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In this paper, uplink of single-cell massive multiple-input multiple-output (mMIMO) system with receiver hardware impairment is considered. Users have limited energy budget in each coherence interval which should be allocated optimally for uplink pilot and data symbol transmission. Also, we assume that for both channel estimation and data transmission phases receiver suffers from hardware impairments. Hence, using the received pilots the estimates of the channels are obtained at the receiver then by use of these estimates and maximum ratio combining (MRC) technique achievable rate of the users are derived for different values of the transmitted pilot and data powers. Next, a fairness optimization problem is proposed so as to maximize the minimum rate of the users by considering energy budget constraint in a coherence interval. The original optimization problem is a nonconvex one. However, we reformulate it such that it can be solved efficiently using geometric programming. Finally, numerical results are provided which signify the considerable improvements by jointly allocating pilot and data powers in comparison with simple equal power allocation or only optimizing the data power.

Keywords: Massive MIMO, uplink, power allocation, channel estimation, hardware impairment, geometric programming, maximum ratio combining (MRC).

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