Problem in Gamma Gamma Distribution PDF of FSO Channel with Strong Atmospheric Turbulence

I am working on FSO channel with strong atmospheric turbulence. This is the code of PDF of Gamma-Gamma Distribution. I am having problem with Bessel Function Graph. Thus my PDF graph is not according to what it should be.

These are the graphs of Gamma-Gamma Distribution and Bessel Function respectively. (PDF vs Irradiance (dB ) & Bessel funct vs Irradiance (dB) )

Can anyone please help me find out what is wrong in my code???

The actual Graph of Gamma-Gamma PDF and its eqn:

%% Parameters & Functions
Rb=10e9; % Data Rate 
B=2e10 ;% Bandwidth 
Lam=1550e-9; % Wavelength
Rd=0.85; %Responsivity
Cs=1e-14; % Refractive Index Parameter for strong turbulence
e=1.6023e-19; % charge of electron 
K=1.38e-23;
Rl=50; % Load Resistance
T=300; % Temperature 
a= 10^(0.02)*1e-3;  %Attenuation Coeff

sigma2= @(x)       (1.23*Cs*((2*pi/Lam)^(7/6))*x.^(11/6)); % Ryotov Variance
alp= @(x)          (exp((0.49*sigma2(x))./(1+1.11*(sigma2(x)).^(6/15)).^(7/6))-1).^(-1); % PDF parameter alpha
beta= @(x)         (exp((0.51*sigma2(x))./(1+0.69*(sigma2(x)).^(6/15)).^(5/6))-1).^(-1); % PDF parameter beta
Bess= @(I,x)       besselk((alp(x)-beta(x)),(2*sqrt(alp(x)*beta(x)*I)),1); % modified bessel function of 2nd kind, order = alpha-beta 
Gam=@(x)           gamma(alp(x))*gamma(beta(x)); % Gamma function of alpha and beta
albe=@(x)          (alp(x)+beta(x))/2;
PDF= @(I,L)        (2*((alp(L).*beta(L)).^(albe(L))).*(I.^((albe(L)-1))).*Bess(I,L))/Gam(L);  % PDF of Gamma-Gamma Distribution

IdB=linspace(-40,40,70); % Irradiance in dB
I=10.^(IdB/10); % Irradiance
L=[4000]; % Link range 4km

figure(1); lw =1.5; 
plot(IdB,Bess(I,L(1)),'-o','LineWidth',lw);
plot(IdB,PDF(I,L(1)),'-o','LineWidth',lw);

[Natasha Pawar]

sir ,what does @(x) in the following line indicates:

sigma2= @(x) (1.23*Cs*((2*pi/Lam)^(7/6))*x.^(11/6)); % Ryotov Variance

[Atrolita afra]

function of x

[Shivangi Shah]

how to plot Irradiance?

Answer 1

[Ayhan Yenilmez]

Your Bessel function must be like this

Bess= @(I,x) besselk((alp(x)-beta(x)),(2*sqrt(alp(x)*beta(x)*I)));

And don't use Irradience in dB, use linear like this

I=0.01:0.01:5;

Finally, use L<=3000 (channel has very strong turbulence for 4km with this parameters), (or change Cs)

L=3000; % or less than 3000 for reducing sigma2

figure(1); lw =1.5;

plot(I,PDF(I,L(1)),'-o','LineWidth',lw);

Answer 2

[Akhtar Saeed]

Dear RUHIN CHOWDHURY,

Could you please share the paper title you are looking into, for "The actual Graph of Gamma-Gamma PDF and its eqn:"?

Many thanks in advance.