Retro-cooperative interference alignment and the DoF region of the (M,N)3 interference network with limited Shannon feedback

The (M,N)×(M,N)×(M,N) interference network (IN), denoted here as the (M,N)³ IN, is a layered, two-hop, two unicast network with two transmitters, two relays, and two receivers with the first hop network between the transmitters and the relays and the second hop network between the relays and the receivers both being multiple-input, multiple-output (MIMO) Gaussian interference channels, and with the first transmitter/receiver pair and the first relay having M antennas each and the second transmitter/receiver pair and the second relay having N antennas each. The setting of limited Shannon feedback is considered where the relay having no fewer antennas than the other is assumed to have delayed knowledge of the coefficients of the second-hop channel and of the received signal of the receiver with fewer antennas. Moreover, while both relays know the channels on the first hop instantaneously and the receivers know the channels on both hops, there is no channel state information at the transmitters (CSIT) whatsoever. For this limited Shannon feedback setting, the degrees of freedom (DoF) region is established by generalizing the retro-cooperative interference alignment (R-CIA) scheme introduced recently by the authors for the equal antenna case, i.e., when M= N. The DoF region thus obtained is also the DoF region for multi-hop (M,N)^l INs and under the more optimistic Shannon feedback assumption.