Zhiwen Liu

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal@?s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs.

Direction finding via biquaternion matrix diagonalization with vector-sensors

Direction-of-arrival (DOA) estimation based on the array of three-component electromagnetic vector-sensors is considered within a biquaternion framework. A relationship is established between the biquaternion covariance and the combination of both complex covariance and cross-product. By exploiting this relationship, the DOA estimates can finally be obtained by diagonalizing the biquaternion covariance matrix of the array outputs in a trilinear PARAFAC manner. This method does not require any a priori knowledge on the position of each sensor, and is shown to offer high robustness to colored noise for direction finding of non-linearly polarized signals. Simulations are provided to illustrate the performance of the proposed method.

Coherent Source Localization: Bicomplex Polarimetric Smoothing with Electromagnetic Vector-Sensors

The work presented here considers coherent source localization with bicomplex. A new polarimetric smoothing variant is proposed by using bicomplex modeled subarrays obtained from complete electromagnetic vector-sensor array, and a MUSIC-like algorithm is further developed. The identifiability, computational complexity, and the choice of selection vectors for the proposed method are also addressed. Simulations show that the proposed method can provide better direction-of-arrival estimates than the complex methods in perturbations caused by noise, short data, and model errors.

Perturbation analysis of conjugate MI-ESPRIT for single acoustic vector-sensor-based noncircular signal direction finding

The closed-form conjugate multiple-invariance ESPRIT (CMI-ESPRIT) algorithm herein analyzed: (1) makes use of redundancy in the nonvanishing conjugated second- and fourth-order cumulants of noncircular signals; (2) recognizes the real-valued two-dimensional directivity inherently achieved by an acoustic vector-sensor in a free-space. It is provided in this correspondence the perturbation analyses on both the norm-penalized and the subspace-constraint ESPRIT matrices that play the key role in the CMI-ESPRIT. It is shown that the norm-penalized ESPRIT matrix is biased (but bounded) and has a minimal mean-squared-error (MSE) for some finite regularization factor, whereas the subspace-constraint ESPRIT matrix is unbiased and its MSE approaches minimum when the regularization factor becomes infinite. These observations are potentially useful for the determination of the regularization parameters which is significant for the performance of CMI-ESPRIT. The results also contribute to the ultimate study of direction-finding accuracy. Simulation results are presented to validate the given analyses.

Biquaternion cumulant-MUSIC for DOA estimation of noncircular signals

Direction-of-arrival (DOA) estimation for noncircular sources is addressed within the hypercomplex framework utilizing fourth-order (FO) cumulants and a MUSIC-like estimator is proposed. Simulation results show the better performance of the proposed method compared to its complex counterpart in terms of both accuracy and robustness to model errors due to the stronger orthogonality in the biquaternion domain.

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.

Quaternion-based worst case constrained beamformer based on electromagnetic vector-sensor arrays

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternionic domain. After defining the uncertainty set of the desired signals quaternionic steering vector, two quaternion-based constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the second-order cone (SOC) programming approach. Numerical simulations show that our quaternion-based robust beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) beamformer and the quaternion Capon (Q-Capon) beamformer in the presence of steering vector mismatches.

Quaternion ESPRIT for direction finding with a polarization sentive array

The problem of direction of arrival (DOA) estimation with a crossed-dipole array is addressed within the quaternionic framework, and a new ESPRIT variant, termed as quaternion-ESPRIT (Q-ESPRIT), is proposed. The proposed algorithm arranges the recorded signals into a quarternion model, and estimates the signal subspace of an array of translational invariance structure via quaternionic low-rank approximation. Then, Q-ESPRIT exploits the underlying rotational invariance between signal subspaces of different sub-arrays with quaternionic matrix operations to obtain the ultimate DOA estimates. Simulations show that Q-ESPRIT significantly outperforms its conventional counterpart in difficult situations with short data length, low signal-to-noise ratio, or unknown model errors.

Adaptive tensorial beamformer based on electromagnetic vector-sensor arrays with coherent interferences

An adaptive beamforming scheme based on vector-sensor arrays is implemented using two different matrix contractions of the 4th order covariance tensor. This tensorial beamformer has a two-stage structure, effectively combining the Bartlett and the minimum-variance-distortionless-response beamformers together. At the first stage, it involves an inherent multi-dimensional data smoothing operation which is capable of suppressing coherent interferences; at the second stage, the fixed Bartlett beamformer provides further enhancement to its robustness against steering vector mismatch errors, such as direction of arrival estimation and element position errors. The effectiveness of the proposed algorithms is verified by numerical simulations.

Noncircularity restoral for multi-antenna blind beamforming

Blind beamforming for extracting noncircular signals without the prior knowledge about the objective steering vector is considered. Three second-order blind techniques via NonCircularity REstoral (NCRE) are proposed to recover a dominant noncircular signal from circular interferences plus sensor noise with arbitrary and unknown correlation structure. These schemes are labeled as NCRE1, NCRE2, and NCRE3, respectively. For the high-rank environments where a number of rectilinear/circular interfering signals are present a Mixed-Order BEamspace (MOBE) technique, using simultaneously the second- and fourth-order cumulants, is developed. The performance of these proposed methods is studied based on numerical simulations. NCRE1 is computationally simple but performs well only in the case of very weak interferences and moderate noise, NCRE3 can provide good performance in the presence of medium or weak interferences, while NCRE2 is very suitable for adverse signal environments. NCRE2 outperforms NCRE1 and NCRE3 in terms of convergence rate, over a wide range of signal to interference plus noise ratio values. It is demonstrated that all the three NCRE methods are better than the traditional sample matrix inversion technique in the presence of look direction mismatch. They are also more attractive than the high-order cumulant method when non-Gaussian circular interferences are encountered. The MOBE method is shown to be competent for handling rectilinear/circular interfering signals, with respect to the attainable output signal to interference plus noise ratio.