  Powering mobiles using microwave \emph{power transfer} (PT) avoids the
inconvenience of battery recharging by cables and ensures uninterrupted mobile
operation. The integration of PT and \emph{information transfer} (IT) allows
wireless PT to be realized by building on the existing infrastructure for IT
and also leads to compact mobile designs. As a result, \emph{simultaneous
wireless information and power transfer} (SWIPT) has emerged to be an active
research topic that is also the theme of this paper. In this paper, a practical
SWIPT system is considered where two multi-antenna stations perform separate PT
and IT to a multi-antenna mobile to accommodate their difference in ranges. The
mobile dynamically assigns each antenna for either PT or IT. The antenna
partitioning results in a tradeoff between the MIMO IT channel capacity and the
PT efficiency. The optimal partitioning for maximizing the IT rate under a PT
constraint is a NP-hard integer program, and the paper proposes solving it via
efficient greedy algorithms with guaranteed performance. To this end, the
antenna-partitioning problem is proved to be one that optimizes a sub-modular
function over a matroid constraint. This structure allows the application of
two well-known greedy algorithms that yield solutions no smaller than the
optimal one scaled by factors $(1-1/e)$ and 1/2, respectively.
