I haven’t really tried to decipher what the problem is, but even assuming that the trig functions are just input data and do not involve optimization variables, it looks like there are products of variables inside an absolute value or norm, which would not satisfy CVX’s rules, and is unlikely to be convex.
Do you have a proof that this problem is convex? I will assume it is not. And if it is not, you should stick with non-convex optimization tools and solvers.