The Loops in the first picture are required, the description is below

%% Suppose I have W and Theta, k=1:K .. K=(any value) let say 10 
%% 
                Alfa_k=zeros(1,k);
                Alfa_i=zeros(1,k);
                Angle_h_w=zeros(1,k);
                Angle_g_h_w=zeros(1,k);
                n0=zeros(1,k);
                
               for t_1=1:k
                   Alfa_k(t_1) = 1/(abs(H(t_1,:)*W(:,t_1)));
                    Angle_h_w(t_1) = angle(H(t_1,:)*W(:,t_1));
                   
                   Alfa_i(t_1) = 0;
                 for t_2=1:k
                     Alfa_i(t_1) = Alfa_i(t_1) + 1/(abs(H(t_2,:)*W(:,t_2)));
                 end
                     Alfa_i(t_1) = Alfa_i(t_1) - Alfa_k(t_1);  % Sum of Alfa_i
               end
               
               L_k = n*(Alfa_k./Alfa_i); % Number of IRS Elements Assigned to UE ..
                               % Total IRS Elements * Proportion of IRS Elements
                    
               r = n-(sum(L_k)); %The Remaining IRS Elements ..
                                 % Are Assigned to The Weakest UE
               [argvalue, argmax] = max(Alfa_k);
               L_k0=L_k(argmax);
               L_k0 = L_k0+r;
               
               
               [Alfa_m,idx]= sort(Alfa_k, 'descend'); % sort UE
               L_m = sort(L_k, 'descend');
               
               F = F(idx,:);  % sort the whole matrix using the sort idx
               W = W(:,idx);  % sort the whole matrix using the sort idx

               for t_3=1:k
                   n0(t_3)=(abs(F(t_3,:)*G*W(:,t_3)))

                   Angle_g_h_w(t_3) = angle(F(t_3,:)*G*W(:,t_3))

               end
               
                
               [argval, arg_max] = max(n0)
               Theta_k = -Angle_h_w-Angle_g_h_w

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Image Analyst]

Original question attached

%% Suppose I have W and Theta, k=1:K .. K=(any value) let say 10

%%

Alfa_k=zeros(1,k);

Alfa_i=zeros(1,k);

Angle_h_w=zeros(1,k);

Angle_g_h_w=zeros(1,k);

n0=zeros(1,k);

for t_1=1:k

Alfa_k(t_1) = 1/(abs(H(t_1,:)*W(:,t_1)));

Angle_h_w(t_1) = angle(H(t_1,:)*W(:,t_1));

Alfa_i(t_1) = 0;

for t_2=1:k

Alfa_i(t_1) = Alfa_i(t_1) + 1/(abs(H(t_2,:)*W(:,t_2)));

end

Alfa_i(t_1) = Alfa_i(t_1) - Alfa_k(t_1); % Sum of Alfa_i

end

L_k = n*(Alfa_k./Alfa_i); % Number of IRS Elements Assigned to UE ..

% Total IRS Elements * Proportion of IRS Elements

r = n-(sum(L_k)); %The Remaining IRS Elements ..

% Are Assigned to The Weakest UE

[argvalue, argmax] = max(Alfa_k);

L_k0=L_k(argmax);

L_k0 = L_k0+r;

[Alfa_m,idx]= sort(Alfa_k, 'descend'); % sort UE

L_m = sort(L_k, 'descend');

F = F(idx,:); % sort the whole matrix using the sort idx

W = W(:,idx); % sort the whole matrix using the sort idx

for t_3=1:k

n0(t_3)=(abs(F(t_3,:)*G*W(:,t_3)))

Angle_g_h_w(t_3) = angle(F(t_3,:)*G*W(:,t_3))

end

[argval, arg_max] = max(n0)

Theta_k = -Angle_h_w-Angle_g_h_w

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

Example with your second set of code. The array sizes are constructed to be consistent with your code

k = 5;
m = 3;
M = 7;
H = randi(9, k, M)

H = 5×7

6 7 4 5 2 8 4 6 1 6 7 2 1 9 8 9 7 6 7 5 1 2 3 7 6 1 1 6 6 4 7 4 3 4 8

W = randi(9, M, k)

W = 7×5

2 3 2 1 9 6 4 6 1 3 5 7 9 3 8 9 1 9 2 9 5 9 9 9 7 2 8 8 8 2 6 7 1 9 3

n = rand()

n = 0.0108

F = randi(9, k, m)

F = 5×3

2 4 5 2 9 4 7 7 8 5 3 5 2 5 2

G = randi(9, m, M)

