Abstrakti
This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Qfunction, and functions thereof, in the form of a weighted sum of exponential functions. They are based on minimizing the maximum absolute or relative error, resulting in globally uniform error functions with equalized extrema. In particular, we construct sets of equations that describe the behaviour of the targeted error functions and solve them numerically in order to find the optimized sets of coefficients for the sum of exponentials. This also allows for establishing a tradeoff between absolute and relative error by controlling weights assigned to the error functions' extrema. We further extend the proposed procedure to derive approximations and bounds for any polynomial of the Qfunction, which in turn allows approximating and bounding many functions of the Qfunction that meet the Taylor series conditions, and consider the integer powers of the Qfunction as a special case. In the numerical results, other known approximations of the same and different forms as well as those obtained directly from quadrature rules are compared with the proposed approximations and bounds to demonstrate that they achieve increasingly better accuracy in terms of the global error, thus requiring significantly lower number of sum terms to achieve the same level of accuracy than any reference approach of the same form.
Alkuperäiskieli  Englanti 

Sivut  65146524 
Sivumäärä  11 
Julkaisu  IEEE Transactions on Communications 
Vuosikerta  68 
Numero  10 
DOI  pysyväislinkit  
Tila  Julkaistu  2020 
OKMjulkaisutyyppi  A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä 
Julkaisufoorumitaso
 Jufotaso 2
Sormenjälki
Sukella tutkimusaiheisiin 'Global Minimax Approximations and Bounds for the Gaussian QFunction by Sums of Exponentials'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.Tietoaineistot

Coefficients for Global Minimax Approximations and Bounds for the Gaussian QFunction by Sums of Exponentials
Tanash, I. (Creator) & Riihonen, T. (Creator), 3 heinäk. 2020
DOI  pysyväislinkki: 10.5281/zenodo.4112978
Tietoaineisto: Dataset