Manifold Separation Technique Research Articles

Polynomial rooting-based parameter estimation for polarimetric monostatic MIMO radar

Compared with conventional multiple-input multiple-output (MIMO) radar, polarimetric MIMO radar has been proven to hold the additional capability to operate data in the joint spatial and polarization domains. However, practical transceivers may involve antenna arrays with classical non-ideal factors (e.g., gain/phase/position errors) and polarimetric non-ideal factors (e.g., polarimetric antenna misorientation), and many current approaches cannot handle such non-ideal factors in real applications. In this study, polynomial rooting-based direction-of-arrival (DOA) and polarization parameter estimation is investigated for polarimetric monostatic MIMO radar with non-ideal transceivers. By incorporating the polarimetric manifold separation (PMS) technique, a joint DOA and polarization parameter estimation method, termed PMS2, is proposed with a closed-form solution. The Cramér-Rao bound for the multi-dimensional parameters involved in the estimation problem is also given. Simulation results demonstrate the performance advantages of the proposed PMS2 approach, which is attributed to the compact structure of polarimetric transceivers and the ability of the PMS2 approach to handle the polarimetric properties of signals.

Underdetermined DOA Estimation Using Arbitrary Planar Arrays via Coarray Manifold Separation

Conventional direction-of-arrival (DOA) estimation algorithms like MUSIC only allow localization of fewer number of sources than the number of physical sensors. In this paper, underdetermined azimuth localization (localizing more sources than the number of sensors) using arbitrary planar arrays has been proposed, using only second-order statistics of the received data. To achieve this, we utilize the difference coarray of the actual array and express the elements of the array covariance matrix as the signal received by the virtual sensors of the coarray. We explore the structure and geometry of the difference coarray of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -element planar array and show that the coarray can provide an increased degree-of-freedom (DOF) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N^{2})$</tex-math></inline-formula> which enables underdetermined localization. Then, we extend the manifold separation (MS) technique to the coarray to express the coarray steering matrix in terms of a Vandermonde structured matrix by designing a signal independent coarray characteristic matrix. As the signal model of a coarray is a single snapshot model, the Vandermonde structure enables us to perform a spatial smoothing type operation to restore the rank of the coarray covariance matrix. This allows us to propose a novel subspace-based algorithm, which we call the coarrayMS-MUSIC, to perform underdetermined source localization using arbitrary planar arrays. We have also introduced the polynomial rooting version of our algorithm called the coarrayMS-rootMUSIC. Finally, we have conducted extensive numerical simulations to verify the effectiveness and usefulness of the proposed methods.

Localization of Mixed Far-field and Near-field Incoherently Distributed Sources Using Two-stage RARE Estimator

In this paper, a mixed source localization method utilizing a two-stage rank-reduction (RARE) estimator is investigated. Different from the existing methods, the proposed one is built on the incoherently distributed (ID) source model, which is more appropriate for multipath and fast time-varying channels. Firstly, a general array manifold (GAM) model is established, where nominal DOAs and nominal ranges are extracted from the initial array manifold. By exploiting the shift invariance property of the far-field (FF) GAM and combining virtual source enumeration result, nominal FF DOA estimation is achieved by a one-dimensional (1-D) RARE spectral search. Secondly, the oblique projection operation is adopted to separate near-field (NF) sources, and the nominal DOA and range parameters of NF sources are subsequently obtained by jointly utilizing the manifold separation technique (MST) and another two 1-D spectral searches. With the estimated nominal DOA and range parameters, the angular spread and range spread are then successfully estimated. Moreover, the Cram&#x00E9;r-Rao bound (CRB) for the considered case is also derived. Simulation results are presented to validate the effectiveness of the proposed method.

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.

DOA Based on Manifold Separation Technique and Dimensionality Reduction

In this paper, we investigate the high resolution of arbitrary array applied to wireless positioning system and propose a Direction of Arrival (DOA) estimation algorithm based on the Manifold Separation Technique (MST). In order to reduce the error of MST model caused by noise, this algorithm uses the MST to decompose the steering vector into sampling matrix (only describing the array itself) and Vandermonde form (only relating to the direction of arrival), the steering vector of arbitrary array is represented by combining the Effective Aperture Distribution Function (EADF). In order to reduce the complexity of Multiple Signal Classification (MUSIC) algorithm of two-dimensional array, the 2D spectral peak search is decomposed into two one-dimensional spectral peak searches using dimensionality reduction methods. Simulation results show that the algorithm not only reduces the computational complexity, but also has good performance of low signal to noise ratio (SNR).

