Noncircular Signals Research Articles

Bounded non-linear covariance based ESPRIT method for noncircular signals in presence of impulsive noise

Among the most important approaches in the study of DOA estimation, ESPRIT-like methods have received considerable attentions and have been widely applied in practical applications. Although many of the latest approaches have considered various performance requirements, the robustness to impulsive noise warrants further investigation. Inspired by the idea of bounded non-linear covariance (BNC), a novel subspace based method for DOA estimation is proposed in this paper. Named NC-BNC-ESPRIT, this method uses the BNC matrix to create a signal subspace of extended array outputs and it can handle the DOA estimation for noncircular (NC) signals in presence of impulsive noise. Simulation experiments and theoretical analysis are provided to verify this methods' superiority over existing approaches and proof of its robustness is provided in the appendix.

Design And Analysis of the Sparse Array for DoA Estimation of Noncircular Signals

Recently, many sparse arrays have been proposed to increase the number of degrees of freedom for direction of arrival (DoA) estimation especially for circular signals. Though many practical signals are noncircular, still the properties of noncircularity are hardly exploited in the design of sparse linear arrays. A new array geometry for noncircular signals, which significantly increases the aperture of the virtual array, has been proposed in this paper. The structure is obtained by systematically placing the two uniform linear array (ULA) side by side. The proposed design provides the largest aperture virtual ULA (VULA) as compared to the existing array structures. The aperture of VULA and corresponding weight function are evaluated analytically. The closed-form expression of the Cramer–Rao bound, the minimum lower bound on the error in the DoA estimation, is also obtained for the proposed structure. The performance of the proposed array is studied by the exhaustive computer simulations.

Two-Dimensional Direction-of-Arrival Estimation of Noncircular Signals in Coprime Planar Array with High Degree of Freedom

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, there are problems of the limited degree of freedom (DOF) and high complexity caused by the spectral peak search. We utilize the time-domain characteristics of signals and present a high DOF algorithm with low complexity based on the noncircular signals. The paper first analyzes the covariance matrix and ellipse covariance matrix of the received signals, vectorizes these matrices, and then constructs the received data of a virtual uniform rectangular array (URA). 2D spatial smoothing processing is applied to calculate the covariance of the virtual URA. Finally, the paper presents an algorithm using 2D multiple signal classification and an improved algorithm using unitary estimating signal parameters via rotational invariance techniques, where the latter solves the closed-form solutions of DOAs replacing the spectral peak search to reduce the complexity. The simulation experiments demonstrate that the proposed algorithms obtain the high DOF and enable to estimate the underdetermined signals. Furthermore, both two proposed algorithms can acquire the high accuracy.

2-D DOA Estimation for Incoherently Distributed Sources Considering Mixed Circular and Noncircular Signals in Massive MIMO System

In practical environment, the received signals cannot be regarded as point sources due to the existence of signal scattering phenomena. Incoherently distributed source model is suitable for this realistic scenarios. The incoherently distributed DOA estimators based on noncircular property can provide a better performance. However, these estimators are not fit for the mixed circular and noncircular signals. In this paper, a conjugate generalized shift invariance algorithm is proposed for incoherently distributed sources comprising of circular and noncircular signals. The general array manifold (GAM) model of incoherently distributed source is established by one-order Taylor series approximation. To utilize the noncircular property, each incoherently distributed circular source is separated as two strictly incoherently distributed noncircular sources. A generalized shift invariance property is derived by dividing the whole uniform rectangular array (URA) into four overlapping subarrays. Then, a modified conjugate generalized least square (CGLS) ESPRIT algorithm is proposed to obtain the central DOAs, which can improve the estimation accuracy without any spectrum searching. In addition, a pair matching method and an angular spreads estimation algorithm are also designed based on the GAM model for this mixed sources scenario. Furthermore, the Cramer-Rao bound (CRB) of proposed algorithm is given and analyzed under the mixed incoherently distributed sources scenario. Numerical results illustrate the validity of the proposed algorithm in this realistic scenario.

Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise

In this paper, a novel direction-of-arrival (DOA) estimation algorithm is proposed for noncircular signals with nonuniform noise by using the unitary matrix completion (UMC) technique. First, the proposed method utilizes the noncircular property of signals to design a virtual array for approximately doubling the array aperture. Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. Next, a novel UMC method is formulated for the DOA estimation to remove the influence of nonuniform noise. Finally, the DOA without the influence of the unknown noncircularity phase is obtained by using the modified estimation of signal parameters via rotational invariance technique (ESPRIT). Especially, for handling the coherent sources, the forward–backward spatial smoothing technique is utilized to reconstruct a full-rank covariance matrix so that the signal subspace and the noise subspace can be correctly separated. Due to utilizing the extended array aperture and the unitary transformation, the proposed method can identify more sources than the number of physical sensors and provides higher angular resolution and better estimation performance. Compared with the existing DOA estimation algorithms for noncircular signals, the proposed one can effectively suppress the influence of the nonuniform noise. The simulation results are provided to verify the effectiveness and superiority of the proposed method.

