The residual frequency offset is intentionally
introduced in the analysis. A square root raised cosine is assumed in the receive path, followed
by despreading and then depiloting. At this point, the modulation has been removed and an
intersymbol phase difference can be used and accumulated over N pilot symbols.
In the block diagram in Fig. 7.98, the received signal is represented as
(7.142) r(t) Scr(t) # p(t) # h(t)
3G WIDEBAND CDMA 421
FIGURE 7.98 FLL block diagram.
X
ej2????†ft
r(t)
RC X
Ts
* Scr
x(t)
FED
X
e??“j( )
X
( )*
LPF ?‰… Q
I
Q
tan??“1 X +
T
X
Pilot
BW
Gain
y(t)
z(t)
SF
??
N
1
N
??›
??› ??›
??›
??
Let??™s assume the spectral down-conversion operation performed by the quadrature demodulator has
a residual frequency offset equal to f Hz. The residual frequency offset manifests itself in the following
manner:
(7.143)
After despreading and depiloting, we have
(7.144)
This signal enters the Frequency Error Discriminator (FED) to produce
(7.145)
(7.146) z(t) > Zh(t) Z2 # ej2pf Ts
z(t) h(t) # h*(t Ts) # ej2pft # ej2pf(tTs)
y(t) ZScr(t) Z2 # Zp(t) Z2 # h(t) # ej2pft
x(t) Scr(t) # p(t) # h(t) # ej2pft
where the frequency offset estimated is equal to f u/2pTs.
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