The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.