Stochastic model for time-varying millimeter-wave beam gains with user orientation changes

Abstract

In the widely used spatial channel model (SCM), the millimeter wave channels encountered by a 5G system are constructed using a stochasto-geometric approach. However, a probabilistic characterization of the time evolution of the gain of any transmit-receive beam pair is not available. We propose a novel modified bivariate Nakagami-m (MBN) model that presents such a characterization. It accurately captures the non-stationary time-variation in the beam gain due to user mobility and user device orientation changes. It applies to both positive and negative correlations between the beam gains. We derive closed-form expressions for the MBN parameters in terms of the SCM parameters. We then apply this tractable model to develop a new, effective, and robust beam selection rule. It predicts in closed-form the signal-to-noise ratios of the beam pairs at the time a beam pair is selected given the beam pair gain measurements that are made at different times.