How to express square constraint, qu and H are variable.
You can use squae_pos(norm(...)).
The 2nd constraint can be handled moving the denominator to the LHS (i.e., multiplying both sides by the denominator), and using square_pos. Squares of scalar variables (or scalar elements) can be handled directly with ^2.
H[n] is a scalar variable. qu[n] is a scalar vector.
I presume you mean “vector”, not “scalar vector”. Anyhow, that is what I figured. So my guidance should be adequate for you to enter this in CVX.