  The evaluation of the performance of clustered cooperative beamforming in
cellular networks generally requires the solution of complex non-convex
optimization problems. In this letter, a framework based on a hypergraph
formalism is proposed that enables the derivation of a performance
characterization of clustered cooperative beamforming in terms of per-user
degrees of freedom (DoF) via the efficient solution of a coloring problem. An
emerging scenario in which clusters of cooperative base stations (BSs) arise is
given by cellular networks with edge caching. In fact, clusters of BSs that
share the same requested files can jointly beamform the corresponding encoded
signals. Based on this observation, the proposed framework is applied to obtain
quantitative insights into the optimal use of cache and backhaul resources in
cellular systems with edge caching. Numerical examples are provided to
illustrate the merits of the proposed framework.
