A low complexity optimal spectrum balancing algorithm for digital subscriber lines

In modern DSL systems, multi-user crosstalk is a major source of performance degradation. Optimal spectrum balancing (OSB) is a centralized algorithm that mitigates the effect of crosstalk by allocating optimal transmit spectra to all interfering DSL modems. By the use of Lagrange multipliers the algorithm decouples the spectrum management problem into per-tone optimization problems. The remaining issues are then finding the Lagrange multipliers that enforce the constraints and solving the per-tone optimization problems. 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 20–50, independent of the number of users. Secondly, the complexity of the per-tone optimization problems grows exponentially with the number of lines in the binder. For multiple-user scenarios this becomes computationally intractable. This paper presents an efficient branch-and-bound approach for the per-tone optimization problem. Simulations show enormous complexity reductions, especially for a large number of users.