You can continue on your path, play around with things, and try to improve the SCA algorithm; or just use a non-convex solver, perhaps under YALMIP. Only you know thee reason why you’re trying to solve this problem using SCA, or trying to solve it at all. The goal of this forum is to help people solve convex optimization problems with CVX; the goal is not to ensure that whatever paper someone tries to replicate will lead to a publishable research paper or thesis.