Least squares null space variational characterization for nonminimum norm solutions

The least-squares estimation problem with non-minimum-norm constraints on the unknown model parameters is considered. Contrary to the quadratic-constraint least-squares solutions the approach presented does not necessarily satisfy the constraint, but rather relies on the nullity of the data matrix to maintain the unconstrained least-squares error value while trading off the minimum-norm solution by another with the shortest distance from the null space of the constraint. The singular value decomposition of the data matrix is used to obtain the necessary information about the minimum-norm solution as well as the basis of the null space. Closed-form expressions are derived for the case in which the constraint of interest is the smoothness of the model parameters. Examples of sinusoids in white noise are given for illustration.Peer ReviewedPostprint (published version

Cepstrum constraints in ME spectral estimation

Current trends in spectral estimation techniques follow basicaly two guidelines; by introducing modifications in the objctive function to be minimized or, keeping the objetive, by modifying the set of constraints in the minimization procedure. This work can be encompassed in the second sense, showing the potential of cepstrum constraints in spectral estimation methods. The special features associated with this constraints allow to use raw approximations in order to linearize or simplify the computations involved in the procedure maintaning within margins of adequate quality the resulting estimate.Peer ReviewedPostprint (published version

The Kolmogorov mapping theorem in signal processing

Since the publication in 1957 of the work of Andrei Kolmogorov 181 in mapping a function of multiple variables by means functions of a single variable, many mathematicians and engineers try , with different degree of success and not without controversy 1191. to find the direct application of it to multiple extremes problems, rooting of multivariate polynomials, neural networks and pattern recognition. This paper revisits the theorem from the optic of a generalised architecture for signal processing 1281. It is envisaged the high potential of the theorem to handle either linear or non-linear processing problems. A specific implementation following the main guide-lines of the theorem is reported, as well as some preliminary results concerning the design, implementation and performance of non-linear systems. The applications cover non linear transmission channels for communications, instantaneous companders and prediction of chaotic series.Peer ReviewedPostprint (published version

The periodogram envelope in parametric and non-parametric spectral estimation

The role of the periodogram envelope as a nonparametric approach for spectral estimation and its potential in parametric spectral estimation using variational approaches are examined. The spectral envelope, or its prior estimate the periodogram envelope, represents a very good candidate for starting any approach to spectral estimation due to its smooth character, its robustness against flat noise spectra, and its statistical stability. Setting envelope constraints in variational spectral estimation increases the statistical stability of the resulting estimate while preserving the high resolution of the best reported methods. The case of line spectra is briefly described to demonstrate the potential of the envelope-associated matrix in the line spectrum. This allows the designer to convert SUD and MUSIC methods to the new starting function.Peer ReviewedPostprint (published version

El procesador adaptativo de Howells-Applebaum

The Howells-Applebaum adaptive processor, working with the asumptions that the desired signal is absent most of the time and the direction of arrival of the desired signal is known, has an associated adaptive loop for each element. Two modifications are introduced in the basic model: the incorporation of aPeer ReviewedPostprint (published version

The variational approach in spectral estimation

This is a very personal point of view of the underlying ideas that yields most of the currently reported spectral estimation techniques, procedures and algorithms. After a brief introduction on non-parametric spectral estimation, which includes a shutle aspect about how to use averaging in DFT based methods, the paper describes the potential of the variational approach in deriving already reported estimates and the way out to obtain new ones. Finally, and as the second approach of high interest in spectral estimation, the design and extensions of data-dependent filters for spectral estimation is reported.Peer ReviewedPostprint (published version

Non-linear spectral estimation

This work describes the use of constraints in variational procedures for spectral analysis. It is reported how the designer in a variational approach for spectral estimation has to select a set of constraints. At the same time it is shown that the selected set of constraints becomes more relevant, as concerns with the resulting quality of the estimate, than the objective function minimized or maximized in the procedure. Finally, some examples are presented which are the result of considering correlation and envelope constraints and minimizing the correlation extrapolation energy.Peer ReviewedPostprint (published version

Decodificador de máxima verosimilitud asistida por procesado digital de señal

This paper deals with the problem of ISI communications channels and the existing tradeoff between channel modeling and channel equalizers. We focus the problem of a TCM system with a 2/3 convolutional coder and PSK-8 signaling. The new scheme reported by the authors supports the weigthed likelihood decoder at every branch by a DSP channel model. This architecture shows a better performance than the classic equalizers both in robustness and resulting complexity.Peer ReviewedPostprint (published version

Conformación de haz con referencia de espectro ensanchado

The multipath propagation is a problem in many communication systems. The adaptive array beamforming is able to reject the interferences when they are decorrelated with the source of information. Therefore, this kind of system is not able to minimise the contributions of correlated signals that come from multipath. One of the applications of the Spread Spectrum signals is to combat the multipath propagation. However, these systems are strongly affected by the near-far problem. Combining spread spectrum signals with adaptive array beam forming results in a more powerful system that rejects interferences, and combats the multipath and the near-far problem.Peer ReviewedPostprint (published version

High performance SVD-like procedure for spectral estimation using Rayleigh function estimates

The author describes how Rayleigh estimates can be viewed as a method which performs singular-value decomposition (SVD) procedure without doing it. As a short cut to get principal-component reduction, Rayleigh quotients allow the resolution of frequency detectors yet preserve the asymptotic behavior of the actual power spectral density. In a filtering framework the estimate is extended to adaptive schemes and 2-D spectral estimation. The resulting estimate provides the means for adaptive processing with low computational complexity. It avoids also the crucial decision between signal subspace and noise subspace which promotes undesired distortion and false peaks in spectral estimation applicationsPeer ReviewedPostprint (published version