Noncircular Signals Research Articles

A class of diagonally loaded robust Capon beamformers for noncircular signals of interest

Diagonal loading is a simple and effective method for robustness enhancement of the Capon beamformer against perturbation in the presumed steering vector of the signal-of-interest (SOI). However, the determination of an appropriate diagonal loading level is not a trivial task. Three noncircularity restoral based methods are herein proposed for selecting the diagonal loading level to recover a noncircular SOI buried in circular and/or noncircular interferences plus circular background noise. Monte Carlo simulations are performed to verify the efficacy of the proposed methods.

Maximum likelihood and signal-selective TDOA estimation for noncircular signals

This paper addresses the issue of time-difference-of-arrival (TDOA) estimation for complex noncircular signals. First, under the wide-sense stationary assumption, we derive the maximum likelihood (ML) estimator and the Cramer-Rao lower bound for Gaussian noncircular signals in Gaussian circular noise. The ML estimator uses the second-order statistics information of a noncircular signal more comprehensively when compared with the cross-correlation (CC) and the conjugate CC estimators. Further, we present a scheme to modify the traditional signal-selective TDOA methods for noncircular signals on the basis of the cyclostationarity of man-made signals. This scheme simultaneously exploits the information contained in both the cyclic cross-correlation (CCC) and the conjugate CCC of a noncircular signal.

Noncircular-PARAFAC for 2D-DOA estimation of noncircular signals in arbitrarily spaced acoustic vector-sensor array subjected to unknown locations

In this paper, we propose a noncircular-parallel factor (NC-PARAFAC) algorithm for two-dimensional direction of arrival (DOA) estimation of noncircular signals for acoustic vector-sensor array. The proposed algorithm enhances the angle estimation performance via utilizing the noncircularity of the signals, and it can be suitable for arbitrary array subjected to unknown locations and achieve automatically paired two-dimensional angle estimation. The proposed algorithm has better angle estimation performance than estimation of signal parameters via rotational invariance technique, PARAFAC algorithm, and propagator method. Furthermore, the proposed algorithm has a lower computational complexity than the PARAFAC algorithm. We also derive the Cramer-Rao bound of DOA estimation of noncircular signal in acoustic vector-sensor array. The simulation results verify the effectiveness of the algorithm.

A New Approach for Estimating the Number of Sources Under the Coexistence of Circular and Various Noncircular Sources

Estimation of source number is a fundamental problem of direction-of-arrival (DOA) estimation. In the problem of DOA estimation under the coexistence of circular and various noncircular signals, the source number should be estimated in order to distinguish the signal subspace from the noise subspace. Thus, a new method for source number estimation is proposed in this paper. Using the approach of k-means clustering, the projections of a one-dimensional reduced covariance matrix are divided into two categories. Then the signal subspace and the noise subspace are separated by the optimal classification boundary of those two categories so as to obtain the equivalent source number. Simulation results show that the proposed method has relatively better performance even in low SNR or in a colored noise environment.

Conjugate ESPRIT for DOA estimation in monostatic MIMO radar

In this paper, a novel conjugate ESPRIT (C-ESPRIT) method for direction of arrival (DOA) estimation in monostatic MIMO radar is proposed. Firstly, a reduced-dimensional matrix is employed to transform the data matrix into a low dimensional space. Then the properties of noncircular signals are utilized to construct a new virtual array, whose elements are twice that of the monostatic MIMO radar virtual array with distinct elements. The rotational invariance properties of the new virtual array are figured out to estimate DOA through ESPRIT. Compared with the reduced-dimensional ESPRIT (RD-ESPRIT), the proposed method improves the angular estimation accuracy significantly and detects more targets. Simulation results verify the effectiveness of the proposed method.

A class of quaternion valued affine projection algorithms

The strictly linear quaternion valued affine projection algorithm (QAPA) and its widely linear counterpart (WLQAPA) are introduced, in order to provide fast converging stochastic gradient learning in the quaternion domain, for the processing of both second order circular (proper) and second order noncircular (improper) signals. This is achieved based on the recent advances in augmented quaternion statistics, which employs all second order information available, together with the associated widely linear models and through performing rigorous gradient calculation (HR-calculus). Further, mean square error analysis is performed based on the energy conservation principle, which provides a theoretical justification for the WLQAPA offering enhanced steady state performance for quaternion noncircular (improper) signals, a typical case in real world scenarios. Simulations on benchmark circular and noncircular signals, and on noncircular real world 4D wind and 3D body motion data support the analysis.

