Coherently Distributed Sources Research Articles

Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC

This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors.

Localization of mixed coherently and incoherently distributed sources based on generalized array manifold

In practice, signals received by an array may be a mixture of coherently distributed (CD) and incoherently distributed (ID) sources, due to some complicated multipath/scattering effects. To localize mixed CD and ID sources, a method based on the generalized array manifold (GAM) is developed in this work. Firstly, source enumeration and source type classification are achieved by jointly employing the minimum description length (MDL) criterion, the covariance matrix difference technique and the second-order statistics of associated eigenvalues. Secondly, with the source enumeration result, the nominal direction of arrival (DOA) of ID sources is estimated by the rank-reduction principle based one-dimensional (1-D) spectral search, where shift invariance of the GAM associated with ID sources is considered. Thirdly, the oblique projection technique is adopted to separate the CD sources from ID ones, and then the nominal DOA of CD sources is estimated via the sparsity-cognizant total least-squares (S-TLS) method. Finally, with aid of the nominal DOA estimates, the corresponding angular spreads are calculated. An analysis of the proposed method is discussed and the approximate Cramér-Rao bound (CRB) is derived. Simulations are provided to demonstrate the performance of the proposed method.

2D DOA Estimation of Coherently Distributed Sources for Planar Arrays Based on Blind Signal Separation

A novel method is presented to estimate the direction-of-arrival (DOA) of coherently distributed (CD) sources for planar arrays. In the proposed method, the two-dimensional (2D) angular parameters are obtained by making use of the estimated generalized array manifold matrix, which is separated from the received observation data based on blind signal separation algorithm. The proposed method offers a number of advantages. First, the 2D central DOAs and angular spread variances can be estimated simultaneously. Second, the deterministic angular distributed functions (DADFs) of the CD sources do not need to know. Third, the special array geometries are not required, as the method is applicable to planar arrays. Computer simulations are shown to verify the efficacy of the proposed method.

Sparse Array Beamforming Design for Coherently Distributed Sources

Recently, nonstructured sparse array designs have attracted wide interest due to their capability of providing optimum performance for environment-dependent adaptive beamforming. In this article, we develop a sparse array design approach for adaptive beamforming in the presence of spatially coherently distributed (CD) sources. The proposed approach formulates the design problem via maximizing the output signal-to-interference-plus-noise ratio (SINR), but it exploits the generalized array manifold of CD sources. Moreover, sequential convex programming is utilized to convert the nonconvex optimization problem into a series of convex subproblems. We also analyze the impact of source distributed shape on optimum array configuration and theoretically prove that when the CD sources are Gaussian-shaped, the uniform linear array (ULA) is exactly the optimum array configuration. The resulting optimum sparse arrays yield higher output SINR and better-shaped beampattern than the structured sparse arrays. Numerical results verify the superiority of the optimum sparse arrays obtained by the proposed approach over the structured sparse arrays.

Parameter estimation for coherently distributed noncircular sources under impulsive noise environments

The signal source generates angular expansion in space due to scattering, reflection and other phenomena in a complex environment, which requires a distributed signal model for processing. This paper extends the method of joint angular estimation for coherently distributed (CD) sources consisting of noncircular signals to the impulsive noise scenario. In an actual wireless passive positioning environment, impulsive noise is very common. However, most algorithms only consider Gaussian noise environments and are not suitable for angle estimation in impulsive noise scenarios. This paper proposes the generalized complex correntropy (GCC) and shows that it can eliminate the effects of outliers in an impulsive noise environment. This is because the complex correntropy is an effective tool to analyze higher-order statistical moments in the impulsive noise environment. In order to improve the accuracy of the estimation, we construct a GCC matrix based on extended array output and apply the subspace techniques to extract the angle information of the CD noncircular sources. The simulation results show that the estimation performance of the proposed algorithms is better than the traditional algorithm applied to the noncircular CD sources.

DOA Estimation of Two-Dimensional Coherently Distributed Sources Based on Spatial Smoothing of Uniform Rectangular Arrays

Aiming at the direction-of-arrival (DOA) estimation of two-dimensional (2D) coherently distributed (CD) sources which are coherent with each other, we explore the propagator method based on spatial smoothing of a uniform rectangular array (URA). The rotational invariance relationships with respect to the nominal azimuth and nominal elevation are obtained under the small angular spreads assumption. A propagator operator is constructed through spatial smoothing of sample covariance matrices firstly. Then, combination of propagator and identical matrix is divided according to rotational operators, and the nominal angles can be obtained through eigendecomposition lastly. Realizing angle matching automatically, the proposed method can estimate multiple DOAs of 2D coherent CD sources without spectral peak searching and prior knowledge of deterministic angular signal distribution function. Simulations are conducted to verify the effectiveness of the proposed method.

