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Table 1 Classes of frequency-selective SOC 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 Delays Gains Freq. Phases WSS   ME   AE    FOS
      Freq. Time Freq. Time Freq. Time Time-Freq. Time
I Det. Det. Det. Det. - - - - - - - -
II Det. Det. Det. Rand. Yes Yes Yes Yes Yes Yes Yes Yes
III Det. Det. Rand. Det. No/Yesc No/Yesc No/Yesc No/Yesc No/Yesc No No No/Yesc
IV Det. Det. Rand. Rand. Yes Yes Yes Yes Yes No No Yes
V Det. Rand. Det. Det. No/Yese No/Yese No/Yese No/Yese No No No No
VI Det. Rand. Det. Rand. Yes No/Yese Yes Yes No No No Yes
VII Det. Rand. Rand. Det. No/Yese No/Yese No/Yese No/Yese No No No No/Yesc
VIII Det. Rand. Rand. Rand. Yes Yes Yes Yes No No No Yes
IX Rand. Det. Det. Det. No/Yesa No/Yesa No/Yesa No/Yesa No No/Yesa No No/Yesa
X Rand. Det. Det. Rand. Yes Yes Yes Yes No Yes No No/Yesb
XI Rand. Det. Rand. Det. No/Yesa No/Yesa No/Yesa/c/d No/Yesa/c/d No No No No/Yesc
XII Rand. Det. Rand. Rand. Yes Yes Yes Yes No No No Yes
XIII Rand. Rand. Det. Det. No/Yesa/e No/Yesa/e No/Yesa/e No/Yesa/e No No No No
XIV Rand. Rand. Det. Rand. Yes Yes Yes Yes No No No Yes
XV Rand. Rand. Rand. Det. No/Yesa/c/e No/Yesa/c/e No/Yesa/c/d/e No/Yesa/c/d/e No No No No/Yesc
XVI Rand. Rand. Rand. Rand. Yes Yes Yes Yes No No No Yes
  1. Freq., frequency; WSS, wide-sense stationary; ME, mean-ergodic; AE, autocorrelation ergodic; FOS, first-order stationary; Rand., random; Det., deterministic. a Only in the limit f→±; b Only in the limit f→0; c Only in the limit t→±; d If the boundary condition n = 1 N c n exp{j θ n }=0 is satisfied; e If the mean of the random gains is equal to zero.