Amplitude Tapers for Planar Arrays Using the McClellan Transformation: Concepts and Preliminary Design Experiments

摘要

The McClellan transformation has been widely studied in image processing since the 1970s, but it is not generally known in the phased-array community. In the array context explored here, the McClellan transformation uses a very small planar array taper - in this report examples ranged from 7 to 31 elements in size - as a 'spreading function' to take the weights of a prototype line-array taper or 1D FIR filter of modest size and spread those weights out spatially to create a large planar array taper of hundreds or thousands of elements. Reasonable 2D tapers can be obtained in this way using common tools for 1D filter design and spreading functions either chosen by hand or designed using simple 2D design techniques. Examples in this report explore the design of 2D tapers of several thousand elements on the triangular grid. The key advantage of the approach is that certain simple changes to the array pattern - modestly broadening the beam, making it elliptical, rotating that ellipse - can often be effected through simple modifications of the spreading function, with the 1D prototype filter left unchanged. Subsequent reapplication of the McClellan transformation is simple enough that such spreading-function changes allow a degree of on-the-fly beam tailoring. The key disadvantage of the approach is that approaching optimal levels of gain or taper loss appears quite difficult. Example designs here all suffered at least a 0.7 dB gain penalty relative to tapers obtained by direct optimization of the whole 2D taper to otherwise similar specifications.