  This paper characterizes the degrees of freedom (DoF) regions for the
multi-user vector broadcast channel with periodic channel state information
(CSI) feedback. As a part of the characterization, a new transmission method
called space-time interference alignment is proposed, which exploits both the
current and past CSI jointly. Using the proposed alignment technique, an inner
bound of the sum-DoF region is characterized as a function of a normalized CSI
feedback frequency, which measures CSI feedback speed compared to the speed of
user's channel variations. One consequence of the result is that the achievable
sum-DoF gain is improved significantly when a user sends back both current and
outdated CSI compared to the case where the user sends back current CSI only.
Then, a trade-off between CSI feedback delay and the sum-DoF gain is
characterized for the multi-user vector broadcast channel in terms of a
normalized CSI feedback delay that measures CSI obsoleteness compared to
channel coherence time. A crucial insight is that it is possible to achieve the
optimal DoF gain if the feedback delay is less than a derived fraction of the
channel coherence time. This precisely characterizes the intuition that a small
delay should be negligible.
