Simple and accurate approximations for marcum Q-function - Feng, Lin (Nanyang Technological University, 2023)
In this project, the computation of the Marcum Q-function is the focus. The function computes the probability that x is greater than a constant R, where x is the distance from a point in a 2-dimensional plane to the origin when the 2 Cartesian coordinates of x are independent Gaussian random variables. The Marcum Q-function is an important function used in radar detection, signal processing and communications. However, the integral in this function cannot be evaluated in terms of ordinary functions. We will first confirm four numerical calculation methods and five boundary pairs used in the literature. After a comprehensive analysis of their computational accuracy and time efficiency, we will recommend good approximations for different ranges and designed accuracy requirements. Finally, the comprehensive performance of the recommended algorithm is analyzed. It also illustrates the shortcomings of this method to the underflow problem and puts forward an outlook for future research. Keywords: Marcum Q-function, numerical calculation methods, boundary pairs, approximations