# Spectral Efficiency of Dynamic Coordinated Beamforming: A Stochastic Geometry Approach

Base station (BS) coordination is regarded as an effective approach to mitigate intercell interference. The idea is to allow multiple BSs to coordinate their transmit and receive strategies (e.g., beamforming, power control, and scheduling) by utilizing channel state information (CSI). A central concept in the implementation of BS coordination with low overheads is to form a cluster, defined as the set of BSs that a given user coordinates with. From the vantage of a user, only those BSs outside the cluster are sources of interference. Intuitively, a larger cluster reduces intercell interference but it also increases the overhead required to acquire the necessary CSI at the BS. Therefore, one of the fundamental questions is to determine the optimal cluster cardinality to assess the true benefits of BS coordination.

Motivated by this question, WNCG PhD. Candidate Namyoon Lee, Universitat Pompeu Fabra (UPF) Barcelona Post-Doc David Morales-Jimenez, UPF Barcelona Professor Angel Lozano, and WNCG Professor Robert Heath characterize the performance of coordinated beamforming with dynamic clustering. To analyze the performance of such BS coordination strategy, they use a tool of stochastic geometry. They derive analytical expressions for the complementary cumulative distribution function (CCDF) of the instantaneous signal-to-interference ratio (SIR) in terms of relevant system parameters, chiefly the number of BSs forming the coordination clusters, the number of antennas per BS, and the pathloss exponent. Using this CCDF, with pilot overheads further incorporated into the analysis, they formulate the optimization of the BS coordination clusters for a given fading coherence. Their results indicate that (i) coordinated beamforming is most beneficial to users that are in the outer part of their cells yet in the inner part of their coordination cluster, and that (ii) the optimal cluster cardinality for the typical user is small and it scales with the fading coherence. They also verify the exactness of the SIR distributions derived for stochastic geometries through simulations, which are further compared with the corresponding distributions for deterministic grid networks.