Optimum unequally spaced arrays and their amplitude shading

In many array applications, a narrow beam is required For regular arrays, beamwidth is inversely proportional to array length. In order to obtain a narrow beam, the array length must be long and the number of elements must be large, making narrow beam arrays expensive. For the unequally spaced array, both the successive approximation method and dynamic program method are presented. The first method can provide the lowest side lobe level; the second method not only can give nearly the lowest side lobe level but it can specify the minimum spacing and all spacings will be an integral multiple of a unit length, making it easy to construct an array. A formula for estimating side lobe level is also presented. On average, the side lobe height obtained with a randomly spaced array will double or triple that obtained by the present methods. An amplitude shading approach for unequally spaced arrays is presented. Unequally spaced planar arrays are also discussed. For example, a 200 kHz circular sparse planar array of 1° beam width can be constructed using only 220 elements and its side lobe level can be suppressed to -20 dB. A fully populated square planar array would require 10,000 elements. Unequally spaced linear arrays designed by the first method have been built