# Adaptive Antenna Array Control Algorithm in Radiocommunication Systems
## 1 Introduction  
An important element of modern telecommunications are wireless radio networks, which enable mobile subscribers to access the fixed telecommunications network and other wireless networks.  
As the number of mobile subscribers served by a single base station increases, the problem of interference related to the operation of the radio link increases. The use of base station antennas with an omnidirectional radiation pattern is not advisable, both from compatibility and energy points of view. When transmitting an antenna with this shape of radiation pattern, an omnidirectional electromagnetic field is generated, which--with the exception of the direction to selected mobile subscribers--is a disturbing field for other stations. At the same time, increasing the number of subscribers does not allow for increasing the frequency spacing of neighboring base stations due to the limited range of the frequency band allocated to a given operator.  
In order to minimize the above disadvantages of omnidirectional antennas, antennas with variable directional radiation patterns, adaptive antennas, were used in base stations [1]. These antennas allow their radiation characteristics to be controlled in such a way as to provide mobile subscribers in a given sector with a connection with specified quality parameters, while limiting interference with other base stations.  
This solution allows you to optimize the operating conditions of the mobile network in terms of reducing the impact of interference, the better management of the frequency spectrum and improving the energy efficiency of the system.  
An adaptive antenna is an antenna that controls its characteristics by controlling the power supply while the antenna is operating [2]. Adaptive antennas are typicallyconstructed from arrays of antennas, with continuous aperture antennas being less common because the characteristics of the antenna array are easily controlled by adjusting the amplitude and phase of the signal from each element before the signals are summed.  
Adaptive antennas are useful in radar technology and communication systems where the fight against jamming and interference is an important issue [3]. These antennas change their characteristics automatically in response to the signal environment. This process occurs in such a way as to optimize the signal-to-noise and interference ratio at the output of the array. This makes them particularly useful in protecting radar and communication systems from interference when the direction of the interference is not known in advance. In communication systems, they are also useful in situations where the angle of arrival of the useful signal is not known. Adaptive antennas can work with any shapes of array elements, polarizations, and arrangement of elements. This property is a great advantage when the antenna system must be designed to operate on irregularly shaped surfaces, such as aircraft.  
The first news about adaptive antennas appeared around 1950. In 1956, [PERSON] and [PERSON] proposed the use of a phase-coupled loop to combine signals from different receiving antennas in a collecting system. These arrays were extensively and intensively researched and developed in the 1960s. As a result of research into the problem of eliminating interference, steering antenna beams and tracking moving radio stations, the first solution for adaptive interference elimination began to be developed, dating back to the late 1950s. This concept consisted of zeroing the antenna's radiation pattern for the directions of space where interference was detected (null steering). The first published results of this research appeared in [PERSON]'s work in 1976.