  This paper investigates joint wireless information and energy transfer in a
two-user MIMO interference channel, in which each receiver either decodes the
incoming information data (information decoding, ID) or harvests the RF energy
(energy harvesting, EH) to operate with a potentially perpetual energy supply.
In the two-user interference channel, we have four different scenarios
according to the receiver mode -- ($ID_1$, $ID_2$), ($EH_1$, $EH_2$), ($EH_1$,
$ID_2$), and ($ID_1$, $EH_2$). While the maximum information bit rate is
unknown and finding the optimal transmission strategy is still open for
($ID_1$, $ID_2$), we have derived the optimal transmission strategy achieving
the maximum harvested energy for ($EH_1$, $EH_2$). For ($EH_1$, $ID_2$), and
($ID_1$, $EH_2$), we find a necessary condition of the optimal transmission
strategy and, accordingly, identify the achievable rate-energy (R-E) tradeoff
region for two transmission strategies that satisfy the necessary condition -
maximum energy beamforming (MEB) and minimum leakage beamforming (MLB).
Furthermore, a new transmission strategy satisfying the necessary condition -
signal-to-leakage-and-energy ratio (SLER) maximization beamforming - is
proposed and shown to exhibit a better R-E region than the MEB and the MLB
strategies. Finally, we propose a mode scheduling method to switch between
($EH_1$, $ID_2$) and ($ID_1$, $EH_2$) based on the SLER.
