  To determine the transmission strategy for joint wireless information and
energy transfer (JWIET) in the MIMO interference channel (IFC), the information
access point (IAP) and energy access point (EAP) require the channel state
information (CSI) of their associated links to both the information-decoding
(ID) mobile stations (MSs) and energy-harvesting (EH) MSs (so-called local
CSI). In this paper, to reduce th e feedback overhead of MSs for the JWIET in
two-user MIMO IFC, we propose a Geodesic energy beamforming scheme that
requires partial CSI at the EAP. Furthermore, in the two-user MIMO IFC, it is
proved that the Geodesic energy beamforming is the optimal strategy. By adding
a rank-one constraint on the transmit signal covariance of IAP, we can further
reduce the feedback overhead to IAP by exploiting Geodesic information
beamforming. Under the rank-one constraint of IAP's transmit signal, we prove
that Geodesic information/energy beamforming approach is the optimal strategy
for JWIET in the two-user MIMO IFC. We also discuss the extension of the
proposed rank-one Geodesic information/energy beamforming strategies to general
K-user MIMO IFC. Finally, by analyzing the achievable rate-energy performance
statistically under imperfect partial CSIT, we propose an adaptive bit
allocation strategy for both EH MS and ID MS.
