Frequency-Domain Analysis of Linear Time-Periodic Systems

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature

Estimation of instantaneous complex dynamics through Lyapunov exponents: a study on heartbeat dynamics

Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the H�non map and R�ssler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations

Performance Analysis of Non-Ideal MIMO Systems in Fading Channels

En esta tesis se aborda el análisis de prestaciones de sistemas MIMO bajo ciertas condiciones no ideales. Se han considerado limitaciones realistas como son las interferencias co-canal, el canal de retorno con velocidad limitada, y la correlación espacial entre antenas. Bajo estas condiciones, se han analizado las probabilidades de error y de outage para sistemas MIMO que incluyen técnicas de conformación de haz en el transmisor y/o distintas técnicas de diversidad espacial en el receptor. Con el fin de obtener expresiones cerradas y exactas par los indicadores de rendimiento mencionados, se han desarrollo nuevos métodos o herramientas matemáticas que facilitan o, en algunos casos, hacen posible el análisis. En primer lugar, se han obtenido nuevas expresiones cerradas para las integrales del tipo Lipschitz-Hankel y para la distribución de los elementos de la diagonal de matrices Wishart complejas. Posteriormente, estos resultados han sido aplicados al análisis de prestaciones de distintos sistemas MIMO en condiciones no-ideales. Concretamente, se han obtenido nuevas expresiones cerrradas de la probabilidad de outage para: sistemas MRC con interferencia co-canal, sistemas MIMO con correlación espacial entre antenas, y sistemas MIMO MRC con un canal de retorno limitado en velocidad. Además, se han obtenido expresiones cerradas para la probabilidad de error en sistemas de diversidad en recepción que emplean modulaciones no coherentes y no ortogonales

MGF Approach to the Analysis of Generalized Two-Ray Fading Models

We analyze a class of Generalized Two-Ray (GTR) fading channels that consist of two line of sight (LOS) components with random phase plus a diffuse component. We derive a closed form expression for the moment generating function (MGF) of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.Comment: 14 pages, 8 Figures and 2 Tables. This work has been accepted for publication at IEEE Transactions on Wireless Communications. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]