Applicability Extension and Calculation Acceleration of Pattern-Multiplication Principle in Far-Field Analysis of Conformal Arrays

Due to the beam-pointing and polarization diversities of carrier-mounted elements, it is widely recognized that the principle of pattern multiplication is not applicable to conformal arrays, particularly when coupling effects are considered. This article proposes a near-field Euler rotation-based technique to transform the far-field calculation of arbitrary conformal arrays into the pattern-multiplication form. Specifically, this technique involves rotating and transforming the electric and magnetic field vectors, along with the position vectors on the near-field sampling surface in the local coordinate system (LCS), to a unified sampling surface encompassing all elements in the global coordinate system (GCS). Based on the Schelkunoff's equivalence principle, the equivalent electric and magnetic currents, which are referred to as equivalent sources, are determined. Consequently, the far fields of the conformal array can be regarded as equivalent to those of arrays composed of these equivalent sources, with the radiation fields of each equivalent-source array conforming to the pattern-multiplication form. Furthermore, the equivalent-source arrays are transformed into 3-D uniform arrays through a virtual expansion operation. To expedite the far-field calculation, the technique incorporates the layer-wise 2-D fast Fourier transform (2D FFT) technique. This is achieved by analyzing the relationship between the array factor of these 3-D arrays and the layer-wise 2D FFT. Finally, several numerical examples, which involve cylindrical and hemispherical-conical arrays and take the mutual coupling (MC) effects into consideration, are provided to validate the advantages of the proposed technique in terms of calculation efficiency and accuracy.