Wireless Channel Modeling Perspectives for Ultra-Reliable Low Latency Communications

Ultra-Reliable Low Latency Communication (URLLC) is one of the distinctive features of the upcoming 5G wireless communication, going down to packet error rates (PER) of $10^{-9}$. In this paper we discuss the statistical properties of the wireless channel models that are relevant for characterization of the lower tail of the Cumulative Distribution Function (CDF). We show that, for a wide range of channel models, the outage probability at URLLC levels can be approximated by a simple power law expression, whose exponent and offset depend on the actual channel model. The main insights from the analysis can be summarized as follows: (1) the two-wave model and the impact of shadowing in combined models lead to pessimistic predictions of the fading in the URLLC region; (2) the CDFs of models that contain single cluster diffuse components have slopes that correspond to the slope of a Rayleigh fading, and (3) multi-cluster diffuse components can result in different slopes. We apply our power law approximation results to analyze the performance of receiver diversity schemes for URLLC-relevant statistics and obtain a new simplified expression for Maximum Ratio Combining (MRC) in channels with power law tail statistics.