A MIMO Relay with Delayed Feedback Can Improve DoF in $k$-User MISO Interference Channel with No CSIT

This paper studies the impact of a multiple-input-multiple-output (MIMO) relay on the K-user multiple-input-single-output (MISO) interference channel (IC) when the relay has delayed feedback (i.e., delayed channel state information (CSI) or delayed channel output feedback) from each receiver, yet each transmitter has no knowledge about CSI. We first develop a new relay-aided retrospective interference alignment (r-RIA) and characterize the optimal sum degrees of freedom (DoFs) for the K-user MISO IC with a MIMO relay by providing a new matching outer bound. It is shown that the sum DoF does not decrease, even in the absence of direct links between transmitters and receivers, as long as K is sufficiently large. We next show that a MIMO relay can provide a sum-DoF gain in the K-user MISO IC with delayed feedback to the relay in the absence of CSI at transmitter (CSIT), whereas relaying is shown to be not useful with instantaneous CSIT from the DoF perspective.