A Schur-saddle function property in CDMA

We consider code division multiaccess (DS-CDMA) with colored additive Gaussian noise. The best “performance” (by an appropriate choice of powers and signature sequences of the users) of this multiple access scheme is a function of the constraints/requirements of the individual users and of the structure of the additive colored noise. The thesis of this paper is that this function has a saddle property: it is convex in the covariance of the additive noise and concave in the user constraints/requirements. By working on a partial order on probability measures (the Schur-order or the order of dilation), we strengthen this thesis by showing that the performance of CDMA is Schur-order preserving. In other words, the more skewed the user constraints/requirements are, the performance decreases. On the other hand, the more skewed the covariance of the additive noise is, the performance increases. In contrast, we show that this saddle function property breaks down if the signature sequences cannot be specifically designed and are instead chosen randomly