Consider the uplink of a single-cell CDMA system with N users active all the time. In the text we have assumed the received powers are controlled such that they are exactly equal to the target level needed to deliver the desired SINR requirement for each user. In practice, the received powers are controlled imperfectly due to various factors such as tracking errors and errors in the feedback links. Suppose that when the target received power level is P, the actual received power of user i is EiP, where Ei are i.i.d. random variables whose statistics do not depend on P. Experimental data and theoretical analysis suggest that a good model for Ei is a log normal distribution, i.e., log(Ei) follows a Gaussian distribution with mean µ and variance a2.

1. Assuming there is no power constraint on the users, give an approximate expression for the achievable spectral efficiency (bits/s/Hz) to support N users for a given outage probability pout and cb/I0 requirement /3 for each user.

2. Plot this expression as a function of N for reasonable values of the parameters and compare this to the perfect power control case. Do you see any interference averaging effect?

3. How does this scenario differ from the users' activity averaging example considered in the text?