Simple and accurate closed-form expressions for Gaussian Q-function

• Main Author: Lei, Hao
• Other Authors: Li Kwok Hung
• Format: Theses and Dissertations
• Language: English
• Published: 2018
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: http://hdl.handle.net/10356/76024
• Institution: Nanyang Technological University

Gaussian functions can be found in the fields of natural science, social science, mathematics and engineering. This type of functions does not have a closed form. It is very difficult to handle mathematically due to its non-elementary integral form which cannot be expressed as a finite composition of simple mathematical functions. For this reason, the development of approximations and tight bounds for the Q -function is quite significant. Generally speaking, researchers may use one acceptable approximation to replace the exact Gaussian integral because that it would take much more time to do the integration, provided that this approximation function performs well. However, depending on different conditions, researchers may choose an approximation according to the actual condition. According to the Gaussian Q -function application requirements this report provided approximation selection scheme, and compared several approximations of the Gaussian Q -function with figures, tables, relative errors, and other aspects. When designing the entire comparison process, the functional modules of the application are considered, and the process is finished through MATLAB simulation. The simulation results in terms of figures and tables, to show the accuracy of approximation functions are talked in Chapter 3, while the applications of the approximation function, such as simulation design of BPSK, QAM modulation are talked in Chapter 4. This report also demonstrated some important codes in Chapter 4. After the simulation part , the conclusion and recommendation in future work are given.