Accurate Computation of Gaussian Quadrature for Tension Powers

2007 ◽  
Author(s):  
Saša Singer ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Gaussian Quadrature ◽  
Accurate Computation

A total positivity property of the Marchenko-Pastur Law

2015 ◽  
Vol 30 ◽  
Author(s):  
Ana Marco ◽  
Jose-Javier Martinez
Keyword(s):  
Orthogonal Polynomials ◽  
Gaussian Quadrature ◽  
Total Positivity ◽  
Quadrature Formulas ◽  
Positivity Property ◽  
Accurate Computation ◽  
Gaussian Quadrature Formulas ◽  
Theoretical Results

A property of the Marchenko-Pastur measure related to total positivity is presented. The theoretical results are applied to the accurate computation of the roots of the corresponding orthogonal polynomials, an important issue in the construction of Gaussian quadrature formulas.

scholarly journals Effect of Correlated Non-Gaussian Quadratures on the Performance of Binary Modulations

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Valentine A. Aalo ◽  
George P. Efthymoglou
Keyword(s):  
Communication Systems ◽  
Gaussian Quadrature ◽  
Wireless Communication Systems ◽  
High Signal ◽  
Random Waves ◽  
The Central Limit Theorem ◽  
Gaussian Quadratures ◽  
Non Gaussian ◽  
Digital Communication Systems ◽  
Composite Signal

The received signal in many wireless communication systems comprises of the sum of waves with random amplitudes and random phases. In general, the composite signal consists of correlated nonidentical Gaussian quadrature components due to the central limit theorem (CLT). However, in the presence of a small number of random waves, the CLT may not always hold and the quadrature components may not be Gaussian distributed. In this paper, we assume that the fading environment is such that the quadrature components follow a correlated bivariate Student-t joint distribution. Then, we derive the envelope distribution of the received signal and obtain new expressions for the exact and high signal-to-noise (SNR) approximate average BER for binary modulations. It also turns out that the derived envelope pdf approaches the Rayleigh and Hoyt distributions as limiting cases. Using the derived envelope pdf, we investigate the effect of correlated nonidentical quadratures on the error rate performance of digital communication systems.

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