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This paper investigated the spectral efficiency (SE) in massive multiple-input multiple-output systems, where all terminals have no fixed power supply and thus need to replenish energy via the received signals from the base station. The hybrid wireless energy harvesting (EH) protocol is applied for each terminal, which can switch to either existing time-switching (TS) protocol or power-splitting (PS) protocol. Based on the hybrid wireless EH protocol, a general system model is developed, which can switch to either only uplink data transmission or only downlink data transmission. As a result, a general analytical framework is formulated. Then, closed-form lower bound expressions on SE for each terminal are obtained on the uplink and downlink, respectively. According to these expressions, the joint SE of uplink and downlink maximization problem is designed with some practical constraints. As the designed optimization problem is non-linear and non-convex, it is hard to solve directly. To provide a solution, an iteration algorithm is proposed by utilizing one-dimensional search technique and successive approximation method based on geometric program. Additionally, the convergence and complexity of the proposed algorithm are discussed as well. Finally, the feasibility of the proposed algorithm is analyzed by simulations. Numerical results manifest that the proposed algorithm can provide good SE by optimizing relevant system parameters, and the system model can help to discuss the TS, PS or hybrid protocol for only uplink data transmission, only downlink data transmission or joint data transmission of uplink and downlink in the considered system.

Joint spectral efficiency optimization of uplink and downlink for massive MIMO-enabled wireless energy harvesting systems