Level Crossing and Fading Statistics
Rice computed joint statistics for a mathematical problem provides simple expressions for computing the average number of level crossing and the duration of fades.Two important statistics are useful for designing error control codes and diversity schemes to be used in mobile communication systems, since it becomes possible to relate the time rate of change of the received signal to the signal level and velocity of the mobile.
Level crossing rate (LCR):
- The level crossing rate (LCR) is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified level in a positive-going direction.
- The number of level crossings persecond is given by:
Average fade duration:
- The average fade duration is defined as the average period of time for which the received signal is below a specified level R
- For a Rayleigh fading signal, this is given by
- Where Pr[r <=R] is the probability that the received signal r is less than R andis given by:
- where is the duration of the fade and T is the observation interval ç)f the fading signal. The probability that the received signal r is less than the thresholdR is found from the Rayleigh distribution as