Spectral Efficiency of Dynamic Coordinated Beamforming: A Stochastic   Geometry Approach
  This paper characterizes the performance of coordinated beamforming with dynamic clustering. A downlink model based on stochastic geometry is put forth to analyze the performance of such base station (BS) coordination strategy. Analytical expressions for the complementary cumulative distribution function (CCDF) of the instantaneous signal-to-interference ratio (SIR) are derived 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. Utilizing this CCDF, with pilot overheads further incorporated into the analysis, we formulate the optimization of the BS coordination clusters for a given fading coherence. Our 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. Simulation results verify the exactness of the SIR distributions derived for stochastic geometries, which are further compared with the corresponding distributions for deterministic grid networks. 
Namyoon Lee, David Morales-Jimenez, Angel Lozano, and Robert W. Heath   Jr
cs.IT math.IT