  Non-Gaussian impulsive noise (IN) with memory exists in many practical
applications. When it is mixed with white Gaussian noise (WGN), the resultant
mixed noise will be bursty. The performance of communication systems will
degrade significantly under bursty mixed noise if the bursty characteristic is
ignored. A proper model for the bursty mixed noise and corresponding algorithms
needs to be designed to obtain desirable performance but there is no such model
reported to the best of our knowledge. The important problem is addressed in
the two-part paper. In the first part, we propose a closed-form heavy-tailed
multivariate probability density function (PDF) that to model the bursty mixed
noise. This model is the weighted addition of gaussian distribution and student
distribution. Then, we present the parameter estimation method based on the
empirical characteristic function of the proposed model and analyze the
performance of the parameter estimation. Numerical results show that our
proposed bursty mixed noise model matches the measured bursty noise well.
Meanwhile, the parameters of the proposed noise model can be accurately
estimated in terms of mean square error (MSE).
