  In the setting of the two-user broadcast channel, where a two-antenna
transmitter communicates information to two single-antenna receivers, recent
work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel
state information at the transmitter (perfect delayed CSIT) can be useful, even
in the absence of any knowledge of current CSIT. Similar benefits of perfect
delayed CSIT were revealed in recent work by Kobayashi et al., Yang et al., and
Gou and Jafar, which extended the above to the case of perfect delayed CSIT and
imperfect current CSIT.
  The work here considers the general problem of communicating, over the
aforementioned broadcast channel, with imperfect delayed and imperfect current
CSIT, and reveals that even substantially degraded and imperfect delayed-CSIT
is in fact sufficient to achieve the aforementioned gains previously associated
to perfect delayed CSIT. The work proposes novel multi-phase broadcasting
schemes that properly utilize knowledge of imperfect delayed and imperfect
current CSIT, to match in many cases the optimal degrees-of-freedom (DoF)
region achieved with perfect delayed CSIT. In addition to the theoretical
limits and explicitly constructed precoders, the work applies towards gaining
practical insight as to when it is worth improving CSIT quality.
