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 sta-tions, can be achieved by optimally allocating transmit pow-ers 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 solu-tion can be reduced to a search in a one-dimensional space. In this paper we rst 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 eort. Because rather than carrying out nu-merical search on a set of intervals, only a few explicitly determined points should now be examined