I understand that you want to plot the output of the attached integral function.
The main equation to focus on is Equation (20), which involves the expansion using the generalized Gauss-Laguerre quadrature.
You need to set up the necessary parameters, such as n, x_i, and H_i, using the information from the equations and any additional context you have.
Follow this script where I have taken example values:
% aber_analysis.m
% Define parameters
n = 10; % Example value for n
gamma = linspace(0, 40, 100); % Example range for gamma
% Pre-allocate ABER result
ABER = zeros(size(gamma));
% Calculate Laguerre polynomial roots and weights
[x_i, w_i] = laguerreL(n, 1/2); % Adjust as needed for generalized Laguerre
% Loop over gamma values
for idx = 1:length(gamma)
% Calculate the integral using Gauss-Laguerre quadrature
sum_terms = 0;
for i = 1:n
H_i = (gamma(i+1) * x_i(i)) / (n * (n+1) * laguerreL(n+1, x_i(i)))^2;
sum_terms = sum_terms + H_i * (1 - exp(-gamma(idx) / (2 * x_i(i))))^R;
end
ABER(idx) = (1 / (2 * sqrt(pi))) * sum_terms;
end
% Plot the results
figure;
semilogy(gamma, ABER, 'b-', 'LineWidth', 2);
xlabel('SNR (dB)');
ylabel('ABER');
title('ABER Performance Analysis');
grid on;
This is the output of the code I got:
I used the "R2021a" model to compute this, you can refer to the following documentation for more help:
Numerical Integration and Differential equation - https://www.mathworks.com/help/releases/R2021a/matlab/numerical-integration-and-differential-equations.html?
