  We study the sum degrees of freedom (DoF) of interference channels with
hybrid beam-forming in which hybrid beam-forming composed of analog and digital
precodings is employed at each node. For the two-user case, we completely
characterize the sum DoF for an arbitrary number of antennas and RF chains by
developing an achievable scheme optimized for the hybrid beam-forming structure
and deriving its matching upper bound. For a general K-user case, we focus on a
symmetric case and obtain lower and upper bounds on the sum DoF, which are
tight for certain cases. The results show that hybrid beam-forming can increase
the sum DoF of interference channel under certain conditions while it cannot
improve the sum DoFs of point-to-point channel, multiple access channel, and
broadcast channel. The key insights on this gain is that hybrid beam-forming
enables users to manage inter user interference better, and thus each user can
increase the dimension of interference-free signal space for its own desired
signals.