2D DOA estimator for coherently distributed sources using one snapshot

A two-dimensional (2D) direction-of-arrival (DOA) estimation method for coherently distributed (CD) sources has been proposed in high real-time situation using only one snapshot. Utilising two uniform linear arrays (ULAs), the proposed algorithm first construct four equivalent matrices with rotational structures using one snapshot, and then a total equivalent covariance is extended by the four matrices. Finally, two rotational invariance matrices can been calculated by ESPRIT-like algorithm, and the eigenvalues which contains of the information of the central DOAs can be obtained by eigen-decomposition of the two matrices. To improve the performance of the proposed method, in-phased accomplished data is proposed. Without snapshots accumulation, peak searching, and correlation process, the 2D DOA estimation method for CD sources can be used for real-time situation. Several simulation results are used to illustrate the performance of the proposed method.

On Spatial Smoothing for DOA Estimation of 2D Coherently Distributed Sources with Double Parallel Linear Arrays

Considering coherently-distributed (CD) sources are correlated with each other, a two-dimensional (2D) coherent CD source model is proposed according to the characteristics of an underwater acoustic channel. Under the assumption of small angular spreads, rotational invariance relationships within and between subarrays of double parallel linear arrays are derived. As the covariance matrix of spatial smoothing obtained from receive vectors expressed by rotational invariance relationships is proven to be full rank, decoherence of the 2D coherent CD source is proposed by spatial smoothing of the double parallel linear arrays. A propagator method base on spatial smoothing (SS-PM) and estimation of signal parameters via rotational invariance techniques (ESPRIT) base on spatial smoothing (SS-ESPRIT) method established by covariance matrix of spatial smoothing are proposed. The proposed methods do not require peak-searching, angles matching and information of deterministic angular signal distribution function. Simulations are conducted to verify the effectiveness of the proposed methods.

Direct Position Determination of Coherently Distributed Noncircular Sources

The existing localization algorithms for coherently distributed (CD) sources fail to achieve the best localization performance because of position information loss and error accumulation. To solve this problem, this study proposed a novel direct position determination (DPD) algorithm that profits from the characteristics of noncircular signals. Based on the parameterization assumption of CD sources, the DPD localization model is initially constructed and an extended subspace data fusion‐based DPD algorithm is subsequently proposed by decomposing the extended covariance matrices, which are constructed by combining the characteristics of noncircular sources. The algorithm achieves a low complexity and a high efficiency by avoiding the calculation of the intermediate variables. Specifically, the closed‐form expression of the Cramer‐Rao lower bound for CD noncircular sources is also derived. Simulation results show that, compared with existing DPD algorithms, the proposed algorithm improves the multitarget localization capability and achieves high‐accuracy results.

Two-Dimensional DOA Estimation for Coherently Distributed Sources with Symmetric Properties in Crossed Arrays.

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

DOA Estimation for Coherently Distributed Sources Considering Circular and Noncircular Signals in Massive MIMO Systems

In mobile communication, the signal that a base station received cannot be regarded as a point source anymore because of the multipath propagation. A distributed source model is more suitable for the realistic scenarios. In this paper, an approach of direction-of-arrival (DOA) estimation is proposed for coherently distributed (CD) sources consisting of circular and noncircular signals in a massive or large-scale multiple-input multiple-output system. The noncircular characteristic can improve the performance of DOA estimation. However, most algorithms are not suitable for DOA estimation where circular and noncircular signals coexist. Based on the analysis of constraint conditions satisfied by the steering vector of mixed signals, a multiple signal classification (MUSIC) like approach is proposed for the DOA estimation of CD sources consisting of circular and noncircular signals. On the conditions of low signal-to-noise ratio, small snapshot numbers, and large source numbers, the pseudopeaking may appear. This phenomenon has been analyzed, and a modified MUSIC-like approach is proposed. Simulation results demonstrate that both two proposed algorithms can estimate more sources than the number of sensors. The estimation performances of the two proposed algorithms outperform the traditional MUSIC algorithm.

