The present invention relates to electromagnetic radiation, more particularly to methods and systems for analytically modeling electromagnetic (e.g., radio frequency) wave propagation between two or more locations.
When radar operates in the presence of any terrain or water surface, radar energy is reflected from that surface. For instance, when there are sea surface interactions, as radar energy propagates from the transmitter to the target and then back again, a portion of that radar energy impinges the sea, thus representing “sea surface interactions.” The term “forward scattering” conventionally refers to the forward propagating energy that is scattered from the surface. Forward scattering is the portion of the sea interaction that scatters in the direction of radar propagation (either to the target or to the receiver). The term “back scattering” (also called “back scatter” or “sea clutter”) conventionally refers to the radar energy from the transmitter that is scattered from the sea surface directly to the receiver. Sea clutter is a kind of environmental noise.
The term “multipath” conventionally refers to the physical phenomenon whereby electromagnetic energy propagates via multiple paths to the target and then returns via multiple paths. Multipath propagation by nature involves surface scattering. In the case of radar, for instance, radio waves propagate via multiple paths from a transmitter, reach a target, and return to a receiver via multiple paths. Forward scattering, as well as the direct path or line-of-sight, illuminates the target. The target then reradiates or scatters the incident radio frequency (RF) energy, and a portion of that energy returns to the receiver (via the direct path and another forward scattering path). According to the traditional “four-route” view, multipath is characterized by four paths taken by RF energy between the transmitter and receiver, viz.: (i) direct path-target-direct path; (ii) direct path-target-forward scatter; (iii) forward scatter-target-direct path; (iv) forward scatter-target-forward scatter.
There are several problems with the traditional four-route multipath notion. The four-route scheme combines everything into three propagation terms, viz., “direct path,” “forward scatter” and “target.” Reflectivity p is assumed equal for all paths; however, water's BRDF, for instance, is strongly angle dependent. The four-route view assumes reciprocity insofar as there being a point source on the departure path and a complex, distributed source on the return path. The four-route view ignores shadowing, wave direction, ducting, etc.; in particular, it assumes only one on-axis specular bounce. The four-route view treats scatterers each as a point scatterer, and thus neglects E-field deviation across the scatterer. The four-route view takes a frequency domain approach, thereby ignoring pulse spreading by path difference, and leaving unknown the sea surface scattering zone.
Currently there are no validated rigorous models for multipath. The dominant methodology of today adopts a physical optics approach that uses ray propagation methods for the direct paths and the forward scattered paths. The direct paths are well understood, but the forward scattered paths are each divided into two components, viz., a coherent portion and an incoherent portion. The coherent portion typically assumes that the terrain or sea is perfectly flat, which yields an analytic answer. The incoherent portion is a random term that does not have an analytic answer, and is typically determined from experimental data. Studies have shown that the experimental data matching cannot be easily extrapolated to terrain and sea surfaces other then those of the experiment; hence, this method is generally not applicable in the absence of a priori forward scattering knowledge.
Other multipath modeling methodologies, which are currently under development and not yet validated, attempt to rigorously solve the electromagnetic field equations at every point between the radar and target. This “total geometry” approach is mathematically valid; nevertheless, for problems of interest where ranges to targets are in the thousands of yards, this geometric manner becomes an untenably large problem to solve.