Shaped-pattern synthesis using pure real distributions

Shaped patterns can be produced by properly excited equispaced linear arrays. An earlier synthesis procedure, which accomplishes this with control ripple in the shaped region and controlled sidelobe levels elsewhere, results in array distributions that are generally complex. It is shown here that if the shaped pattern is symmetric and has 2M filled nulls, there are 2^M complex symmetric distributions, and 2^M pure real asymmetric distributions, and 2^2M-2^M+1 complex asymmetric distributions that will produce the desired pattern. By adding 2M elements to the array, one can find a symmetric pure real distribution that will achieve the same result. A representative example illustrates the procedure. The results have application to standing-wave-fed planar arrays with quadrantal symmetry via use of the collapsed distribution principle