Low-complexity optimal discrete-rate spectrum balancing in digital subscriber lines

Discrete-rate spectrum balancing in interference-limited multi-user and multi-carrier digital subscriber lines (DSL) is a large-scale, non-convex and combinatorial problem. Previously proposed algorithms for its (dual) optimal solution are only applicable for networks with few users, while the suboptimality of less complex bit-loading algorithms has not been adequately studied so far. We deploy constrained optimization techniques as well as problem-specific branch-and-bound and search-space reduction methods, which for the first time give a low-complexity guarantee of optimality in certain multi-user DSL networks of practical size. Simulation results precisely quantify the suboptimality of multi-user bit-loading schemes in a thousand ADSL2 scenarios under measured channel data.

► Low-complexity optimal methods for discrete-rate spectrum balancing in DSL. ► Problem-specific branch-and-bound search with linear memory requirements. ► Dependency of the combinatorial search complexity on the Lagrange multipliers. ► Convex problem relaxation effective for low target-rates and low-bandwidth systems. ► Greedy multi-user bit-loading is provably near-optimal under real cable measurements.