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.Comment: Submitted to Transactions on Information Theory - November 2012 18
double column page