Complex Independent Component Analysis Research Articles

Fast gradient algorithm for complex ICA and its application to the MIMO systems

This paper proposes a new gradient-descent algorithm for complex independent component analysis and presents its application to the Multiple-Input Multiple-Output communication systems. Algorithm uses the Lie structure of optimization landscape and toral decomposition of gradient matrix. The theoretical results are validated by computer simulation and compared to several classes of algorithms, gradient descent, quasi-Newton as well as complex JADE. The simulations performed showed excellent results of the algorithm in terms of speed, stability of operation and the quality of separation. A characteristic feature of gradient methods is their quick response to changes in the input signal. The good results of the proposed algorithm indicate potential use in on-line applications.

Understanding Water Level Changes in the Great Lakes by an ICA-Based Merging of Multi-Mission Altimetry Measurements

Accurately monitoring spatio-temporal changes in lake water levels is important for studying the impacts of climate change on freshwater resources, and for predicting natural hazards. In this study, we applied multi-mission radar satellite altimetry data from the Laurentian Great Lakes, North America to optimally reconstruct multi-decadal lake-wide spatio-temporal changes of water level. We used the results to study physical processes such as teleconnections of El Niño and southern oscillation (ENSO) episodes over approximately the past three-and-a-half decades (1985–2018). First, we assessed three reconstruction methods, namely the standard empirical orthogonal function (EOF), complex EOF (CEOF), and complex independent component analysis (CICA), to model the lake-wide changes of water level. The performance of these techniques was evaluated using in-situ gauge data, after correcting the Glacial Isostatic Adjustment (GIA) process using a contemporary GIA forward model. While altimeter-measured water level was much less affected by GIA, the averaged gauge-measured water level was found to have increased up to 14 cm over the three decades. Our results indicate that the CICA-reconstructed 35-year lake level was more accurate than the other two techniques. The correlation coefficients between the CICA reconstruction and the in situ water-level data were 0.96, 0.99, 0.97, 0.97, and 0.95, for Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario, respectively; ~7% higher than the original altimetry data. The root mean squares of errors (RMSE) were 6.07 cm, 4.89 cm, 9.27 cm, 7.71 cm, and 9.88 cm, respectively, for each of the lakes, and ~44% less than differencing with the original altimetry data. Furthermore, the CICA results indicated that the water-level changes in the Great Lakes were significantly correlated with ENSO, with correlation coefficients of 0.5–0.8. The lake levels were ~25 cm higher (~30 cm lower) than normal during EI Niño (La Niña) events.

An Approach for Determining Voltage Imbalance Contributions Based on Complex Independent Component Analysis

In the context of power quality problems, the voltage imbalance index is relevant, given its harmful impacts on the networks and loads. Thus, reliable and viable methodologies for practical use are necessary to determine agents’ contributions. This article presents a noninvasive method for sharing responsibility for imbalances based on the principle of superposing the individual voltage imbalance produced by the parties. A procedure based on the Complex Independent Component Analysis (CICA) technique is proposed to meet the parameters required by the superposition method. Based on the measurements of voltages and currents carried out on the point of common coupling (PCC), the negative sequence impedances are determined using the CICA method under the terms needed by the superposition principle. The methodology’s effectiveness is evaluated through performance comparisons carried out over the process, in light of the response from the methods for sharing responsibilities currently published in the literature of this domain. The results obtained through the proposed approach show good adherence to the procedures presented with solid conceptual bases. However, unlike these, this article’s methodology offers practical perspectives for application in the field.

Neural Network Detection for Bandwidth-Limited Non-Orthogonal Multiband CAP UVLC System

In this paper, we propose a novel sparse data-to-symbol neural network (SDSNN) receiver for bandwidth-limited underwater visible light communication (UVLC) based on non-orthogonal multi-band carrierless amplitude and phase modulation (NM-CAP). Bandwidth limited NM-CAP signals usually carry severe inter-symbol interference (ISI) and inter-band interference (IBI). The SDSNN receiver directly converts the received NM-CAP data with ISI and IBI into quadrature amplitude modulation symbols without distortion for each sub-band. In contrast, the conventional receiver requires the least mean square (LMS) equalizer to cancel ISI, and the subcarrier component extraction with complex independent component analysis (SCE-ICA) to cancel IBI, respectively. SDSNN provides a novel receiving structure to replace post-equalization, matched filtering, and SCE-ICA. A blue-LED based UVLC system has been demonstrated utilizing NM-CAP16 with 3 sub-bands. The experimental results show that NM-CAP with the SDSNN receiver case reaches the highest spectral efficiency, where an enhancement of 43%, 20%, 6% has been measured over the orthogonal multi-band CAP case, NM-CAP with LMS equalizer case, and NM-CAP with joint LMS equalizer and SCE-ICA case, respectively. Compared with joint LMS equalizer and SCE-ICA case, the proposed SDSNN receiver can achieve 98% reduction of computational complexity.

