Analytical array polynomial method for linear antenna arrays with phase-only control

A new analytical synthesis technique is developed for the phase-only control of linear antenna arrays and is based on the Schelkunoff's unit circle. The array factor is formulated as an array polynomial in the complex z-plane and as a product of corresponding subpolynomials such that their roots are located on the unit circle. A constraint is derived such that the expansion of the subpolynomials yields current excitations with unity magnitudes. In general, the constraint of phase-only control forces some element excitations to be zero for an arbitrary number of array elements. The subpolynomial with the largest degree is used to synthesize the main beam characteristics. The null steering for interference suppression is obtained by using only one subpolynomial to steer only one null. The results verify the developed analytical solution to synthesize the prescribed patterns using the phase shifters of the linear antenna arrays.