**Abstract**

In this chapter, the physical propagation environment of radio waves is described in terms of scattering clusters, in which each cluster could include many scattering objects. We use each single distant scattering cluster to study the characteristics of channel second-order statistics (CSOS) and build the multiple-input and multiple-output (MIMO) radio channels in accordance with the correlation properties of the channel. In this approach, each distant scattering cluster contributes a portion to the Doppler spectrum and corresponds to a state-space single-input and singleoutput (SISO) channel model. A MIMO channel model is then constructed by connecting multiple SISO channel models in parallel, in which a coloring matrix is used to adjust the channel spatial correlation properties between the SISO channels. A MIMO-OFDM (orthogonal frequency-division multiplexing) channel model is obtained in the same manner. This time, however, another matrix is used to adjust the channel spectral correlation properties between the MIMO channels. This approach has three advantages: Simple, the entire Doppler power spectrum can be formed from multiple uncorrelated distant scattering clusters, and the channels contributed by these clusters can be obtained by summing up the individual channels. In this way, we can reassemble the radio wave propagation environment in a simulated manner.

**Keywords:** channel second-order statistics, Cauchy-Rayleigh cluster, Rayleigh cluster, AOA, AOD, TOA, AR model, phase-shift method, SISO, MIMO, MIMO-OFDM, state-space model
