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

CVX does not allow the formation of that product.

However, depending on what you want to do with the resulting covariance matrix, there may be a way to accomplish that without explicitly forming the covariance matrix. For instance,x'*w*w'*x = square_pos(norm(w'*x)), which will be accepted by CVX (presuming w is a CVX variable and x is input data). And if that term appears by itself in the objective function. there is no need to apply square_pos.