When using integral function to calculate MeijerG function, Matlab will get stuck.

Question

Sicong 2024-4-8

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https://ww2.mathworks.cn/matlabcentral/answers/2104376-when-using-integral-function-to-calculate-meijerg-function-matlab-will-get-stuck

回答： Torsten 2024-4-8

采纳的回答： Torsten

在 MATLAB Online 中打开

When using integral function to calculate MeijerG function, Matlab will get stuck.

Does anyone have same problem?

How can I figure that?

alpha_value = 4.399688384728341;
beta_value = 2.571722827839187;
g_value = 0.749154464911330;
A0 = 0.1172;
hl = 0.9033;
Pt = 3.1632;
Energy_Efficiency = 0.5;
h_rain = 1;
N0 = 1.0e-07;
function pdf = pdf_of_ht(ht, alpha_value, beta_value, g_value, A0, hl)
pdf = alpha_value * beta_value * (g_value^2) / (A0 * hl) / ...
    (gamma(alpha_value) * gamma(beta_value)) * ...
    meijerG([], [g_value^2], [g_value^2 -1], [alpha_value - 1, beta_value - 1], (alpha_value * beta_value * ht) / (A0 * hl));
end
function pdf = pdf_of_SNR(SNR, alpha_value, beta_value, g_value, A0, hl, Pt, Energy_Efficiency, h_rain, N0)
h_to_SNR = 2 * Pt^2 * Energy_Efficiency^2 * h_rain^2 / N0^2;
ht = sqrt(SNR ./ h_to_SNR);
pdf = pdf_of_ht(ht, alpha_value, beta_value, g_value, A0, hl) .* (1 ./ (2 .* sqrt(SNR * h_to_SNR)));
end
function ber = ber_func(x)
ber = 0.5 * erfc(sqrt(x) / sqrt(2));
end
% Get stuck on the following line
average_ber = integral(@(SNR) ber_func(SNR) .* pdf_of_SNR(SNR, alpha_value, beta_value, g_value, A0, hl, Pt, Energy_Efficiency, h_rain, N0), 0, Inf, 'RelTol',1e-3, 'AbsTol',1e-6);

Thanks a lot

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Answer 1

Torsten 2024-4-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2104376-when-using-integral-function-to-calculate-meijerg-function-matlab-will-get-stuck#answer_1438341

在 MATLAB Online 中打开

meijerG has a division by 0 at SNR = 0. If you are sure the integral exists at SNR = 0, start with a small value > 0, e.g.

average_ber = integral(@(SNR) ber_func(SNR) .* pdf_of_SNR(SNR, alpha_value, beta_value, g_value, A0, hl, Pt, Energy_Efficiency, h_rain, N0), 1e-8, Inf)