Underdetermined Direction of Arrival Estimation of Non-Circular Signals via Matrix Completion in Nested Array

Direction-of-arrival (DOA) estimation using nested linear array ignores the information from repeated sensors, thus involves the problem of losing accuracy. Moreover, non-circular feature of signals is rarely considered and it results in discontinuity of the virtual array, namely, holes appear. This paper first provide an improved data averaging method to increase the accuracy of DOA estimation by fusing data from covariance and elliptic covariance. And then an algorithm based on matrix completion theory in nested array that greatly extends the degrees of freedom (DOF) and is able to find more sources than number of physical sensors is presented. The algorithm reconstructs the covariance matrix of the virtual linear array, which exactly has the same shift invariance as the uniform linear array but a higher aperture. Considering about the missing elements of the virtual array covariance matrix, we apply matrix completion theory to solve the problem. Finally, true DOAs of multiple signals can be obtained through subspace algorithms. Numerical results demonstrate that the proposed algorithms can obtain high accuracy while underdetermined DOA estimation is realized.

RSNT-cFastICA for Complex-Valued Noncircular Signals in Wireless Sensor Networks

RSNT-cFastICA for Complex-Valued Noncircular Signals in Wireless Sensor Networks

Widely Linear Adaptive Instantaneous Frequency Estimation in Vector Hydrophones

To solve the problem that the time-frequency resolution of Short-Time Fourier Transform (STFT) is constrained by the window length and the moving step of the short time window, and to utilize the merits of a widely linear method, a novel instantaneous frequency estimation method in vector hydrophone was proposed. In this paper, a complex variable was constructed. It is composed of sound pressure and particle velocity as its real part and imaginary part, respectively. The constructed variable was approved to be second order noncircular (improper). For the modelling of noncircular signals, the standard linear estimation is not adequate and the pseudo-covariance matrix should also be taken into consideration. As a result, a widely linear adaptive instantaneous frequency estimation algorithm and its three solutions based on the augmented complex least mean square (ACLMS) method are presented to estimate the instantaneous frequency in vector hydrophones. The results of simulations and laboratory experiments prove that this approach based on a widely linear model performs better compared to STFT and strict linear filter methods.

Hybrid Joint Diagonalization Algorithms

This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation. We introduce new Jacobi-like algorithms using Givens or a combination of Givens and hyperbolic rotations. These algorithms are compared with state-of-the-art methods and their performance gain, especially in the high dimensional case, is assessed through simulation experiments including examples related to blind separation of non-circular sources.

Tensor based angle estimation scheme for strictly noncircular sources in bistatic MIMO radar

In this paper, joint direction of departure (DOD) and direction of arrival (DOA) estimation for strictly noncircular sources in multiple-input multiple-output (MIMO) radar is dealt with by a novel tensor based subspace method. The proposed method firstly formulates a novel augmented tensor for capturing both the noncircularity and inherent multidimensional structure of strictly noncircular signals, and then a tensor based signal subspace is constructed by utilizing the high-order singular value decomposition (HOSVD). Finally, the DODs and DOAs are achieved by calculating the rotational invariance factors corresponding to the augmented steering matrix. The proposed method provides better angle estimation performance than the existing subspace based algorithms, especially in the case of low SNR and a small number of snapshots. In addition, the DODs and DOAs are paired automatically. The effectiveness and advantages of the proposed method are demonstrated via simulation results.

Parameter Estimation of Coexisted Circular and Strictly Noncircular Sources Using Diversely Polarized Antennas

The problem of closed-form parameter estimation using a diversely polarized antenna array of arbitrary configurations is considered, under the coexistence of the circular and strictly noncircular signals used in the communication/radar systems. By incorporating the noncircularity difference and polarization diversity of the signals with the augmented polarimetric manifold decoupling, the conventional polynomial rooting polarimetric element space subspace technique is enhanced for direction-of-arrival, polarization, and noncircularity phase (for strictly noncircular sources) estimation. A subspace constraint method is also presented to improve parameter estimation of the strictly noncircular sources. Simulation results are included to illustrate the performance of the proposed methods.

