  Based on the distinguishing features of multi-tier millimeter wave (mmWave)
networks such as different transmit powers, different directivity gains from
directional beamforming alignment and path loss laws for line-of-sight (LOS)
and non-line-of-sight (NLOS) links, we introduce a normalization model to
simplify the analysis of multi-tier mmWave cellular networks. The highlight of
the model is that we convert a multi-tier mmWave cellular network into a
single-tier mmWave network, where all the base stations (BSs) have the same
normalized transmit power 1 and the densities of BSs scaled by LOS or NLOS
scaling factors respectively follow piecewise constant function which has
multiple demarcation points. On this basis, expressions for computing the
coverage probability are obtained in general case with beamforming alignment
errors and the special case with perfect beamforming alignment in the
communication. According to corresponding numerical exploration, we conclude
that the normalization model for multi-tier mmWave cellular networks fully
meets requirements of network performance analysis, and it is simpler and
clearer than the untransformed model. Besides, an unexpected but sensible
finding is that there is an optimal beam width that maximizes coverage
probability in the case with beamforming alignment errors.
