  In this paper, we consider a time-switching (TS) co-located simultaneous
wireless information and power transfer (SWIPT) system consisting of multiple
multi-antenna access points which serve multiple single antenna users. In this
scenario, we propose a multi-objective optimization (MOO) framework to design
jointly the Pareto optimal beamforming vector and the TS ratio for each
receiver. The objective is to maximize the utility vector including the
achieved data rates and the harvested energies of all users simultaneously.
This problem is a non-convex rank-constrained MOO problem which is relaxed and
transformed into a non-convex semidefinite program (SDP) based on the weighted
Chebycheff method. The majorization-minimization algorithm is utilized to solve
the nonconvex SDP and the optimal solution is proved to satisfy the rank
constraint. We also study the problem of optimizing the beamforming vectors in
a fixed TS ratio scenario with the same approach. Numerical results are
provided for two coordinated access points with MISO configuration. The results
illustrate the trade-off between harvested energy and information data rate
objectives and show the effect of optimizing the precoding strategy and TS
ratio on this trade-off.
