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ICC
2009
IEEE

Arbitrarily Tight Upper and Lower Bounds on the Gaussian Q-Function and Related Functions

9 years 1 days ago
Arbitrarily Tight Upper and Lower Bounds on the Gaussian Q-Function and Related Functions
—We present a new family of tight lower and upper bounds on the Gaussian Q-function Q(x). It is first shown that, for any x, the integrand ϕ(θ; x) of the Craig representation of Q(x) can be partitioned into a pair of complementary convex and concave segments. As a consequence of this property, integrals of ϕ(θ; x) over arbitrary intervals within its convex region can be lower-bounded by Jensen’s inequality and upper-bounded by Cotes’ quadrature rule, with the opposite occurring for the concave region ϕ(θ; x). The combination of these complementary bounds yield a complete family of both lower and upper bounds on Q(x), which are expressed in terms of elementary transcendental functions and can be made arbitrarily tight by finer segmentation. A by-product of the method is that various other functions, such as the squared Gaussian Q-function Q2 (x), the 2D joint Gaussian Q-function Q(x, y, ρ), and the generalized Marcum Q-function QM (x, y), can also be both upper and lower ...
Giuseppe Thadeu Freitas de Abreu
Added 21 May 2010
Updated 21 May 2010
Type Conference
Year 2009
Where ICC
Authors Giuseppe Thadeu Freitas de Abreu
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