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

11 .6 Code Division Multiple-Access (CDMA) of DSSS 635
The Near-Far Problem
The Gaussian approximation of the MAI has limitations when used to predict system performance.
While the central limit theorem implies that /pi will tend toward a Gaussian distribution
near the center of its distribution, convergence may require very large number of CDMA
users M. In a typical CDMA system, the user number M is only in the order of 64 to 128.
When M is not sufficiently large, the Gaussian approximation of the MAI may be highly
inaccurate, particularly in a near-far environment.
The so-called near-fa r environment describes the following scenario.
The desired transmitter is much farther away from its receivers than some interfering
transmitters.
The spreading codes are not mutually orthogonal; that is, R;,j (k) 'I- 0 when i f- j.
If we assume identical user transmission power in all cases, (i.e., P j
= P 0 ), in the near-far
environment the desired signal channel gain g; is much smaller than some interferers' channel
gains. In other words, there may exist some user set :J such that
j E J (11.36)
As a result, Eq. (11.31) becomes
(11.37)
where we have defined an equivalent noise term
(11.38)
that is approximately Gaussian.
In a near-far environment, it becomes likely that the smaller signal channel gain and the
nonzero cross-correlation result in the domination of the (far) signal component
by the strong (near) interference
(i)
g;R;,; (k)s k
The Gaussian approximation analysis of the BER in Eq. (11.35) no longer applies.
Exam pie l l . 3 Consider a CDMA system with two users (M = 2). Both signal transmission powers are 10 mW .
The receiver for user 1 can receive signals from both user signals. To this receiver, the two
signal channel gains are