Dear experts,

I am new with CVX and cannot understand the point:

Here is my original problem(about communication channel capacity):

I have to find the Best S(matrix) to maximize 𝑙𝑜𝑔|𝑰+𝑯𝑺𝑯^𝐻 |

subject to trace(GSG^𝐻)>=specific value (4.8933e-04W)

trace(S)<=1(transmit power W)

S>=0(semidefinite matrix)

(*G and H matrix are channels)

Hre is my code:

```
s_p3 = randn(4,4);
nRx =4;nTx = 1
H_p3 = 1/sqrt(2)*sqrt(1e-4)*(randn(nRx,nTx)+1i*randn(nRx,nTx));
G_p3= (1/sqrt(2))*sqrt(1e-8)*(randn(nRx,nTx)+1i*randn(nRx,nTx));
cvx_begin
variable s_p3(4,4) semidefinite
maximize((log_det(eye(r)+H_p3*s_p3*H_p3'*1e10))*bandwidth )
subject to
trace(G_p3*s_p3*G_p3') == 4.8933e-04
trace(s_p3) <= 1%P
%s_p3>=0
cvx_end
cvx_optval
```

However, the result is Status: Unbounded

Optimal value (cvx_optval): +Inf

I feel very strange because I went to check this term trace(G_p3*s_p3*G_p3’) and found that this condition was not met(far less than the value I gave)

Ask the experts to help me,

Thanks!