An Exact Solution for the Level-Crossing Rate and the Average Duration of Fades of the Envelope of Sum-of-Cisoids Processes

Sum-of-cisoids (SOC) processes provide a physically and numerically appealing framework for the modelling and simulation of a wide class of mobile radio channels. This paper is concerned with the problem of finding a general solution for the level-crossing rate (LCR) and the average duration of fades (ADF) of the envelope of SOC processes. Exact expressions are derived for the LCR and the ADF by taking into account that the inphase component, the quadrature component, and the time derivatives of the inphase and quadrature components of SOC processes are in general mutually correlated. The validity of the theoretical results is confirmed by simulation results. This study reveals new insight into the fading behaviour of SOS-based multipath fading channel models. The results of this study are indispensable for the performance assessment of mobile radio channel simulators employing the SOC principle.