A novel stochastic model and fast generation method for Nakagami fading channels

Nakagami fading channels are widely accepted to model a variety of wireless channels. They are parameterized by the m-factor, which can take on any value m > 0. The case m = 1 subsumes Rayleigh fading, while 0 < m < 1 models channels that exhibit a larger percentage of deep fades. The Nakagami amplitude distribution is closely related to the gamma distribution, which describes the instantaneous intensity. In this paper, we address generation of random samples from the univariate Nakagami or equivalently, the gamma distribution. When m takes on integral values, a simple stochastic description in terms of exponential variates is commonly employed. Recently acceptance-rejection techniques have been described that hold for non-integral m. We describe a little known stochastic description as the product of uniform variates, and provide a simple approximate description which allows for rapid generation of Nakagami variates with very few random degrees of freedom. The stochastic model is also of interest in that it suggests new interpretations of Nakagami fading as a random product model.