G = 3×7

1 2 3 3 1 1 5 2 7 2 9 8 3 8 2 1 4 8 5 4 8

                Alfa_k=zeros(1,k);
                Alfa_i=zeros(1,k);
                Angle_h_w=zeros(1,k);
                Angle_g_h_w=zeros(1,k);
                n0=zeros(1,k);
                
               for t_1=1:k
                   Alfa_k(t_1) = 1/(abs(H(t_1,:)*W(:,t_1)));
                    Angle_h_w(t_1) = angle(H(t_1,:)*W(:,t_1));
                   
                   Alfa_i(t_1) = 0;
                 for t_2=1:k
                     Alfa_i(t_1) = Alfa_i(t_1) + 1/(abs(H(t_2,:)*W(:,t_2)));
                 end
                     Alfa_i(t_1) = Alfa_i(t_1) - Alfa_k(t_1);  % Sum of Alfa_i
               end
               
               L_k = n*(Alfa_k./Alfa_i); % Number of IRS Elements Assigned to UE ..
                               % Total IRS Elements * Proportion of IRS Elements
                    
               r = n-(sum(L_k)); %The Remaining IRS Elements ..
                                 % Are Assigned to The Weakest UE
               [argvalue, argmax] = max(Alfa_k);
               L_k0=L_k(argmax);
               L_k0 = L_k0+r;
               
               
               [Alfa_m,idx]= sort(Alfa_k, 'descend'); % sort UE
               L_m = sort(L_k, 'descend');
               
               F = F(idx,:);  % sort the whole matrix using the sort idx
               W = W(:,idx);  % sort the whole matrix using the sort idx

               for t_3=1:k
                   n0(t_3)=(abs(F(t_3,:)*G*W(:,t_3)))

                   Angle_g_h_w(t_3) = angle(F(t_3,:)*G*W(:,t_3))

               end

n0 = 1×5

1903 0 0 0 0

Angle_g_h_w = 1×5

0 0 0 0 0

n0 = 1×5

1903 2771 0 0 0

Angle_g_h_w = 1×5

0 0 0 0 0

n0 = 1×5

1903 2771 2025 0 0

Angle_g_h_w = 1×5

0 0 0 0 0

n0 = 1×5

1903 2771 2025 1674 0

Angle_g_h_w = 1×5

0 0 0 0 0

n0 = 1×5

1903 2771 2025 1674 3997

Angle_g_h_w = 1×5

0 0 0 0 0

               
                
               [argval, arg_max] = max(n0)

argval = 3997

arg_max = 5

               Theta_k = -Angle_h_w-Angle_g_h_w

Theta_k = 1×5

0 0 0 0 0

[Matthew Worker]

Thank you, but is the code that I wrote is compatible with the Loops and equation in the first picture because I think that there is something missing.

[Walter Roberson]

No, this code is incompatible. This code works. Your previous code did not work.

N = (6:10).^2; %Number of Elements IRS
K = 1:10; %Number of Single Antennas UE

Those are vectors.

for k = K
  for i=1:k
        G = complex(rand(K, N), rand(K,N)); % KxN Where gk = [g1;k; g2;k;....; gN;k] ..... gk is (1xN)
        %% 
        H_dk = complex(rand(K, M), rand(K,M)); % KxM Where  h_dk is (1xM)
    end

K and N are vectors, but you are trying to use them as sizes for rand()

The natural idea would be to try rand(K(i),N(i)) . Except that for i=1:k is not iterating over the length of K, since k = K tells MATLAB to iterate k over the content of K, not over the length of K. For example of K = [5, 10] then 1:k would be 1:5 and then 1:10, but K(i) would exceed matrix dimensions.

Supposing that you managed to escape from exceeding matrix dimenions (which can happen if you use rand(K(i),N(i)) and K is consecutive integers from 1), then notice that i has no role inside the loop: you generate random numbers k times, but only keep the last set of them.

You use H in your second set of code, but there is no H in your first set of code. It looks most likely that you would instead use HT rather than H

F = F(idx,:);  % sort the whole matrix using the sort idx
W = W(:,idx);  % sort the whole matrix using the sort idx

Those lines are from your second set of code.. but what is F in this context? I cannot match it to anything in the first code.

[Matthew Worker]

thank you again, do you know how to make this code compatible with the first picture, because that is the main problem for me.

[Walter Roberson]

No, I do not know how to make it compatible with the first picture. If I were coding it, I would start over without your existing code.