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The paper focuses on designing precoding matrices in multi-cell multiple-input multiple-output (MIMO) simultaneous wireless information and power transfer networks (SWIPT) where the sets of users are selected for data transmission in each time slot and the unselected users are dedicated to energy harvesting. The precoding design for the SWIPT problem is formulated as a general multi-objective maximization problem, in which the sum-rate (SR) and sum harvested energy (SHE) are maximized simultaneously under the transmit power constraints. Since the objective function of the maximization problem is not concave in the design matrix variables, it is difficult to directly obtain the optimal solutions. To tackle this challenge, we recast the SR function into one more amenable by applying the connection between the minimum mean square error and achievable data rate. In addition, to deal with the non-concavity of the harvested energy function, we derive its concave minorant. Then, we develop an efficient iterative algorithm based on alternating optimization (AO) to obtain the optimal precoders. We also analyze the convergence and computational complexity of the proposed algorithm. Finally, by numerical simulation results we investigate the trade-offs between the SR and SHE.

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