Cultural quantum-inspired shuffled frog leaping algorithm for direction finding of non-circular signals

In order to resolve complex continuous optimisation problem, a cultural quantum-inspired shuffled frog leaping CQSFL algorithm is proposed. The proposed CQSFL applies the quantum knowledge strategy and new quantum leaping equations to shuffled frog leaping algorithm, and thus has the advantages of low computational complexity and fast convergence. As a key step of CQSFL algorithm, leaping movement is modelled as guided cultural behaviour and thus may improve the capability of SFLA to find the optimal solution. Then we applied the proposed CQSFL algorithm in direction finding problem of non-circular signals, which is a hot spot in domain of communication. Then, based on CQSFL algorithm and non-circular maximum likelihood NML algorithm, a new direction finding method is proposed, which is called CQSFL-NML algorithm. Monte-Carlo simulations have proved that the CQSFL-NML method has good performance for non-coherent and coherent non-circular signals.

Optimal combination of fourth-order cumulant based contrasts for blind separation of noncircular signals

In this paper, we have considered the problem of blind source separation of noncircular signals. We have proposed a new Jacobi-like algorithm that achieves optimization of the optimal combination of complex fourth-order cumulant based contrasts. We have investigated the application to separation of non-Gaussian sources using fourth order cumulants. And computer simulations applied to noncircular signals illustrate the proposed approach.

Time-difference-of-arrival estimation for noncircular signals using information theory

This paper addresses the time-difference-of-arrival (TDOA) estimation problem for a noncircular source, which is usually encountered in the context of radio communications. To exploit the second-order statistics (SOS) noncircularity of such signals, an information-theoretical measure is employed in designing the new TDOA estimator. While the classical cross-correlation (CC) method uses only the correlation measure of a source, the proposed method simultaneously uses both the correlation and conjugate correlation measures of a source. Since the SOS of a noncircular signal is not only determined by the correlation function but also by the conjugate correlation function, the proposed method utilizes the SOS information of a noncircular signal more comprehensively than the popular CC method. Simulation results demonstrated the effectiveness of the new algorithm compared to the CC algorithm.

Direction-of-Arrival Estimation of Noncircular Signals via Sparse Representation

This correspondence addresses the problem of direction-of-arrival (DOA) estimation of noncircular signals, and a new method named noncircular covariance matrix sparse representation (NC-CMSR) is proposed. NC-CMSR realizes DOA estimation by jointly representing the covariance and elliptic covariance matrices of the array output on overcomplete dictionaries subject to sparsity constraint. The new method relies less on the a priori information of the incident signal number than its subspace-based counterparts, and also achieves identification of simultaneous circular and noncircular signals without any extra processes. Simulation results demonstrate the performance of NC-CMSR in DOA estimation and circular-and-noncircular signal identification.

Class of Widely Linear Complex Kalman Filters

Recently, a class of widely linear (augmented) complex-valued Kalman filters (KFs), that make use of augmented complex statistics, have been proposed for sequential state space estimation of the generality of complex signals. This was achieved in the context of neural network training, and has allowed for a unified treatment of both second-order circular and noncircular signals, that is, both those with rotation invariant and rotation-dependent distributions. In this paper, we revisit the augmented complex KF, augmented complex extended KF, and augmented complex unscented KF in a more general context, and analyze their performances for different degrees of noncircularity of input and the state and measurement noises. For rigor, a theoretical bound for the performance advantage of widely linear KFs over their strictly linear counterparts is provided. The analysis also addresses the duality with bivariate real-valued KFs, together with several issues of implementation. Simulations using both synthetic and real world proper and improper signals support the analysis.

Adaptive Beamforming for Noncircular Signals

Many manmade signals have nonzero noncircularity coefficients such as those used in AM, BPSK, and ASK systems. They are called noncircular signals which have coexisted moment and conjugate moment at the second-order. This redundancy is herein exploited to derive a blind scheme for source separation and classification based on the NonCircularity REstoral (NCRE4) filtering. The present blind scheme has three major advantages: 1) involves only the second-order statistics (SOS) and has a faster convergence speed than the traditional high-order statistics (HOS) methods; and 2) does not require any a prioriknowledge about the content and/or direction of the signal-of-interest (SOI).

An Adaptive Diffusion Augmented CLMS Algorithm for Distributed Filtering of Noncircular Complex Signals

An adaptive diffusion augmented complex least mean square (D-ACLMS) algorithm for collaborative processing of the generality of complex signals over distributed networks is proposed. The algorithm enables the estimation of both second order circular (proper) and noncircular (improper) signals within a unified framework of augmented complex statistics. The analysis shows that the performance advantage of the widely linear D-ACLMS over the strictly linear D-CLMS increases with the degree of noncircularity while maintaining similar performance for proper data. Simulations on both synthetic benchmark and real world noncircular data support the approach.

On Testing the Extent of Noncircularity

In this correspondence, we provide a multiple hypothesis test to detect the number of latent noncircular signals in a complex Gaussian random vector. Our method sequentially tests the results of individual generalized likelihood ratio test (GLRT) statistics with known asymptotic distributions to form the multiple hypothesis detector. Specifically, we are able to set a threshold yielding a precise probability of error. This test can be used to statistically determine if a given complex observation is circular Gaussian, and if not, how many latent signals in the observation are noncircular. Simulations are used to quantify the performance of the detector as compared to a detector based on the minimum description length (MDL) criterion. The utility of the detector is shown by applying it to a beamforming application using independent component analysis (ICA).

