An efficient Lagrange multiplier search algorithm for Optimal Spectrum Balancing in crosstalk dominated xDSL systems

In modern DSL systems, multi-user crosstalk is the major source of performance degradation. Optimal Spectrum Balancing (OSB) is a centralized algorithm that optimally allocates the available transmit power over frequencies, thereby mitigating the effect of crosstalk. OSB uses Lagrange multipliers to enforce constraints that are coupled over frequencies. However, finding the optimal Lagrange multipliers can become complex when more than two users are considered. Starting from the single user case, this paper presents a number of properties, which are then extended to the multi-user case and lead to an efficient search algorithm for the Lagrange multipliers. Simulations show that the number of Lagrange multiplier evaluations is as small as 40, independent of the number of users, which is much faster than currently known search algorithms.