  In this paper, we study the multiple-input and multiple-output (MIMO)
wireless power transfer (WPT) system so as to enhance the output DC power of
the rectennas. To that end, we revisit the rectenna nonlinearity considering
multiple receive antennas. Two combining schemes for multiple rectennas at the
receiver, DC and RF combinings, are modeled and analyzed. For DC combining, we
optimize the transmit beamforming, adaptive to the channel state information
(CSI), so as to maximize the total output DC power. For RF combining, we
compute a closed-form solution of the optimal transmit and receive beamforming.
In addition, we propose a practical RF combining circuit using RF phase shifter
and RF power combiner and also optimize the analog receive beamforming adaptive
to CSI. We also analytically derive the scaling laws of the output DC power as
a function of the number of transmit and receive antennas. Those scaling laws
confirm the benefits of using multiple antennas at the transmitter or receiver.
They also highlight that RF combining significantly outperforms DC combining
since it leverages the rectenna nonlinearity more efficiently. Two types of
performance evaluations, based on the nonlinear rectenna model and based on
realistic and accurate rectenna circuit simulations, are provided. The
evaluations demonstrate that the output DC power can be linearly increased by
using multiple rectennas at the receiver and that the relative gain of RF
combining versus DC combining in terms of the output DC power level is very
significant, of the order of 240% in a one-transmit antenna ten-receive antenna
setup.

Signal Processing