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Digital Communication over Fading Channels P2

FADING CHANNEL CHARACTERIZATION AND MODELING and hence, following (2.3), the instantaneous SNR per symbol of the channel, , is distributed according to an exponential distribution given by p D 1 exp , ½0 2.7 The MGF corresponding to this fading model is given by M s D 1 s 1 2.8 In addition, the moments associated with this fading model can be shown to be given by 2.9 E[ k ] D 1 C k k where Ð is the gamma function. The Rayleigh fading model therefore has an AF equal to 1 and typically agrees very well with experimental data for mobile. | 20 FADING CHANNEL CHARACTERIZATION AND MODELING and hence following 2.3 the instantaneous SNR per symbol of the channel y is distributed according to an exponential distribution given by _ 1 Py y exp y y y y 0 2.7 The MGF corresponding to this fading model is given by M s 1 - sy 1 2.8 In addition the moments associated with this fading model can be shown to be given by E yk T 1 C k yk 2.9 where T - is the gamma function. The Rayleigh fading model therefore has an AF equal to 1 and typically agrees very well with experimental data for mobile systems where no LOS path exists between the transmitter and receiver antennas 3 . It also applies to the propagation of reflected and refracted paths through the troposphere 7 and ionosphere 8 9 and to ship-to-ship 10 radio links. 2.2.1.2 Nakagami-q Hoyt Model. The Nakagami-q distribution also referred to as the Hoyt distribution 11 is given in Nakagami 12 Eq. 52 by Pa a q a exp qQ 1 q V 1- q4 a2 4q2Q 0 4q2Q 0 2.10 where I0 - is the zeroth-order modified Bessel function of the first kind and q is the Nakagami-q fading parameter which ranges from 0 to 1. Using 2.3 it can be shown that the SNR per symbol of the channel y is distributed according to 1 C q2 pr y o _ exp 2qy 1 q-Q 1- q4 y 4q2y 4q2y y 0 2.11 It can be shown that the MGF corresponding to 2.11 is given by My s 2sy 2q2 1 - 2sy C ------7-7 1 C q2 2_ 2.12 Also the moments associated with this model are given by 12 Eq. 52 E r 1 c k 2F1 k- 1 2 1 - q2 1 C q2 k 1 2 yk 2.13 MODELING OF FLAT FADING CHANNELS 21 where 2F1 - is the Gauss hypergeometric function and the AF of the Nakagami-q distribution is therefore given by AF 1 q41 q 1 C q2 2 0 q 1 2.14 and hence ranges between 1 q 1 and 2 q 0 . The Nakagami-q distribution spans the range from one-sided Gaussian fading q 0 to Rayleigh fading q 1 . It is typically observed on satellite links subject to strong ionospheric scintillation 13 14 . Note that one-sided Gaussian fading corresponds to the worst-case fading or equivalently