Sum capacity of DS-CDMA with colored noise

We consider a Direct Sequence Code Division Multiple Access (DS-CDMA) channel in colored additive Gaussian noise and focus on the sum capacity of this channel. Sum Capacity is the maximum sum of rates at which users can jointly reliably transmit, in an information theoretic sense. We completely characterize optimum sum capacity, which is obtained by choosing the signature sequences of the users appropriately. Our characterization is constructive in that we provide a combinatorial algorithm to generate the optimum signature sequences as a function of the covariance of the additive background noise and power constraints of the users. The characterization also allows us to identify a saddle property of the optimum sum capacity: convexity in the covariance matrix of the additive noise and concavity in the vector of user power constraints.