry, where a uniform line array is also required. However, due to the requirements in terms of the system coverage/resolution and installation space constraints, an MBES system usually employs a receiving array with a special shape, which means that high-resolution algorithms cannot be applied directly. In addition, the short-term stationary echo signals make it difficult to estimate the covariance matrix required by the high-resolution approaches, which further increases the complexity when applying the high-resolution algorithms in the MBES systems. The ESPRIT with multiple-angle subarray beamforming is employed to reduce the requirements in terms of the signal-to-noise ratio, number of snapshots, and computational effort. The simulations show that the new processing method can provide better fine-structure resolution. Then a highresolution bottom detection (HRBD) algorithm is developed by combining the new processing method with virtual array transformation. The application of the HRBD algorithm to a U-shaped array is also discuss. The computer simulations and experimental data processing results verify the effectiveness of the proposed algorithm.

Joint DOD and DOA estimation for bistatic multiple‐input multiple‐output radar target discrimination based on improved unitary ESPRIT method

Target position estimation of radar system has attracted much attention. Researchers have proposed a variety of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation algorithms over the last few decades for this well-known problem. However, traditional estimation algorithms require a pairing process between the DOD and DOA estimation. In this study, the authors propose an improved unitary estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm for joint DOD and DOA estimation without a pairing operation. The waveforms are transmitted by an array with M sensors and received by two detached sub-arrays with and sensors, respectively. Specifically, the proposed algorithm eliminates a pairing process via sharing the eigenvectors of DOD and DOA. Theoretical derivation demonstrates that the proposed algorithm requires less computational complexity than two-dimensional multiple signal classification (MUSIC), reduced-dimension MUSIC, and ESPRIT. Simulation results show that the proposed algorithm can effectively enhance the accuracy of identifying and locating targets for the bistatic multiple-input multiple-output radar system.

Performance analysis of propagator‐based ESPRIT for direction of arrival estimation

Compared with the standard estimation of signal parameters via rotational invariance technique (ESPRIT) for direction of arrival estimation, the propagator-based ESPRIT is a more computationally efficient method since it requires no eigenvalue decomposition when calculating the signal subspace. In this study, the propagator-based ESPRIT method is analysed by deriving its theoretical asymptotic error. With first-order perturbation analysis, it is shown that both propagator-based ESPRIT and standard ESPRIT have the same asymptotic error with high signal-to-noise ratio. Simulation results of both the propagator-based ESPRIT and the standard ESPRIT are presented, and they are shown to be consistent with the theoretical derivations.

Research on ESPRIT estimation algorithm for the central frequency of gain spectrum in Brillouin optical time-domain reflectrometry

In fiber-optic Brillouin optical time-domain reflectometer (BOTDR) system, the estimation of the center frequency of Brillouin scattering spectrum in fiber is the key and the most time-consuming part of the measurement, which makes BOTDR system difficult to achieve fast response. In this paper, estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm is proposed to estimate the center frequency of Brillouin scattering spectrum in BOTDR system. Due to fairly low requirement on data length, ESPRIT algorithm can obtain good frequency estimation over short data length, and makes it possible to increase measurement speed at high spatial resolution and measurement performance.

Wave forecast and its application to the optimal control of offshore floating wind turbine for load mitigation

Abstract Control algorithms play an important role in energy capture and load mitigation for offshore floating wind turbines (OFWTs). One of the advanced and effective control techniques is the feedforward or model predictive control approach, which requires the forecast of incoming environment conditions. For OFWTs, wave loading is one of the dominant sources to excite structural responses. This study is thus motivated to develop forecasting algorithms for wave elevations and wave excitation forces with the purpose of applying feedforward controllers on OFWTs. Two forecasting algorithms, the approximate Prony Method based on ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) and SVM (Support Vector Machine) regression, are developed and validated using wave records from tank tests. Utilizing the forecasted wave elevations and wave excitation forces, a feedforward LQR controller is designed to mitigate structural loads of an OFWT system.

Wireless channel parameter estimation algorithms: Recent advances and future challenges

Temporal and three-dimensional (3D) spatial information is important for the characterization of wireless channels. In this paper, the commonly used array signal processing (ASP) methods to estimate channel parameters are summarized. Firstly, algorithms that can be used to estimate azimuth angle of arrival (AAoA) and elevation AoA (EAoA) are introduced. They include multiple signal classification (MUSIC), estimation of signal parameter via rotational invariance techniques (ESPRIT), and Unitary ESPRIT algorithms. Secondly, algorithms that can be used to jointly estimate delay, AAoA, and EAoA are given. They include joint angle and delay estimation (JADE) MUSIC, JADE ESPRIT, shift-invariance (SI) JADE, and space-alternating generalized expectation-maximization (SAGE) algorithms. We also propose an improved SI-JADE algorithm to further reduce computation complexity by incorporating with the Unitary ESPRIT algorithm. Performance of the above algorithms to extract only spatial information and to jointly extract temporal and spatial information is compared in both synthetic and 60 GHz real channel environments. Simulation results show that with the inclusion of delay estimation, the joint temporal and spatial estimation algorithms can provide better resolution than algorithms estimating only angles. Measurement data processing results show that MUSIC algorithm can provide comparable results with SAGE algorithm in estimating AAoA and EAoA. SI-JADE and the improved SI-JADE algorithms are also applicable to process 60 GHz channel measurement data. However, MUSIC, SI-JADE, and the improved SI-JADE algorithms can greatly reduce computational burden compared with SAGE algorithm. At last, some future directions are pointed out.

