On the Performance of Cell-Free Massive MIMO with Short-Term Power   Constraints
  In this paper we consider a time-division duplex cell-free massive multiple-input multiple-output (MIMO) system where many distributed access points (APs) simultaneously serve many users. A normalized conjugate beamforming scheme, which satisfies short-term average power constraints at the APs, is proposed and analyzed taking into account the effect of imperfect channel information. We derive an approximate closed-form expression for the per-user achievable downlink rate of this scheme. We also provide, analytically and numerically, a performance comparison between the normalized conjugate beamforming and the conventional conjugate beamforming scheme in [1] (which satisfies long-term average power constraints). Normalized conjugate beamforming scheme reduces the beamforming uncertainty gain, which comes from the users' lack of the channel state information knowledge, and hence, it improves the achievable downlink rate compared to the conventional conjugate beamforming scheme. 
Giovanni Interdonato, Hien Quoc Ngo, Erik G. Larsson, P{\aa}l Frenger
cs.IT eess.SP math.IT