On the Achievable Degrees of Freedom of a K-User MIMO Interference Channel with a MIMO Relay

This paper investigates the achievable degrees of freedom (DoF) of a fully connected K-user multiple-input-multiple-output (MIMO) interference channel with a MIMO relay, where each transmitter (Tx) has M antennas and each receiver (Rx) has N antennas (K-user M × N channel). For the special case where M = N, previous works showed that even with the presence of relays, the sum DoF is still KM/2 and is achieved by interference alignment, assuming all Txs and Rxs have global channel state information (CSI). While this result showed that relays cannot increase the achievable DoF, we find that relay eliminates the CSI requirement at the Txs if global CSI is available at the relay. We propose a two-time-slot transmission scheme through which interference can be aligned, provided that the relay has enough antennas. We obtain the minimum number of antennas required at the relay for each Tx-Rx pair to achieve the maximum DoF and this number is less than that needed in the decode-and-forward approach and all other reported approaches in existing literature. Moreover, this can be achieved with just linear processing at the relay. Then the interference alignment based scheme is generalized to M ≠ N case, where we focus on the achievable symmetric DoF. A lower bound for the number of antennas required at the relay is derived and is shown to be tight in some cases.