Convolutive Complex-Valued Independent Component Analysis for Nonlinear Radar Signal Processing and Maritime Weak Target Detection

This paper first establishes a new complex independent component analysis (cICA) algorithm based on the spatiotemporal extension of complex-valued entropy bound minimization (CEBM) to separate received complex-valued radar signals. Next, we propose a new cICA-based detector with an open structure to find Swerling model targets, lognormal targets, and sea-surface small floating targets in coherent high-resolution maritime surveillance radars. The detector encountered three major problems when adopting cICA for detection and solved them using three effective suggestions. After performing cICA on the time series received by the radar, we obtained two different sources. Using the first and second theoretical and empirical moment estimates of the K-distribution, the target was selected between these two output source signals. Detector performance was verified quantitatively and qualitatively using the real-life IPIX radar database. Comprehensive experiments on this database with synthetic injected targets showed promising results. The computational time and sample size dependency of the proposed cICA algorithm were also discussed. Finally, a comparison of the detector with several novel detectors for detecting sea-surface floating small targets of the IPIX radar database demonstrated the proposed detector’s superiority.

Novel Process Monitoring Approach Enhanced by a Complex Independent Component Analysis Algorithm with Applications for Wastewater Treatment

Novel Process Monitoring Approach Enhanced by a Complex Independent Component Analysis Algorithm with Applications for Wastewater Treatment

Inter-Band Interference Cancellation Based on Complex ICA for 100Gbit/s/λ Non-Orthogonal m-CAP NGFI-II Fronthaul Data Transmission

Next generation fronthaul interface (NGFI) has been adopted as the mobile fronthaul (FH) transportation solution of the next generation (NG) mobile network, which requires high bandwidth and architecture flexibility. Spectral efficiency (SE) is a key performance indicator that worth discussion for NG mobile FH. In this paper, a novel inter-band interference (IBI) cancellation method based on complex independent component analysis (ICA) is proposed in non-orthogonal multiband CAP (NO-m-CAP) system. The interfering distortion caused by spectral overlapping between adjacent sub-bands in non-orthogonal multi-band CAP is mitigated by the proposed method, and the overall SE has been improved. As a proof of concept, an experimental demonstration of 100Gb/s/λ NGFI-II data transmission over 25km SSMF is carried out. Simple intensity modulator at central unit (CU) and a coherent detection at distributed unit (DU) are applied to achieve high-performance, low-cost and flexible mobile FH data transmission. A maximum SE improvement of 15% is obtained with the proposed method for both 4-band and 8-band assuming a 7% HD-FEC limit. Flexible data rate allocating, from 12.5Gb/s to 100Gbps with a bandwidth granularity of 12.5Gb/s, is also demonstrated.

Performance analysis for complex-valued FastICA and its improvement based on the Tukey M-estimator

Independent component analysis (ICA) is increasingly utilized to modern digital signal processing. Complex-valued FastICA, a fast fixed-point algorithm for ICA, is one of the most non-trivial algorithms for solving the ICA problems in the complex domain. Hitherto, there have been several attempts to give performance analysis for complex-valued FastICA. Rigorous theoretical analysis, however, still has room for improvement further. Consequently, the purposes of this paper are threefold: Firstly, the uniformity of the complex-valued FastICA estimator is constructed for the first time. Secondly, the stability of the complex-valued ICA algorithm is rigorously deduced based on the augmented generating matrix. Meanwhile, the local convergence of complex-valued FastICA algorithm is derived based on circular source signals. Finally, for improving the performance of separation, we select a novel alternative for nonlinearity based on the Tukey M-estimator in the complex-valued FastICA algorithm. Further, we prove the existence of local optimal solution and stability of the complex ICA problem based on the Tukey M-estimator. Simulations are presented to demonstrate the accuracy of our analysis. Additionally, the experimental results with synthetic data and complex-valued wind signal show the superiorities of the improved method.