Efficient Data Transmission Strategy for IIoTs With Arbitrary Geometrical Array

Various kinds of data are generated from industrial Internet of Things, and these data can be applied for connecting production equipment, identifying and locating items, etc. These data should be forwarded to the decision center for further analyses, especially in wartime. Thus, the channel status information (CSI) for industrial big data transmission has to be acquired. In this article, we develop a system architecture for industrial big data (BD) transmission based on radar-communication integration with arbitrary geometrical array. The traditional channel estimation method, which usually utilizes the regular antenna array to estimate the CSI, cannot be applied to the arbitrary geometrical array. Here, we use the manifold separation technique to transform the complex array configuration into regular array and the downlink channel covariance matrix is estimated by exploiting the frequency calibration technique when the uplink channel covariance matrix is received. The computational complexity for the proposed method and other state-of-the-art methods are analyzed. The simulation results prove that the proposed method can achieve excellent estimation performance for its application in radar-communication integration.

Low-Complexity Joint 2-D DOA and TOA Estimation for Multipath OFDM Signals

The multiple signal classification (MUSIC) algorithmis computationally expensive in the application to joint two-dimensional (2-D) direction-of-arrival (DOA) and time-of-arrival (TOA) estimation based on uniform circular array (UCA) using orthogonal frequency-division multiplexing (OFDM) signal. This letter proposed an efficient way to compute the 3-D spatial-temporal spectrum. We extended the manifold separation technique, by which we obtained the 3-D discrete Fourier transform (DFT) form of the spectrum. On this basis, we proposed two 2-D DOA and TOA estimators called FFT-MUSIC and Two-step FFT-MUSIC. The former computed the spectrum by large size fast Fourier transform (FFT) to reduce the grid error in searching DOAs and TOAs. The latter roughly located the DOAs and TOAs by relatively small size FFT, followed by the subspace-based technique for a fine-grained searching within a local grid. Simulation results showed that both estimators can reduce the computation cost by one to two orders of magnitude, as compared to their conventional counterparts, while maintaining a similar accuracy.

DOA estimation with extended sparse and parametric approach in multi‐carrier MIMO HFSWR

To obtain a higher angle resolution of multiple-in multiple-out high-frequency surface wave radar (MIMO HFSWR) for direction of arrival (DOA) estimation with a limited number of antenna sensors, multiple working frequencies are proposed to enlarge the aperture of the virtual array of the MIMO HFSWR. The scenario that all targets have the identical reflection at all working frequencies is studied, which permits the abstraction of a virtual received data vector by using all frequencies. This virtual data vector can be taken as the measurement of a virtual non-uniform linear array (VNLA) with a single reference working frequency. To extend the sparse and parametric approach (SPA) to the VNLA for DOA estimation, the manifold separation technique is utilised to decompose the array steering vector of the VNLA into two different parts, one is a characteristic matrix that is related to the array itself. The other is a Vandermonde vector that contains the DOAs of the targets. Then the authors use the Vandermonde structure to develop a SPA-liked method for the DOA estimation. Simulation results are provided to confirm the validity of the proposed method.

Combined root‐MUSIC algorithms for multi‐carrier MIMO radar with sparse uniform linear arrays

In this study, sparse uniform linear arrays are used to improve the direction-of-arrival (DOA) estimation accuracy for the multiple-input multiple-output radar. With a suitable choice of multi-carrier frequencies, the DOA estimation ambiguity problem caused by spatial under-sampling can be resolved. Two kinds of search-free DOA estimation algorithms based on root-multiple signal classification (MUSIC) are proposed. The first algorithm directly applies the root-MUSIC to each carrier frequency separately for the true DOAs as well as their spurious DOAs, then, a novel DOA replicas matching algorithm is proposed to obtain the true DOAs from the ambiguous ones. The second algorithm utilises the manifold separation technique (MST) to align the noise subspaces of all multi-carrier frequencies. Using the MST, the separable representation of the array manifold vector of each carrier frequency is obtained, then the root-MUSIC polynomials of all multi-carrier frequencies are combined to construct a new polynomial, the true DOAs can be obtained directly by applying polynomial rooting without any matching processing. The two proposed algorithms are both practical, computationally efficient and robust. Numerical simulations verify the effectiveness of the proposed algorithms in terms of root-mean-squared error.

