Root Multiple Signal Classification Research Articles

Robust DOA estimation for two‐level nested arrays in unknown mutual coupling

AbstractAiming at solving the problem that the capability of direction of arrival method for estimation of nested arrays decreases sharply under unknown mutual coupling, an iterative weighted low‐rank matrix reconstruction algorithm is proposed here. First, the received data covariance matrix is extended, and a weighted low‐rank matrix recovery problem is formulated for joint estimations of the Toeplitz matrix and mutual coupling coefficients. Next, the direction of arrival from recovered Toeplitz matrix is retrieved by using the root multiple signal classification algorithm. Simulation results show that iterative weighted low‐rank matrix reconstruction algorithm can effectively avoid the influence of mutual coupling while solving the grid‐mismatch problem so that the accuracy and the resolution of estimation are improved.

Research on Direction Finding Method under Impulsive Noise Based on Nonuniform Linear Array

Direction of arrival (DOA) estimation under impulsive noise has always been an important research area in array signal processing. The traditional methods under impulsive noise mostly rely on prior parameters and have high computational complexity. Based on the filtering theory, we present an effective pretreatment filtering technology to cut out the impulse mixed in the array received data and employ the nonuniform linear array to improve the estimation performance further. First, according to the amplitude characteristics of impulse noise, the pretreatment filtering technology is proposed to cut out the impulse based on the median filter and sliding average filter, which is valid for both strong and weak impulsive noise. Second, the minimum redundant array is adopted to carry out array virtual expansion so that the array aperture can be increased and the estimation performance can be improved. Finally, based on the idea of matrix reconstruction, we propose the improved estimation of signal parameters via rotational invariance techniques algorithm and an improved root multiple signal classification algorithm for DOA estimation. Theoretical analysis and simulation results show that the proposed method has a simple processing process, small calculation load, good array expansion ability, and excellent noise adaptability. Moreover, the proposed methods greatly improve the direction-finding performance under the condition of low signal-to-noise ratio and strong impulsive noise.

Self-Position Determination Based on Array Signal Subspace Fitting under Multipath Environments

A vehicle’s position can be estimated with array receiving signal data without the help of satellite navigation. However, traditional array self-position determination methods are faced with the risk of failure under multipath environments. To deal with this problem, an array signal subspace fitting method is proposed for suppressing the multipath effect. Firstly, all signal incidence angles are estimated with enhanced spatial smoothing and root multiple signal classification (Root-MUSIC). Then, non-line-of-sight (NLOS) components are distinguished from multipath signals using a K-means clustering algorithm. Finally, the signal subspace fitting (SSF) function with a P matrix is established to reduce the NLOS components in multipath signals. Meanwhile, based on the initial clustering estimation, the search area can be significantly reduced, which can lead to less computational complexity. Compared with the C-matrix, oblique projection, initial signal fitting (ISF), multiple signal classification (MUSIC) and signal subspace fitting (SSF), the simulated experiments indicate that the proposed method has better NLOS component suppression performance, less computational complexity and more accurate positioning precision. A numerical analysis shows that the complexity of the proposed method has been reduced by at least 7.64dB. A cumulative distribution function (CDF) analysis demonstrates that the estimation accuracy of the proposed method is increased by 3.10dB compared with the clustering algorithm and 11.77dB compared with MUSIC, ISF and SSF under multipath environments.

3D Localization With a Single Partially-Connected Receiving RIS: Positioning Error Analysis and Algorithmic Design

In this paper, we introduce the concept of partially-connected receiving reconfigurable intelligent surfaces (R-RISs), which refers to metasurfaces designed to efficiently sense electromagnetic waveforms impinging on them, and perform localization of the users emitting them. The presented R-RIS hardware architecture comprises subarrays of meta-atoms, with each of them incorporating a waveguide assigned to direct the waveforms reaching its meta-atoms to a reception radio-frequency (RF) chain, enabling signal/channel parameter estimation. We particularly focus on the scenarios where the user is located in the far-field of all the R-RIS subarrays, and present a three-dimensional (3D) localization method which is based on narrowband signaling and angle of arrival (AoA) estimates of the impinging signals at each single-receive-RF R-RIS subarray. For the AoA estimation, which relies on spatially sampled versions of the received signals via each subarray's phase configuration of meta-atoms, we devise an off-grid atomic norm minimization approach, which is followed by subspace-based root multiple signal classification (MUSIC). The AoA estimates are finally combined via a least-squared line intersection method to obtain the position coordinates of a user emitting synchronized localization pilots. Our derived theoretical Cramér Rao lower bounds (CRLBs) on the estimation parameters, which are compared with extensive computer simulation results of our localization approach, verify the effectiveness of the proposed R-RIS-empowered 3D localization system, which is showcased to offer cm-level positioning accuracy. Our comprehensive performance evaluations also demonstrate the impact of various system parameters on the localization performance, namely the training overhead and the distance between the R-RIS and the user, as well as the spacing among the R-RIS's subarrays and its partitioning patterns.

Deep Learning-Based Multipath DoAs Estimation Method for mmWave Massive MIMO Systems in Low SNR

To realize the direction-of-arrivals (DoAs) estimation without the prior information about the multipath number, a novel method using the deep learning is introduced for the millimeter (mmWave) massive multiple-input and multiple-output (MIMO) systems. In particular, the DoAs estimation is decomposed into three sub-problems, which are solved by the corresponding convolutional neural network (CNN), respectively. The estimation of multipath number is achieved by a multi-label classification model using the proposed CNN-I. Then, the proposed CNN-II is introduced for the DoA estimation of the line-of-sight (LOS) path. Based on the predicted multipath number obtained by the CNN-I, a regression model using the proposed CNN-III is applied for the DoAs estimation of non-line-of-sight (NLOS) paths. The proposed DoAs estimation method is implemented by learning the non-linear relationship between the sample covariance matrix of the received signal and the angles, thus reconstructing the mapping model. A series of results validate the superiority of the proposed DoAs estimation method in low signal-to-noise-ratio (SNR) regimes. The CNN-I is capable of achieving the good multipath number estimation performance across a range of SNRs. The classification model based on the proposed CNN-II and the regression model using the proposed CNN-III achieve the lower DoAs estimation root mean square error (RMSE) compared with some deep learning-based methods, estimation of signal parameters via rotational invariance techniques (ESPRIT) and Root-MUltiple SIgnal Classification (Root-MUSIC) methods. Remarkably, the proposed method using the CNN-II exhibits the good robustness in the DoA estimation of the LOS path. Furthermore, the low DoAs estimation RMSE is also achieved in the uniform planar array.

Two Low-Complexity DOA Estimators for Massive/Ultra-Massive MIMO Receive Array

Eigen-decomposition-based direction finding methods of using large-scale/ultra-large-scale fully-digital receive antenna arrays lead to a high or ultra-high complexity. To address the complexity dilemma, in this letter, three low-complexity estimators are proposed: partitioned subarray auto-correlation combining (PSAC), partitioned subarray cross-correlation combining (PSCC) and power iteration max correlation successive convex approximation (PI-Max-CSCA). Compared with the conventional no-partitioned direction finding method like root multiple signal classification (Root-MUSIC), in the PSAC method, the total set of antennas are equally partitioned into subsets of antennas, called subarrays, each subarray performs independent DOA estimation, and all DOA estimates are coherently combined to give the final estimation. For a better performance, the cross-correlation among sub-arrays is further exploited in the PSCC method to achieve the near-Cramer-Rao lower bound (CRLB) performance with the help of auto-correlation. To further reduce the complexity, in the PI-Max-CSCA method, using a fraction of all subarrays to make an initial coarse direction measurement (ICDM), the power iterative method is adopted to compute the more precise steering vector (SV) by exploiting the total array, and a more accurate DOA value is found using ICDM and SV through the maximum correlation method solved by successive convex approximation. Simulation results show that as the number of antennas goes to large-scale, the proposed three methods can achieve a dramatic complexity reduction over conventional Root-MUISC. Particularly, the PSCC and PI-Max-CSCA can reach the CRLB while the PSAC shows a substantial performance loss.

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.

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.

Multiple Source Angle of Arrival Estimation Through Phase Interferometry

The evaluation of the Angle of Arrival (AoA) of a received signal is a basic tool for many RF location systems. This brief introduces a new technique for estimating the AoA via a phase interferometric approach when multiple sources are present. After briefly recalling some widespread algorithms and methods, the proposed technique is described from a mathematical point of view. This brief also reports the results of an experimental campaign, along with a comparison of the results with those obtained using the Estimation of Signal Parameters via Rotational Invariant Techniques (ESPRIT) and Root MUltiple SIgnal Classification (RMUSIC) algorithms. The experiments demonstrate that the proposed approach gives accurate results with low computational complexity, thus being eligible for direct implementation in digital custom hardware.

