The theory of fractional order calculus is applied to construct variations of the fundamental Pareto clutter model density, used in X-band maritime surveillance radar. Such data are characterised, at high resolution, by spiky clutter returns whose density function possesses heavy tails. By an application of fractional calculus to the Pareto distribution function, together with optimisation applied to determine the fractional derivative order, it is possible to obtain a new model for radar clutter. This is shown to fit real radar clutter returns better than a standard Pareto model. Additionally, it accounts for receiver thermal noise without the complexity of an additional noise distribution.

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Abstract-We consider how an electromagnetic field propagating to a target alters the radar cross section of the target relative to an observer. We derive the optimum high-frequency path for the fields using the calculus of variations and by using a realistic refractive index profile for the atmosphere obtain closed form solutions. It is found that the predicted nulls and peaks in the radar cross section of a scattering object relative to an observer are shifted from those normally expected from just the isolated object. Hence, for predictive purposes at least, radar cross section results need to incorporate the effects of atmospheric propagation.

By averaging over pairs of hyperspheres, we have obtained the dielectric function for a binary mixture containing hyperspherical inclusions up to order c 2 , where c is the volume fraction of inclusions. The method used is based on multipole expansions for the potential of two spheres in a uniform field and is a generalization of the method of Jeffrey to d-dimensional space. Numerical results are presented for the second-order coefficient κ in the low-c expansion of the dielectric constant for arbitrary d; these verify earlier known results, as well as showing the dependence of κ on dimensionality, which is particularly simple as d → 1 and as d → ∞.

The paper extends one-body effective-medium theory to incorporate the correct second-order interactions in a two-dimensional Maxwell-Garnett theory. The two-body inclusion problem is solved using the averaged dipole moments that are induced by the scattering electromagnetic field on the medium/inclusion system. By incorporating the appropriate polarizability factor in the solutions, conventional right-handed media with binary embeddings are analyzed while a different form for the polarizability term allows the study of the effective properties of a metasurface. In both cases, it is shown that the two-body coefficient to second order in the low area fraction of inclusions is exact, while the corresponding results of the Maxwell-Garnett and Bruggeman theories are incorrect. This is especially true in the superconducting and holes limits, respectively. In the study of metasurfaces, the requirement for electromagnetic screening of the inclusions as well as the requirement needed to achieve the Fröhlich condition are stated. Negative permittivity and permeability are presented for strong-scattering showing negative resonances for a given frequency spectrum. It is shown that these resonances disappear when we derive the weak-scattering limit. The possibility of obtaining doubly negative effective permittivity and permeability is discussed by using an appropriate polarization for the applied electromagnetic field propagating in the metasurface. Finally, the potential difference and hence voltage and capacitance between binary inclusions is determined for surfaces/metasurfaces which allows, in the case of metasurfaces, the behavior of split-ring-type resonators to be investigated.