On the DoF of Parallel MISO BCs with Partial CSIT: Total Order and Separability

We study the degrees of freedom (DoF) of a $K$-user parallel MISO broadcast channel with arbitrary levels of partial CSIT over each subchannel. We derive a sum-DoF upperbound which depends on the average CSIT quality of each user. This upperbound is shown to be tight under total order, i.e. when the order of users with respect to their CSIT qualities is preserved over all subchannels. In this case, it is shown that separate coding over each subchannel is optimum in a sum-DoF sense.