Subspace Based Hierarchical Channel Clustering in Massive MIMO

This work proposes a hierarchical clustering method for wireless users based on a similarity measure between the subspaces spanned by their channel matrices. Specifically, the channel subspaces are seen as points in Grassmann manifolds and their similarity is measured in terms of the squared projection-Frobenius distance. The asymptotic (in the number of antennas) analysis of the first- and second-order statistics of the similarity measure provides a tool for effectively comparing Grassmann manifolds of different sizes and allows for a proper similarity measure between clusters of different number of users/antennas, as corroborated by numerical results.