Column Generation for Discrete-Rate Multi-User and Multi-Carrier Power Control

We consider a constrained multi-carrier power allocation problem in interference-limited multi-user systems with a finite set of transmission rates. The Lagrange relaxation is a common technique for decomposing such problems into independently solvable per-subcarrier problems. Deviating from this approach our main contribution is the proposal of a novel spectrum management framework based on a Nonlinear Dantzig-Wolfe problem decomposition. It allows for suboptimal initialization and suboptimal power allocation methods with low complexity. While we show that the combinatorial per-subcarrier problems have polynomial complexity in the number of users, we find that such suboptimal methods are indispensable in large systems. Thus we give an overview of various basic dual heuristics and provide simulation results on a set of thousand digital subscriber line (DSL) networks which show the superior performance of our framework compared to previous power control algorithms.