Cell-free Massive MIMO (multiple-input multipleoutput) refers to a distributed Massive MIMO system where all the access points (APs) cooperate to coherently serve all the user equipments (UEs), suppress inter-cell interference and mitigate the multiuser interference. Recent works 1, 2 demonstrated that, unlike co-located Massive MIMO, the channel hardening is, in general, less pronounced in cell-free Massive MIMO, thus there is much to benefit from estimating the downlink channel. In this study, we investigate the gain introduced by the downlink beamforming training, extending the analysis in 1 to non-orthogonal uplink and downlink pilots. Assuming singleantenna APs, conjugate beamforming and independent Rayleigh fading channel, we derive a closed-form expression for the peruser achievable downlink rate that addresses channel estimation errors and pilot contamination both at the AP and UE side. The performance evaluation includes max-min fairness power control, greedy pilot assignment methods, and a comparison between achievable rates obtained from different capacitybounding techniques. Numerical results show that downlink beamforming training, although increases pilot overhead and introduces additional pilot contamination, improves significantly the achievable downlink rate. Even for large number of APs, it is not fully efficient for the UE relying on the statistical channel state information for data decoding.

We propose a strategy for orthogonal downlink pilot assignment in cell-free massive MIMO (multiple-input multiple-output) that exploits knowledge of the channel state information, the channel hardening degree at each user, and the mobility conditions for the users. These elements, properly combined together, are used to define a user pilot utility metric, which measures the user's real need of a downlink pilot for efficient data decoding. The proposed strategy consists in assigning orthogonal downlink pilots only to the users having a pilot utility metric exceeding a predetermined threshold. Instead, users that are not assigned with an orthogonal downlink pilot decode the data by using the statistical channel state information. The utility-based approach guarantees higher downlink net sum throughput, better support both for high-speed users and shorter coherent intervals than prior art approaches.

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.

Cell-free Massive multiple-input multiple-output (MIMO) ensures ubiquitous communication at high spectral efficiency (SE) thanks to increased macro-diversity as compared cellular communications. However, system scalability and performance are limited by fronthauling traffic and interference. Unlike conventional precoding schemes that only suppress intra-cell interference, full-pilot zero-forcing (fpZF), introduced in [1], actively suppresses also inter-cell interference, without sharing channel state information (CSI) among the access points (APs). In this study, we derive a new closed-form expression for the downlink (DL) SE of a cell-free Massive MIMO system with multi-antenna APs and fpZF precoding, under imperfect CSI and pilot contamination. The analysis also includes max-min fairness DL power optimization. Numerical results show that fpZF significantly outperforms maximum ratio transmission scheme, without increasing the fronthauling overhead, as long as the system is sufficiently distributed.