A DOA Estimation Approach for Transmission Performance Guarantee in D2D Communication

In Device-to-Device (D2D) communications of massive Multiple-Input Multiple-Output (MIMO) system, the inter-channel interference (ICI) can severely deteriorate the entire system performance. The beamforming technique can be used to alleviate this situation. Thus the localization of the users’ equipment (UE) should be known as a prior. In wireless communication, due to the effect of multipath, the model of incident signal should be regarded as distributed sources instead of point sources. In this paper, we propose a 2-D DOA estimation algorithm for coherently distributed (CD) sources based on conformal array. First, three rational invariance relationships are constructed based on generalized steering vectors (GSVs). Then the propagator method (PM) is used for estimating three rational invariance matrices. Finally, the 2-D DOA of CD sources can be obtained from the eigenvalues of three rational invariance matrices. Without spectrum peaking searching, and estimation and eigendecomposition of sampling covariance matrix, the proposed algorithm has low computational complexity. For the condition with a large amount of data, the distributed and parallel PM is proposed to deal with this problem. Simulation results verify the effectiveness of the proposed algorithm.

Joint Angle Estimation and Signal Reconstruction for Coherently Distributed Sources in Massive MIMO Systems Based on 2-D Unitary ESPRIT

We consider the challenging problem of joint angle estimation and signal reconstruction for coherently distributed (CD) sources in massive multiple-input–multiple-output (MIMO) systems employing uniform rectangular arrays. A simplified method inspired by the two-dimensional (2-D) unitary estimating signal parameters via rotational invariance technique (ESPRIT) is proposed to estimate both the central angle and the angular spread without the need for a spectrum peak search and covariance matrix matching process. We first approximate the 2-D generalized steering vector expressed as a Schur-Hadamard product by a pair of one-dimensional generalized steering vectors. Then, we obtain two approximate rotational invariance relationships with respect to the central angles of the CD sources using a linear approximation of the individual generalized steering vectors of the azimuth and elevation subarrays. With the aid of this approximate decomposition, a new unitary ESPRIT-inspired algorithm is conceived to automatically pair the 2-D central angle estimations and a novel method capable of bypassing the high-complexity search process is proposed for angular spread estimation. Furthermore, the closed-form approximate Cramer-Rao lower bounds are derived for the estimators of both the central angles and the angular spreads. The complexity of the proposed estimator is also analyzed. Additionally, the orthogonality of the generalized steering vectors is proved, which enables us to propose a low-complexity method to reconstruct the CD signal matrix by replacing the inversion operator with the conjugate transpose operator. The simulation results demonstrate the efficiency of our proposed approach.

Wearable Sensor Localization Considering Mixed Distributed Sources in Health Monitoring Systems.

In health monitoring systems, the base station (BS) and the wearable sensors communicate with each other to construct a virtual multiple input and multiple output (VMIMO) system. In real applications, the signal that the BS received is a distributed source because of the scattering, reflection, diffraction and refraction in the propagation path. In this paper, a 2D direction-of-arrival (DOA) estimation algorithm for incoherently-distributed (ID) and coherently-distributed (CD) sources is proposed based on multiple VMIMO systems. ID and CD sources are separated through the second-order blind identification (SOBI) algorithm. The traditional estimating signal parameters via the rotational invariance technique (ESPRIT)-based algorithm is valid only for one-dimensional (1D) DOA estimation for the ID source. By constructing the signal subspace, two rotational invariant relationships are constructed. Then, we extend the ESPRIT to estimate 2D DOAs for ID sources. For DOA estimation of CD sources, two rational invariance relationships are constructed based on the application of generalized steering vectors (GSVs). Then, the ESPRIT-based algorithm is used for estimating the eigenvalues of two rational invariance matrices, which contain the angular parameters. The expressions of azimuth and elevation for ID and CD sources have closed forms, which means that the spectrum peak searching is avoided. Therefore, compared to the traditional 2D DOA estimation algorithms, the proposed algorithm imposes significantly low computational complexity. The intersecting point of two rays, which come from two different directions measured by two uniform rectangle arrays (URA), can be regarded as the location of the biosensor (wearable sensor). Three BSs adopting the smart antenna (SA) technique cooperate with each other to locate the wearable sensors using the angulation positioning method. Simulation results demonstrate the effectiveness of the proposed algorithm.

