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2 results for “Gaussian Q-function”
Optimized Coefficients for the Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function with Optimized Coefficients," in<em> IEEE Communications Letters</em>, in press.</p> <p>The dataset contains the sets of the optimized coefficients for the novel GKL minimax approximations and bounds of the Gaussian Q-function, and the optimized coefficients for the GKL approximations in terms of the total error. The corresponding optimized coefficients are found up to 10 terms (N=10) for the two variations of the absolute error and for the relative error in terms of the minimax and the total errors.</p> <p>The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected optimization_criterion, error_type, number of terms, the bound or approximation type, and the variation. See help func_extract_coef for more information.</p> <p>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 minimax absolute error function which is shown by figure Example.jpg. Another example is given in the same script to extract the coefficients of the total relative error.<br> </p>
Coefficients for Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials
<p>This is a supplementary dataset for the publication:</p> <p>I. M. Tanash and T. Riihonen, "Global Minimax Approximations and Bounds for the Gaussian Q-Function by Sums of Exponentials," in <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 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.</p> <p>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.</p> <p>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.</p> <p> </p>
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