I don’t know what is done with this stuff, once defined. Nor do I understand the symbols and conventions used. Are you applying real(....) everywhere it is needed? You can’t divide by a variable or CVX expression in CVX, but you can use inv_pos if you follow its rules (its argument must be concave, which includes affine as a special case of concave, and only makes sense if the expression to which it is applied is known to be positive).
Have you proven the problem is convex? That is the first step. Don’t answer that you have proven it is convex until you carefully read