Constrained optimization of the performance indices of arbitrary array antennas

The solution to the optimization of performance indices of array antennas such as directive gain, efficiency index, and signal-to-noise ratio, do not provide information regarding the sidelobe region of the radiation pattern. It is shown that, with proper constraints on the sidelobes, a given performance index can be optimized to give a radiation pattern with desired sidelobe levels. As most of the performance indices of an array antenna can be expressed as a ratio of two Hermitian quadratic forms, an eigenvalue method is used for the constrained optimization. This method gives explicit expressions for the excitation vector and constrained values of the performance indices. An iterative technique is used to ensure that the specified field values occur at the sidelobe peak positions. The element excitations obtained by this technique for maximum gain and uniform sidelobe level are similar to these obtained by the Dolph-Chebyshev technique.