Can feedback increase the degrees of freedom of a wireless network with delayed CSIT?

There is no known network with instantaneous channel state information at the transmitters (CSIT) for which (output) feedback enhances the degrees of freedom (or the signaling dimensions) of the network. In this paper, we show that the DoF of wireless networks with delayed CSIT however, can increase with output feedback. This result is shown by obtaining the degrees of freedom (DoF) region for the multiple- input multiple-output (MIMO) fast fading interference channel (IC) with an arbitrary number of antennas at each node, under the Shannon feedback setting wherein the channel matrices (i.e., the channel state) and the channel outputs are available at the transmitters with a finite delay. While for most numbers of antennas at the four terminals, it is shown that the DoF region with Shannon feedback is the same as the DoF region with just delayed CSIT, it is shown that this is not always the case. For a specific class of MIMO ICs characterized by a certain relationship between the numbers of antennas at the four nodes, the DoF region with Shannon feedback is strictly bigger than the DoF region with just delayed CSIT. To realize these DoF gains attainable with Shannon feedback, a new retrospective interference alignment scheme is developed wherein transmitter cooperation made possible by output feedback in addition to delayed CSIT is employed to effect a more efficient form of interference alignment than feasible with previously known schemes that require just delayed CSIT.