Note that \mathop{\textrm{Tr}}(AB)=\mathop{\textrm{Tr}}(BA) whenever the multiplication commutes. Therefore,$$\mathop{\textrm{Tr}}(w_1w_1^H+w_2w_2^H) =
\mathop{\textrm{Tr}}(w_1w_1^H)+\mathop{\textrm{Tr}}(w_2w_2^H)=
\mathop{\textrm{Tr}}(w_1^Hw_1)+\mathop{\textrm{Tr}}(w_2^Hw_2)=|w_1|_2^2+|w_2|_2^2.$$
So this constraint is equivalent to

sum_square_abs(w_1)+sum_square_abs(w_2) <= P_R.

If P_R is a constant, then itâ€™s a bit better to use norms instead: