  This paper deals with fading and/or near-far effects with or without power
control on the evaluation of the sum capacity of finite dimensional Code
Division Multiple Access (CDMA) systems for binary and finite nonbinary inputs
and signature matrices. Important results of this paper are that the knowledge
of the received power variations due to input power differences, fading and/or
near-far effects can significantly improve the sum capacity. Also traditional
power controls can not improve the sum capacity; for the asymptotic case, any
type of power control on the near-far effects is equivalent to the case without
any power control. Moreover, for the asymptotic case, we have developed a
method that determines bounds for the fading/near-far sum capacity with
imperfect power estimation from the actual sum capacity of a CDMA system with
perfect power estimation. To show the power and utility of the results, a
number of sum capacity bounds for special cases are numerically evaluated.
