Analysis of the Level-Crossing Rate and Average Duration of Fades of WSSUS Channels

Studies of the level-crossing rate (LCR) and the average duration of fades (ADF) are so far only devoted to stochastic processes being a function of one independent variable, which is usually time or in some few cases frequency. In this paper, we study the LCR (ADF) of wide-sense stationary uncorrelated scattering (WSSUS) processes in the time-frequency domain. A closed-form solution will be derived for the so-called time-frequency LCR (ADF) of the absolute value of the time-variant transfer function (TVTF) of WSSUS processes. It is shown that the LCR (ADF) is circularly symmetric in the normalized time-frequency domain. The derived time-frequency LCR contains the time LCR and frequency LCR well known in the literature as special cases. The importance of the introduced time-frequency LCR is demonstrated by introducing a new method for the estimation of the Doppler spread and the delay spread from measured TVTFs of WSSUS channels.