Heinz Mathis

Joint diagonalization of correlation matrices by using gradient methods with application to blind signal separation

Joint diagonalization of several correlation matrices is a powerful tool for blind signal separation. The paper addresses the blind signal separation problem for the case where the source signals are non-stationary and/or non-white, and the sensors are possibly noisy. We present cost functions for jointly diagonalizing several correlation matrices. The corresponding gradients are derived and used in gradient-based joint-diagonalization algorithms. Several variations are given, depending on the desired properties of the separation matrix, e.g., unitary separation matrix. These constraints are either imposed by adding a penalty term to the cost function or by projecting the gradient onto the desired manifold. The performance of the proposed joint-diagonalization algorithm is verified by simulating a blind signal separation application.

An FFT-based algorithm for multichannel blind deconvolution

A new update equation for the general multichannel blind deconvolution (MCBD) of a convolved mixture of source signals is derived. It is based on the update equation for blind source separation (BSS), which has been shown to be an alternative interpretation of the natural gradient applied to the minimization of some mutual information criterion. Computational complexity is held at a minimum by carrying out the separation/equalization task in the frequency domain. The algorithm is compared to similar known blind algorithms and its validity is demonstrated by simulations of real-world acoustic filters. In order to assess the performance of the algorithm, performance measures for multichannel blind deconvolution of signals are given in the paper.

Combined blind/nonblind source separation based on the natural gradient

It is a known fact that blind algorithms have convergence times of an order of magnitude longer than their nonblind counterparts. However, as shown in this letter, the knowledge of a subset of signals can greatly accelerate the convergence of blind source separation. The convergence behavior of the proposed algorithm is compared with the blind-only case.

On the kurtosis of digitally modulated signals with timing offsets

Beside being a renowned parameter in signal classification, the kurtosis of a source signal is an indicator of the separation difficulty in blind signal separation and deconvolution. Whereas the maximum kurtosis is unbounded, the lower bound on the minimum kurtosis is -2. This means that the family of sub-Gaussian signals, to which most modulated communication signals belong, have an inherent limit in their suitability for blind techniques. Furthermore, the kurtosis of a composite signal has bounds which depend on the kurtoses of the constituent signals. Exact expressions for the kurtoses for a number of digital modulation formats are derived, and the influence of sampling-time accuracy to the kurtosis of the sampled signal is investigated.

On optimal and universal nonlinearities for blind signal separation

The search for universally applicable nonlinearities in blind signal separation has produced nonlinearities that are optimal for a given distribution, as well as nonlinearities that are most robust against model mismatch. This paper shows yet another justification for the score function, which is in some sense a very robust nonlinearity. It also shows that among the class of parameterizable nonlinearities, the threshold nonlinearity with the threshold as a parameter is able to separate any non-Gaussian distribution, a fact that is also proven in this paper.

A simple threshold nonlinearity for blind separation of sub-Gaussian signals

A computationally simple nonlinearity in the form of a threshold device for the blind separation of sub-Gaussian signals is derived. Convergence is shown to be robust, fast, and comparable to that of more complex polynomial nonlinearities. Together with the known signum nonlinearity for super-Gaussian distributions, which basically is a threshold device with the threshold set to zero, the general threshold nonlinearity (with an appropriate threshold) can separate any non-Gaussian signals.

Elementary cost functions for blind separation of non-stationary source signals

Blind source separation (BSS) is a problem found in many applications related to acoustics or communications. This paper addresses the blind source separation problem for the case where the source signals are non-stationary and the sensors are noisy. To this end, we propose several useful elementary cost functions which can be combined to an overall cost function. The elementary cost functions might have different objectives, such as uncorrelated output signals or power normalization of the output signals. Additionally, the corresponding gradients with respect to the adjustable parameters are given. We discuss the design of an overall cost function and also give a simulation example.

Indoor positioning using LTE signals

This paper presents an experiment using real Long-Term Evolution (LTE) signals to extend positioning from outdoors to indoors. LTE signals are of interest for positioning applications because of their availability indoors, where GNSS signal reception is limited. Different approaches for time of arrival (TOA) extraction are evaluated for their positioning performance, combined with an extended Kalman filter (EKF) for movement tracking. The paper shows that the performance is surprisingly good, with high visibility of cellular signals even in the difficult indoor test environment, and with a positioning error once indoors smaller than 8m in 50% of cases.

Unbiased blind separation using the threshold nonlinearity

The stability analysis of blind signal separation algorithms using the threshold nonlinearity is extended to discrete distributions, such as used in digital communication systems. Conditions for the threshold parameter are derived. An extension to the standard algorithm mitigates separation coefficient bias, which is introduced by additive noise at the sensors. Simulations quantify the improvement in terms of steady-state interchannel interference.

Blind deconvolution of impulsive signals using a modified Sato algorithm

Many blind deconvolution algorithms have been designed to extract digital communications signals corrupted by inter-symbol interference. Such algorithms generally fail when applied to signals with impulsive characteristics, such as acoustic signals. In this paper, we provide a theoretical analysis and explanation as to why Bussgang-type algorithms are generally unsuitable for deconvolving impulsive signals. We then propose a novel modification of one such algorithm, the Sato algorithm, to enable it to deconvolve such signals. Sufficient conditions on the source signal to guarantee local stability of the modified Sato algorithm about a deconvolving solution are derived. Computer simulations show the efficiency of the proposed approach as compared to the Shalvi-Weinstein algorithm for deconvolving impulsive signals.