A decomposition technique for efficient generation of correlated Nakagami fading channels

Correlated Nakagami m-fading is commonly encountered in wireless communications. Its generation in a laboratory, environment is therefore of theoretical and practical importance. However, no generic technique for this purpose is available in the literature. Correlated Rayleigh fading is easy to simulate since it has a simple relationship with a complex Gaussian process, Unfortunately, this is not the case for Nakagami fading, The difficulty lies in that the fading parameter call be a real number and there is no general theory linking a Nakagami vector to a finite set of correlated Gaussian vectors. In this paper, by introducing a direct-sum decomposition principle and determining the statistical mapping between the correlated Nakagami process and a set of Gaussian vectors for its generation, a simple general procedure is derived for the generation of correlated Nakagami channels with arbitrary parameters. A key parameter in the statistical mapping can he determined by using an iterative method. The validity of the new technique is examined through the generation of a correlated Nakagami sequence, as encountered in U.S. digital cellular, and a multibranch vector channel as encountered in diversity reception.