Tc
0
??«
dt
2P ?· b(t??“t) ?· c(t??“t) ?· S(t??“t) =
cos[2pfct ??“ t]
The first operation performed in the above receiver is to spectrally down convert the received signal
s(t ) to the baseband z(t), which is given below with the assumption of ideal carrier recovery.
(7.3)
Once this signal is multiplied by the locally generated PN sequence, appropriately shifted in time
to account for the propagation time delay, we get the following intermediate value, assuming is an
estimate of the propagation time delay t:
(7.4)
If , there is no timing offset and perfect synchronization occurs. In this case, we have the
despreader output signal represented as
(7.5) I(t) P # b
^
(t t) # PG
t t^
x(t) P # b(t t) # c(t t) # c(t t^
)
t^
z(t) P # b(t t) # c(t t)
assuming the autocorrelation of the PN sequence has been set to the PG value. A point worth mentioning
here is if the time delay between two arriving multipath rays is less than the chip time Tc ,
then the received signals are difficult to be resolved due to the interchip interference (ICI). This is
commonly called interpath interference (IPI). On the other hand, if Tc, we can resolve the multipaths
with the conventional RAKE receiver.
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