Rational Gauss-Chebyshev Quadratures for Wireless Performance Analysis

Abstract

The convergence rate of the classical GaussChebyshev quadrature (GCQ) rule for wireless performance as a function of the signal-to-noise ratio (SNR) is analyzed. The convergence rate is found to decline as the SNR varies from high to low. Thus, at low SNR, the number of nodes needed to achieve the desired accuracy is extremely high. A generalized rational GCQ rule is thus adopted. The nodes and weights are then computed from a system of orthogonal rational functions. The rational GCQ is much more accurate than the classical GCQ over the entire SNR range. Especially at low SNR, the accuracy is extremely high.Index Terms-Error probability, Gauss-Chebyshev quadrature, moment generating function, outage probability, signal-tonoise ratio.