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

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/Yes^a,b	No/Yes^a	No	No/Yes^b
III SOS	Det.	Rand.	Det.	No/Yes^c,d,e	No/Yes^c,d	No	No/Yes^b,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/Yes^f	No/Yes^f	No	No
V SOS	Rand.	Det.	Det.	No	No/Yes^f	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/Yes^b/f	No/Yes^a/b/f	No	No/Yes^b
VII SOS	Rand.	Rand.	Det.	No/Yes^c,d,e	No/Yes^f/c,d	No	No/Yes^b,c,d,e
VIII SOC	Rand.	Rand.	Rand.	Yes	Yes	No	Yes
VIII SOS	Rand.	Rand.	Rand.	Yes	Yes	No	Yes

WSS, wide-sense stationary; ME, mean-ergodic; AE, autocorrelation ergodic; FOS, first-order stationary; Rand., random; Det., deterministic. ^aIf the boundary condition $\sum_{n = 1}^{N} c_{n} exp {j θ_{n}} = 0$ is satisfied; ^bOnly in the limit t→±∞; ^cIf the density of the random Doppler frequencies is an even function; ^dIf the boundary condition $\sum_{n = 1}^{N_{i}} cos (θ_{i, n}) = 0$ is satisfied; ^eIf the boundary condition $\sum_{n = 1}^{N_{i}} cos (2 θ_{i, n}) = 0$ is satisfied; ^f If the mean value of the random gains is equal to zero.