3-D Spatial Spread Quantifiers for Multipath Fading Wireless Channels

This letter proposes a novel generalized method to quantify the angular dispersion of radiated energy in realistic 3-D space. Based on the first three coefficients of the 2-D Fourier transform, simple mathematical expressions are derived to independently or jointly quantify the angular dispersion of energy in a reduced 2-D or realistic 3-D space, respectively. The proposed quantifiers include mean direction of arrival, circular variance, true standard deviation, angular spreads, angular constriction, and direction of maximum fading. The proposed quantifiers are helpful in establishing an appropriate mechanism to measure the angular dispersion in 3-D space. These quantifiers provide results in radians with true physical meaning unlike their counterparts in the literature. Moreover, an analysis on the impact of distribution truncation/distortion on the degree of accuracy in measuring the angular dispersion is presented which signifies the importance of true angular spread quantification. The proposed quantifiers can thus be considered as an appropriate goodness-of-fit criterion in the characterization of spatial statistics of multipath fading channels.