Theoretical limitation of fading reduction by space or frequency diversity

Theoretical relations among Rayleigh, normal and dB-normal distributions are investigated, and a dB-normal distribution is derived from short term median values of Rayleigh fading. From the relation between Rayleigh and dB-normal distributions, limitations of fading reduction by space or frequency diversity are found, which are 1.8, 6.7, 13.0, 19.8 and 27.1 dB at 10, 1, 0.1, 0.01 and 0.001 percent of the cumulative distribution values, respectively. These numerical values will be valid for a diversity system which keeps the median value constant and reduces Rayleigh fading by averaging the received signals of independent levels with respect to the space or frequency. The calculated values are compared with experimental values of a frequency-hopping multilevel FSK system.