Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Statistical analysis of extreme values
Statistical analysis of extreme values
Minimum mean squared error impulse noise estimation andcancellation
IEEE Transactions on Signal Processing
IEEE Journal on Selected Areas in Communications
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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 u 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.