Iterative algorithm for finding optimal resource allocations in symbol-asynchronous CDMA channels with different SIR requirements

In this paper, we consider the problem of admissibility in a symbol-asynchronous CDMA (A-CDMA) channel with random signal delays and different SIR requirements. We say that users are admissible in a CDMA channel with the power constraints if one can assign sequences to the users and control their power so that each user meets its SIR requirement. The problem is shown to be equivalent to minimizing the spectral radius of a certain primitive matrix with respect to all sequence sets. Since a closed form solution is notoriously difficult to obtain, we propose an iterative algorithm that is shown to monotonically converge to a local minimum.