Wavelet expansion of the antenna far field for "beam-based" pattern synthesis

Many antenna applications require the design of antennas of the multiple-beam type, possibly involving reconfiguration. A typical example is satellite antennas for telecommunication applications. Various synthesis methods have been devised in the past to deal with this problem, however little attention has been paid to the issue of how best to describe the far field of the antenna. We present and discuss the construction of a "wavelet" basis to describe the far field of an array. The information of the desired far field is concentrated on a limited number of wavelet basis functions, potentially improving the behaviour of synthesis algorithms and speeding up the synthesis process. We describe a wavelet basis able to concentrate the information required for the beam synthesis in a few terms of the far field expansion. The reduction of the number of significant terms offers valuable advantages in "power synthesis" problems, when suitable adaptive algorithms are used. Furthermore, an adjoint basis is made available for 2D problems, facilitating also the use of other synthesis methods.