MISO Broadcast Channel with Delayed and Evolving CSIT
  The work considers the two-user MISO broadcast channel with gradual and delayed accumulation of channel state information at the transmitter (CSIT), and addresses the question of how much feedback is necessary, and when, in order to achieve a certain degrees-of-freedom (DoF) performance. Motivated by limited-capacity feedback links that may not immediately convey perfect CSIT, and focusing on the block fading scenario, we consider a progressively increasing CSIT quality as time progresses across the coherence period (T channel uses - evolving current CSIT), or at any time after (delayed CSIT).   Specifically, for any set of feedback quality exponents a_t, t=1,...,T, describing the high-SNR rates-of-decay of the mean square error of the current CSIT estimates at time t<=T (during the coherence period), the work describes the optimal DOF region in several different evolving CSIT settings, including the setting with perfect delayed CSIT, the asymmetric setting where the quality of feedback differs from user to user, as well as considers the DoF region in the presence of a imperfect delayed CSIT corresponding to having a limited number of overall feedback bits. These results are supported by novel multi-phase precoding schemes that utilize gradually improving CSIT.   The approach here naturally incorporates different settings such as the perfect-delayed CSIT setting of Maddah-Ali and Tse, the imperfect current CSIT setting of Yang et al. and of Gou and Jafar, the asymmetric setting of Maleki et al., as well as the not-so-delayed CSIT setting of Lee and Heath. 
Jinyuan Chen and Petros Elia
cs.IT math.IT