Can anyone please help how to simulate closed form expression in Matlab?

How to simulate closed form expression in Matlab?

[Walter Roberson]

Please explain your question in more detail ?

[Dhawal Beohar]

Hi Walter! I am sharing my code below.

I want to calculate closed form for mu_o_fix. I have solved this mathematically and got equation (1) as final expression. Can please anyone help how to perform the simulation for closed form expression.

clc
clear all;

%Parameters defined
 
N_0=10^-11.4;                                                               
Xsr=1;                                                                      
Bmax=50;                                                                    
Bslot=3;                                                                
PmaxdB=[15];                                                                
Pmax=10.^(PmaxdB/10);                                                       
 
Qu=[-3:0.1:-1];
QoS_Component_u=10.^(Qu);

% Starting For Loop for QoS Component u  
  
for m=1:length(QoS_Component_u)
    u=QoS_Component_u(m);
% Starting For Loop for Expectation
    
    for n=1:100000                                                          % First Monte-Carlo Simulations  
 
% Equations for Rayleigh Fading h1
        hx1=(1/sqrt(2))*randn(1,1);
        hy1=(1/sqrt(2))*randn(1,1);
        h1=hx1.^2+hy1.^2; 
% Ending Rayleigh Fading h1                      
    end
    
% Ending Loop for Expectation 
        ee(m)=(-u*((Pmax*h1)+N_0)-h1);                                      %exponent expression
        mu_o_fix(m) = ((1/u)*log(ee(m))/(Pmax*u)+1);                   % equation (1)
        mu_o_fix_snr(m) = mu_o_fix(m)/N_0;
        mu_o_fix_dB(m)=10*log(mu_o_fix_snr(m))/log(10);
        mu_o_fix_dB_real(m) = real(mu_o_fix_dB(m));
end

[Walter Roberson]

?? You appear to already be doing numeric simulation of the system. I do not understand where the "closed form" comes in?

Are you trying to derive the expression mu_o_fix = ((1/u)*log(ee)/(Pmax*u)+1) symbolically ? If so then what are you starting with?

[Dhawal Beohar]

equation 1 is the closed expression i derived and now i want to simulate in Matlab. I don't know if this is the correct way i am doing.

[Dhawal Beohar]

i want to calculate closed form expression for the following equation:

; where

in Matlab.

Answer 1

[Walter Roberson]

Ten = sym(10);
N_0 = Ten^sym(-11.4);
PmaxdB = sym(15);
Pmax = Ten.^(PmaxdB/Ten);                                                       
syms gamma Qu
assume(Qu < 0)
QoS_Component_u = Ten.^(Qu);
u = QoS_Component_u;
Q = -1/u * log(int(exp(-u*(Pmax*gamma + N_0))*exp(-gamma), gamma, 0, inf));
Qs = simplify(Q);
disp(char(Qs))

(log(10*10^(1/2)*10^Qu + 1) + (10^(3/5)*10^Qu)/1000000000000)/10^Qu

disp(char(vpa(Qs,5)))

(log(31.623*10.0^Qu + 1.0) + 3.9811e-12*10.0^Qu)/10.0^(1.0*Qu)

[Dhawal Beohar]

Thank you Walter for your help.