The degrees of freedom of the 2×2×2 interference network with delayed CSIT and with limited Shannon feedback

The 2×2×2 interference network, which is a layered two-hop, two-user interference channel, consists of two transmitters, two relays, and two receivers with both the first hop network between the transmitters and the relays and the second hop network between the relays and the receivers being i.i.d. Rayleigh fading Gaussian interference channels. Two feedback models are studied. In the first one, called the delayed channel state information at the transmitters (delayed CSIT) model, the transmitters are assumed to know the first and second hop channel coefficients with a finite delay but the relays have no side information whatsoever. In the second feedback model, referred to as the limited Shannon feedback model, one of the two relays knows the first and second hop channel coefficients with a finite delay and the received signal of one of the receivers with a finite delay and the other relay and the transmitters have no side information whatsoever. It is shown in this paper that under both these settings, the 2×2×2 interference network has 4/3 degrees of freedom. The result is obtained by developing a broadcast- channel-type upper-bound and two new achievability schemes termed retro-cooperative interference alignment. Generalizations of the results are provided for networks with multiple but fully-connected layers, multiple relays per layer, and M -antenna source and destination terminals with the total number of antennas at the relays being no less than 2M.