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 can 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 be 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.