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

634 SPREAD SPECTRUM COMMUNICATIONS
Recall that the QAM symbols sfl are independent with zero mean and unit variance, that is,
sfl = 0
sk (j) sk (i)* = 0
I
sk (j)
12
= l
Hence, we can approximate the MAI as Gaussian with mean
(11.33)
and variance
(11.34)
The effect of this MAI approximation is a strengthened channel noise. Effectively, the
performance of detection based on decision variable rk i J is degraded by the additional Gaussian
MAL Based on single-user analysis, the new equivalent SNR is degraded and becomes
For the special case ofBPSK or polar signaling, the BER of the ith CDMA user is approximately
(11.35)
Observe that when a single user is present (M = 1 ), Eq. (11.35) becomes the well-known
polar BER result of
as expected. The same result is also true when all spreading codes are mutually orthogonal
such that R;j (k) = 0, i =f- j.
In the extreme case of noise-free systems, when the signal-to-noise ratio is very high
(Eb/N ➔ oo), we obtain
This shows the presence of an irreducible error floor for the MAI limited case. This noise floor
vanishes when the spreading codes are mutually orthogonal such that R;,; (k) = 0 if i =f- j.