GMRES algorithm for large-scale vectoring in DSL systems

We propose an iterative crosstalk cancellation scheme based on the generalized minimal residual (GMRES) algorithm for large-scale digital subscriber line (DSL) systems. The proposed scheme does not require channel inversion and stores fewer vectors for crosstalk cancellation. We analyze the convergence of the GMRES algorithm and derive computable bounds on the residual error and signal-to-noise ratio in terms of system parameters at each iteration for upstream DSL systems. We show that the GMRES algorithm typically requires a single iteration for very large vectored systems to achieve crosstalk-free performance for the very high-speed DSL (VDSL) frequencies and only a few more in the highest frequency bands of the G.fast spectrum. This yields significant complexity savings and reduction in memory storage, compared to the zero forcing scheme under certain conditions.