Three-dimensional multipath shape factors for spatial modeling of wireless channels

This paper develops a generalized theory of multipath shape factors used to study the small-scale fading statistics in three-dimensional non-omnidirectional multipath channels. Previous results for horizontal propagation channels are special cases of the present framework when the multipath angular power density (APD) and the travel direction of the mobile unit are confined to a plane. The three-dimensional multipath shape factors are derived in terms of the first three degrees of unnormalized spherical harmonics of the APD. Based on the so derived shape factors, analytical expressions for the level crossing rate, average fade duration and approximate envelope correlation are derived for a Rayleigh fading three-dimensional channel.

[1]  R. Clarke,et al.  3-D mobile radio channel statistics , 1997 .

[2]  R.A. Kennedy,et al.  Spatial correlation for general distributions of scatterers , 2002, IEEE Signal Processing Letters.

[3]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[4]  Bernard H. Fleury,et al.  First- and second-order characterization of direction dispersion and space selectivity in the radio channel , 2000, IEEE Trans. Inf. Theory.

[5]  E. Bonek,et al.  Directional macro-cell channel characterization from urban measurements , 2000 .

[6]  Jaunty T. Y. Ho.  Generalized Doppler power spectrum for 3D non-isotropic scattering environments , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[7]  M. Gans.  A power-spectral theory of propagation in the mobile-radio environment , 1972 .

[8]  S.A. Kotsopoulos,et al.  A Small Scale Fading Model with Sectored and Three Dimensional Diffuse Scattering , 2008, 2008 5th IEEE Consumer Communications and Networking Conference.

[9]  Outi Kivekäs,et al.  Angular power distribution and mean effective gain of mobile antenna in different propagation environments , 2002, IEEE Trans. Veh. Technol..

[10]  W. W. Bell,et al.  Special Functions for Scientists and Engineers , 1968 .

[11]  Donald C. Cox,et al.  A generalized Doppler power spectrum for wireless environments , 1999, IEEE Communications Letters.

[12]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[13]  Theodore S. Rappaport,et al.  Theory of multipath shape factors for small-scale fading wireless channels , 2000 .

[14]  R. Clarke.  A statistical theory of mobile-radio reception , 1968 .

[15]  E. Bonek,et al.  High-resolution 3-D direction-of-arrival determination for urban mobile radio , 1997 .

[16]  Andrew R. Nix,et al.  A Novel Quantification of 3D Directional Spread from Small-Scale Fading Analysis , 2006, 2006 IEEE International Conference on Communications.