B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

the maximum Doppler shift is bounded by
12.1 1 Time-Varying Channel Distortions Due to Mobility 713
Based on the Doppler analysis, each path has a Doppler frequency shift w;, delay Ti , and
path attenuation ai . The signal from the ith path can be written as
ai [ Re {sk }p(t - kT - T;)] cos [(we + Wi)(t - Ti)J
+ a; [ Im {sk )p(t - kT - r;)] sin [(we + w;)(t - r;)]
(12.76)
As a result, the baseband receiver signal after demodulation is now
! y(t) = I>k t l
ai exp [-j(wc + Wi)ril exp (-jw;t) p(t - kT - r;)
k l=O
{J; (t)
=
Sk [t, /3; (t) p(t - kT - T;)] (12.77)
Frequency-Selective Fading Channel
Recall that the original baseband transmission is
x(t) = L sk p(t - kT)
k
In the channel output of Eq. (12.77), if the mobile velocity is zero, then w; = 0 and /3;(t) = /3i
are constant. In the case of zero mobility, the baseband channel output simply becomes
This means that corresponding channel is linear time-invariant with impulse response
K
h(t) = L /3; 8(t - r;)
i=O
( 1 2.78)
and transfer function
H (f) = L/3; exp(-j2n:fr;)
i=O
(12.79)
This is a frequency-selective channel with intersymbol interference (ISI).