The Impact of Subspace-Based Pilot Decontamination in User-Centric Scalable Cell-Free Wireless Networks

We consider a scalable user-centric wireless network with dynamic cluster formation as defined by Bj\"ornsson and Sanguinetti. Several options for scalable uplink (UL) processing are examined including: i) cluster size and SNR threshold criterion for cluster formation; ii) UL pilot dimension; iii) local detection and global (per cluster) combining. We use a simple model for the channel vector spatial correlation, which captures the fact that the propagation between UEs and RRHs is not isotropic. In particular, we define the ideal performance based on ideal but partial CSI, i.e., the CSI that can be estimated based on the users to antenna heads cluster connectivity. In practice, CSI is estimated from UL pilots, and therefore it is affected by noise and pilot contamination. We show that a very simple subspace projection scheme is able to basically attain the same performance of perfect but partial CSI. This points out that the essential information needed to pilot decontamination reduces effectively to the dominant channel subspaces.