Resumen
In this paper we introduce a Gaussian approximation for the achievable downstream bit rate per user in modern broadband and ultra-broadband digital subscriber loop-based access systems. The considered formulation allows one to account for the main characteristics of the interference scenario (e.g., number and positions of interferers along the cable), the far-end crosstalk (FEXT) fluctuations, bit loading limitation per sub-carrier, and approximated zero forcing in vectoring pre-coding. Formulas are obtained assuming log-normal statistics for the signal-to-interference plus noise ratio per sub-carrier. The validity of the considered approximation has been assessed by computer calculation. A very good agreement between the exact and the approximated bit rates is obtained. The bit rate approximation is then used to analyze the performance of a very high-speed digital subscriber line type 2 (VDSL2, Profile 35b) with vectoring and used to assess G.fast performance degradation when approximated zero forcing in vectoring pre-coding is applied. It is observed for G.fast performance that degradation due to residual FEXT after vectoring pre-coding can be relevant. A significant performance improvement can be achieved at the expense of increased computational complexity of the vectoring pre-coding.