For example, consider this simple PN generator with the polynomial given as g(x) 1 x3 x4.
The linear feedback shift register (LFSR) block diagram is shown in Fig. 7.8.
348 CHAPTER SEVEN
FIGURE 7.8 LFSR example of PN code generation.
+
Tc Tc Tc Tc
Output Chip
Sequence
XOR
In this PN code generator, the state is updated by the combination of shifting the contents of the
registers at the chip rate and exclusive ORing certain register outputs to form the feedback signal.
It is well known that the autocorrelation of a square pulse is a triangular waveform [5]. Also, the
autocorrelation of a periodic signal is periodic; these two comments explain the autocorrelation function
Rcc() of the above PN sequence. In Fig. 7.9, we plot the autocorrelation function of the above
PN sequence, where T is used to denote the period of the PN sequence.
0 T
Rcc(t)
1
T
??“
t
FIGURE 7.9 Autocorrelation function of the PN sequence.
Next let us provide the mathematical equations used to describe the autocorrelation function. The
autocorrelation of a periodic signal is given as follows (assuming the time difference between the PN
sequences is equal to ):
(7.6)
where T is the period of the signal. The average power of the received signal is denoted as
(7.
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