Deep Alternating Projection Networks for Gridless DOA Estimation With Nested Array

Recently, deep unfolding networks with interpretable parameters have been widely utilized in direction of arrival (DOA) estimation due to the faster convergence speed and better generalization ability. However, few consider the nested array for gridless DOA estimation. In this letter, we propose a deep alternating projection network to address the problem. We first convert the covariance matrix into a measurement vector in the form of atomic norm, which can reduce the matrix dimension during projection. We then train the proposed network to alternately obtain the positive semi-definite matrix and the corresponding irregular Hermitian Toeplitz matrix, where the loss function is derived by employing the trace of network output. Finally, we apply the irregular root Multiple Signal Classification (MUSIC) method to obtain gridless DOA via nested array. We demonstrate that the proposed networks can accelerate the convergence rate and reduce computational cost. Simulations verify the performance of proposed networks in comparison with the existing methods.

Root high-order cumulant MUSIC

The (p,q)th order circularity and non-circularity of non-Gaussian signals are developed for the first time in this paper. The polynomial rooting implementation of the high-order cumulant based multiple signal classification (MUSIC) methods are then investigated, concentrating on the direction-of-arrival estimation of the (p,q)th order circular and noncircular non-Gaussian signals, where different signal cases are studied. The proposed methods are based on manifold separation technique, which are the extensions of the current noncircular root MUSIC to the high-order and to the arbitrary array structure. Theoretical computational complexity analysis for the methods is also given. The effectiveness of the methods is evaluated by Monte Carlo simulations.

A Low-Complexity Three-Stage Estimator for Low-Rank mmWave Channels

This paper investigates the estimation of low-rank multiple-input multiple-output (MIMO) channels in millimeter wave (mmWave) communications. Hybrid MIMO transceivers equipped with uniform linear arrays (ULAs) and phase shifter networks are considered. We propose a novel three-stage channel estimator by exploiting the low-rankness of the channel matrix and knowledge of the array response: We first obtain a low-rank estimate of the channel matrix using inductive matrix completion (IMC); then estimate the angle of arrival (AoA) and angle of departure (AoD) for the propagation paths by solving two one-dimensional spectrum estimation problems using Toeplitz rectification and the root multiple signal classification (MUSIC) algorithm; and finally pair the AoAs and AoDs and estimate the channel gains by solving a sparse recovery problem. Each stage is implemented at a low complexity and thus the overall complexity is kept low. A priori knowledge about the channel is exploited progressively to enhance the performance. The simulation results suggest significant gains in the channel estimation performance along with sparse representations of the estimated channel.

Adaptive Sparse Cyclic Coordinate Descent for Sparse Frequency Estimation

The frequency estimation of multiple complex sinusoids in the presence of noise is important for many signal processing applications. As already discussed in the literature, this problem can be reformulated as a sparse representation problem. In this letter, such a formulation is derived and an algorithm based on sparse cyclic coordinate descent (SCCD) for estimating the frequency parameters is proposed. The algorithm adaptively reduces the size of the used frequency grid, which eases the computational burden. Simulation results revealed that the proposed algorithm achieves similar performance to the original formulation and the Root-multiple signal classification (MUSIC) algorithm in terms of the mean square error (MSE), with significantly less complexity.

Gridless Multiple Measurements Method for One‐Bit DOA Estimation with a Nested Cross‐Dipole Array

The gridless one‐bit direction of arrival (DOA) estimator is proposed to estimate electromagnetic (EM) sources on a nested cross‐dipole array, and the multiple measurement vectors (MMV) mode is introduced to improve the reliability of parameter estimation. The gridless method is based on atomic norm minimization, solved by alternating direction multiplier method (ADMM). With gridless method used, sign inconsistency caused by one‐bit measurements and basis mismatches by traditional grid‐based algorithms can be avoided. Furthermore, the reconstructed denoising measurements with fast convergence and stable recovery accuracy are obtained by ADMM. Finally, spatial smoothing root multiple signal classification (SSRMUSIC) and dual polynomial (DP) methods are used, respectively, to estimate the DOAs on the reconstructed denoising measurements. Numerical results show that our method one‐bit ADMM‐SSRMUSIC has a better performance than that of one‐bit SSRMUSIC used directly. At low signal to noise ratio (SNR) and low snapshot, the one‐bit ADMM‐DP has an excellent performance which is even better than that of unquantized MUSIC. In addition, the proposed methods are also suitable for both completely polarized (CP) signals and partially polarized (PP) signals.

DoA Estimation for Lens Antenna Array via Root-MUSIC, Outlier Detection, and Clustering

Lens antenna arrays have become attractive for mmWave MIMO systems due to their energy-focusing and path-division properties. However, when the signals cannot be well differentiated at different array elements due to their similar incident angles, we cannot estimate their DoAs separately. In this paper, we present a DoA estimation algorithm for this situation. Our algorithm has three main steps: a special version of root multiple signal classification (MUSIC) for lens antenna arrays, outlier detection, and clustering. Numerical results show that our algorithm can achieve good performance even with a large number of signal sources, a large number of array elements, and a small number of snapshots.

