  Enabling the high data rates of millimeter wave (mmWave) cellular systems
requires deploying large antenna arrays at both the basestations and mobile
users. The beamforming weights of these large arrays need to be tuned to
guarantee sufficient beamforming gains. Prior work on coverage and rate of
mmWave cellular networks focused mainly on the case when basestations and
mobile users beamfomring vectors are perfectly designed for maximum beamforming
gains. Designing beamforming/combining vectors, though, requires training which
may impact both the SINR coverage and rate of mmWave cellular systems. This
paper characterizes and evaluates the performance of mmWave cellular networks
while accounting for the beam training/association overhead. First, a model for
the initial beam association is developed based on beam sweeping and downlink
control pilot reuse. To incorporate the impact of beam training into system
performance, a new metric, called the effective reliable rate, is defined and
adopted. Using stochastic geometry, the effective reliable rate of mmWave
cellular networks is derived for two special cases: with near-orthogonal
control pilots and with full pilot reuse. Analytical and simulation results
provide insights into the answers of three important questions: (i) What is the
impact of beam association on mmWave network performance? (ii) Should
orthogonal or reused control pilots be employed in the initial beam association
phase? (iii) Should exhaustive or hierarchical search be adopted for the beam
training phase? The results show that unless the employed beams are very wide
or the system coherence block length is very small, exhaustive search with full
pilot reuse is nearly as good as perfect beam alignment.