A Novel Algorithm for Improving the Spectrum Efficiency of Non-Orthogonal Multiband CAP UVLC Systems

Nowadays, how to further enhance the spectrum efficiency is one of the key technologies for band limited scenarios in underwater visible light communication (UVLC) systems. In this article, a novel subcarrier component extraction (SCE) with complex independent component analysis (ICA) algorithm is proposed in the non-orthogonal multiband CAP UVLC systems. With the proposed SCE-ICA algorithm, the non-orthogonal multiband CAP system can support a higher overlapping level in contrast to the conventional CAP scheme and therefore hold a higher spectral efficiency. In the simulation, varying degrees of performance enhancement is achieved in comparison with the conventional CAP scheme with different roll-off, compression factor (CF) and signal-noise ratio (SNR). Then, we first discover that in the simulated frequency-selective fading channels, moderate overlapping among subcarriers can achieve the best performance in system-level in contrast to the non-overlapping case. Moreover, the UVLC system experimental investigation of overlapping 2-CAP and 5-CAP scheme is carried out. The experiment demonstration shows that the utmost spectral efficiency enhancement of 40% and 18% are achieved compared with the non-compression CAP case and the conventional demodulation of the overlapping CAP case, respectively. Finally, with the low computational complexity of O(N), the proposed algorithm can be a potential candidate to handle the equalization of non-orthogonal multiband CAP schemes.

Multi‐harmonic sources location based on sparse component analysis and complex independent component analysis

With the large-scale deployment of power electronic equipment, harmonic sources in the power system are gradually increasing. Traditional harmonic source location methods are inaccurate and they usually require prior information of the location, which is difficult to obtain. This study presents a novel method of harmonic source location that can use less prior information to accurately locate the location of harmonic sources. First, a linear screening criterion is constructed using sparse component analysis. Then, the source signals separated by complex independent component analysis are filtered by linear and non-Gaussian secondary screening, improving the accuracy of source signals and mixing matrix. Finally, the precise location of the harmonic is obtained by matching the mixing matrix with the columns of the matrix, which related to the system topology. Three IEEE systems are used to validate the proposed method. The simulation results show the high accuracy of the proposed method in the harmonic source location.

Evaluation of Harmonic Contributions for Multi Harmonic Sources System Based on Mixed Entropy Screening and an Improved Independent Component Analysis Method

Evaluating the harmonic contributions of each nonlinear customer is important for harmonic mitigation in a power system with diverse and complex harmonic sources. The existing evaluation methods have two shortcomings: (1) the calculation accuracy is easily affected by background harmonics fluctuation; and (2) they rely on Global Positioning System (GPS) measurements, which is not economic when widely applied. In this paper, based on the properties of asynchronous measurements, we propose a model for evaluating harmonic contributions without GPS technology. In addition, based on the Gaussianity of the measured harmonic data, a mixed entropy screening mechanism is proposed to assess the fluctuation degree of the background harmonics for each data segment. Only the segments with relatively stable background harmonics are chosen for calculation, which reduces the impacts of the background harmonics in a certain degree. Additionally, complex independent component analysis, as a potential method to this field, is improved in this paper. During the calculation process, the sparseness of the mixed matrix in this method is used to reduce the optimization dimension and enhance the evaluation accuracy. The validity and the effectiveness of the proposed methods are verified through simulations and field case studies.

An improved complex ICA based method for wind farm harmonic emission levels evaluation

Wind farms, as typical renewable energy infrastructure, provide clean energy to the power grid but also inevitably generate harmonic pollution. In the case of a multi-wind farms system, evaluating the harmonic emissions for each farm is essential for the division of harmonic responsibility and the design of the harmonic mitigation scheme. However, this evaluation process faces two challenges. First, the background harmonics of a single wind farm might be unstable. In addition, the harmonic impedance of wind farm side is reduced by the installation of filters. As a result, traditional evaluation methods are no longer applicable. Complex independent component analysis is a well-known method for evaluating harmonic emissions. To make this method feasible in the above situations, we analyze its shortcomings. Furthermore, an improved method is proposed by introducing two screening mechanisms based on sparse component analysis and the maximization of hybrid negentropy. Additionally, the results of simulations and field case verification indicate that the traditional methods have large calculation errors when the background harmonics fluctuate greatly or the harmonic impedance of the wind farm side is not far larger than that of the utility side. In contrast, our novel evaluation method has high precision in the above cases.

