Theory of Multipath Shape Factors for Small-Scale Fading Wireless Channels

This paper presents a new theory of multipath shape factors that greatly simplifies the description of small-scale fading statistics of a wireless receiver. A method is presented for reducing a multipath channel with arbitrary spatial complexity to three shape factors that have simple intuitive geometrical interpretations. Furthermore, these shape factors are shown to describe the statistics of received signal fluctuations in a fading multipath channel. Analytical expressions for level-crossing rate, average fade duration, envelope autocovariance, and coherence distance are all derived using the new shape factor theory and then applied to several classical examples for comparison.