On dimensionality of multipath fields: Spatial extent and richness

We establish that an arbitrary narrowband multipath field in any circular region in two dimensional space has an intrinsic functional dimensionality of (πe)R/λ ≈ 8.54 R/λ that scales only linearly with radius R/λ in wavelengths. This result implies there is no such thing as an arbitrarily complicated multipath field. That is, a field generated by any number of nearfield and farfield, specular and diffuse multipath reflections is no more complicated than a field generated by a limited number plane waves. As such, there are limits on how rich multipath can be. This result has significant implications including means: i) to determine a parsimonious parameterization for arbitrary multipath fields, ii) of synthesizing arbitrary multipath fields with arbitrarily located nearfield or farfield, spatially discrete or continuous sources. We give examples of multipath field analysis and synthesis.