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

<p>This is a supplementary&nbsp;dataset for&nbsp;the publication:</p> <p>I. M. Tanash and T. Riihonen, &quot;Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials,&quot; in&nbsp;<em>IEEE Transactions on Communications</em>, vol. 68, no. 10, pp. 6514-6524, Oct. 2020, doi: 10.1109/TCOMM.2020.3006902.</p> <p>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&nbsp;average symbol error probability (SEP) in optimal detection of 4-QAM&nbsp;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&nbsp;optimized coefficients are found up to twenty-five exponential terms with the right boundary of the finite interval on the x-axis&nbsp;(x_K+1) ranging from 1 to 10 in steps of 0.1 for the relative error.</p> <p>The Matlab function (func_extract_coef.m)&nbsp;extracts the required set of optimal coefficients from the provided dataset&nbsp;according to the selected error type, variation, number of terms and the right end-point in case of relative error. See help&nbsp;func_extract_coef for more information.</p> <p>A Matlab script (Example.m) is also provided as an example to illustrate&nbsp;the use&nbsp;of the provided&nbsp;Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding relative error&nbsp; which is shown by&nbsp;figure&nbsp;Example.jpg.</p> <p>&nbsp;</p>