Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials

This is a supplementary dataset for the publication:

I. M. Tanash and T. Riihonen, "Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials," in IEEE Transactions on Communications, vol. 68, no. 10, pp. 6514-6524, Oct. 2020, doi: 10.1109/TCOMM.2020.3006902.

The dataset contains the sets of the optimized coefficients for the novel minimax approximations and bounds of the Gaussian Q-function, its first four integer powers and for the case of average symbol error probability (SEP) in optimal detection of 4-QAM that is actually a polynomial of the Q-function. The proposed approximations and bounds have the form of a weighted sum of exponential functions. The corresponding optimized coefficients are found up to twenty-five exponential terms with the right boundary of the finite interval on the x-axis (x_K+1) ranging from 1 to 10 in steps of 0.1 for the relative error.

The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected error type, variation, number of terms and the right end-point in case of relative error. See help func_extract_coef for more information.

A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding relative error  which is shown by figure Example.jpg.