Log-Normal Approximation for VDSL Performance Evaluation

A performance analysis of VDSL2 technologies in FttC or FttC/FttDp hybrid scenarios requires knowledge of the access network geometry, propagation, and crosstalk interference models. A simulation-based approach is commonly adopted for performance assessment. In this paper, we introduce a performance evaluation framework based on the log-normal approximation for the probabilistic description of the signal-to-interference plus noise ratio (SINR), which is then used to obtain the statistics of the achievable bit rate per user. A very good agreement has been observed between the exact and the approximated calculations of the bit rate up to 600 m from the Cabinet. In addition, the log-normal approximation has allowed to define a simple procedure, based on the equivalent number of co-located interferers, to evaluate the bit rate per user for generic access network geometry. Furthermore, two approximated formulas for bit rate have been obtained under high SINR and dominant far-end crosstalk (FEXT) conditions. They evidence the logarithmic decrease of the bit rate with the distance from the Cabinet and provide the accurate results for distances up to 400 m. Finally, when FEXT fluctuations are modeled in accordance with Beta distribution, we have observed the log-normal approximation still provides valid probabilistic description of the SINR