Throughout the history of wireless communications, spatial antenna diversity has been important in improving the radio link between wireless users. Historically, microscopic antenna diversity has been used to reduce the fading seen by a radio receiver, whereas macroscopic diversity provides multiple listening posts to ensure that mobile communication links remain intact over a wide geographic area. In recent years, the concepts of spatial diversity have been expanded to build foundations for emerging technologies, such as smart (adaptive) antennas and position location systems. Smart antennas hold great promise for increasing the capacity of wireless communications because they radiate and receive energy only in the intended directions, thereby greatly reducing interference. To properly design, analyze, and implement smart antennas and to exploit spatial processing in emerging wireless systems, accurate radio channel models that incorporate spatial characteristics are necessary. In this tutorial, we review the key concepts in spatial channel modeling and present emerging approaches. We also review the research issues in developing and using spatial channel models for adaptive antennas.

With the introduction of antenna array systems into wireless communication networks comes the need to better understand the spatial characteristics of the channel. Scattering models provide both angle of arrival (AOA) and time of arrival (TOA) statistics of the channel. A number of different scattering models have been proposed in the literature including elliptical and circular models. These models assume that scatterers lie within an elliptical and circular region in space, respectively. In this paper, the joint TOA/AOA, the marginal TOA, and the marginal AOA probability density functions (pdf's) are derived for the elliptical and circular scattering models. These pdf's provide insight into the properties of the spatial wireless channel.

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