Noncircular Signals Research Articles

WLB-DSCA method for strictly non-circular signals in coprime array

Widely linear beamforming (WLB) performs better than conventional adaptive beamforming, however its performance is restricted by array geometry. Coprime array can improve the beamforming performance compared with uniform linear array given the number of sensors. In this paper, a WLB with difference-sum co-array (WLB-DSCA) is devised for strictly non-circular (SNC) signals in coprime array. We vectorize the augmented covariance matrix of coprime array to produce a DSCA. To efficiently exploit all information of continuous and discontinuous virtual sensors in DSCA, we introduce the sparse representation of DSCA. A norm minimization optimization problem is formulated and then solved to localize the SNC signals in DSCA. We formulate a joint covariance and pseudo covariance matrices optimization problem to determine the powers of SNC signals. The augmented interference-plus-noise covariance matrix (AINCM) is reconstructed. Lastly, the augmented weight vector of the proposed WLB-DSCA is computed. Numerical results validate that the proposed WLB-DSCA is capable of handling SNC signals in coprime array.

Fast DOA Estimation of IGS Noncircular Signals Under Coprime Arrays

Traditional direction-of-arrival (DOA) estimation methods often encounter challenges such as low accuracy and high computational complexity, particularly in complex signal environments with multiple sources. To address these issues, this paper proposes a fast DOA estimation method for improper Gaussian signaling (IGS) non-circular signals, based on a coprime array; this approach involves extending the array model by leveraging the unique properties of non-circular signals. Subsequently, this study introduces the ANCM algorithm, a method designed for fast DOA estimation of IGS non-circular signals within a non-uniform noise background. The proposed ANCM algorithm is then compared to classical algorithms, through simulations in a non-uniform noise environment. Experimental results demonstrate that the ANCM algorithm significantly outperforms traditional methods in such conditions. Therefore, the development of new, efficient DOA estimation methods holds substantial theoretical and practical value.

An Enhanced Direct Position Determination of Mixed Circular and Non-Circular Sources Using Moving Virtual Interpolation Array.

In this study, a moving single-station direct position determination (DPD) algorithm based on virtual interpolated arrays is proposed. Existing moving single-station algorithms face challenges such as the incomplete utilization of sparse array apertures and insufficient consideration of mixed circular and non-circular signals. To address these issues, we propose an enhanced gridless DPD algorithm, suitable for multiple mixed circular and non-circular sources. Through constructing a non-zero unconjugated covariance matrix from the non-circular components of the mixed signals, the data dimensionality is expanded, and the gridless method is used to fill the voids in the coarray, significantly improving localization performance. Additionally, a unitary transformation method is applied to reduce computational complexity. This method transforms complex operations into real operations by applying unitary transformations to steering vectors and subspaces. Simulation results demonstrate that the proposed algorithm offers significant advantages in terms of array degrees of freedom and localization accuracy.

An augmented complex-valued gradient-descent total least-squares algorithm for noncircular signals

In this paper, we propose a novel augmented complex-valued gradient-descent total least-squares (ACGDTLS) adaptive filter for processing noisy input and output noncircular complex-valued signals. First, a Rayleigh quotient cost function is formulated by incorporating augmented complex-valued statistics and the output-to-input-noise-ratio within the widely linear error-in-variable model, whereby the ACGDTLS is developed using the gradient-descent approach. Next, rigorous analysis is conducted to establish a conservative step-size bound guaranteeing mean convergence, a closed-form expression for the steady-state mean-squared deviation, and the algorithm’s computational complexity. Finally, through simulations conducted in system identification, wind/speech prediction, and stereophonic acoustic echo cancellation, the analytical findings are validated, and the proposed ACGDTLS filter demonstrates superior estimation accuracy compared to the augmented complex-valued least-mean-square algorithm and two state-of-the-art bias-compensated methods. Remarkably, this performance advantage persists across a wide range of step-sizes, input noise variances, and output noise variances.

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.

DOA estimation of noncircular signals with direction-dependent mutual coupling

In this paper, a reweighted sparse recovery algorithm based on the optimal weighted subspace fitting (WSF) for non-circular signals in direction-dependent mutual coupling (MC) is proposed. Firstly, a new augmented model is constructed by leveraging the characteristics of non-circular signals. Next, a new direction matrix without mutual coupling coefficients is obtained by a novel transformation method. Then, two sparse recovery models are constructed by utilizing the WSF technique, and the sparsity of the solution is increased by constructing a weighted matrix. Finally, the direction of arrival (DOA) is achieved by a sparse recovery approach. For both coherent and incoherent signals, the developed approach can achieve precise DOA estimation in the case of direction-dependent MC. The robustness and advantage of the developed approach are testified by various experiments.

An enhanced direct position determination of non-circular sources via sparse Bayesian inference and grid refinement strategy

In this study, an off-grid sparse Bayesian inference (OGSBI) based direct position determination (DPD) algorithm is investigated. Existing SBI-based DPD algorithms are confronted with the challenge of excessive computational loads and lack of consideration for non-circular (NC) signals. To address these limitations, we present an enhanced OGSBI-based DPD algorithm for multiple non-circular sources. By utilizing the conjugate information of the NC signals, we expand the dimensionality of the data matrix to achieve a significant improvement in the localization performance. Additionally, a grid refinement strategy is developed to alleviate the computational loads, which involves an initial search to determine the approximate source locations, followed by fine localization using a denser grid. Moreover, the computational complexity and Cramér-Rao lower bound are derived to provide a comprehensive analysis of the proposed algorithm. Numerical simulations demonstrate the superiority of the proposed algorithm in terms of both localization accuracy and computational efficiency.

