In this paper, we propose a relative channel estimation error (RCEE) metric, and derive closed-form expressions for its expectation Exprcee and the achievable uplink rate holding for any number of base station antennas M, with the least squares (LS) and minimum mean squared error (MMSE) methods. It is found that RCEE and Exprcee converge to the same constant value when M ! 1, which renders the pilot power allocation (PPA) substantially simplified and a PPA algorithm is proposed to minimize the average Exprcee per user with a total pilot power budget P in multi-cell massive multiple-input multipleoutput systems. Numerical results show that the PPA algorithm brings considerable gains for the LS estimation compared with equal PPA (EPPA), while the gains are significant only with large frequency reuse factor (FRF) for the MMSE estimation. Moreover, for large FRF and large P, the performance of the LS approaches to the MMSE. Besides, a scheduling strategy is proposed to allocate pilot power in the whole system, which can approach the optimal performance. For the achievable uplink rate, the PPA scheme delivers almost the same average achievable uplink rate and improves the minimum achievable uplink rate compared with the EPPA scheme.
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