I don’t see \chi anywhere explicitly in the objective function. Do some of the symbols in the objective function depend on \chi? We are not mindreaders, so you’ll have to tell us. Or perhaps \chi only appears in constrains (if there are any) which you haven’t shown?
Presuming that everything other than the stated optimization variables are input data, which I don’t know to be true, the log term can be entered essentially “as is” except for using log(...)/log(2) instead of log2.
As for the term in the <...,...>, is that trace of inner product? Is the \partial some kind of gradient operator I have no idea, so you have to be very explicit about all of it. I have no idea what superscript (n) means. Make sure you thoroughly understand exactly what the objective function is, to include the answers to all my questions. It will not serve you well to lift an optimization problem statement from a book or paper without thoroughly understanding it. That would be true no matter what optimization tools you used. Given your use of CVX, you have the extra obligation of proving your optimization problem is convex Given my lack of understanding of what your problem is, I don’t know whether it is convex, but you need to.