Exponential and generalized Dolph-Chebyshev functions for flat-top array beampattern synthesis

For the flat-top array beampattern synthesis, a conceptually simple closed-form method without iterative work and heavy numerical calculations is desired. We are therefore motivated to look for a good template function for flat-top beampattern synthesis, such as Dolph-Chebyshev Function (DCF) for pencil-beam pattern synthesis. In this paper, two new template functions, Exponential Dolph-Chebyshev Function (EDCF) and Generalized Dolph-Chebyshev Function (GDCF) are derived from the original DCF, and the corresponding synthesis procedures in the Quadratic Programming (QP) method are also presented. From the simulation results using the proposed templates, it is shown that although the resultant beampatterns are not equi-ripple, both the mainbeam width and the Side-Lobes Level (SLL) of the synthesized beampatterns are controlled well, simultaneously, and the proposed methods can also be applied to synthesize arrays of different geometries including Uniform Linear Arrays (ULA) and Uniform Circular Arrays (UCA). The comparison between the two proposed template functions is also presented so that one can choose the proper synthesis template based on specified requirements.