Based on the distinguishing features of multi-tier millimeter wave (mmWave)networks such as different transmit powers, different directivity gains fromdirectional beamforming alignment and path loss laws for line-of-sight (LOS)and non-line-of-sight (NLOS) links, we introduce a normalization model tosimplify the analysis of multi-tier mmWave cellular networks. The highlight ofthe model is that we convert a multi-tier mmWave cellular network into asingle-tier mmWave network, where all the base stations (BSs) have the samenormalized transmit power 1 and the densities of BSs scaled by LOS or NLOSscaling factors respectively follow piecewise constant function which hasmultiple demarcation points. On this basis, expressions for computing thecoverage probability are obtained in general case with beamforming alignmenterrors and the special case with perfect beamforming alignment in thecommunication. According to corresponding numerical exploration, we concludethat the normalization model for multi-tier mmWave cellular networks fullymeets requirements of network performance analysis, and it is simpler andclearer than the untransformed model. Besides, an unexpected but sensiblefinding is that there is an optimal beam width that maximizes coverageprobability in the case with beamforming alignment errors.
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