A method and transmitter unit in a multi-tone multi-line based transmission system such as a digital subscriber line system for determining a Power Spectral Density (PSD) of a plurality of users over a physical channel for at least one tone. Each of the users has a minimum required data rate and a maximum allowed power. A Power Minimization Problem (PMP) is formulated mathematically introducing Lagrangian multipliers and by utilizing a dual decomposition approach for the objective function of the PMP in order to solve the PMP on a per-tone basis.