Broadcast channel optimal spectrum balancing (BC-OSB) with per-modem total power constraints for downstream DSL

In this paper we investigate the problem of optimal power allocation in a BC by exploiting the duality with MAC. We first describe an algorithm for power allocation under a total power constraint. Then, the BC-OSB algorithm is devised for BC power allocation under per-modem total power constraints, where the Lagrange multipliers of the dual problem formulation are transferred into the optimization function by means of a precoding matrix, such that the MAC-BC duality can again be exploited. Simulation results are given for a VDSL2 scenario, and also for a theoretical multi-user independent flat-fading Rayleigh environment.