How to maximize achievable Rate for spectrum sharing in MIMO?

Hi @Nasrin ,

After analyzing your error you encountered regarding cvx_begin, I did some research and find out that you probably need to make sure that the CVX package is correctly installed and initialized in your MATLAB environment.

CVX installation instructions

Download the CVX package from

https://cvxr.com/cvx/download/

Unzip the downloaded files into your directory then add the CVX folder to your Matlab path using:

   addpath('path_to_cvx_directory');

Afterwards, initialize CVX by running the command:

   cvx_setup;

This command will set up CVX and check for any missing components.

Update Code

Here’s an updated version of your code with additional checks for clarity and error handling:

% Define constants

Ns = 4; % Number of secondary users

Ms = 20;

Nup = 200; % value for Nup

Nt = 12; % value for Nt

Np = 200; % value for Np

sigma2_dBm = -104; % Noise power in dB

tilde_P2_dBW = 20; % Maximum power constraint for secondary users

xi_k = rand(Ns, 1); % Example values for xi_k, replace with actual values

hat_zeta1_l = rand(Np, 1); % Example values for hat_zeta1_l, replace with 
actual values

% Convert dB to linear

tilde_P2 = 10^(tilde_P2_dBW/10);

sigma2 = 10^(sigma2_dBm/10 - 3);  % Convert dBm to mW then to W

% Initialize CVX optimization

cvx_begin quiet

    variables P2(Ns,1) W2(Ms,Ns)

    expression gamma_2k(Ns)

    expression log_terms(Ns)

     % Calculate gamma_2k and log terms

     for k = 1:Ns

        gamma_2k(k) = P2(k) / (sigma2 * square_pos(W2(k)));

        log_terms(k) = log(1 + gamma_2k(k));

      end

      % Objective function

       maximize((Nup - Nt) / Nup * sum(log_terms))

      % Constraints
       subject to

        for k = 1:Ns

            0 <= P2(k) <= tilde_P2 / Ns;

            for l = 1:Np

                sum(P2(k) .* xi_k) <= hat_zeta1_l(l);

            end

        end

cvx_end

% Check if optimization was successful

    if strcmp(cvx_status, 'Solved')

    disp('Optimization successful!');

else

    disp('Optimization failed!');

end

In the code, you will see the addition of a check on cvx_status which allows you to identify whether the optimization was successful. Also, make sure that square_pos is defined elsewhere in your code or replace it with a suitable function if it's not recognized and when you are working with larger datasets or more complex models, consider optimizing your constraints or objective function further to improve performance.

Hope this helps. Please let us know if you have any further questions.