An example of such components will be provided next.
With respect to the above AFC block diagram, let us represent the differential detector output as
(assuming the compensation loop is open)
(6.112)
where T the time separation between samples compared and residual frequency offset present
on the signal.
(6.113) d(t) h(t) # h*(t T) # ej[u(t)u(tT )vT ]
d(t) 5h(t) # ej[u(t)vt]6# 5h(t T) # ej[u(tT )v(tT )]6*
RECEIVER DIGITAL SIGNAL PROCESSING 331
LPF X
BPF
X LPF
ADC Filter
ADC Filter
Baseband
Section
~
LNA GCA
90?°
LPF DAC
RI(t)
RQ(t)
AFC
COS[wct + ??†wt]
FIGURE 6.41 Typical receiver architecture with emphasis on frequency control.6
6 LNA Low Noise Amplifier, BPF Band Pass Filter, and GCA Gain Control Amplifier.
Assuming differential encoding this can be represented as
(6.114)
We discuss two options: first without differential encoding modulation and second with differential
encoding. In the absence of modulation the expectation of the differential detector output produces
the channel autocorrelation function.
(6.115)
where d the maximum Doppler spread, 2
h fading channel power. The frequency error can then
be easily determined as
(6.116)
(6.117)
The second option is when the modulation is present and is discussed next.
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