Variational inequality approach to spectrum balancing in vectoring xDSL networks

We study the multi-user and multi-carrier power allocation (spectrum balancing) problem in digital subscriber line (DSL) networks under inter-carrier and inter-user interference as well as self-interference. The key assumption of this work is that we do not have knowledge of the interference coefficients, but only have access to the total per-line interference noise power. Furthermore, lines may support different technologies or be part of linear crosstalk cancellation (Vectoring) groups, which implies coupling among lines through per-transceiver sum-power and spectral mask constraints. We propose a novel generalized Nash equilibrium formulation for spectrum balancing in a virtual network with modified selfinterference coefficients and an associated variational inequality problem. The latter allows for intuitive analytical criteria for algorithms' convergence to a unique solution in the virtual network as well as in the real network, related to the sum of interference coefficients. Exemplarily a fully autonomous projected gradient algorithm is proposed which requires no information exchange among Vectoring groups and obeys transmit power limitations throughout its run-time. The applicability of the proposed framework is demonstrated by testing this algorithm on two previously studied power allocation problems in Vectoring G.fast networks.