Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

The joint eigenvalue decomposition algorithm based on first-order Taylor expansion via the exterior penalty function method

Parallel factor analysis (PARAFAC) is a branch of multi-way signal processing that has received increased attention recently. This is due to the large class of applications as well as the milestone identifiability results demonstrating the superiority to matrix (two-way) analysis approaches. A significant amount of research was dedicated to iterative methods to estimate the factors from noisy data. In many situations these require many iterations and are not guaranteed to converge to the global optimum. Therefore, suboptimal closed-form solutions were proposed as initializations. In this contribution we derive a closed-form solution to completely replace the iterative approach by transforming PARAFAC into several joint diagonalization problems. Thereby, we obtain several estimates for each of the factors and present a new matching scheme to select the best estimate for each factor. In contrast to the techniques known from the literature, our closed-form solution can efficiently exploit symmetric as well as Hermitian symmetric models and solve the underdetermined case, if there are at least two modes that are non-degenerate and full rank. This closed-form solution achieves approximately the same performance as previously proposed iterative solutions and even outperforms them in critical scenarios.

One approach to the analysis of the high signal-to-noise ratio (SNR) capacity of noncoherent wireless communication systems is to ignore the noise component of the received signal in the computation of its differential entropy. In this paper, we consider the error incurred by this approximation when the transmitter and the receiver have one antenna each and when the noise has a Gaussian distribution. We consider the complex and real cases, and we show that when the probability density function (pdf) of the signal component of the received signal is piecewise differentiable, the approximation error decays as 1/SNR, which tightens the available result that the error decays as o(1). In addition, we consider the special instance in which the signal component of the received signal corresponds to a signal transmitted over a channel with a Gaussian fading coefficient. For that case, we provide explicit expressions for the first nonconstant term of the Taylor expansion of the differential entropy, and we invoke Schwartz's inequality to obtain an efficiently computable bound on it. Our results are supported by numerical examples.

The goal of independent component analysis (ICA) is to decompose observed signals into components as independent as possible. In linear instantaneous blind source separation, ICA is used to separate linear instantaneous mixtures of source signals into signals that are as close as possible to the original signals. In the estimation of the so-called demixing matrix one has to distinguish two different factors: 1. Variance of the estimated inverse mixing matrix in the noiseless case due to randomness of the sources. 2. Bias of the demixing matrix from the inverse mixing matrix: This chapter studies both factors for circular and noncircular complex mixtures. It is important to note that the complex case is not directly equivalent to the real case of twice larger dimension. In the derivations, we aim to clearly show the connections and differences between the complex and real cases. In the first part of the chapter, we derive a closed-form expression for the CRB of the demixing matrix for instantaneous noncircular complex mixtures. We also study the CRB numerically for the family of noncircular complex generalized Gaussian distributions (GGD) and compare it to simulation results of several ICA estimators. In the second part, we consider a linear noisy noncircular complex mixing model and derive an analytic expression for the demixing matrix of ICA based on the Kullback-Leibler divergence (KLD). We show that for a wide range of both the shape parameter and the noncircularity index of the GGD, the signal-to-interference-plus-noise ratio (SINR) of KLD-based ICA is close to that of linear MMSE estimation. Furthermore, we show how to extend our derivations to the overdetermined case (\(M>N\)) with circular complex noise.

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at learning data representations suited to NMF. In this work, we relate TL-NMF to the classical matrix joint-diagonalization (JD) problem. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach -- termed as JD+NMF -- that estimates the transform through JD, prior to NMF computation. In contrast, we found that when the number of data realizations is limited, not only is JD+NMF no longer equivalent to TL-NMF, but the inherent low-rank constraint of TL-NMF turns out to be an essential ingredient to learn meaningful transforms for NMF.

