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

EURASIP Journal on Wireless Communications and Networking

Table 1 Classes of frequency-selective SOC models and their stationary and ergodic properties

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/Yes^c	No/Yes^c	No/Yes^c	No/Yes^c	No/Yes^c	No	No	No/Yes^c
IV	Det.	Det.	Rand.	Rand.	Yes	Yes	Yes	Yes	Yes	No	No	Yes
V	Det.	Rand.	Det.	Det.	No/Yes^e	No/Yes^e	No/Yes^e	No/Yes^e	No	No	No	No
VI	Det.	Rand.	Det.	Rand.	Yes	No/Yes^e	Yes	Yes	No	No	No	Yes
VII	Det.	Rand.	Rand.	Det.	No/Yes^e	No/Yes^e	No/Yes^e	No/Yes^e	No	No	No	No/Yes^c
VIII	Det.	Rand.	Rand.	Rand.	Yes	Yes	Yes	Yes	No	No	No	Yes
IX	Rand.	Det.	Det.	Det.	No/Yes^a	No/Yes^a	No/Yes^a	No/Yes^a	No	No/Yes^a	No	No/Yes^a
X	Rand.	Det.	Det.	Rand.	Yes	Yes	Yes	Yes	No	Yes	No	No/Yes^b
XI	Rand.	Det.	Rand.	Det.	No/Yes^a	No/Yes^a	No/Yes^a/c/d	No/Yes^a/c/d	No	No	No	No/Yes^c
XII	Rand.	Det.	Rand.	Rand.	Yes	Yes	Yes	Yes	No	No	No	Yes
XIII	Rand.	Rand.	Det.	Det.	No/Yes^a/e	No/Yes^a/e	No/Yes^a/e	No/Yes^a/e	No	No	No	No
XIV	Rand.	Rand.	Det.	Rand.	Yes	Yes	Yes	Yes	No	No	No	Yes
XV	Rand.	Rand.	Rand.	Det.	No/Yes^a/c/e	No/Yes^a/c/e	No/Yes^a/c/d/e	No/Yes^a/c/d/e	No	No	No	No/Yes^c
XVI	Rand.	Rand.	Rand.	Rand.	Yes	Yes	Yes	Yes	No	No	No	Yes

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 $\sum_{n = 1}^{N} c_{n} exp {j θ_{n}} = 0$ is satisfied; ^e If the mean of the random gains is equal to zero.