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

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

Answer 1

[Torsten]

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)