Complex Blind Source Separation

Blind source separation (BSS) techniques aim at recovering the original source signals from observed mixtures without a priori information. The bivariate empirical mode decomposition (BEMD) algorithm combined with complex independent component analysis by entropy bound minimization (ICA-EBM) technique is proposed as an alternative to separate convolutive mixtures of speech signals. The empirical mode decomposition (EMD) is a local self-adaptive decomposition method that allows analyzing data from non-stationary and/or nonlinear processes. Its principle is based on the sequential extraction of different amplitude and frequency modulation single-component contributions called intrinsic mode functions (IMFs). The BEMD is an extension of the EMD to complex-valued signals. First, the convolutive mixtures in the frequency domain are decomposed into a set of IMFs using the BEMD algorithm, and then, the complex ICA-EBM method is applied to extract the independent sources. The performance of the proposed approach is tested on real speech sounds chosen from available databases and compared to the results obtained via conventional frequency ICA and BEMD-ICA-based separation for convolutive mixtures. Simulation results show that the proposed method of BSS outperforms the BEMD-ICA separation technique for convolutive mixtures and conventional frequency ICA.

Decoding Method Based on Complex ICA for a Multicell Massive MIMO Uplink System

Pilot signal reuse in neighboring cells causes the pilot contamination, and performance will be degraded significantly in a multicell, massive multiple-input, multiple-output (MIMO) uplink system. In this letter, a new decoding method is proposed to alleviate the degradation. In the proposed method, the principal component analysis (PCA) is used to reduce the dimension of the received signals from both intercell and intracell. Then, the complex independent component analysis (ICA) is implemented to estimate the channels, and the mean minimum square error (MMSE) decoder is employed to decode the transmitted signals. At last, few pilot signals are used to overcome the ambiguity caused by the complex ICA. In our method, orthogonality or asymptotic orthogonality of the channels is not required. Moreover, the path-loss and shadowing factors can be unknown. Simulation results show that the performance of our decoder is better than the MMSE channel estimation-based MMSE decoder. Moreover, error floor does not appear even when signal-to-noise ratio (SNR) is high, while it occurs if the MMSE decoder is used.

Fixed-point ICA algorithm for blind separation of complex mixtures containing both circular and noncircular sources

Fixed-point algorithms are widely used for independent component analysis (ICA) owing to its good convergence. However, most existing complex fixed-point ICA algorithms are limited to the case of circular sources and result in phase ambiguity, that restrict the practical applications of ICA. To solve these problems, this paper proposes a two-stage fixed-point ICA (TS-FPICA) algorithm which considers complex signal model. In this algorithm, the complex signal model is converted into a new real signal model by utilizing the circular coefficients contained in the pseudo-covariance matrix. The algorithm is thus valid to noncircular sources. Moreover, the ICA problem under the new model is formulated as a constrained optimization problem, and the real fixed-point iteration is employed to solve it. In this way, the phase ambiguity resulted by the complex ICA is avoided. The computational complexity and convergence property of TS-FPICA are both analyzed theoretically. Simulation results show that the proposed algorithm has better separation performance and without phase ambiguity in separated signals compared with other algorithms. TS-FPICA convergences nearly fast as the other fixed-point algorithms, but far faster than the joint diagonalization method, e.g. joint approximate diagonalization of eigenmatrices (JADE).

The role of diversity in complex ICA algorithms for fMRI analysis

BackgroundThe widespread use of data-driven methods, such as independent component analysis (ICA), for the analysis of functional magnetic resonance imaging data (fMRI) has enabled deeper understanding of neural function. However, most popular ICA algorithms for fMRI analysis make several simplifying assumptions, thus ignoring sources of statistical information, types of “diversity,” and limiting their performance. New methodWe propose the use of complex entropy rate bound minimization (CERBM) for the analysis of actual fMRI data in its native, complex, domain. Though CERBM achieves enhanced performance through the exploitation of the three types of diversity inherent to complex fMRI data: noncircularity, non-Gaussianity, and sample-to-sample dependence, CERBM produces results that are more variable than simpler methods. This motivates the development of a minimum spanning tree (MST)-based stability analysis that mitigates the variability of CERBM. Comparison with existing methodsIn order to validate our method, we compare the performance of CERBM with the popular CInfomax as well as complex entropy bound minimization (CEBM). ResultsWe show that by leveraging CERBM and the MST-based stability analysis, we are able to consistently produce components that have a greater number of activated voxels in physically meaningful regions and can more accurately classify patients with schizophrenia than components generated using simpler models. ConclusionsOur results demonstrate the advantages of using ICA algorithms that can exploit all inherent types of diversity for the analysis of fMRI data when coupled with appropriate stability analyses.