During recent decades new routing paradigms based on policies and quality of service provisioning have been proposed. The aim of these constraint-based path selection algorithms is to satisfy a set of quality of service constraints. This can help to reduce costs and balance network load. Path computation algorithms pose new challenges when extending them to larger inter-domain networks. The process of path computation in these complex cases could be delivered to the external nodes like PCEs. In inter-domain cases, path computation schemes are more prone to blocking due to the long response time of the requests. To address this issue, we propose an algorithm to find the domain sequences in computing the end-to-end path from the source to the destination. The proposed algorithm also increases the number of successful requests while minimizing the blockage in network. The main advantage of the algorithm is to improve the overall network utilization, which can be seen in simulation results.

This paper addresses the problem of detecting and estimating hidden periodicity from noisy observations when the noise distribution is asymmetric with heavy tail on one side. The ordinary periodogram is less effective in handling such noise. In this paper, we introduce an alternative periodogram-like function, called the quantile periodogram. The quantile periodogram is constructed from trigonometric regression where a specially designed objective function is used to substitute the squared l 2 norm that leads to the ordinary periodogram. Simulation results are provided to demonstrate the superior performance of the quantile periodogram in comparison with the ordinary periodogram when the noise is asymmetrically distributed with a heavy tail. The asymptotic distribution of the quantile periodogram is derived under the white noise assumption. Extensions to the multivariate case and the complex case are also discussed.

Monte Carlo simulation of NovalisTx linear accelerator using GATE/Geant4 code for dosimetry analysis

The construction of the Routh's table in both real and complex cases is extended to the special situations of vanishing leading array elements without introducing arbitrary parameters. It is shown that it is always possible to associate to any polynomial with real or complex coefficients an extended Rough's table and that the number of sign changes in the first column of this table equals the number of zeros of this polynomial with positive real part. >

Differential evolution-based optimized hierarchical extreme learning machines for fault section diagnosis of large-scale power systems

A new Jacobi-like method for joint diagonalization of arbitrary non-defective matrices

This article deals with the problem of joint diagonalization of hermitian and/or complex symmetric matrices. Within the framework of gradient algorithms, we develop various algorithms which are based on different levels of approximation of the classical diagonalization criterion. The algorithms are based on a multiplicative update and on the derivation of an optimal step-size. One of the algorithms is a generalization of DOMUNG to the complex case. Finally, in the blind source separation context, computer simulations illustrate the relative performances of some proposed algorithms in comparison to the true gradient one.

Polynomial numerical indices of Banach spaces with 1-unconditional bases

This paper describes user location and tracking on indoor scenarios based on the pattern recognition of IEEE 802.11 signal strength measurements by means of a fuzzy inference system. Signal fluctuation makes difficult and imprecise the trilateration of the user location, so we propose the use of fuzzy techniques to deal with such imprecision. To implement the location system, deterministic wireless channel characterisation is obtained by means of in–house implemented 3D ray launching code. Several scenarios are analysed, since their size strongly impacts on algorithm convergence. The limitations and solution, based on subdivision of the scenario in sub–zones, are analysed and applied to the case of a new emergency hospital complex in Navarra. Simulation and measurement results are presented showing good agreement. The results can aid in the determination of an optimised WiFi–based location system providing efficient positioning and communication services in complex indoor scenarios.

In this paper we consider the problem of joint wideband spectrum sensing and direction-of-arrival (DoA) estimation, where a number of uncorrelated narrowband sources spread over a wide frequency band impinge on a sparse linear array (SLA). To overcome the sampling rate bottleneck for wideband spectrum sensing, we rely on sub-Nyquist sampling for the receiver, and to resolve the sources both in the angle and frequency domain, an additional delayed branch is included for every antenna to gain an extra degree of freedom (DoF). Appropriately designing the delays at the different antennas allows us to use the contemporary machinery of co-array processing. We accordingly propose a joint eigenvalue decomposition (EVD) based algorithm to jointly estimate the angles and frequencies of the different sources with automatic pairing. Furthermore, as a consequence of the co-array processing, we can handle more sources than the number of physical antennas. Simulation results are included to corroborate our findings.