Optimization of the directivity of sum and shaped patterns using circular Taylor and Ludwig distributions

The use of Taylor and Ludwig circular distributions are two useful approaches to the synthesis of sum and shaped patterns using planar arrays with circular boundaries. The excitations of the discrete arrays are determined by conventional sampling of these continuous distributions. These two techniques use a transition parameter (n̅) that controls the number of nulls manipulated in order to afford a specific side lobe level for the n̅ −1 innermost lobes whereas the remaining lobes decay as u^{#x2212;3 2} for Taylor and u^−5/2 for Ludwig.