Wideband Direction-of-Arrival Estimation With Arbitrary Array via Coherent Annihilating

In this paper, a new wideband DOA estimation method for arbitrary array application is proposed. The arbitrary array manifold is approximately decomposed under the concept of manifold separation technique (MST) and a linear combination of the equal interval sampling complex exponentials (EISCE) can be synthesized. Since the EISCEs at all frequencies contain the same DOA information, they can be annihilated by the same spatial annihilating filter. So, the coherent annihilating scheme is proposed, and all narrowband components are coherently combined to construct an optimization problem under the structural total least squares framework. During the optimization problem construction, the general solution method is proposed to enable the model approximation error in MST to be reduced to a negligible level. Finally, the optimization problem is solved through the multiple measurement vectors structural total least norm (MMV-STLN) approach and the DOAs are estimated from the reconstructed spatial annihilating filter. The new method is free of frequency focusing and is capable of handling both incoherent and coherent signals. The simulation results verify that the proposed method surpasses the existing methods largely in resolution and estimation performance under the low SNR, snapshot deficient, and closely spaced sources scenarios.

Application of Manifold Separation to Parametric Localization for Incoherently Distributed Sources

By using the manifold separation technique (MST), we develop a computationally efficient yet accurate estimator for localization of multiple incoherently distributed (ID) sources. In this paper, we have made the following main contributions: first, we use the MST to derive a closed-form expression for the ID signal covariance matrix that is applicable to the case with arbitrary array geometries or large angular spreads; second, we find that the two-dimensional spatial spectrum can be computed efficiently by using the discrete Fourier transform algorithms coupled with the unweighted (or Gaussian-weighted) moving average for the uniformly (or Gaussian) distributed ID sources; finally, we employ the first-order Taylor expansion to formulate a weighted least-squares approach that can improve the estimation performance significantly. Numerical results demonstrate that with less complexity, the proposed estimator offers better estimation performance compared with several classical estimators.

Joint Estimation of Azimuth and Elevation via Manifold Separation for Arbitrary Array Structures

Direction-of-arrival estimation is a ubiquitous task in array processing. The conventional MUltiple SIgnal Classification (MUSIC) method is often computationally expensive, particularly in the application of joint azimuth and elevation estimation. In this paper, we propose an efficient way to compute the two-dimentional (2D) spatial spectrum. By using the manifold separation technique, we find that the 2-D null-spectrum has the form of discrete Fourier transform (DFT). Moreover, the coefficients of the DFT form can be truncated and computed in parallel. Then by exploiting the fact that the nonzero coefficients are concentrated only at the top-left corner, we present a partial 2-D DFT to compute the 2-D spatial spectrum, which can reduce the latency significantly. In order to improve the estimation performance, we formulate an iterative multidimensional-subspace-fitting estimator in which we apply the first-order Taylor expansion to expand the projection operator. At each iteration, the estimation errors can be computed by solving a set of linear equations. Numerical results demonstrate that the proposed estimator offers better estimation performance compared with the classical 2-D MUSIC.

Distributed DOA Estimation for Arbitrary Topology Structure of Mobile Wireless Sensor Network Using Cognitive Radio

In order to improve the frequency spectrum availability and evade insecurity frequency range, the cognitive radio is introduced in wireless sensor network (WSN), which constructs the cognitive wireless network (CWN). The dynamic spectrum access (DSA) is used in CWN as the spectrum access scheme. In this paper, sensor nodes of mobile wireless sensor network (MWSN) are deployed based on the prior information of the deployment environment. The idea of CWN is introduced in MWSN. A distributed direction-of-arrival (DOA) estimation algorithm is proposed. The clustering of nodes constructs a sub-NWSN which acts as the sensor array used for DOA estimation. The Fourier domain (FD) root multiple signal classification (root-MUSIC) algorithm is applied for DOA estimation of sub-MWSN with arbitrary topology structure. The weight values of sub-MWSNs can be formulated as a function of the number of nodes, snapshot number and battery capacity of nodes. The total cost spectrum function is achieved finally. The improved performance of distributed FD root-MUSIC algorithm is verified by comparing with the manifold separation technique.

Full polarimetric sum and difference patterns synthesis for conformal array

A convex optimisation-based full polarimetric sum and difference patterns synthesis method for a conformal array is proposed. The method adopts a manifold separation technique and a co-polarisation and cross-polarisation basis to model the conformal array response in a closed-form expression from array calibration measurements, and then formulates the full polarisation sum and difference patterns synthesis as convex optimisation problems. The method is applied to a simulated conformal spherical conformal array composed of 176 antenna elements; the low sidelobe and low cross-polarisation level sum and difference patterns are presented.

