Isophoric arrays-massively thinned phased arrays with well-controlled sidelobes

Traditional filled phased arrays have an element placed in every location of a uniform lattice with half-wavelength spacing between the lattice points. Massively thinned arrays have fewer than half the elements of their filled counterparts. Such drastic thinning is normally accompanied by loss of sidelobe control. This paper describes a class of massively thinned linear and planar arrays that show well-behaved sidelobes in spite of the thinning. The term isophoric is derived from Greek roots to denote uniform weight. In isophoric arrays, element placement based on difference sets forces uniformly weighted spatial coverage. This constraint forces the array power pattern to pass through V uniformly spaced, equal, and constant values that are less than 1/K times the main beam peak, where V is the aperture size in half-wavelengths and K is the number of elements in the array. The net result is reduced peak sidelobes, especially when compared to cut-and-try random-placement approaches. An isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that K is approximately the square root of V. Where more than one beam must be generated at a time, isophoric array designs may be used to advantage even within a traditional filled array. By “interweaving” two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time, two independent antenna power patterns can be generated, each with a sidelobe region that is approximately a constant value of 1/(2K) relative to the main beam, where K is the number of elements in the subarray