Recent works on the analysis of linear multiuser receivers for DS-CDMA applications have
led to capacity-relevant expressions that are the solution of an integral equation
involving Stieltjes transforms of the distribution of transmit powers. The key tools
employed in these works are new results on the asymptotic eigenvalue distributions of
random matrices. Unfortunately, it is only in the particular case of the transmit powers
being equal that the integral
equation has a closed form solution. This paper addresses the same problems pioneered
in the afore-mentioned works, but demonstrates
how an alternative solution is available that, while appealing to
simpler mathematical ideas (principally, the law of large numbers),
also offers flexibility in that the results obtained apply for arbitrary (as opposed to
strictly constant) received powers. An additional advantage is
that the convergence rate of the approximation used here can also be
quantified.