Tensor-Based Angle Estimation Approach for Strictly Noncircular Sources with Unknown Mutual Coupling in Bistatic MIMO Radar

In the paper, the estimation of joint direction-of-departure (DOD) and direction-of-arrival (DOA) for strictly noncircular targets in multiple-input multiple-output (MIMO) radar with unknown mutual coupling is considered, and a tensor-based angle estimation method is proposed. In the proposed method, making use of the banded symmetric Toeplitz structure of the mutual coupling matrix, the influence of the unknown mutual coupling is removed in the tensor domain. Then, a special enhancement tensor is formulated to capture both the noncircularity and inherent multidimensional structure of strictly noncircular signals. After that, the higher-order singular value decomposition (HOSVD) technology is applied for estimating the tensor-based signal subspace. Finally, the direction-of-departure (DOD) and direction-of-arrival (DOA) estimation is obtained by utilizing the rotational invariance technique. Due to the use of both noncircularity and multidimensional structure of the detected signal, the algorithm in this paper has better angle estimation performance than other subspace-based algorithms. The experiment results verify that the method proposed has better angle estimation performance.

The augmented complex-valued extreme learning machine

Abstract As an emerging learning model, extreme learning machine (ELM) has attracted more and more attention due to its fast learning and powerful data processing ability. By extending ELM to complex domain, complex ELM (CELM) has been proposed to process complex-valued data. However, the existing CELMs can not fully capture the second-order statistics of complex signals, thus providing only suboptimal solutions in real world applications when dealing with noncircular (or improper) signals. To this end, this paper proposes two augmented CELM models by incorporating the conjugate information of the complex input and the hidden layer, respectively. The approximation capability and the ability to capture the second-order statistics of signals are theoretically analysed. Moreover, based on Wirtinger calculus, the corresponding regularized models are derived for the sake of overcoming the possible overfitting problem. The superiority of the proposed models is verified by simulation results.

Efficient DOA estimation of noncircular signals in the presence of multipath propagation

The noncircularity of uncorrelated signals can improve the performance of direction of arrival (DOA) estimation using antenna arrays. However, due to reflection from surfaces or malicious jamming, the received noncircular signals may be a mixture of uncorrelated and coherent components in practice, which has not been considered by existing algorithms. This paper addresses the issue of DOA estimation for noncircular signals under multipath fading in smart antenna systems, and a novel two-stage processing method is proposed accordingly. By expanding the signal subspace from augmented array output, the DOA estimates of uncorrelated sources are first obtained, and then the covariance matrix of uncorrelated signals is reconstructed and removed from that of the mixed signals afterwards. Secondly, a spatial smoothing technique is performed on a denoised covariance to restore rank deficiency in the covariance of the remaining coherent signals. The resultant algorithm can resolve more signals than array elements with higher accuracy and better classification of signal type than previous methods. Additionally, a new deterministic direction estimation Cramér–Rao lower bound (CRLB) is derived for the considered mixture model. Simulation results demonstrate the validity and efficiency of the proposed method.

DOA estimation of rectilinear signals with a partly calibrated uniform linear array

This paper investigates the problem of direction-of-arrival (DOA) estimation of rectilinear or strictly second-order noncircular signals with a partly calibrated uniform linear array (ULA). Consider that the uncalibrated portion of the array suffers from unknown gains and phases, an extended data model corresponding to a virtual (extended) array is presented by taking the noncircularity of the signals into account. On this basis and given the signal subspace matrix associated with the virtual array, a linear equation is derived to determine the unknown gains and phases. Then, the DOAs are found through the eigenvalue decomposition of a matrix related to the signal subspace matrix and array gains and phases. Since spatial spectrum search is not required, the proposed method is computationally efficient. Moreover, it is able to handle at most 2M−3 rectilinear signals with a partly calibrated ULA of M elements, even though only two neighboring elements of the array are calibrated. Numerical results also demonstrate that the proposed method has remarkable performance superiority brought by the rectilinearity.

An Efficient Direct Position Determination Method for Multiple Strictly Noncircular Sources.

This paper focuses on the localization methods for multiple sources received by widely separated arrays. The conventional two-step methods extract measurement parameters and then estimate the positions from them. In the contrast to the conventional two-step methods, direct position determination (DPD) localizes transmitters directly from original sensor outputs without estimating intermediate parameters, resulting in higher location accuracy and avoiding the data association. Existing subspace data fusion (SDF)-based DPD developed in the frequency domain is computationally attractive in the presence of multiple transmitters, whereas it does not use special properties of signals. This paper proposes an improved SDF-based DPD algorithm for strictly noncircular sources. We first derive the property of strictly noncircular signals in the frequency domain. On this basis, the observed frequency-domain vectors at all arrays are concatenated and extended by exploiting the noncircular property, producing extended noise subspaces. Fusing the extended noise subspaces of all frequency components and then performing a unitary transformation, we obtain a cost function for each source location, which is formulated as the smallest eigenvalue of a real-valued matrix. To avoid the exhaustive grid search and solve this nonlinear function efficiently, we devise a Newton-type iterative method using matrix Eigen-perturbation theory. Simulation results demonstrate that the proposed DPD using Newton-type iteration substantially reduces the running time, and its performance is superior to other localization methods for both near-field and far-field noncircular sources.