Mxpfit: A library for finding optimal multi-exponential approximations

mxpfit is a library implemented in C++ to find optimal approximations of functions by multi-exponential sums with complex-valued parameters. The library provides an interface for evaluating exponents and coefficients from sampling data on a uniform grid using the fast Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm originally proposed by Potts and Tasche (2015). The parameters can be estimated efficiently from a sampling data even including noise. A modified balanced truncation algorithm to find the multi-exponential sum with a smaller order is also provided. These features are useful for finding optimal exponential sum approximations of analytic functions or large-scale numerically sampled data set. Program summaryProgram Title: mxpfitProgram Files doi:http://dx.doi.org/10.17632/vjygkwpss4.1Licensing provisions: MITProgramming language: C++Nature of problem: Nonlinear curve fitting by multi-exponential function, frequency estimation of signals, and reduction of multi-exponential sumSolution method: The modified fast Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm originally proposed in [1] is utilized for the parameter estimation of multi-exponential sums from sampled data on a uniform grid. In this method, partial Lanczos bidiagonalization is used to find a low-rank approximation of a Hankel matrix constructed from sampled data. An overdetermined Vandermonde system is solved by the conjugate gradient least square (CGLS) method with preconditioner to obtain the coefficients of the multi-exponential sum. The truncation of the multi-exponential sum is performed by a modified balanced truncation method in [2]. The projection matrix to obtain the truncated system is determined by computing con-eigenvalues of a Gramian matrix, which can be computed efficiently with highly relative accuracy using the algorithm in [3].Additional comments: A C++ compiler supporting the C++11 standard is required to compile programs using the mxpfit library. mxpfit depends on the Eigen (http://eigen.tuxfamily.org/) and FFTW3 (http://www.fftw.org/) libraries. CMake (https://cmake.org/) is used for building example programs.

Angle Estimation in Monostatic MIMO Radar with Low-Complexity Beamspace Unitary ESPRIT

A low-complexity angle estimation method for multiple-input multiple-output (MIMO) radar using beamspace unitary estimation of signal parameters via rotational invariance techniques (ESPRIT) is presented. Reduced-dimensional transformation is firstly utilized as a pre-processing to obtain the reduced-dimensional data matrix, and then a conjugate centrosymmetric discrete Fourier transform (DFT) matrix is employed to map the received data into lower-dimensional beamspace and transforms the complex covariance matrix into a realvalued one. At last, the rotational invariance structure of the real-valued signal subspace is constructed in the beamspace to obtain the estimation of direction of arrival (DOA). Compared with the other ESPRIT algorithms, the proposed method can achieve improved estimation performance with a significantly reduced computational complexity. Simulation results are presented to demonstrate the effectiveness of the proposed method.

Wide area damping of electromechanical low frequency oscillations using phasor measurement data

A wide area controller using modern multi-band power system stabilizer (PSS) is proposed to damp low frequency oscillations (LFOs) in the presence of wind power penetration. The proposed scheme is perfected in two stages. In the first stage, as the online stage, the generation re-dispatch is utilized to improve the damping of LFOs. In the second stage, as the real-time stage, the modern multiband PSSs are tuned in a wide area basis using ambient synchro-phasor measurements. A hybrid subspace identification approach based on estimation of signal parameters via rotational invariance technique (ESPRIT) and robust project approximation subspace tracking (PAST) technique is developed for online estimation of electromechanical modal properties using ambient phasor measurement data. The estimated modal information is then utilized for optimal wide area tuning of multi-band PSSs. Performance of the proposed scheme is then compared with local and global conventional PSSs. The proposed wide area damping controller is simulated over the IEEE-39 Bus test systems.

Successive ESPRIT Algorithm for Joint DOA-Range-Polarization Estimation With Polarization Sensitive FDA-MIMO Radar

Polarization sensitive frequency and frequency diversity array (FDA)-MIMO (PSFDA-MIMO) hybrid radar is an emerging technology. The existing algorithms for parameter estimation with PSFDA-MIMO radar need multiple-dimensional searches, whose computational complexity is high. To reduce the computational complexity, in this paper, a search-free algorithm is proposed to estimate 4-D parameters with PSFDA-MIMO radar. First, direction of arrival (DOA) is estimated with the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm using the rotational invariance of the receiving array. Second, based on the estimated DOA parameter, range estimation is obtained with the ESPRIT algorithm using the rotational invariance of the transmitting array. Finally, polarization parameters are estimated with the ESPRIT algorithm using the rotational invariance of the polarization domain. Thus, the proposed algorithm is termed the successive ESPRIT algorithm. Simulation results demonstrate the effectiveness of the proposed algorithm.

Time Delay and Interface Roughness Estimation Using Modified ESPRIT With Interpolated Spatial Smoothing Technique

In civil engineering, ground penetrating radar is a common technique for evaluating the structure and quality of road pavement. This paper focuses on the estimation of the time delay and interface roughness of civil engineering structure, like pavements. The influence of interface roughness is taken into account in the signal model. A modified estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm combined with an interpolated spatial smoothing technique is proposed. It allows us to jointly and efficiently estimate the time delay and interface roughness by ultrawideband radar (the upper frequency up to 8–10 GHz) with low computational complexity. The proposed algorithm is tested on both numerical and experimental data. Simulation and experimental results show the good performance of the proposed algorithm.