Chaotic maps as parsimonious bit error models of wireless channels

The error patterns of a wireless digital communication channel can be described by looking at consecutively correct or erroneous bits (runs and bursts) and at the distribution function of these run and burst lengths. A number of stochastic models exist that can be used to describe these distributions for wireless channels, e.g., the Gilbert-Elliot model. When attempting to apply these models to actually measured error sequences, they fail: measured data gives raise to two essentially different types of error patterns which can not be described using simple error models like Gilbert-Elliot. These two types are distinguished by their run length distribution; one type in particular is characterized by a heavy-tailed run length distribution. This paper shows how the chaotic map model can be used to describe these error types and how to parameterize this model on the basis of measurement data. We show that the chaotic map model is a superior stochastic bit error model for such channels by comparing it with both simple and complex error models. Chaotic maps achieve a modeling accuracy that is far superior to that of simple models and competitive with that of much more complex models, despite needing only six parameters. Furthermore, these parameters have a clear intuitive meaning and are amenable to direct manipulation. In addition, we show how the second type of channels can be well described by a semiMarkov model using a quantized lognormal state holding time distribution.