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

TL;DR

This paper investigates the degrees of freedom in a multi-user parallel MISO broadcast channel with varying partial CSIT, establishing bounds and conditions for optimal separate coding strategies based on user orderings.

Contribution

It derives a sum-DoF upper bound dependent on average CSIT quality and proves its tightness under total order, showing separate coding is optimal in this scenario.

Findings

Sum-DoF upper bound depends on average CSIT quality.

Tightness of the bound is established under total order.

Separate coding over subchannels is optimal under total order.

Abstract

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.