B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

11 .6 Code Division Multiple-Access (CDMA) of DSSS 633
short code CDMA systems, the cross-correlation coefficient between two spreading codes is a
constant
Note that the decision variable of the ith receiver is
(11.30)
(11.31)
The term I i ) is an additional term resulting from the multiple-access interference of the M - 1
interfering signals. When the spreading codes are selected to satisfy the orthogonality condition
then the CDMA multiple-access interference is zero, and each CDMA user obtains performance
identical to that of the single DSSS user or a single baseband QAM user.
There are various ways to generate orthogonal spreading codes. Walsh-Hadamard codes
are the best-known orthogonal spreading codes. Given a code length of L identical to the
spreading factor, there are a total of L orthogonal Walsh-Hadamard codes. A simple example
of the Walsh-Hadamard code for L = 8 is given here. Each row in the matrix of Eq. (11.32) is
a spreading code of length 8:
+1 +1 +l +1 +1 +l +1 +l
+1 -1 +l -1 +l -1 +l -1
+1 +l -1 -1 +l +1 -1 -1
Ws = +l -1 -1 +l +l -1 -1 +1
+l +1 +1 +1 -1 -1 -1 -1
+1 -1 +1 -1 -1 +1 -1 +1
+1 +1 -1 -1 -1 -1 +1 +1
+1 -1 -1 +1 -1 +1 +1 -1
(11.32)
At the next level, Walsh-Hadamard code has length 16, which can be obtained from Ws via
In fact, starting from W 1 = [ 1 ] with k = 0, this recursion can be used to generate length
L = 2 k Walsh-Hadamard codes.
Gaussian Approximation of Nonorthogonal MAI
In practical applications, many user spreading codes are not fully orthogonal. As a result, the
effect of MAI on user detection performance may be serious. To analyze the effect of MAI on a
single-user receiver, we need to study the MAI probability distribution. The exact probability
analysis of h is difficult. An alternative is to use a good approximation. When M is large, one
may invoke the central limit theorem to approximate the MAI as a Gaussian random variable.