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.