Derivation of orthogonal beams and their application to beamforming in small phased arrays

It is a difficult problem to synthesise beams with the desired characteristics (low sidelobe levels, narrow main beam) from small phased arrays with few elements, Mutual coupling between elements means that conventional tapering algorithms are corrupted. In the paper a technique is presented whereby weights are calculated by point matching measured element radiation patterns to an ideal sine function. It is found that a very close approximation to an ideal sine beam can be synthesised by point matching to the nulls and main beam peak value of the ideal. Moreover, an orthogonal set of sine beams can be synthesised using this technique, which in turn are used to construct a low sidelobe beam using the main beam gain of orthogonal sine beams as sampling points. This technique gives insight into the limits of how far sidelobe levels can be reduced in arrays with few elements. No knowledge of the coupling coefficients of the array is required.