Finding the parameters of a Bernoulli-Gaussian Model
A transmission medium perturbed by an additive noise from which the estimated noise power is all information known, is better modeled as a Gaussian channel. Since the Gaussian channel is, according to Information Theory, the worst channel to transmit information through, this is the most pessimistic assumption. When noise samples are available though, choosing to model the transmission medium using a more sophisticated model pays off. The Bernoulli-Gaussian channel, would be one such a choice. Finding the three parameters that characterize the Bernoulli-Gaussian stochastic process which mathematically models the noise is a task of paramount importance. Many algorithms can be used to estimate the parameters of this model based on numerical methods. In the current work a closed form expression to estimate the model parameters is presented. All that is required besides the estimation of the power of Bernoulli-Gaussian process from the available noise samples is the estimation of two additional quantities: the expected value of the absolute value of the amplitude of the process—the first absolute moment—plus the third absolute moment, viz., the expected value of the third power of the absolute value of the process. An alternative option, often used for power line communication, is to model the transmission medium as a channel in which the noise is represented by a three parameter stochastic process called Middleton Class A. Other models (like generalized-Bernoulli-Gaussian, or Bernoulli- Gaussian with memory) might render a better medium model than the Bernoulli-Gaussian channel. Estimating the parameters of these processes is however a cumbersome task and, as we show in the current work, the rate harvested by using the simple, yet more sophisticated, Bernoulli-Gaussian channel is increased as compared to the, more pessimistic, Gaussian channel, allowing one thus to more closely approach the true capacity. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the true noise. The incorporation of the Bernoulli-Gaussian channel in the communication system model leads to a better design as corroborated by the computer simulation results presented.