Doubt in solving nested integral
I have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciatedI have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciated I have a query regarding MATLAB code to plot SOP using analytical expression given by :
where
begin{equation}
begin{aligned}
Theta(u,y,v)
&= frac{1}{A_k(u,y,v)}
exp!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
– A_k(u,y,v)frac{1}{bar{gamma}} right. \
&quad left.
– lambda_U u – lambda_V v
right)
E_1!left(
frac{lambda_Y lambda_Z}{alpha A_k(u,y,v)}
right).
end{aligned}
end{equation}
Here is what i tried for code of SOP (analytical):
% This code is for analytical expression of SOP of user k
clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 1*1e5; % samples
t2 = 1e4;
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_ana = [];
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
accum = 0;
for iter = 1:t1
% Generate all RVs together
y = exprnd(1/lambda_Y);
u = exprnd(1/lambda_U);
v = exprnd(1/lambda_V);
% Gamma_e
Gamma_e = (beta * a(k) * u) / …
(u*D + alpha*y*v + (1/snr_eve));
% t(u,y,v)
t_val = (2^R(k))*(1 + Gamma_e) – 1;
% A_k
if beta*a(k) – t_val*D <= 0
continue;
end
A_k = (lambda_X * t_val) / (beta*a(k) – t_val*D);
% Theta
arg = (lambda_Y * lambda_Z)/(alpha*A_k);
Theta = (1/A_k) * …
exp(arg – A_k*(1/snr_user) …
– lambda_U*u – lambda_V*v) …
* expint(arg);
accum = accum + Theta;
end
SOP = 1 – (lambda_U * lambda_V * lambda_Y * lambda_Z / alpha) …
* (accum / t1);
SOP_ana = [SOP_ana SOP];
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_ana, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
The output of above code should match the simulation of SOP whose code is given by
% This code is for simulation expression of SOP of user k
%clc; clear all; close all;
%% Parameters
lambda_X = 1; % rate parameter of the exponential distribution
lambda_Y = 1;
lambda_Z = 1;
lambda_U = 1;
lambda_V = 1;
alpha = 0.1;
k = 1;
a1 = 0.1;
a2= 0.3;
a3 = 0.6;
a = [a1 a2 a3];
R1 = 0.1; % nearest
R2 = 0.2; % middle
R3 = 0.3; % farthest
R = [R1 R2 R3];
beta = 0.8;
t1 = 10*1e4; % samples
D = (1 – beta) + beta * sum(a(1:k-1));
SOP_sim = []; count = 0;
for snr_user_dB = 0:5:80
snr_user = 10^(snr_user_dB/10);
snr_eve_dB = 0; % in dB
snr_eve = 10^(snr_eve_dB/10);
for iter = 1:t1
X = exprnd(1/lambda_X); % mean is 1/lambda
Y = exprnd(1/lambda_Y);
Z = exprnd(1/lambda_Z);
U = exprnd(1/lambda_U);
V = exprnd(1/lambda_V);
Gamma_k = (beta * a(k) * X) / …
( X * D + alpha * Y * Z + (1/snr_user));
Gamma_e = (beta * a(k) * U) / …
( U * D + alpha * Y * V + (1/snr_eve));
if Gamma_k < ((2^R(k))*(1+Gamma_e)-1)
%if Gamma_k < (2^R(k)-1)
count = count + 1;
end
end
SOP = count / t1;
SOP_sim = [SOP_sim SOP];
count = 0;
end
snr_axis = 0:5:80;
figure;
%semilogy(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
plot(snr_axis, SOP_sim, ‘r-o’,’LineWidth’,1.5);
grid on;
xlabel(‘SNR (dB)’);
ylabel(‘SOP’);
title(‘SOP vs SNR’);
I am not getting what wrong i am doing in analytical SOP code…
Any help in this regard is highly appreciated for loop, mathematics MATLAB Answers — New Questions
