In this paper we consider a time-division duplex cell-free massivemultiple-input multiple-output (MIMO) system where many distributed accesspoints (APs) simultaneously serve many users. A normalized conjugatebeamforming scheme, which satisfies short-term average power constraints at theAPs, is proposed and analyzed taking into account the effect of imperfectchannel information. We derive an approximate closed-form expression for theper-user achievable downlink rate of this scheme. We also provide, analyticallyand numerically, a performance comparison between the normalized conjugatebeamforming and the conventional conjugate beamforming scheme in [1] (whichsatisfies long-term average power constraints). Normalized conjugatebeamforming scheme reduces the beamforming uncertainty gain, which comes fromthe users' lack of the channel state information knowledge, and hence, itimproves the achievable downlink rate compared to the conventional conjugatebeamforming scheme.
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