```
clear on
clc
% Initialization
Nr = 6;
Nt = 1;
device_num = 3;
gamma = randn(device_num);
alpha = 1;
h = [];
for j = 1:1:device_num
h(:,j) = randn(Nr, Nt) + 1i*randn(Nr, Nt);
m = h(:,j);
M = m*m';
end
% subgradient M
v = max_eig(M);
sg_M = v*v';
X = randi([0, 5], device_num, 1);
x_sg = X;
% calculate k-norm
X = sort(X,'descend');
k_norm = 0;
device_index = 0;
number_k = 0;
I = 0;
for k = 1:1:length(X)
k_norm = k_norm + X(k);
if norm(X,1) == k_norm
number_k = k;
break;
end
end
% subgradient X
for j = 1:1:length(X)
abs(X(j));
abs(X(number_k));
if abs(X(j)) >= abs(X(number_k))
value = sign(X(j));
else
value = 0;
end
x_sg(j,1) = value;
end
% I
for i = 1:1:device_num
h_hermitian = h';
if real(trace(M)) - real(gamma(i)*h_hermitian(i,:)*M*h(:,i)) <= X(i) && (real(trace(M)) >= 1) && all(X(:) > 0)
I = 0;
else
I = 100000000;
end
end
cvx_begin
variable X(device_num, 1)
variable M(Nr, Nr) complex semidefinite
minimize norm(X,1) + real(trace(M)) + I + alpha/2*(norm(X,2) + real(norm(M,2))) - ( trace(x_sg'*X) + alpha*trace(norm(X,2)) + real(trace(sg_M'*M)) + alpha*real(norm(M,2)) )
subject to
for i = 1:1:device_num
real(trace(M)) - real(gamma(i)*h_hermitian(i,:)*M*h(:,i)) <= X(i);
X(i) >= 0
end
real(trace(M)) >= 1;
cvx_end
```

function value = max_eig(M)

```
[x,y] = eig(M);
eigenvalue = diag(y);
lamda = max(eigenvalue);
for i=1:length(M)
if lamda == eigenvalue(i)
break;
end
end
y_lamda = x(:,i);
value = y_lamda;
```

end

Hi, could anyone help me find out why matlab keeps sending me following error :

Disciplined convex programming error:

Illegal operation: {convex} - {convex}

- ( trace(x_sg’
*X) + alpha*trace(norm(X,2)) + real(trace(sg_M’*M)) + alpha*real(norm(M,2)) )

This part has some problem, but I do not know why ? Thanks.