This article outlines the basic theory of adaptive antenna arrays. The basic elements of an adaptive antenna array such as a diagramforming device and an adaptive processor are presented. The task of the adaptive processor is to control the diagram forming device, which provides the required processing of the input observation based on the available a priori information on the signal-interference environment. When such information is insufficient, the adaptive processor must have the ability to automatically adjust to the receiving conditions. In other words, the adaptive processor must implement some adaptation algorithm based on the initial data bank and the signal processing efficiency criterion. To quantitatively evaluate the performance of adaptive antenna arrays when receiving a useful signal, one of the ways of quality indicator has been considered: the RMS value of the deviation of the useful signal from the reference.