A Millimeter-Wave Broadband Multi-Mode Substrate-Integrated Gap Waveguide Traveling-Wave Antenna with Orbit Angular Momentum.

Orbit angular momentum (OAM) has been considered a new dimension for improving channel capacity in recent years. In this paper, a millimeter-wave broadband multi-mode waveguide traveling-wave antenna with OAM is proposed by innovatively utilizing the transmitted electromagnetic waves (EMWs) characteristic of substrate-integrated gap waveguides (SIGWs) to introduce phase delay, resulting in coupling to the radiate units with a phase jump. Nine "L"-shaped slot radiate elements are cut in a circular order at a certain angle on the SIGW to generate spin angular momentum (SAM) and OAM. To generate more OAM modes and match the antenna, four "Π"-shaped slot radiate units with a 90° relationship to each other are designed in this circular array. The simulation results show that the antenna operates at 28 GHz, with a -10 dB fractional bandwidth (FBW) = 35.7%, ranging from 25.50 to 35.85 GHz and a VSWR ≤ 1.5 dB from 28.60 to 32.0 GHz and 28.60 to 32.0 GHz. The antenna radiates a linear polarization (LP) mode with a gain of 9.3 dBi at 34.0~37.2 GHz, a l = 2 SAM-OAM (i.e., circular polarization OAM (CP-OAM)) mode with 8.04 dBi at 25.90~28.08 GHz, a l = 1 and l = 2 hybrid OAM mode with 5.7 dBi at 28.08~29.67 GHz, a SAM (i.e., left/right hand circular polarization (L/RHCP) mode with 4.6 dBi at 29.67~30.41 GHz, and a LP mode at 30.41~35.85 GHz. In addition, the waveguide transmits energy with a bandwidth ranging from 26.10 to 38.46 GHz. Within the in-band, only a quasi-TEM mode is transmitted with an energy transmission loss |S21| ≤ 2 dB.

A Design Method and Application of Meta-Surface-Based Arbitrary Passband Filter for Terahertz Communication.

A meta-surface-based arbitrary bandwidth filter realization method for terahertz (THz) future communications is presented. The approach involves integrating a meta-surface-based bandstop filter into an ultra-wideband (UWB) bandpass filter and adjusting the operating frequency range of the meta-surface bandstop filter to realize the design of arbitrary bandwidth filters. It effectively addresses the complexity of designing traditional arbitrary bandwidth filters and the challenges in achieving impedance matching. To underscore its practicality, the paper employs silicon substrate integrated gap waveguide (SSIGW) and this method to craft a THz filter. To begin, design equations for electromagnetic band gap (EBG) structures were developed in accordance with the requirements of through-silicon via (TSV) and applied to the design of the SSIGW. Subsequently, this article employs equivalent transmission line models and equivalent circuits to conduct theoretical analyses for both the UWB passband and the meta-surface stopband portions. The proposed THz filter boasts a center frequency of 0.151 THz, a relative bandwidth of 6.9%, insertion loss below 0.68 dB, and stopbands exceeding 20 GHz in both upper and lower ranges. The in-band group delay is 0.119 ± 0.048 ns. Compared to reported THz filters, the SSIGW filter boasts advantages such as low loss and minimal delay, making it even more suitable for future wireless communication.

Dynamic functional network connectivity based on spatial source phase maps of complex-valued fMRI data: Application to schizophrenia.

BACKGROUND: Dynamic spatial functional network connectivity (dsFNC) has shown advantages in detecting functional alterations impacted by mental disorders using magnitude-only fMRI data. However, complete fMRI data are complex-valued with unique and useful phase information. METHODS: We propose dsFNC of spatial source phase (SSP) maps, derived from complex-valued fMRI data (named SSP-dsFNC), to capture the dynamics elicited by the phase. We compute mutual information for connectivity quantification, employ statistical analysis and Markov chains to assess dynamics, ultimately classifying schizophrenia patients (SZs) and healthy controls (HCs) based on connectivity variance and Markov chain state transitions across windows. RESULTS: SSP-dsFNC yielded greater dynamics and more significant HC-SZ differences, due to the use of complete brain information from complex-valued fMRI data. COMPARISON WITH EXISTING METHODS: Compared with magnitude-dsFNC, SSP-dsFNC detected additional and meaningful connections across windows (e.g., for right frontal parietal) and achieved 14.6% higher accuracy for classifying HCs and SZs. CONCLUSIONS: This work provides new evidence about how SSP-dsFNC could be impacted by schizophrenia, and this information could be used to identify potential imaging biomarkers for psychotic diagnosis.

