Analysis of Zero-Forcing Vectoring for VDSL2 and Long Reach VDSL Technologies

A Normal approximation for the downstream bit rate per user in modern Fiber-to-the-Cabinet DSL-based access systems such as Very high-speed Digital Subscriber Line type 2 (VDSL2) and Long Reach VDSL (LR-VDSL) is presented in this paper. It accounts for the positions of subscribers along the main cable from the Cabinet, for the Far-end cross-talk (FEXT) fluctuations, for the transmitter power spectra of subscribers and for zero forcing vectoring. A stochastic model relating the FEXT to residual FEXT after zero forcing vectoring pre-coding is also presented. The proposed Normal model is derived by assuming Log-normal statistics of the signal-to-interference plus noise ratio per sub-carrier. Its validity is assessed by computer calculation by superimposing the cumulative distribution functions obtained from exact bit rate calculation with those obtained with the Normal model. Differences of few Mbit/s have been observed for high percentiles thus proving the effectiveness of the proposed model. We applied the model to assess coexistence among different DSL technologies such as VDSL2 and LR-VDSL sharing the same copper cable from the Cabinet and even to evaluate the downstream bit rate for G.fast with zero forcing vectoring.