  In this paper, we propose a generalized framework that combines the cognitive
radio (CR) techniques for spectrum sharing and the simultaneous wireless
information and power transfer (SWIPT) for energy harvesting (EH) in the
conventional multi-user MIMO (MuMIMO) channels, which leads to an
MuMIMO-CR-SWIPT network. In this system, we have one secondary base-station
(S-BS) that supports multiple secondary information decoding (S-ID) and
secondary EH (S-EH) users simultaneously under the condition that interference
power that affects the primary ID (P-ID) receivers should stay below a certain
threshold. The goal of the paper is to develop a generalized precoder design
that maximizes the sum-utility cost function under the transmit power
constraint at the S-BS, and the EH constraint at each S-EH user, and the
interference power constraint at each P-ID user. Therefore, the previous
studies for the CR and SWIPT systems are casted as particular solutions of the
proposed framework. The problem is inherently non-convex and even the weighted
minimum mean squared error (WMMSE) transformation does not resolve the
non-convexity of the original problem. To tackle the problem, we find a
solution from the dual optimization via sub-gradient ellipsoid method based on
the observation that the WMMSE transformation raises zero-duality gap between
the primal and the dual problems. We also propose a simplified algorithm for
the case of a single S-ID user, which is shown to achieve the global optimum.
Finally, we demonstrate the optimality and efficiency of the proposed
algorithms through numerical simulation results.