An Augmented Complex-Valued Least-Mean Kurtosis Algorithm for the Filtering of Noncircular Signals

In this paper, a novel augmented complex-valued least-mean kurtosis (ACLMK) algorithm is proposed for processing complex-valued signals. The negated kurtosis of the complex-valued error signal is defined as a cost function by using augmented statistics. As a result of the minimization of this cost function, the ACLMK algorithm containing all second-order statistical properties is obtained for processing noncircular complex-valued signals. Moreover, in this paper, convergence and misadjustment conditions of the proposed ACLMK algorithm are derived from the steady-state analysis. The simulation results on complex-valued system identification, prediction, and adaptive noise cancelling problems show that the use of the cost function defined by the negated kurtosis of the complex-valued error signal based on augmented statistics enables the processing of the noncircular complex-valued signals, and significantly improves the performance of the proposed ACLMK algorithm in terms of the mean square deviation, the mean square error, the prediction gain and the convergence rate when compared to other algorithms.

DOA Estimation of Noncircular Signals for Unfolded Coprime Linear Array: Identifiability, DOF and Algorithm (May 2018)

An ambiguity-free direction of arrival (DOA) estimation method is presented for unfolded coprime linear array (UCLA) in this paper to resolve noncircular signals. Unlike the existing methods which process the two subarrays of coprime linear array separately, we stack the received signals of the two subarrays and derive the total subspace to produce the MUSIC spectrum. Specifically, we demonstrate that the ambiguity problem can be suppressed owing to the coprime property and the true DOA estimates can be obtained immediately. As the self-information and mutual information are jointly employed, the proposed method can achieve the full degrees of freedom (DOFs) and improved DOA estimation performance. Meanwhile, the extended aperture of UCLA can be feasibly exploited, which endows the proposed method with an enhanced identifiability. In addition, the non-circularity is utilized to double the available DOF and further improve the estimation accuracy of the proposed method. Simulation results verify the effectiveness and superiority of the proposed method.

Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis

We provide a complete study on the direction-of-arrival (DOA) estimation of noncircular (NC) signals for uniform linear array (ULA) via Vandermonde constrained parallel factor (PARAFAC) analysis. By exploiting the noncircular property of the signals, we first construct an extended matrix which contains two times sampling number of the received signal. Then, taking the Vandermonde structure of the array manifold matrix into account, the extended matrix can be turned into a tensor model which admits the Vandermonde constrained PARAFAC decomposition. Based on this tensor model, an efficient linear algebra algorithm is applied to obtain the DOA estimation via utilizing the rotational invariance between two submatrices. Compared with some existing algorithms, the proposed method has a better DOA estimation performance. Meanwhile, the proposed method consistently has a higher estimation accuracy and a much lower computational complexity than the trilinear alternating least square- (TALS-) based PARAFAC algorithm. Finally, numerical examples are conducted to demonstrate the effectiveness of the proposed approach in terms of estimation accuracy and computational complexity.

Robust Widely Linear Beamforming via the Techniques of Iterative QCQP and Shrinkage for Steering Vector Estimation

For non-circular signals, the existing robust widely linear (WL) beamforming algorithms either suffer from performance degradation at high signal-to-noise ratio or have high computational complexities. In order to cope with this problem, three low-complexity robust WL beamformers, i.e., the WL-IQCQP, the WL-RBLW, and the WL-OAS, are proposed in this paper. First, based on the spatial spectrum of non-circularity coefficient, the augmented interference-plus-noise covariance matrix is reconstructed to remove the signal-of-interest’s component from the augmented sample covariance matrix. Then, the method of iterative quadratically constrained quadratic programming, the modified Rao-Blackwell Ledoit-Wolf estimator, and oracle approximating shrinkage estimator are developed, respectively, to estimate the desired signal’s extended steering vector. Only the prior knowledge of the antenna array geometry and the angular sector in which the desired signal is located are utilized in the proposed algorithms. Compared with several representative robust WL beamformers, numerical simulations demonstrate that the proposed beamformers can achieve better performances.