Low‐complexity 2D DOA estimator for multiple coherently distributed sources

PurposeThe purpose of this paper is to develop a new method for the two‐dimensional direction‐of‐arrival (DOA) estimation of multiple coherently distributed (CD) sources, which can provide lower computational complexity while sustaining the estimation performance within a tolerable level.Design/methodology/approachUsing three parallel uniform linear arrays (ULAs), a new method for parametric estimation of multiple coherently distributed sources is proposed. The proposed method is based on the Taylor approximation to the generalized steering vectors (GSVs) of shifted ULAs, and utilizes the special array geometry. In addition, a simple parameter matching procedure is also given in this paper.FindingsSeveral numerical experiments have been designed. The experiments are based on coherently distributed source model, and the noise is assumed to be zero‐mean and spatially and temporally white and Gaussian. Numerical results show that the proposed method can exhibit good estimation performance under small angular spread and be applicable to the multisource scenario with different angular distributions.Research limitations/implicationsThis research is limited to CD sources. Furthermore, the proposed method is based on the small angular approximation to GSV. Hence, it is fitter for the case of small angular extension.Originality/valueWithout any spectrum‐peak searching, the proposed method provides lower computational cost compared to the classical spectrum‐based methods. Moreover, it does not depend on the prior knowledge about angular distribution shape and is hence robust to mismodeling.

2D DOA Estimator for Multiple Coherently Distributed Sources Using Modified Propagator

In this paper, we propose a new algorithm for estimating the two-dimensional (2D) nominal direction-of-arrivals (DOAs) of multiple coherently distributed (CD) sources by utilizing three parallel uniform linear arrays (ULAs). The proposed algorithm firstly shows that some rotational eigenstructures exist approximately for three pair of shifted ULAs. And then a modified propagator method is used to estimate three rotational invariance matrices which denote the rotational eigenstructures. Finally, the nominal angular parameters of CD sources are obtained from the eigenvalues of the rotational invariance matrices. Without spectrum searching, the estimation and eigendecomposition of the sample covariance matrix, our approach is computationally more attractive compared with the earlier algorithms. In addition, it can be applied to the scenario with multiple sources that may have different angular distribution shapes. Simulation results illustrate the performance of the algorithm.

Simplified Estimation of 2D DOA for Coherently Distributed Sources

In mobile communications, local scattering in the vicinity of the mobile results in angular spreading as seen from a base station antenna array. In this paper, we consider the problem of estimating the two-dimensional (azimuth and elevation) direction-of-arrival (DOA) parameters of spatially distributed sources. Based on double parallel uniform linear arrays (ULAs), a simplified method without spectrum-peak searching is proposed for the 2D DOA estimation of multiple coherently distributed (CD) sources. The proposed method firstly obtains two approximate rotational invariance relations with respect to the nominal DOAs of CD sources by using one-order Taylor approximation to the generalized steering vectors (GSVs) of two pairs of shifted subarrays. And then a new ESPRIT-based method is utilized to estimate the nominal azimuth DOA and nominal elevation DOA. In addition, a simple parameter matching approach is also given. Compared with the conventional methods, our method has significantly reduced the computational cost and can sustain the estimation performance within a tolerable level. Moreover, our method is a blind estimator without any prior knowledge about angular distribution shape. Numerical examples illustrate the performance of the method.

Decoupled Estimation of 2D DOA for Coherently Distributed Sources Using 3D Matrix Pencil Method

A new 2D DOA estimation method for coherently distributed (CD) source is proposed. CD sources model is constructed by using Taylor approximation to the generalized steering vector (GSV), whereas the angular and angular spread are separated from signal pattern. The angular information is in the phase part of the GSV, and the angular spread information is in the module part of the GSV, thus enabling to decouple the estimation of 2D DOA from that of the angular spread. The array received data is used to construct three-dimensional (3D) enhanced data matrix. The 2D DOA for coherently distributed sources could be estimated from the enhanced matrix by using 3D matrix pencil method. Computer simulation validated the efficiency of the algorithm.

Distributed source localization using ESPRIT algorithm

A new algorithm based on ESPRIT is proposed for the estimation of the central angle and angular extension of distributed sources. The central angles are estimated using TLS-ESPRIT for both incoherently distributed (ID) and coherently distributed (CD) sources. For CD sources, the extension width is estimated by constructing a one-dimensional (1-D) distributed source parameter estimator (DSPE) spectrum for each source. For ID sources, the extension widths are estimated using the central moments of the distribution. The algorithm can be used for sources with different angular distributions.