Low-complexity near-optimal spectrum balancing for digital subscriber lines

This paper investigates the multiuser spectrum optimization problem for digital subscriber lines. We propose an iterative and low-complexity spectrum optimization technique that improves upon the recently proposed optimal spectrum balancing (OSB) algorithm. In the optimal spectrum balancing algorithm, the Lagrange multipliers are used to decouple the constrained optimization problem into a series of per-tone unconstrained optimization problems. However, each per-tone problem still has a computational complexity that is exponential in the number of users. This paper proposes an iterative algorithm for the per-tone optimization problem to further reduce the computational complexity of spectrum balancing. The essential idea resembles that of iterative water-filling. In each step of the algorithm, each individual user iteratively optimizes the joint objective function with a fixed set of Lagrange multipliers. The new algorithm has a computational complexity that is polynomial in the number of users. Simulation results show that the new algorithm has a near-optimal performance.