Efficient Optimization of Reference-Based Negentropy for Noncircular Sources in Complex ICA

Bingham proposed a complex fast independent component analysis (c-FastICA) algorithm to approximate the nengentropy of circular sources using nonlinear functions. Novey proposed extending the work ...

Method for determining utility and consumer harmonic contributions based on complex independent component analysis

This study presents a new method for determining the harmonic contributions (HCs) of utility and consumer at the point of common coupling (PCC). The proposed method is based on a well-known statistical signal processing technique, the so-called complex independent component analysis (ICA). The complex ICA technique is applied to the harmonic voltage and current measured at the PCC to estimate the parameters of the Northon equivalent circuit model. Then, the HCs of utility and consumer are calculated through quantitative indices defined by the superposition method. The proposed method is robust against the background harmonic disturbances and works well in resonance condition. Moreover, the impact of consumer harmonic impedance is appropriately considered in calculations. The effectiveness of the proposed method is verified through the computer simulation and the real case study.

PWC-ICA: A Method for Stationary Ordered Blind Source Separation with Application to EEG.

Independent component analysis (ICA) is a class of algorithms widely applied to separate sources in EEG data. Most ICA approaches use optimization criteria derived from temporal statistical independence and are invariant with respect to the actual ordering of individual observations. We propose a method of mapping real signals into a complex vector space that takes into account the temporal order of signals and enforces certain mixing stationarity constraints. The resulting procedure, which we call Pairwise Complex Independent Component Analysis (PWC-ICA), performs the ICA in a complex setting and then reinterprets the results in the original observation space. We examine the performance of our candidate approach relative to several existing ICA algorithms for the blind source separation (BSS) problem on both real and simulated EEG data. On simulated data, PWC-ICA is often capable of achieving a better solution to the BSS problem than AMICA, Extended Infomax, or FastICA. On real data, the dipole interpretations of the BSS solutions discovered by PWC-ICA are physically plausible, are competitive with existing ICA approaches, and may represent sources undiscovered by other ICA methods. In conjunction with this paper, the authors have released a MATLAB toolbox that performs PWC-ICA on real, vector-valued signals.

Pharmacokinetic analysis of prostate cancer using independent component analysis

Dynamic contrast enhanced (DCE)-MRI combined with pharmacokinetic (PK) modeling of a tumor provides information about its perfusion and vascular permeability. Most PK models require the time course of contrast agent concentration in blood plasma as an input, which cannot be measured directly at the tissue of interest, and is approximated with an arterial input function (AIF). Variability in methods used in estimating the AIF and inter-observer variability in region of interest selection are major sources of discrepancy between different studies. This study had two aims. The first was to determine whether a local vascular input function (VIF) estimated using an adaptive complex independent component analysis (AC-ICA) algorithm could be used to estimate PK parameters from clinical dynamic contrast enhanced (DCE)-MRI studies. The second aim was to determine whether normalizing the input function using its area under the curve would improve the results of PK analysis. AC-ICA was applied to DCE-MRI of 27 prostate cancer patients and the intravascular signal was estimated. This signal was converted into contrast agent concentration to give a local vascular input function (VIF) which was used as the input function for PK analysis. We compared Ktrans values for normal peripheral zone (PZ) and tumor tissues using the local VIF with those calculated using a conventional AIF obtained from the femoral artery. We also compared the Ktrans values obtained from the un-normalized input functions with the KNtrans values obtained after normalizing the AIF and local VIF. Normalization of the input function resulted in smaller variation in PK parameters (KNtrans vs. Ktrans for normal PZ tissue was 0.20±0.04mM.min−1 vs. 0.87±0.54min−1 for local VIF and 0.21±0.07mM.min−1 vs. 0.25±0.29min−1 for AIF) and better separation of the normal and tumor tissues (effect-size of this separation using KNtrans vs. Ktrans was 0.89 vs. 0.75 for local VIF and 0.94 vs. 0.41 for AIF). The AC-ICA and AIF-based analyses provided similar (KNtrans) values in normal PZ tissue of prostate across patients. Normalizing the input function before PK analysis significantly improved the reproducibility of the PK parameters and increased the separation between normal and tumor tissues. Using AC-ICA allows a local VIF to be estimated and the resulting PK parameters are similar to those obtained using a more conventional AIF; this may be valuable in studies where an artery is not available in the field of view.