Xiaoming Gou

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.

Three-dimensional wind profile prediction with trinion-valued adaptive algorithms

The problem of three-dimensional (3-D) wind profile prediction is addressed based a trinion wind model, which inherently reckons the coupling of the three perpendicular components of a wind field. The augmented trinion statistics are developed and employed to enhance the prediction performance due to its full exploitation of the second-order statistics. The proposed trinion domain processing can be regarded as a more compact version of the existing quaternion-valued approach, with a lower computational complexity. Simulations based on recorded wind data are provided to demonstrate the effectiveness of the proposed methods.

Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals

A polynomial-rooting based fourth-order cumulant algorithm is presented for direction-of-arrival(DOA) estimation of second-order fully noncircular source signals, using a uniform linear array(ULA). This algorithm inherits all merits of its spectralsearching counterpart except for the applicability to arbitrary array geometry, while reducing considerably the computation cost.Simulation results show that the proposed algorithm outperforms the previously developed closed-form second-order noncircular ESPRIT method, in terms of processing capacity and DOA estimation accuracy, especially in the presence of spatially colored noise.

Fully automatic robust adaptive beamforming using the constant modulus feature

The diagonal loading (DL) technique is the most widely used method to improve the robustness of the Capon beamformer in the presence of imprecise knowledge of the covariance matrix and the desired signals steering vector. The selection of the DL level is challenging in practice and might depend on some user-defined parameters which are possibly hard to be determined. A fully automatic and training-free method for the DL level selection is herein presented to extract the desired signal with constant modulus, which is a common feature for communication signals. Simulated results of the beamforming performance have demonstrated the efficacy of the proposed method.

Filtering and tracking with trinion-valued adaptive algorithms

A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared to the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind recordings and synthetic data sets are provided to demonstrate the potential of this new modeling method.

Biquaternion noncircular MUSIC

A biquaternion-based direction-finding algorithm for noncircular sources is presented. The covariance and conjugate covariance matrices of the array output are utilized symmetrically within a frame of biquaternions. The direction-of-arrivals are found where the biquaternion steering vectors are orthogonal to the noise subspace in the biquaternion domain. Simulations show the improved performance of the proposed method compared to its complex counterparts.

Biquaternion Capon beamformer using four-component vector-sensor arrays

A hypercomplex variant of Capon beamformer, called biquaternion Capon BQ-Capon, is herein proposed for signal strengthening with four-component vector-sensor arrays. This BQ-Capon beamformer extracts the signal-of-interest SOI while rejecting interferences plus noise in a multiple-input-multiple-output MIMO fashion. Simulation results show that BQ-Capon beamformer outperforms the standard long-vector counterpart in convergence and sensitivity to mismatch in SOI steering vector.

Blind Separation of Noncircular Sources Via Approximate Joint Diagonalization of Augmented Charrelation Matrices

An augmented charrelation matrix (ACM), which can utilize both the conventional and the conjugate statistical information in the complex domain, is proposed. The ACM additionally makes use of the conjugate Hessian matrix (namely conjugate charrelation matrix) of the observations of noncircular sources. A blind separation scheme built on the approximate joint diagonalization (AJD) principle is introduced, which precedes some numerical examples to demonstrate the improved performance of the ACM-AJD approach compared with some algorithms in the literature.

Quaternion-valued single-phase model for three-phase power system

Abstract In this work, a quaternion-valued model is proposed in lieu of the Clarke’s α, β transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion detection in three-phase power systems. In particular, the proposed model maps all the harmonic frequencies into frequencies in the quaternion domain, while the Clarke’s transformation-based methods will fail to detect the zero sequence voltages. Based on the quaternion-valued model, the Fourier transform, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are presented as examples to detect harmonic distortion. Simulations are provided to demonstrate the potentials of this new modeling method.

Sparse antenna array design for directional modulation

Directional modulation (DM) can be achieved based on uniform linear arrays (ULAs), where the maximum half wavelength spacing is needed to avoid spatial aliasing. To exploit the degrees of freedom (DOFs) in the spatial domain, sparse arrays can be employed for more effective DM design. In this paper, the problem of antenna location optimisation for sparse arrays in the context of DM is addressed for the first time, where compressive sensing based formulations are proposed employing the group sparsity concept. Design examples are provided to verify the effectiveness of the proposed designs.