Probability distributions for multiplicative noise in internet associated wireless cells and in speckled images

Multiplicative noise degrades the performance of internet-associated wireless peripheral systems, most notably small femto- and pico-cells in a WPAN environment. In addition, multiplicative noise also complicates the processing of images in coherent systems such as ultrasound and synthetic aperture radars (SAR). When the target resolution cell is very small, the statistics of multiplicative noise is not analytically tractable and pose a serious challenge to developing closed canonical forms that can be analyzed and used in the design of efficient and optimal receivers. In this context, noise is referred to as stochastically local fading in the case of wireless channels and partially developed speckle in the case of coherent imaging systems. In many analytical investigation of multiplicative noise, the exponential or Gamma statistics are invoked. More recent advances by the primary author of this paper have utilized a Poisson modulated and weighted generalized Laguerre polynomials with floating parameters and uncorrelated noise assumptions. In this paper, we provide improved stochastic models for this type of multiplicative noise, we estimate the model parameters using a moment matching structure, and we generalize the results to the case of correlated noise.