A flexible method to approximate Marcum Q-function based on geometric way of thinking

Geometrical approaches used in Marcum Q-function have been successfully applied in former works to find its bounds. However, this bound is still not tight enough for mainly two reasons: first, those approximations contain only two different radiuses of arcs; second, the approximation is restricted at the form of circle whose radius is a constant, while the radius varies continuously with the direction. In this paper, we have two main aims: first, we want to have a deeper analytical reasoning on why the geometrical way works; second, we try to solve those two drawbacks and propose two new methods based on that. We test our new results on the Marcum Q-function and gain some very promising results.