Denoising brain networks using a fixed mathematical phase change in independent component analysis of magnitude-only fMRI data.

Brain networks extracted by independent component analysis (ICA) from magnitude-only fMRI data are usually denoised using various amplitude-based thresholds. By contrast, spatial source phase (SSP) or the phase information of ICA brain networks extracted from complex-valued fMRI data, has provided a simple yet effective way to perform the denoising using a fixed phase change. In this work, we extend the approach to magnitude-only fMRI data to avoid testing various amplitude thresholds for denoising magnitude maps extracted by ICA, as most studies do not save the complex-valued data. The main idea is to generate a mathematical SSP map for a magnitude map using a mapping framework, and the mapping framework is built using complex-valued fMRI data with a known SSP map. Here we leverage the fact that the phase map derived from phase fMRI data has similar phase information to the SSP map. After verifying the use of the magnitude data of complex-valued fMRI, this framework is generalized to work with magnitude-only data, allowing use of our approach even without the availability of the corresponding phase fMRI datasets. We test the proposed method using both simulated and experimental fMRI data including complex-valued data from University of New Mexico and magnitude-only data from Human Connectome Project. The results provide evidence that the mathematical SSP denoising with a fixed phase change is effective for denoising spatial maps from magnitude-only fMRI data in terms of retaining more BOLD-related activity and fewer unwanted voxels, compared with amplitude-based thresholding. The proposed method provides a unified and efficient SSP approach to denoise ICA brain networks in fMRI data.

Isobutyric acid promotes colorectal cancer metastasis through activating RACK1.

Colorectal cancer (CRC) metastasis plays a crucial role in disease progression, yet the regulatory mechanisms underlying metastasis remain incompletely understood. Isobutyric acid (IBA), a short-chain fatty acid found at high levels in serum of CRC patients, has been shown to be a critical metabolite influencing CRC proliferation. However, its role in tumor metastasis remains unknown. Here, utilizing liquid chromatography tandem mass spectrometry (LC-MS/MS) analysis, we found that levels of IBA were significantly higher in patients with distant organ metastasis of CRC than in those without. Furthermore, IBA promoted CRC metastasis both in vitro and in vivo. Mass spectrometry, immunofluorescence, and cellular thermal shift assay revealed that IBA interacts with RACK1. Mechanistically, IBA binding to and activating RACK1 promotes regulation of downstream Akt and FAK signaling and CRC metastasis. Collectively, our study highlights the critical interplay between IBA and RACK1 and its impact on tumor metastasis. This study suggests that targeting the IBA-RACK1 signaling axis may be an effective therapeutic strategy for controlling CRC metastasis.

Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares.

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- R and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- R least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- R least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- R and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

SSPNet: An interpretable 3D-CNN for classification of schizophrenia using phase maps of resting-state complex-valued fMRI data.

Convolutional neural networks (CNNs) have shown promising results in classifying individuals with mental disorders such as schizophrenia using resting-state fMRI data. However, complex-valued fMRI data is rarely used since additional phase data introduces high-level noise though it is potentially useful information for the context of classification. As such, we propose to use spatial source phase (SSP) maps derived from complex-valued fMRI data as the CNN input. The SSP maps are not only less noisy, but also more sensitive to spatial activation changes caused by mental disorders than magnitude maps. We build a 3D-CNN framework with two convolutional layers (named SSPNet) to fully explore the 3D structure and voxel-level relationships from the SSP maps. Two interpretability modules, consisting of saliency map generation and gradient-weighted class activation mapping (Grad-CAM), are incorporated into the well-trained SSPNet to provide additional information helpful for understanding the output. Experimental results from classifying schizophrenia patients (SZs) and healthy controls (HCs) show that the proposed SSPNet significantly improved accuracy and AUC compared to CNN using magnitude maps extracted from either magnitude-only (by 23.4 and 23.6% for DMN) or complex-valued fMRI data (by 10.6 and 5.8% for DMN). SSPNet captured more prominent HC-SZ differences in saliency maps, and Grad-CAM localized all contributing brain regions with opposite strengths for HCs and SZs within SSP maps. These results indicate the potential of SSPNet as a sensitive tool that may be useful for the development of brain-based biomarkers of mental disorders.

Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition With Spatial Sparsity Constraint.

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an lp norm ( ), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts.

BACKGROUND: Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data. NEW METHODS: We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise. RESULTS: The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method. COMPARISON WITH EXISTING METHODS: Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps. CONCLUSIONS: The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint.

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l0 norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Spatial source phase: A new feature for identifying spatial differences based on complex-valued resting-state fMRI data.

Spatial source phase, the phase information of spatial maps extracted from functional magnetic resonance imaging (fMRI) data by data-driven methods such as independent component analysis (ICA), has rarely been studied. While the observed phase has been shown to convey unique brain information, the role of spatial source phase in representing the intrinsic activity of the brain is yet not clear. This study explores the spatial source phase for identifying spatial differences between patients with schizophrenia (SZs) and healthy controls (HCs) using complex-valued resting-state fMRI data from 82 individuals. ICA is first applied to preprocess fMRI data, and post-ICA phase de-ambiguity and denoising are then performed. The ability of spatial source phase to characterize spatial differences is examined by the homogeneity of variance test (voxel-wise F-test) with false discovery rate correction. Resampling techniques are performed to ensure that the observations are significant and reliable. We focus on two components of interest widely used in analyzing SZs, including the default mode network (DMN) and auditory cortex. Results show that the spatial source phase exhibits more significant variance changes and higher sensitivity to the spatial differences between SZs and HCs in the anterior areas of DMN and the left auditory cortex, compared to the magnitude of spatial activations. Our findings show that the spatial source phase can potentially serve as a new brain imaging biomarker and provide a novel perspective on differences in SZs compared to HCs, consistent with but extending previous work showing increased variability in patient data.

Model order effects on ICA of resting-state complex-valued fMRI data: Application to schizophrenia.

BACKGROUND: Component splitting at higher model orders is a widely accepted finding for independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data. However, our recent study found that intact components occurred with subcomponents at higher model orders. NEW METHOD: This study investigated model order effects on ICA of resting-state complex-valued fMRI data from 82 subjects, which included 40 healthy controls (HCs) and 42 schizophrenia patients. In addition, we explored underlying causes for distinct component splitting between complex-valued data and magnitude-only data by examining model order effects on ICA of phase fMRI data. A best run selection method was proposed to combine subject averaging and a one-sample t-test. We selected the default mode network (DMN)-, visual-, and sensorimotor-related components from the best run of ICA at varying model orders from 10 to 140. RESULTS: Results show that component integration occurred in complex-valued and phase analyses, whereas component splitting emerged in magnitude-only analysis with increasing model order. Incorporation of phase data appears to play a complementary role in preserving integrity of brain networks. COMPARISON WITH EXISTING METHOD(S): When compared with magnitude-only analysis, the intact DMN component obtained in complex-valued analysis at higher model orders exhibited highly significant subject-level differences between HCs and patients with schizophrenia. We detected significantly higher activity and variation in anterior areas for HCs and in posterior areas for patients with schizophrenia. CONCLUSIONS: These results demonstrate the potential of complex-valued fMRI data to contribute generally and specifically to brain network analysis in identification of schizophrenia-related changes.

DOA Estimation for Underwater Wideband Weak Targets Based on Coherent Signal Subspace and Compressed Sensing.

Direction of arrival (DOA) estimation is the basis for underwater target localization and tracking using towed line array sonar devices. A method of DOA estimation for underwater wideband weak targets based on coherent signal subspace (CSS) processing and compressed sensing (CS) theory is proposed. Under the CSS processing framework, wideband frequency focusing is accompanied by a two-sided correlation transformation, allowing the DOA of underwater wideband targets to be estimated based on the spatial sparsity of the targets and the compressed sensing reconstruction algorithm. Through analysis and processing of simulation data and marine trial data, it is shown that this method can accomplish the DOA estimation of underwater wideband weak targets. Results also show that this method can considerably improve the spatial spectrum of weak target signals, enhancing the ability to detect them. It can solve the problems of low directional resolution and unreliable weak-target detection in traditional beamforming technology. Compared with the conventional minimum variance distortionless response beamformers (MVDR), this method has many advantages, such as higher directional resolution, wider detection range, fewer required snapshots and more accurate detection for weak targets.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data.

