7) Rxx(0)
1
T 3
T
2
T
2
x2(t) dt
(` t `) Rxx(t)
1
T 3
T
2
T
2
x(t) # x(t t)dt
Normalizing the above autocorrelation by the average signal power gives the following:
(7.8)
This can also be described by the following formula:
(7.9)
Here we count the number of chip positions where the values agree or have the same sign, and we
subtract from this the number of chip positions where the values are not the same or disagree. This is
used to explain the value of Rcc() being equal to 1/15 for the previous example. In this case, the allzero
PN sequence is not a valid sequence which can be easily confirmed if one sets the state of the
above PN generator to the all-zero state. Also, the autocorrelation waveform drawn above assumes no
pulse-shaping filter was used in the comparison. In reality, an LPF needs to be used, and this will
result in widening the width as well as changing the general shape of the autocorrelation function to
resemble the windowed sinc(x) function.
7.3 2G IS-95 CDMA DISCUSSION
CDMA is a multiple-access technique, where multiple users can share the same time and frequency
domains while remaining distinct in the code domain (e.g., applying the orthogonality principle).
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