Skip to main content

Table 3 Classes of SOC and SOS models and their stationary and ergodic properties

From: Classes of sum-of-cisoids processes and their statistics for the modeling and simulation of mobile fading channels

Class Gains Frequency Phases WSS ME AE FOS
I SOC Det. Det. Det. - - - -
I SOS Det. Det. Det. - - - -
II SOC Det. Det. Rand. Yes Yes Yes Yes
II SOS Det. Det. Rand. Yes Yes Yes Yes
III SOC Det. Rand. Det. No/Yesa,b No/Yesa No No/Yesb
III SOS Det. Rand. Det. No/Yesc,d,e No/Yesc,d No No/Yesb,c,d,e
IV SOC Det. Rand. Rand. Yes Yes No Yes
IV SOS Det. Rand. Rand. Yes Yes No Yes
V SOC Rand. Det. Det. No/Yesf No/Yesf No No
V SOS Rand. Det. Det. No No/Yesf No No
VI SOC Rand. Det. Rand. Yes Yes No Yes
VI SOS Rand. Det. Rand. Yes Yes No Yes
VII SOC Rand. Rand. Det. No/Yesb/f No/Yesa/b/f No No/Yesb
VII SOS Rand. Rand. Det. No/Yesc,d,e No/Yesf/c,d No No/Yesb,c,d,e
VIII SOC Rand. Rand. Rand. Yes Yes No Yes
VIII SOS Rand. Rand. Rand. Yes Yes No Yes
  1. WSS, wide-sense stationary; ME, mean-ergodic; AE, autocorrelation ergodic; FOS, first-order stationary; Rand., random; Det., deterministic. aIf the boundary condition n = 1 N c n exp{j θ n }=0 is satisfied; bOnly in the limit t→±; cIf the density of the random Doppler frequencies is an even function; dIf the boundary condition n = 1 N i cos( θ i , n )=0 is satisfied; eIf the boundary condition n = 1 N i cos(2 θ i , n )=0 is satisfied; f If the mean value of the random gains is equal to zero.