Noncircular Principal Component Analysis and Its Application to Model Selection

One of the most commonly used data analysis tools, principal component analysis (PCA), since is based on variance maximization, assumes a circular model, and hence cannot account for the potential noncircularity of complex data. In this paper, we introduce noncircular PCA (ncPCA), which extends the traditional PCA to the case where there can be both circular and noncircular Gaussian signals in the subspace. We study the properties of ncPCA, introduce an efficient algorithm for its computation, and demonstrate its application to model selection, i.e., the detection of both the signal subspace order and the number of circular and noncircular signals. We present numerical results to demonstrate the advantages of ncPCA over regular PCA when there are noncircular signals in the subspace. At the same time, we note that since a noncircular model has more degrees of freedom than a circular one, there are cases where a circular model might be preferred even though the underlying problem is noncircular. In particular, we show that a circular model is preferred when the signal-to-noise ratio (SNR) is low, number of samples is small, or the degree of noncircularity of the signals is low. Hence, ncPCA inherently provides guidance as to when to take noncircularity into account.

Efficient detection algorithms for multi-input/multi-output systems by exploiting the non-circularity of transmitted signal source

In this study, several new detection algorithms are proposed for multi-input/multi-output (MIMO) communication systems transmitting non-circular signals. Unlike the conventional receivers, the proposed detectors estimate the transmitted signal from both the received signal and its complex conjugate version. Analytical results quantifying the performance improvement are provided. As a typical example, extended zero-forcing (EZF) detector and extended minimum mean square error (EMMSE) detector are derived for the real signals. Computational complexity of the proposed algorithms remains the same order as that of the conventional zero-forcing (ZF). Simulation results show that both EZF and EMMSE detectors significantly outperform the conventional minimum mean square error (MMSE) detector, and that the ordered-successive-interference-cancelling (OSIC) version of the EZF (or EMMSE) detector has a quasi-optimal performance in terms of bit error rate (BER).

A New Forth-Order Direction Finding Algorithm for Noncircular Signals

对通信系统中大量使用的BPSK等非圆信号测向，可以采用共轭扩展MUSIC(CE-MUSIC)算法，也可以采用基于四阶累积量的MUSIC-like算法。CE-MUSIC算法没有利用高阶信息，MUSIC-like算法没有利用信号的非圆信息，性能均受限。该文提出的四阶扩展MUSIC(FO-EMUSIC)算法利用了非圆信号在四阶累积量中的信息，分辨力和测角精度明显优于MUSIC-like算法，略优于CE-MUSIC算法，可测向阵元数大于CE-MUSIC算法和MUSIC-like算法。针对均布线阵，为减小计算量，还提出了FO-EMUSIC/ULA算法。仿真实验验证了FO-EMUSIC算法的优良性能。

Estimation of 2-D DOA using non-circular music method for Uniform Circular and Rectangular Arrays

This paper extends the Non-Circular MUltiple SIgnal Classification (MUSIC) (NC-MUSIC) method for the common array geometries including Uniform Circular Arrays (UCAs) and Uniform Rectangular Arrays (URAs), which enables the algorithm to estimate 2-D Direction Of Arrival (DOA). A comparison between UCAs and URAs of NC-MUSIC is made in this paper. The simulations show that the NC-MUSIC method doubles the maximum estimation number of standard MUSIC. Using non-circular signals, the performance of URAs is improved remarkably while the improvement of UCAs is not so significantly. Moreover, the influence of arrays structures on the NC-MUSIC method is discussed.

Kurtosis-Based Blind Source Extraction of Complex Non-Circular Signals with Application in EEG Artifact Removal in Real-Time

A new class of complex domain blind source extraction algorithms suitable for the extraction of both circular and non-circular complex signals is proposed. This is achieved through sequential extraction based on the degree of kurtosis and in the presence of non-circular measurement noise. The existence and uniqueness analysis of the solution is followed by a study of fast converging variants of the algorithm. The performance is first assessed through simulations on well understood benchmark signals, followed by a case study on real-time artifact removal from EEG signals, verified using both qualitative and quantitative metrics. The results illustrate the power of the proposed approach in real-time blind extraction of general complex-valued sources.

Conjugate ESPRIT algorithm for bistatic MIMO radar

A novel conjugate ESPRIT (C-ESPRIT) algorithm is proposed to estimate the direction of arrival (DOA) and direction of departure (DOD) for bistatic MIMO radar. It employs the properties of noncircular signals to construct a new virtual array first, the virtual antenna number of which is twice that of the MIMO virtual array. It then exploits the rotational invariance property of the new virtual array to estimate DOAs and DODs of multiple targets through ESPRIT which are paired automatically in a new way. This algorithm can provide more precise angle estimation and can detect more targets than well-known classical subspace methods. Simulation results validate these conclusions.