Since you mentioned before, h \overline{R} =(h_0r_0 - h_1r_1) + (h_0r_1 + h_1r_0) i, it can be seen as a complex vector where the real part is (h_0r_0 - h_1r_1) and the imaginary part is (h_0r_1 + h_1r_0), and the Euation (6) is the regularizer.
But why in your code the ||h \overline{R}||_2^2 = h^2 * r^2 = (lhs[0] ^ 2 + lhs[1] ^ 2) * (rel[0] ^ 2 + rel[1] ^ 2) = (h_0 ^2 + h_1 ^ 2) * (r_0 ^ 2 + r_1 ^ 2)
Since h \overline{R} is a new complex vector, where the real part is (h_0r_0 - h_1r_1) and the imaginary part is (h_0r_1 + h_1r_0), are you sure that its L2 norm's square ||h \overline{R}||_2^2 = (h_0 ^2 + h_1 ^ 2) * (r_0 ^ 2 + r_1 ^ 2)= ||h||_2^2 * ||r||_2^2 ?
Did I misunderstand anything about the L2 norm of a complex vector?