Shifted super transformed nested array for DOA estimation of non-circular signals with increased uDOFs and reduced mutual coupling

In this work, a scheme for array structure design is proposed to maximize uniform degrees of freedom (uDOFs) and reduce mutual coupling. It starts by exchanging the positions of two subarrays within the nested array, followed by mitigating mutual coupling through sensor relocation due to the dense subarray, and ultimately increasing uDOFs by globally shifting the entire array to the right. Following this scheme, the concept of Shifted Super Transformed Nested Array (SSTNA) is introduced and general guidelines for the construction of SSTNA are provided. Analytical expressions for the continuous region of the virtual apertures and uDOFs are derived. Furthermore, the optimal shifting parameter and the first three weight functions are determined for SSTNA. Theoretical analysis shows that SSTNA can effectively reduce mutual coupling while maintaining high uDOFs. In strong mutual coupling scenarios, simulation results are provided to demonstrate the effectiveness and superiority of the proposed design.

Sparse representation based DOA estimation of mixed circular and non-circular signals

Sparse representation based DOA estimation of mixed circular and non-circular signals

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Maximum likelihood based direction estimation for noncircular signals

In the direction estimation for the signals incident on a sensor array, maximum likelihood (ML) based methods can provide superior performance than subspace based ones such as the multiple signal classification (MUSIC). When the incoming signals are noncircular the exploitation of the property can allow us to improve estimation performance. Based on the deterministic ML criterion, a direction estimation method for strictly noncircular signals is proposed that can outperform the conventional alternating maximization (AM) with no use of noncircularity. Using a generalized Gaussian probability density function, we approach the ML estimation, which is formulated as a nonlinear multidimensional problem. The application of the alternating projection to the multidimensional problem leads to the maximization of an objective function of two variables associated with the direction and the initial phase of a noncircular signal. Theoretically optimizing the phase variable, we obtain the maximum through one-dimensional search with respect to the direction variable only. The complexity of the proposed noncircular AM (NC-AM) is far less than that of the existing ML based method, noncircular decoupled maximization (NC-DM). Moreover, simulation results demonstrate that NC-AM outperforms NC-DM as well as the noncircular MUSIC.

Robust DOA Estimation of Incoherently Distributed Sources Considering Mixed Circular and Noncircular Signals in Impulsive Noise

Robust DOA Estimation of Incoherently Distributed Sources Considering Mixed Circular and Noncircular Signals in Impulsive Noise

GLRT-based Spectrum Sensing for Non-circular Signals in Cognitive Radios with Multiple Antennas

GLRT-based Spectrum Sensing for Non-circular Signals in Cognitive Radios with Multiple Antennas

Direct Position Determination of Non-Circular Signals for Distributed Antenna Arrays: Optimal Weight and Polynomial Rooting Approach

Direct Position Determination of Non-Circular Signals for Distributed Antenna Arrays: Optimal Weight and Polynomial Rooting Approach

Noncircular Signal Tracking With Distributed Passive Arrays: Combining Data Fusion and Extended Kalman Filter

Noncircular Signal Tracking With Distributed Passive Arrays: Combining Data Fusion and Extended Kalman Filter

Widely Linear Momentum LMS Algorithm for Second Order Noncircular Signals and Performance Analysis

Widely Linear Momentum LMS Algorithm for Second Order Noncircular Signals and Performance Analysis

Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise

Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Design of relocating sparse nested arrays for DOA estimation of non-circular signals

Recently, the ability of sparse arrays to achieve higher degrees of freedom (DOFs) and to be less sensitive to the mutual coupling (MC) effect has aroused increasing attention. Aiming at this, we investigate the sparse array design problem for direction of arrival (DOA) estimation of non-circular (NC) signals. Then, we propose two novel relocating sparse nested array (RSNA) structures, named RSNA-I and RSNA-II, respectively, and derive simple explicit expressions for their array locations and DOFs. Specifically, the RSNA-I is composed of two subarrays plus a separate sensor. By utilizing the separate sensor to enable the virtual sum and difference co-array (SDCA) with a longer consecutive segment and to alleviate the MC effect. In addition, to further make the array structure more robust to the MC effect, RSNA-II relocates the dense subarray of RSNA-I. Theoretical analysis and numerical simulation results demonstrate that the proposed RSNA-I and RSNA-II achieve a better balance between DOFs and the MC effect, which in turn effectively solves DOA estimation of NC signals and yields better DOA estimation performance.

A Mixed-Field Circular and Non-Circular Source Localization Algorithm Based on Exact Spatial Propagation Geometry.

In passive localization techniques, as the scale of the array of the sensors used increases, the source distribution may be a coexistence of near-field (NF) and far-field (FF) sources. Most of the existing algorithms dedicated to the localization of mixed-field sources are based on a simplified model, which has model errors and cannot make good use of non-circular properties when non-circular signals are present in the sources. In this paper, we present a mixed-field circular and non-circular source localization algorithm based on exact spatial propagation geometry. First, we make an initial estimate of the source parameters using exact spatial geometry relations. The MUSIC algorithm is then used in combination with the non-circular properties of the signal to achieve an accurate estimate. The algorithm does not lose performance due to model mismatch and is able to make good use of the non-circular properties of the sources to improve the estimation accuracy. The simulation results show that the proposed algorithm can effectively distinguish between sources and that the algorithm performs satisfactorily.