Fast and robust method for flow analysis using GPU assisted diffractive optical element based background oriented schlieren (BOS)

The paper introduces a method for studying flow dynamics using diffractive optical element based background-oriented schlieren (BOS). Our method relies on fringe demodulation using root multiple signal classification technique which provides high robustness against noise. Further, a graphics processing unit (GPU) based implementation is proposed which offers significant improvement in computational efficiency, and thus enables high speed analysis of flows. The performance of the method is demonstrated via numerical simulations and the practical applicability is also shown by analyzing a diffusion phenomenon in liquids by BOS.

Super Resolution Sub-space based ROOT- MUSIC technique for Direction of Arrival Evaluation in MIMO Radar

In this paper, subspace based on DOA evaluation with high resolution ROOT-Multiple Signal Classification (MUSIC) method is proposed for MIMO radar. In order to achieve a desired transmitting power distribution, the main component is the fundamental vector was made such that the transmitted power is focuses on power to be transmitted inside the required sectors eliminating the power of off-sector. Using the designed algorithm, population in associate weight-vectors is created which has almost equal size division. These associate vectors utilized in forming multiple transmitting ways, over which an orthogonal waveform is transmitted. Match filtering is done for the collected information and perpendicular transmitted waves. Many of the information vectors similar to the perpendicular waves are generated. Now, carefully taking these waves, virtual information output covariance matrix that enhances the use in super resolution direction of arrival prediction methods. This technique decomposes the eigenvectors in correlation. Signal estimation is performed by taking the maximum values in the signal, corresponding to base in the polynomial. The software output display ROOT MUSIC technique giving best DOA prediction presentation compared to existing techniques that have been used for comparison.

Gold-MUSIC Based DOA Estimation and Multiuser Detection of DS-CDMA System with Optimal Beamformer ULA Antenna

gold-MUSIC based direction of arrival (DOA) estimation and multiuser detection (MUD) overcoming near–far problem are achieved concurrently for direct-sequence code division multiple access (DS-CDMA). The optimal beamformer uniform linear array (ULA) antenna is exploited for mitigating the multiple access interference and increasing signal to noise ratio. Multiple signal classification (MUSIC) algorithms are employed for DOA estimation of equal propagation delay signal sources in the presence of additive white Gaussian noise. Bit error rate (BER) of quadriphase shift keying transmission is taken as analytical reference in emphasizing the performance of CDMA users for different ULA elements. Advantages of gold-MUSIC over Root MUSIC and MUSIC algorithms are established through spatial spectrum, computational efficiency and root mean square error (RMSE) of DOA estimation. Impact of arrival angle, ULA elements and data length on RMSE and algorithm complexity of DOA estimation are also enumerated here. Signal constellation and BER analysis utilizing MUD decision feedback, MUD decorrelator and single-user receivers are investigated for equal DOA and different DOA DS-CDMA sources.

An Experimental Study of the Angular Superresolution of Two Correlated Signals Using the Minimum-Polynomial Method

We present experimental results on the superresolution of two closely located signal sources, which were obtained using an automotive millimeter-wave radar. The signal sources were mutually correlated and the input process consisted of only one sample. The minimum-polynomial method (the root variant) was compared with the Minimum Description Length (MDL) criterion when determining the number of sources and the root MUltiple Signal Classification (MUSIC) method when estimating their angular location. The minimum-polynomial method is shown to have a higher efficiency compared with the MDL criterion and ensures the source superresolution for the angular distance which is a factor of 4–5 smaller than the width of the antenna-array pattern. In terms of accuracy of estimating the coordinates of the signal sources, the efficiency of this method almost coincides with that of the root-MUSIC method if the number of sources is considered to be known in the latter method.

Direction of arrival estimation using combined coprime and nested array

A combined coprime and nested array geometry is designed and a corresponding direction of arrival (DOA) method is proposed. The proposed array has three subarrays, where two are prototype coprime subarrays, and both of them are nested to the third one. Then the vectorisations of two covariance matrices yield two virtual coprime subarrays, which show a much larger aperture compared to the physical ones. Thereafter, through Toeplitz matrix reconstruction and root multiple signal classification, two coprime estimations are obtained and they are combined to obtain the final unique DOA estimation. Multiple analysis and simulations verify that the proposed method achieves larger aperture, better DOA estimation accuracy and higher angular resolution compared to other coprime array-based methods.