Semidefinite matrix as a constraint

it appears that you are trying to constrain the LHS to be psd,i.e., in spd mode. The inclusion of x*x', with x a decision variable, makes that a BMI (Bilinear Matrix Inequality), which is non-convex, and can’t be handled with CVX.

The only semidefinite constraints which are convex, and which CVX can handle, are affine (linear) in the decision variables.