The multi-beam antenna systems become increasingly important in moden communi-cations, so in this paper, according to the properties of array radiation space, the LMS adaptive techniques are generalized for multi-beam antenna systems. And the follow-ing theoretical aspects of the said arrays are discussed: the radiation pattern of three-dimensional adaptive arrays, the evolution of radiation pattern of the adaptive arrays, the signal-to-noise ratio of the array system output, and the structure of the adaptive multi-beam networks.
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