Hi

I am regenerating the results of a paper published in IEEE transactions in wireless communications where they used CVX to solve a convex optimization problem. They are minimizing the following function

Minimize

log_2 (1+\frac{\alpha}{b^H X b +1})+ \lambda. tr(X)

S.T.:

X is a postive semi-definite matrix (covariance matrix).

where \alpha and \lambda are constant scalars. and b is a constant vector.

The above problem is convex. Since X is positive semi-definite, therefore b^H X b > 0.

I tried many ways to formulate this problem using CVX. However, none of them succeeded. e.g.

cvx_begin

variable X(N,N) complex semidefinite

expression summation

summation=summation+log(1+alpha*inv_pos(b’ Xb+1))/log(2)
minimize(summation+lmda*trace(X) )

cvx_end

But I obtain the following error

Error using cvx/log (line 64)

Disciplined convex programming error:

Illegal operation: log( {convex} ).

The authors mentioned that they used CVX to solve this problem. So, I am sure it can be implemented using CVX. Can someone help?

Thanks