Xiao-Feng Gong

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.

Generalized Non-Orthogonal Joint Diagonalization With LU Decomposition and Successive Rotations

Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset, and thus is insufficient to handle multiple datasets with inter-set dependences, a scenario often encountered in joint BSS (J-BSS) applications. As such, we present a generalized NJD (GNJD) algorithm to simultaneously perform asymmetric NJD upon multiple sets of target matrices with mutually linked loading matrices, by using LU decomposition and successive rotations, to enable J-BSS over multiple datasets with indication/exploitation of their mutual dependences. Experiments with synthetic and real-world datasets are provided to illustrate the performance of the proposed algorithm.

Complex non-orthogonal joint diagonalization based on LU and LQ decompositions

In this paper, we propose a class of complex non-orthogonal joint diagonalization (NOJD) algorithms with successive rotations. The proposed methods consider LU or LQ decompositions of the mixing matrices, and propose to solve the NOJD problem via two successive stages: L-stage and U (or Q)-stage. Moreover, as the manifolds of target matrices in these stages could be appropriately parameterized by a sequence of simple elementary triangular or unitary matrices, which depend on only one or two parameters, the high-dimensional minimization problems could be replaced by a sequence of lower-dimensional ones. As such, the proposed algorithms are of simple closed-form in each iteration, and do not require the target matrices to be Hermitian nor positive definite. Simulations are provided to compare the proposed methods to other complex NOJD methods.

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.

Simultaneous Source Localization and Polarization Estimation via Non-Orthogonal Joint Diagonalization with Vector-Sensors

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

Antenna Selection in Space Time Block Coded MC-CDMA Systems

Antenna selection (AS) is herein applied to space-time block coded (STBC) multi-carrier code division multiple access (MC-CDMA) system to improve the downlink system performance while reducing system cost, by choosing a subset of antennas from all available ones. Optimal antenna subset is obtained at the receiver with channel state information (CSI) estimated, and then fed back through a low bit rate, zero-delay and error-free path. The STBC scheme is applied to the system with antennas selected from available. The system structure of the transmitter and the receiver is illustrated. The downlink performance of such a system in frequency selective, spatially independent and correlated fading channels is analyzed. Some representative simulations are taken to validate the analysis

Joint canonical polyadic decomposition of two tensors with one shared loading matrix

We present an algorithm for jointly performing canonical polyadic decomposition (J-CPD) upon two tensors with one shared loading matrix. Target tensors are firstly matricized and factorized into two components each, and a joint nonorthogonal joint diagonalization based scheme is performed secondly to restore the joint Khatri-rao structures of the results obtained in the first step. Lastly, estimates of loading matrices could be obtained by singular value decomposition based scheme. The proposed algorithm could be used to extract common structures shared with different tensors, and such problem would occur in applications that involve joint utilization of multiple datasets or multiple statistics such as covariance and pseudo-covariance. Simulations are provided to examine the performance of the proposed algorithm.

Spatially constrained parallel factor analysis for semi-blind beamforming

Parallel factor analysis (PARAFAC) has found numerous applications in blind signal processing, mainly due to its nice identifiability. However, the standard PARAFAC decomposition does not use prior information on the mixing procedure, which could actually be roughly estimated. As a result, the standard PARAFAC is ambiguious in permutation, and may converge slowly in the presence of collinearity. In this paper, we assume that the steering vector of the target source is coarsely known, and propose a spatially constrained PARAFAC algorithm by using this prior information. In addition, a semi-blind beamformer with multiple-invariance array is presented based on the above spatially constrained PARAFAC. Simulations are provided to verify the efficacy of the proposed method.

On the Equivalence of Tensor-MUSIC and Matrix-MUSIC

Most previous work on direction finding with an electromagnetic vector-sensor array characterizes the collection with vector and/or matrix manipulation although it is inherently of multidimensional structure. The vector-MUSIC method, which is referred to as Tensor-MUSIC in this contribution, represents the first direction finding algorithm that is based on tensor formulation and is claimed to offer quite improved direction of arrival estimation than the conventional MUSIC does. In this paper, we thoroughly examine the tensor-MUSIC with theoretical analysis and numerical examples. It is found that the tensor-MUSIC is actually equivalent to matrix-MUSIC which is based on matrix operations only.