Homework 10
Problem 1
Consider a system with 3 CDMA users.
a.
Use a coin to generate a random sequence of length 32 for each of the 3 users.
b.
Find the correlation of the sequence of the first user with itself (answer: 32) and with
each of the other two users (call that
1
N
and
2
N
). Also, find the value of
2
1
N
N
+
.
c.
If the first user sent 1, he would receive a value
2
1
N
N
N
Y
+
+
=
? If instead he sent
1, he would have received instead
2
1
N
N
N
Y
+
+

=
. Suppose in the above
experiment, he sent 1. What would be a reasonable way to decide if 1 or 1 was sent?
In your experiment, would he have made an error in deciding?
d.
In general, we may have
K
users and each user uses a random sequence of length
N
as
its CDMA code. It can be shown that the correlations of the first sequence with any
one of the
K1
other sequences is a sum of
N
Bernoulli random variables (values = 1
or 1 with equal probability of ½). Therefore the correlation of the first sequence with
any other sequence has mean zero and variance
N
. In order words, after despreading,
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 Spring '09
 Hui
 2 K, Code division multiple access, Random sequence, 1000 bits, DS spread spectrum

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