possitive solution for set of three nonlinear eqations where t_1 t_2 and pi_2 are varaibles

Hi guys,

I have provided a code to solve a set of nonlinear equation where t_1, t_2 and Pi_2 are variables. We know all the variable should be positive.

for my case, I consider

Inputs Parameters

K = 4

K = 4

N = 1

N = 1

P_max = 2

P_max = 2

T = 2

T = 2

Noise_Prdb = -100

Noise_Prdb = -100

a= 1e-21

a = 1.0000e-21

BW = 10

BW = 10

epsilon = 0.0001

epsilon = 1.0000e-04

For different values of T, my code works but the solution is wrong becuase it gives me a similar values for t_1 which is impossible.

Could you please help me in this regard or give me an alternative to solve this set of equations.

Thank you inadvance

 
for q = 1:length(P_max)
    for r = 1:length(T)  
 Minimum1 = 0;
   P_3 = P_max(q);
   R_3 = BW*log2(1+(P_3*h_worst^2)/(BW*Noise_Pr));
   t_3 = L3/R_3;
   t_1 = 0.0001; 
   OP_Point = zeros(6,K);
   
   while t_1<T(r)-t_3
         Sum = 0;
         P_2 = zeros(1,K+1); 
         for i = K:-1:1
             Sum = Sum+P_2(1,i+1)*h(i);     
             t_2 = T(r)-t_1-t_3;
             P_2(1,i) = (2^(L2/(t_2*BW))-1)*(Sum+(BW*Noise_Pr))/(h(i)^2);
             if P_2(1,i)>0 && abs(P_max(q)*h(i)*t_1^3-P_2(1,i)*t_2*t_1^2-a*L1^3)<epsilon
                OP_Point(1,i) =  t_1; OP_Point(2,i) = t_1;  OP_Point(3,i) = t_2;
                OP_Point(4,i) =  t_3; OP_Point(5,i) = P_2(1,i); OP_Point(6,i) = P_3;
             else
                 t_1 = t_1 + 0.0001;
                 break
             end 
         end
         if nnz(OP_Point) == 6*K
            break
         end
   end
    end
end

Unrecognized function or variable 'h_worst'.

[Matt J]

What does the orange shading in your equations signify?

[Hossein Alishahi]

It means that they are constant!

It is notworthy to mention that m should be j. I just understood this typo!

[Matt J]

Your code is hard to unpack because you have included all kinds of extra lines which handle data set-up and display, and which have nothing to do with the solving the actual equations. You should show us just the part of your code dedicated to solving the equations. Additonal variables needed to run that part of the code can be attached in a .mat file.

[Hossein Alishahi]

Thank you for your comment.

Do you have any suggestion to solve this set of equations?

Here is the main part of code for solving th equations

for q = 1:length(P_max)

for r = 1:length(T)

P_3 = P_max(q);

R_3 = BW*log2(1+(P_3*h_worst^2)/(BW*Noise_Pr));

t_3 = L3/R_3;

t_1 = 0.0001;

while t_1<T(r)-t_3

Sum = 0;

P_2 = zeros(1,K+1);

for i = K:-1:1

Sum = Sum+P_2(1,i+1)*h(i);

t_2 = T(r)-t_1-t_3;

t_11(i) = t_1;

P_2(1,i) = (2^(L2/(t_2*BW))-1)*(Sum+(BW*Noise_Pr));

if P_2(1,i)>0 && abs(P_max(q)*h(i)*t_11(i)^2*t_1-P_2(1,i)*t_11(i)^2-a*L1^3)<epsilon

OP_Point1(1,i) = t_1; OP_Point1(2,i) = t_11(i); OP_Point1(3,i) = t_2;

OP_Point1(4,i) = t_3; OP_Point1(5,i) = P_2(1,i); OP_Point1(6,i) = P_3;

else

t_1 = t_1+0.0001;

break

end

end

if nnz(OP_Point1) == 6*K

break

end

end

end

end

Answer 1

[Torsten]

Solve the first equation for t_i2.

Solve the second equation for P_i2 and insert the expression for t_i2 from the first equation.

Both t_i2 and P_i2 now should only depend on t1.

Insert the expressions for both in the third equation.

I think you arrive at

Li2/(T-Li3/Ri3-t1) - log2(1 + (Pmax*hi*t1^3-a*Li1^3)*hi^2/(t1^2*(T-Li3/Ri3-t1))/(sum_{m>i}...)) = 0

This is one equation in one unknown.

Use fzero to solve for t1.

Insert t1 in the expressions for t_i2 and P_i2 to get these variables, too.