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In massive MIMO systems, energy efficiency (EE) and spectral efficiency (SE) can be balanced by tuning the number of the transmit antennas and the transmit power. However, two key parameters i.e. the modulation order and the bit-error-rate (BER) are seldom considered in the conventional EE-SE tradeoff for the massive MIMO systems. To address this problem, the throughput-based EE (TEE) and SE (TSE) tradeoff for both the conventional massive MIMO and the full-dimensional (FD) massive MIMO systems are investigated. Firstly, a TEE and TSE tradeoff problem is formulated and the transition property of the modulation order is analysed. The analysis reveals that due to the discrete property of the modulation order, the TEE-TSE tradeoff curve is continuously non-differentiable at the transition point of the modulation order. By utilising the transition property, a modified normal-boundary-intersection particle-swarm-optimisation (NBI-PSO) algorithm is developed to solve the TEE-TSE problem effectively. From the numerical results, it is found that the throughput-based problem has a relatively smaller EE and SE on the Pareto front than the capacity-based one and selecting an improper combination of the modulation order, the transmit power and the number of the antennas may cause the EE-SE relation sub-optimal from the point view of Pareto efficiency. Through the numerical results, the most energy efficient modulation order is obtained and it is not the commonly assumed low-order modulation scheme.

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Full‐dimensional (FD) massive MIMO can overcome the limitation of the physical space at the base station (BS) and meet the increasing capacity requirement for future wireless communications. However, the pilot overhead for the acquisition of the channel state information (CSI) at the BS could be prohibitively high due to the large number of antennas. In this letter, exploiting the Kronecker property of the channel, we propose a low‐rank matrix fitting based channel estimation (LMFCE) scheme to reduce the pilot overhead in FD massive MIMO systems. The simulation results illustrate that the proposed LMFCE scheme can significantly reduce the pilot overhead for the channel estimation.