New Insights on Channel Hardening in Cell-Free Massive MIMO Networks

The cell-free (CF) massive multiple-input multiple-output (M-MIMO) architecture has recently emerged as a key technology for future wireless networks that is shown to outperform alternative network deployments such as those based on small-cells. Despite the many characteristics CF-M-MIMO shares with conventional M-MIMO (i.e., centralized) systems, its distributed nature brings along new issues that need to be carefully accounted for. In particular, the so-called channel hardening effect that postulates that the variance of the compound wireless channel experienced by a given user from a large number of transmit antennas tends to vanish, effectively making the channel deterministic. This critical assumption, which permeates most theoretical results of M-MIMO, has been well investigated and validated in centralized architectures, however, it has received little attention in the context of CF-M-MIMO networks. Hardening in CF-M-MIMO is potentially compromised by the different large-scale gains each access point (AP) impinges to the transmitted signal to each user, a condition that is further stressed when not all APs transmit to all users as proposed in the user-centric (UC) variations of CF-M-MIMO. This paper aims at presenting a comprehensive study of the channel-hardening effect in CF-M-MIMO under realistic operational conditions (e.g, presence of pilot contamination, power control, different precoders). Closed-form expressions of the hardening coefficient for different precoding schemes are provided showing that the precoder's choice, the number of antennas at each AP and the geographical density of APs play a key role in achieving this property.