Jointly optimal power and signature sequence allocation for fading CDMA

We solve for the optimum signature sequence and power allocation policies that maximize the information theoretic ergodic sum capacity of a code division multiple access (CDMA) system subject to fading. We show that at most N users may transmit at any given channel state, where N is the processing gain; and those users who are transmitting should be assigned orthogonal signature sequences. We also show that the power allocation policy that maximizes the capacity together with the choice of these signature sequences is single user waterfilling over sets of channel states that are favorable to each user. That is, the capacity maximizing signalling scheme is shown to dictate that the users allocate their powers and signature sequences in such a way that they always avoid interference from each other.