  In this paper, coordinated beamforming based on relaxed zero forcing (RZF)
for K transmitter-receiver pair multiple-input single-output (MISO) and
multiple-input multiple-output (MIMO) interference channels is considered. In
the RZF coordinated beamforming, conventional zero-forcing interference leakage
constraints are relaxed so that some predetermined interference leakage to
undesired receivers is allowed in order to increase the beam design space for
larger rates than those of the zero-forcing (ZF) scheme or to make beam design
feasible when ZF is impossible. In the MISO case, it is shown that the
rate-maximizing beam vector under the RZF framework for a given set of
interference leakage levels can be obtained by sequential orthogonal projection
combining (SOPC). Based on this, exact and approximate closed-form solutions
are provided in two-user and three-user cases, respectively, and an efficient
beam design algorithm for RZF coordinated beamforming is provided in general
cases. Furthermore, the rate control problem under the RZF framework is
considered. A centralized approach and a distributed heuristic approach are
proposed to control the position of the designed rate-tuple in the achievable
rate region. Finally, the RZF framework is extended to MIMO interference
channels by deriving a new lower bound on the rate of each user.
