Multiple solutions starting from real shaped beams in equispaced linear arrays

In the present work, the theoretical basis of the multiplicity of solutions obtained from an initial real symmetric distribution is derived. This initial solution is devoted to generating an equivalent pure real shaped-beam pattern for a concrete synthesis scenario. However, these new solutions are not based on real symmetric distributions; hence, not based on the generation of pure real patterns. The bandwidth performances and tolerance to errors provided by the multiple solutions in the array design are analyzed by considering different architectures, also including mutual coupling models and element factor expressions due to accuracy purposes. In addition, a technique to obtain efficient linear arrays by designing resonant structures is addressed. Examples involving both standard linear arrays of half-wavelength cylindrical dipoles and resonant linear arrays generating flat-top beam patterns are reported and discussed. Additionally, an extension to planar arrays performed by means of a generalisation of the Baklanov transformation through collapsed distribution techniques inspired in the well-known method devised by Tseng and Cheng is performed. In such a way, an analysis of the quality of solutions for generating circular and elliptical footprints with controlled both SLL and ripple which are highly interesting in the framework of space vehicle applications.