Level-Crossing Rate and Average Duration of Fades of the Envelope of a Sum-of-Cisoids

For the modelling and simulation of mobile radio channels, one often uses a sum of complex sinusoids (cisoids). This paper analyses in detail the level-crossing rate (LCR), the average duration of the fades (ADF), and the cumulative distribution function (CDF) of the envelope of a sum-of-cisoids (SOC). For these statistical quantities, exact and simple approximate solutions are derived by taking into account that the inphase and quadrature components of SOC models are generally correlated. The correctness of all theoretical results is confirmed by simulations. The results are not only important for getting a better fundamental understanding of the statistical behaviour of SOC models, but also for the performance evaluation of SOC-based mobile radio channel simulators.