Efficient Two-Dimensional Direction Finding via Auxiliary-Variable Manifold Separation Technique for Arbitrary Array Structure

A polynomial rooting direction of arrival (DOA) algorithm for multiple plane waves incident on an arbitrary array structure that combines the multipolynomial resultants and matrix computations is proposed in this paper. Firstly, a new auxiliary-variable manifold separation technique (AV-MST) is used to model the steering vector of arbitrary array structure as the product of a sampling matrix (dependent only on the array structure) and two Vandermonde-structured wavefield coefficient vectors (dependent on the wavefield). Then the propagator operator is calculated and used to form a system of bivariate polynomial equations. Finally, the automatically paired azimuth and elevation estimates are derived by polynomial rooting. The presented algorithm employs the concept of auxiliary-variable manifold separation technique which requires no sector by sector array interpolation and thus does not suffer from any mapping errors. In addition, the new algorithm does not need any eigenvalue decomposition of the covariance matrix and exhausted search over the two-dimensional parameter space. Moreover, the algorithm gives automatically paired estimates, thus avoiding the complex pairing procedure. Therefore, the proposed algorithm shows low computational complexity and high robustness performance. Simulation results are shown to validate the effectiveness of the proposed method.

Direction of Arrival Estimation using EM-ESPRIT with Nonuniform Arrays

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows one to improve the interpolation using the previously estimated DOA. One of this method’s novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with a smaller number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array.

Direction of arrival estimation for monostatic multiple-input multiple-output radar with arbitrary array structures

Compared with other systems with a single transmit antenna, multiple-input multiple-output (MIMO) radar systems have additional degrees of freedom that can enhance space resolution, improve parameter identifiability and enhance flexibility for transmit beam pattern design. The computational complexity for direction of arrival (DOA) estimation using sensor arrays increases very rapidly with the number of channels. The polynomial-rooting version of multiple signal classification algorithm (root-MUSIC) is computationally more efficient than spectral MUSIC. However, this algorithm can only be applied to uniform linear arrays. The manifold separation technique allows arrays of any geometry to be used with fast DOA estimators designed for linear arrays. In this study, a DOA estimation method that uses manifold separation and polynomial rooting technique is presented for monostatic MIMO radar with arbitrary array configuration. The algorithm offers a low computation complexity and an improved resolution capability for closely spaced sources as compared to conventional spectral MUSIC. Moreover, the wavefield modelling for monostatic MIMO radar and the number of mode selection of the proposed method are also analysed in the study. Finally, the simulation results are presented and the performances of the proposed algorithm are investigated and discussed.

Robust Beamformer Using Manifold Separation Technique for Semispherical Conformal Array

Conventional beamformers suffer from problems of finite samples, desired signal pointing errors, as well as imperfect array. A simple and robust beamformer based on the manifold separation technique (MST) is proposed in this letter to alleviate these problems. Using MST, the steering vector of an arbitrary array can be modeled as the product of an array sampling matrix and a vector with a Vandermonde structure. Robust characteristics are found by using this transformation. The analysis is verified via simulations based on a real-world semispherical conformal antenna array.

Direction-of-Arrival Estimation for Nonuniform Sensor Arrays: From Manifold Separation to Fourier Domain MUSIC Methods

In this paper, the problem of spectral search-free direction-of-arrival (DOA) estimation in arbitrary nonuniform sensor arrays is addressed. In the first part of the paper, we present a finite-sample performance analysis of the well-known manifold separation (MS) based root-MUSIC technique. Then, we propose a new class of search-free DOA estimation methods applicable to arrays of arbitrary geometry and establish their relationship to the MS approach. Our first technique is referred to as Fourier-domain (FD) root-MUSIC and is based on the fact that the spectral MUSIC function is periodic in angle. It uses the Fourier series to expand this function and reformulate the underlying DOA estimation problem as an equivalent polynomial rooting problem. Our second approach applies the zero-padded inverse Fourier transform to the FD root-MUSIC polynomial to avoid the polynomial rooting step and replace it with a simple line search. Our third technique refines the FD root-MUSIC approach by using weighted least-squares approximation to compute the polynomial coefficients. The proposed techniques are shown to offer substantially improved performance-to-complexity tradeoffs as compared to the MS technique.

DoA Estimation Via Manifold Separation for Arbitrary Array Structures

In this paper, we consider the manifold separation technique (MST), which stems from the wavefield modeling formalism developed for array processing. MST is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2-D or 3-D geometry. It is the product of a sampling matrix (dependent on the antenna array only) and a Vandermonde structured coefficients vector depending on the wavefield only. This allows fast direction-of-arrival (DoA) algorithms designed for linear arrays to be used on arrays with arbitrary configuration. In real-world applications, the calibration measurements used to determine the sampling matrix are corrupted by noise. This impairs the performance of MST-based algorithms. In particular, we study the effect of noisy calibration measurements on subspace-based DoA algorithms using MST. Expressions describing the error in the DoA estimates due to calibration noise and truncation are derived. This allows predicting the performance of MST-based algorithms in real-world applications. The analysis is verified by simulations. We established a link between the optimal number of selected modes and the statistics of calibration noise. We analyze the modeling error when MST is used for 1-D (azimuth) DoA estimation.