Hello, I’m trying the sum-rate maximization problem in CVX. So far I was able to implement my problem in CVX without SINR constraints.

However, still, I’m struggling to write the following constraint in CVX. Can someone help me to write this in CVX?

The constraint is attached. The variable is vec(w).

It is not a convex constraint, so it can’t be expressed with CVX. For example, when `f1=0`

, it becomes a form of `square norm>=a constant`

, which is not convex.

Thank you for your comment. Yes, I do understand that this is not convex constraint. Is there any method to make it convex?

I don’t know if there’s a way. I saw people handling SINR constraints by treating it as difference of convex function (DC Program？)， which means you can move your denominator to the right, and then move everything to the right, it will become a DCP. Then it is handled by convex approximation, replacing the second convex function with its taylor first-order expansion.

I don’t know how (or if at all) your problem can be fit in this form, but the typical approach to SINR modeling is via geometric programming (GP)

Like I said your model looks more complicated so it is possible what I said makes no sense, or that you need some more clever reformulation of the whole problem, not just the one constraint.

I have tried the method you suggested before (I mean DCP). But, it did not work here. Anyway, thanks for your comment.