Cosine pattern synthesis for single and multiple main beam uniformly spaced linear arrays

The method of cosine pattern synthesis for single- and multiple-main-beam equispaced linear arrays is introduced. The cosine pattern function is characterized by the position of the main beam in the θ-domain and its half-power beamwidth. The Fourier series and Woodward-Lawson methods are applied to the special cases of single- or multiple-main-beam cosine pattern synthesis. The patterns produced by application of these classical shaped-beam synthesis methods can then be used as initial patterns for iterative and perturbational techniques. Examples are presented and discussed, including the use of multiple-main-beam cosine pattern synthesis to design a high-power, high-frequency, ground-based transmitter for the creation of an array of `wireless´ ionospheric dipoles