Coefficients for Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals

This is a supplementary dataset for the publication:

I. M. Tanash and T. Riihonen, "Tight Logarithmic Approximations and Bounds for Generic Capacity Integrals and Their Applications to Statistical Analysis of Wireless Systems," in IEEE Transactions on Communications, 2022, doi: 10.1109/TCOMM.2022.3198435.

The dataset contains the sets of optimized coefficients for the novel minimax approximations of the Nakagami and lognormal capacity integrals in terms of absolute error. The proposed approximations have the form of a weighted sum of logarithmic functions. The optimized coefficients are found for a wide range of the corresponding fading parameters, namely m for the Nakagami capacity integral and σ (standard deviation) for the lognormal capacity integral. Please note that the optimized coefficients in the provided dataset for the lognormal capacity integral are calculated for σdB (standard deviation in decibels) so σ=0.1 log_e(10) σdB in Eq. 5.

The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected capacity integral, the parameter's value, and the number of terms. See help func_extract_coef for more information.

The Matlab script (general_any_func) implements the theory presented in the corresponding journal paper: More specifically, it implements solving Eq. 22 to calculate the optimized coefficients of Eq. 7 for the Nakagami capacity integral. The code also provides general comments on how to generalize it to obtain the optimized coefficients of any communication system in terms of absolute error. Number of supplementary Matlab functions (general_any_func, func_abs_gen_any_func, calc_d_gen, calc_Cappr_gen, calc_d_gen_derivative, calc_Cappr_gen_derivative, Gauss_Laguerre, and peakseek) are provided herein and are used in the main Matlab script.

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