Using continuous aperture illuminations discretely

An iterative procedure is described for fitting a continuous aperture illumination function to a small discrete element array such that the far-field antenna pattern has prescribed sidelobe behavior. Control of successive sidelobe levels in the array factor pattern is used to minimize an error expression comprised of the sum of the squares of the differences between calculated and specified levels for a selected number of sidelobes. The coefficients of a finite series defining the continuous aperture illumination are the variables employed in a Newton-Raphson solution. A sum beam aperture excitation for meeting the 20/30 dB sidelobe requirements of the 1973 OTP manual is derived for a small array and shown to be a useful approximation for a larger array situations. The procedure has been extended to difference beam illumination functions. Extensions to other aperture illuminations are indicated.