Improved Chernoff Bound of Gaussian Q-function with ABC algorithm and its QAM applications to DB SC and MRC systems over Beaulieu–Xie channels

Bilim, Mehmet; Karaboğa, Derviş

doi:10.1016/j.phycom.2023.102034

Cited by 3 publications

(1 citation statement)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The cumulative distribution function (CDF) and its various forms (see Table 1 in the appendix) have significant applications in a wide range of fields [30], such as engineering [14,27,29], Mathematics [21], Statistics [4] computer science [15], diffusion theory [5], communication theory [26], physics [6], and chemistry [24]. Due to the mathematical complexity of the integral form, various approximations have been presented in the literature [19,11].…”

Section: Introductionmentioning

confidence: 99%

New Mathematical Approximations for the Cumulative Normal Distribution Function

Etesami,

Madadi,

Keynia

et al. 2024

Preprint

View full text Add to dashboard Cite

The normal cumulative distribution function and its derivatives, such as the error function, the Q-function, and the Mills ratio, are widely used in engineering, mathematics, statistics, computer science, diffusion theory, communication theory, physics, and chemistry. However, their non-closed form nature has led to the development of new approximations with varying levels of accuracy and complexity. These new approximations are often more accurate; nevertheless, they can also be more complex, which may limit their practical utility. In this article, a new approach for approximating is proposed. which combines Taylor series expansion and logistic function to create an initial approximation, to enhance the accuracy of the initial approximation, the Hunter-Prey Optimization algorithm is utilized to minimize both the maximum absolute error and the mean absolute error, leading to a significantly more precise approximation. Furthermore, this algorithm is employed to enhance the accuracy of other existing approximations introduced by researchers. The results showed that the improved approximations have much higher accuracy. To show the effectiveness of the new findings of this article, two case studies with applications are presented.

show abstract