The Degrees of Freedom of Two-Unicast Layered MIMO Interference Networks With Feedback

Abstract

Two-unicast layered interference networks under the Shannon feedback and limited Shannon feedback settings are studied from a degrees of freedom (DoF) perspective. The main focus is on the archetypal two-hop multiple-input, multiple-output (MIMO) $(M,N)\, \times \, (M,N) \,\times \, (M,N) $ network, denoted here as the $(M,N)^{3}$ network, which is a layered 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 MIMO Gaussian interference channels. In particular, the first transmitter–receiver pair and the first relay have $M$ antennas each and the second transmitter–receiver pair and the second relay having $N$ antennas each. The (full) Shannon feedback setting for the $(M,N)^{3}$ network is one in which the transmitters have delayed knowledge of the first and second hop channel coefficients and the relay and destination outputs and the relays have delayed knowledge of the second hop channel coefficients and destination outputs. The DoF region under this setting is established. A key result in this paper shows that this Shannon feedback DoF region can in fact be achieved with much less side information—under what we refer to as the limited Shannon feedback setting—wherein the transmitters have no channel state or output feedback whatsoever and only the $M$ -antenna relay (assuming $M \geq N$ ) has delayed knowledge of the coefficients of the second-hop channel and of only the received signal of the $N$ -antenna receiver. For this limited Shannon feedback setting, the DoFs region of the $(M,N)^{3}$ network is established by introducing a retro-cooperative interference alignment scheme. These DoF region results for the $(M,N)^{3}$ network with feedback are also extended to more general layered interference networks including the two-unicast $l$ -hop layered networks as well as layered networks with more general numbers of antennas at the various terminals.