Chernoff-Type Bounds for the Gaussian Error Function

We study single-term exponential-type bounds (also known as Chernoff-type bounds) on the Gaussian error function. This type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form. We derive the conditions for a...

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Bibliographic Details
Published inIEEE transactions on communications Vol. 59; no. 11; pp. 2939 - 2944
Main Authors Seok-Ho Chang, Cosman, P. C., Milstein, L. B.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.11.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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Summary:We study single-term exponential-type bounds (also known as Chernoff-type bounds) on the Gaussian error function. This type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form. We derive the conditions for a general single-term exponential function to be an upper or lower bound on the Gaussian error function. We prove that there exists no tighter single-term exponential upper bound beyond the Chernoff bound employing a factor of one-half. Regarding the lower bound, we prove that the single-term exponential lower bound of this letter outperforms previous work. Numerical results show that the tightness of our lower bound is comparable to that of previous work employing eight exponential terms.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2011.072011.100049