In this thesis, we simulate multipath fading which is assumed to have Rayleigh or Rician distribution under the non-line-of sight or line-of-sight condition respectively; as well as spatial shadowing process, assumed to be log-normally distributed. We propose a low-complexity high performance Rayleigh fading simulator, an autoregressive moving average (ARMA)(3,3) model. This proposed method is a variant of the method of filtering of the white Gaussian noise where the filter design is accomplished in the analog domain and transferred into the digital domain. The proposed model is compared with improved Jakes. model, autoregressive (AR) filtering and inverse discrete Fourier transform (IDFT) techniques, in performance and computational complexity. The proposed method outperforms AR(20) filter and modified Jakes. generators in performance. Although IDFT method achieves the best performance, it brings a significant cost in storage which is undesirable.The proposed method achieves high performance with the lowest complexity.Additionally, we apply the quantized filter extension of our proposed filter design, since quantized filters are generally used in hardware implementations due to their minimum power consumption, minimum heat generation and their computational efficiency. We simulate spatial shadowing process, via the simulation method proposed by Patzold and Nguyen. This method is derived from a reference model by using the sum of sinusoids principle. There are two methods enabling the fitting of the simulation model to the reference model with respect to the probability density function (pdf) of the received signal strength as well as to a given autocorrelation function with a decaying exponential shape.Furthermore we use our predicted autocorrelation function obtained via the site-specific radio propagation prediction software named Wireless InSite in order to determine the model parameters.