Closed form solution for QoS: constrained information--theoretic sum capacity of reverse link CDMA systems

The information-theoretic maximum system capacity in a CDMA network, which guarantees fairness to mobile stations,can be achieved by optimally allocating transmit powers to the mobile stations while imposing individual QoS constraints. Even though this optimization is carried out in a multi-dimensional space we show that the optimal solution can be reduced to a search in a one-dimensional space. In this paper we first show that the previous results can be obtained by a simpler and more intuitive approach. Also, we show that the optimal solution is actually bang--bang. In addition, we show that the candidate solutions can be determined in a closed form. This considerably reduces the computational effort. Because rather than carrying out numerical search on a set of intervals, only a few explicitly determined points should now be examined