A Comprehensive Framework for Performance Analysis of Cooperative Multi-Hop Wireless Systems over Log-Normal Fading Channels

International audienceIn this paper, we propose a comprehensive framework for performance analysis of multi–hop multi–branch wireless communication systems over Log–Normal fading channels. The framework allows to estimate the performance of Amplify and Forward (AF) relay methods for both Channel State Information (CSI–) assisted relays, and fixed–gain relays. In particular, the contribution of this paper is twofold: i) first of all, by relying on the Gauss Quadrature Rule (GQR) representation of the Moment Generation Function (MGF) for a Log–Normal distribution, we develop accurate formulas for important performance indexes whose accuracy can be estimated a priori and just depends on GQR numerical integration errors; ii) then, in order to simplify the computational burden of the former framework for some system setups, we propose various approximations, which are based on the Improved Schwartz–Yeh (I–SY) method. We show with numerical and simulation results that the proposed approximations provide a good trade–off between accuracy and complexity for both Selection Combining (SC) and Maximal Ratio Combining (MRC) cooperative diversity methods

Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations

This paper is concerned with polynomial approximations of the spectral abscissa function (the supremum of the real parts of the eigenvalues) of a parameterized eigenvalue problem, which are closely related to polynomial chaos approximations if the parameters correspond to realizations of random variables. Unlike in existing works, we highlight the major role of the smoothness properties of the spectral abscissa function. Even if the matrices of the eigenvalue problem are analytic functions of the parameters, the spectral abscissa function may not be everywhere differentiable, even not everywhere Lipschitz continuous, which is related to multiple rightmost eigenvalues or rightmost eigenvalues with multiplicity higher than one. The presented analysis demonstrates that the smoothness properties heavily affect the approximation errors of the Galerkin and collocation-based polynomial approximations, and the numerical errors of the evaluation of coefficients with integration methods. A documentation of the experiments, conducted on the benchmark problems through the software Chebfun, is publicly available.Comment: This is a pre-print of an article published in Numerical Algorithms. The final authenticated version is available online at: https://doi.org/10.1007/s11075-018-00648-