The Degrees of Freedom Regions of Two-User and Certain Three-User MIMO   Broadcast Channels with Delayed CSIT
  The degrees of freedom (DoF) region of the fast-fading MIMO (multiple-input multiple-output) Gaussian broadcast channel (BC) is studied when there is delayed channel state information at the transmitter (CSIT). In this setting, the channel matrices are assumed to vary independently across time and the transmitter is assumed to know the channel matrices with some arbitrary finite delay. An outer-bound to the DoF region of the general $K$-user MIMO BC (with an arbitrary number of antennas at each terminal) is derived. This outer-bound is then shown to be tight for two classes of MIMO BCs, namely, (a) the two-user MIMO BC with arbitrary number of antennas at all terminals, and (b) for certain three-user MIMO BCs where all three receivers have an equal number of antennas and the transmitter has no more than twice the number of antennas present at each receivers. The achievability results are obtained by developing an interference alignment scheme that optimally accounts for multiple, and possibly distinct, number of antennas at the receivers. 
Chinmay S. Vaze and Mahesh K. Varanasi
cs.IT math.IT