A Dual Decomposition Approach to the Sum Power Gaussian Vector Multiple Access Channel Sum Capacity Problem

The Gaussian vector multiple access channel with a sum-power constraint across all users, rather than the usual individual power constraint on each user, has recently been shown to be the dual of a Gaussian vector broadcast channel (1) (2). Further, a numerical algorithm for the sum capacity under the sum power constraint has been proposed in (3). This paper proposes a different algorithm for this prob- lem based on a dual decomposition approach. The proposed algorithm works in the Lagrangian dual do- main; it is based on a modified iterative water-filling algorithm for the multiple access channel; and it is guaranteed to converge to the sum capacity in all cases. This spectrum optimization problem for the sum-power multiple access channel is also applicable to the optimal power allocation problem for an OFDM system with correlated noise.