Synthesis of linearly polarised patterns of conical arrays by the method of least square

Abstract

Method of least squares is employed for pattern synthesis of non-uniform conical arrays using Euler rotation of coordinate axes. Design specifications involve beam-width of main-lobe, side-lobe and cross-polarisation levels. This method is effective for conformal arrays, because pattern multiplication is not applicable for them. Constructed error function depends on element spacing and current excitations (amplitudes and phases of input currents). Combination of conjugate gradient and genetic algorithms is used for its miniaturisation to determine element spacing and excitations. Recent literature on non-uniform arrays mostly deals with non-uniform excitations with complicated input networks. The non-uniformly spaced arrays will realise any specification obtained by non-uniform excitations. Two examples of non-uniform current excitations are presented. First example leads to reduction of side-lobe level (SLL) from 12 to 20 dB. Second example deals with different upper and lower SLLs. Third example treats non-uniform spacing, which results in the reduction of SLL from 12 to 18 dB. Fourth example synthesises both non-uniform spacing and unequal excitations, which provides the SLL reduction from 12 to 25 dB, besides the reduction of cross-polarisation level from 12 to 25 dB, compared with Qing- Qjang et al. 2011, which decreased SLL by only 8 dB.