Higher Order Statistics in a mmWave Propagation Environment

A thorough measurement campaign in an indoor environment at the millimeter-wave band is carried out with an aim at characterizing the short-term fading channel in terms of its higher-order statistics. The measurements are conducted in a variety of scenarios, with frequencies ranging from 55 to 65 GHz, in line-of-sight and non-line-of-sight conditions, and combinations of horizontal and vertical polarizations at both the transmitter and the receiver. A number of fading models are tested, namely Rayleigh, Rice, Nakagami-<inline-formula> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>. The main second-order statistics under analysis are the level crossing rate (LCR) and average fade duration (AFD) both given per distance unit. From the experimental data, the parameters of these statistics are estimated, and the corresponding curves of the theoretical models are compared with the empirical ones and the best model is selected. Additionally, the study of the very general distribution, namely <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>, is advanced, in which new expressions for time-/distance-domain LCR and AFD are derived using an envelope-based approach. Such an approach leads to integral-form formulations with much less computational complexity and computes rapidly compared with the already existing ones presented elsewhere, also given in the integral form. Furthermore, a series of expansion expression for the <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> time-/distance-domain LCR is then derived that improves even further the computational time.