  We present an approach to solve the nonconvex optimization problem that
arises when designing the transmit covariance matrices in multiuser
multiple-input multiple-output (MIMO) broadcast networks implementing
simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT
problem is formulated as a general multi-objective optimization problem, in
which data rates and harvested powers are optimized simultaneously. Two
different approaches are applied to reformulate the (nonconvex) multi-objective
problem. In the first approach, the transmitter can control the specific amount
of power to be harvested by power transfer whereas in the second approach the
transmitter can only control the proportion of power to be harvested among the
different harvesting users. The computational complexity will also be
different, with higher computational resources required in the first approach.
In order to solve the resulting formulations, we propose to use the
majorization-minimization (MM) approach. The idea behind this approach is to
obtain a convex function that approximates the nonconvex objective and, then,
solve a series of convex subproblems that will converge to a locally optimal
solution of the general nonconvex multi-objective problem. The solution
obtained from the MM approach is compared to the classical
block-diagonalization (BD) strategy, typically used to solve the nonconvex
multiuser MIMO network by forcing no interference among users. Simulation
results show that the proposed approach improves over the BD approach both the
system sum rate and the power harvested by users. Additionally, the
computational times needed for convergence of the proposed methods are much
lower than the ones required for classical gradient-based approaches.
