Bounds on the spatial extrapolation of multipath in long-range prediction of mobile signals

A bound is derived for the extent to which narrowband knowledge of a multipath field inside a spatially limited region can be extrapolated beyond that region. The bound is independent of any model which may be applied to the multipath field, relying on the field being a solution to the homogeneous Helmholtz wave equation. The bound has implications for the extent and reliability of long range channel prediction particularly when the multipath is diffuse.