BACKGROUND: Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. NEW METHOD: To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. RESULTS: Results from simulated and experimental fMRI data demonstrated the efficacy of our method. COMPARISON WITH EXISTING METHOD(S): Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. CONCLUSIONS: The proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Multi-subject fMRI analysis via combined independent component analysis and shift-invariant canonical polyadic decomposition.

BACKGROUND: Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability. NEW METHOD: This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA as an initialization step to provide the aggregating mixing matrix for shift-invariant CPD to estimate shared TCs with subject-dependent delays and intensities. We then estimate shared SMs using a least-squares fit post shift-invariant CPD. RESULTS: Using simulated fMRI data as well as actual fMRI data we demonstrate that the proposed approach improves the estimates of the shared SMs and TCs, and the subject-dependent TC delays and intensities. The default mode component illustrates larger TC delays than the task-related component. COMPARISON WITH EXISTING METHOD(S): The proposed approach shows improvements over tensor PICA in particular when TC delays are large, and also outperforms SCP with SM orthogonality constraint and SCP with ICA-based SM initialization. CONCLUSIONS: TCs with subject-dependent delays conform to the true situation of multi-subject fMRI data. The proposed approach is suitable for decomposing multi-subject fMRI data with large inter-subject temporal and spatial variability.

ICA of full complex-valued fMRI data using phase information of spatial maps.

BACKGROUND: ICA of complex-valued fMRI data is challenging because of the ambiguous and noisy nature of the phase. A typical solution is to remove noisy regions from fMRI data prior to ICA. However, it may be more optimal to carry out ICA of full complex-valued fMRI data, since any filtering or voxel-based processing may disrupt information that can be useful to ICA. NEW METHOD: We enable ICA of the full complex-valued fMRI data by utilizing phase information of estimated spatial maps (SMs). The SM phases are first adjusted to properly represent spatial phase changes of all voxels based on estimated time courses (TCs), and then these are used to segment the voxels into BOLD-related and unwanted voxels based on a criterion of TC real-part power maximization. Single-subject and group phase masks are finally constructed to remove the unwanted voxels from the individual and group SM estimates. RESULTS: Our method efficiently estimated not only the task-related component but also the non-task-related component DMN. COMPARISON WITH EXISTING METHOD(S): Our method extracted 139-331% more contiguous and reasonable activations than magnitude-only infomax for the task-related component and DMN at |Z|>2.5, and detected more BOLD-related voxels, but eliminated more unwanted voxels than ICA of complex-valued fMRI data with pre-ICA de-noising. Our TC-based phase de-ambiguity exhibited higher accuracy and robustness than the SM-based method. CONCLUSIONS: The TC-based phase de-ambiguity is essential to prepare the SM phases. The SM phases provide a new post-ICA index for reliably identifying and suppressing the unwanted voxels.

Tensor decomposition of EEG signals: a brief review.

Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higher-order partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously.

How to validate similarity in linear transform models of event-related potentials between experimental conditions?

BACKGROUND: It is well-known that data of event-related potentials (ERPs) conform to the linear transform model (LTM). For group-level ERP data processing using principal/independent component analysis (PCA/ICA), ERP data of different experimental conditions and different participants are often concatenated. It is theoretically assumed that different experimental conditions and different participants possess the same LTM. However, how to validate the assumption has been seldom reported in terms of signal processing methods. NEW METHOD: When ICA decomposition is globally optimized for ERP data of one stimulus, we gain the ratio between two coefficients mapping a source in brain to two points along the scalp. Based on such a ratio, we defined a relative mapping coefficient (RMC). If RMCs between two conditions for an ERP are not significantly different in practice, mapping coefficients of this ERP between the two conditions are statistically identical. RESULTS: We examined whether the same LTM of ERP data could be applied for two different stimulus types of fearful and happy facial expressions. They were used in an ignore oddball paradigm in adult human participants. We found no significant difference in LTMs (based on ICASSO) of N170 responses to the fearful and the happy faces in terms of RMCs of N170. COMPARISON WITH EXISTING METHOD(S): We found no methods for straightforward comparison. CONCLUSIONS: The proposed RMC in light of ICA decomposition is an effective approach for validating the similarity of LTMs of ERPs between experimental conditions. This is very fundamental to apply group-level PCA/ICA to process ERP data.

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.