Rate-Memory Trade-Off for the Cache-Aided MISO Broadcast Channel with Hybrid CSIT

One of the famous problems in communications was the so-called "PN" problem in the Broadcast Channel, which refers to the setting where a fixed set of users provide perfect Channel State Information (CSI) to a multi-antenna transmitter, whereas the remaining users only provide finite-precision CSI or no CSI. The Degrees-of-Freedom (DoF) of that setting were recently derived by means of the Aligned Image Set approach. In this work, we resolve the cache-aided variant of this problem (i.e., the "PN" setting with side information) in the regime where the number of users providing perfect CSI is smaller or equal to the number of transmit antennas. In particular, we derive the optimal rate-memory trade-off under the assumption of uncoded placement and characterize the same trade-off within a factor of 2.01 for general placement. The result proves that the "PN" impact remains similar even in the presence of side information, but also that the optimal trade-off is not achievable through independently serving the two sets of users.