How much Training is Needed in Downlink Cell-Free mMIMO under LoS/NLoS channels?

The assumption that no LoS channels exist between wireless access points~(APs) and user equipments~(UEs) becomes questionable in the context of the recent developments in the direction of cell free massive multiple input multiple output MIMO~(CF-mMIMO) systems. In CF-mMIMO systems, the access point density is assumed to be comparable to, or much larger than the the user density, thereby leading to the possibility of existence of LoS links between the UEs and the APs, depending on the local propagation conditions. In this paper, we compare the rates achievable by CF-mMIMO systems under probabilistic LoS/ NLos channels, with and without acquiring the channel state information~(CSI) of the fast fading components. We show that, under sufficiently large AP densities, statistical beamforming that does not require the knowledge about the fast fading components of the channels, performs almost at par with full beamforming, utilizing the information about the fast fading channel coefficients, thus potentially avoiding the need for training during every frame. We validate our results via detailed Monte Carlo simulations, and also elaborate the conditions under which statistical beamforming can be successfully employed in massive MIMO systems with LoS/ NLoS channels.