Do you have a proof that the constraint is convex (some kind of second order cone thing?)? I will presume it is non-convex unless you show otherwise, in which case the non-convex designation will be removed (edit: the non-convex designation has now been removed).

Per the CVX Users’ Guide and Why isn’t CVX accepting my model? READ THIS FIRST! , you are not allowed to enter the constraint as you have. And if it is somehow convex, reformulation will be required for entry into CVX.

Even presuming the joint convexity proof (in the transformed variables) is correct, there is no concrete formulation provided in a form suitable for entry into CVX. I suggest you contact the authors and request them to provide you with their CVX code and allow you to post if here for the benefit of forum readers.