The statistical nature of impulse noise interarrival times in digital subscriber loop systems

The increasing demand for reliable, high-speed data transmission over the local loop utilizing xDSL technologies has prompted fresh studies into the nature and statistics of impulse noise. With a given dB margin specified on other noise (e.g. AWGN, NEXT, FEXT, etc.), impulse noise is known to be the most likely cause of error on a DSL in operation. The interarrival statistics of real impulse noise events are examined; from this examination and subsequent analysis, a Markov renewal process (MRP) model (wherein ranges of interarrival times are the Markov states) is proposed. Within this model. Poisson or Pareto probability distributions are assigned to Markov states as appropriate thereby accommodating the insights of prior studies as well as current findings. Importantly, the MRP model mirrors the clustering exhibited in real data. For events in excess of a threshold it a heavy-tailed distribution is observed. Such excesses fit a generalized Pareto distribution and are accommodated naturally within the overall MRP model as the highest Markov state. (C) 2002 Elsevier Science B.V. All rights reserved.