How to deal with the product of column vector and its conjugate transpose?

The constraint in your CVX code is non-convex, because the inequality is going the wrong direction to be convex. concave >= affine is convex. convex <= affine is convex. The reverse direction nequalities are non-convex.

I can’t say for sure that (c1) is non-convex because I’m not clear on what are optimization variables and what’s input data. That’s for you tro figure out.

Before trying to use CVX, you should read the CVX User’s Guide. Perhaps you should also study the first several chapters of Convex Optimization – Boyd and Vandenberghe .

Start by carefully reading Why isn't CVX accepting my model? READ THIS FIRST! which you either didn’t do or didn’t understand when I posted the link earlier.