Signal processing for G.fast+

The first version of G.fast occupies frequencies up to 106 MHz and uses relatively simple linear channel-inverting matrix precoders to cancel the crosstalk in a multi-pair telephone cable. However, to truly deliver Gbps+ data rates to most customers, even higher frequencies should be used; where the crosstalk can be stronger than the signal, and so more advanced non-linear signal processing is envisioned. This paper derives optimum signal processing structures for G.fast crosstalk cancelling precoders, and compares approximate and optimum linear and non-linear structures for G.fast running up to 212 MHz. The optimum linear and non-linear precoders are derived. Simulations compare the performance of optimum and QR-decomposition based non-linear precoders, and find that the QR-decomposition with Tomlinson-Harishima precoding is practically optimal. An algorithm is shown for maximizing the minimum bit rate for line ordering of nonlinear precoders; this algorithm is shown to have max-min performance near the optimum.