Non-uniform sampling and polynomial interpolation for array synthesis

Two techniques are presented for array synthesis, based on the non-uniform sampling of the array factor, in order to control its shape. In the first technique, the ideal excitation distribution is truncated with an appropriated window function in order to obtain an initial approximation for the array factor. After that, certain points of the array factor are used for further control, usually the peaks of the ripple structure and of the sidelobes. The number of points used for this control is equal to the number of array elements and, imposing appropriated positions and values to these points, the polynomial interpolation allows the user to generate an array factor that approximates to the desired one. The second technique also uses polynomial interpolation, but the number of points is greater than the number of elements. In this case, the array factor matches some desired points and approximates to the other ones with the least minimum square error criterion. Both techniques consider the Fourier relation method, in order to realise the calculations efficiently. Among other applications, these techniques permit to define the level of each sidelobe in an array factor, to control the ripple structure of shaped patterns and to impose nulls in prescribed directions of any array factor, with minimum computation times, thereby permitting real-time applications.