On spatial power gradients

The variation of the instantaneous power versus distance for a narrowband channel is an important parameter in modern digital systems, relevant for variations during a burst and for power control algorithms. This paper gives the statistical distribution for the power gradient, both in decibels and in natural units for a Rayleigh fading channel. The former has been known for some time to be Student's t distribution, and the latter has a Laplacian distribution, a new result. Both results are proven here. They are in variance with an approximation given in a previous publication.