Mathematics & Physics 2016, 9(2), 258–267 УДК 519.873 The Synthesis of Spatial Filtering Algorithm with a Constant Level of Useful Signal Valeriy N.Tyapkin∗ Dmitry D. Dmitriev† Yuri L.Fateev‡ Nikolay S.Kremez§ Military Engineering Institute Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Received 10.02.2016, received in revised form 26.02.2016, accepted 22.03.2016 The theoretical basis of two classical recursive algorithms is considered in the paper. <...> They are beamforming algorithm based on the Kalman filter and the least squares algorithm based on QR decomposition. <...> An algorithm that minimizes the noise at the output of an antenna array is proposed on the basis of these two algorithms. <...> The algorithm allows one to maintain a constant level of the received useful signal. <...> Keywords: phased array, adaptive algorithm, Kalman filter, recursive least squares method, QR decomposition. <...> Introduction Modern navigation receivers of global satellite systems have a significant drawback – low interference immunity [1]. <...> To solve this problem, navigation receivers are based on phased array antennas that use adaptive beamforming techniques. <...> Pattern control is widely used in applications such as navigation, radar, wireless communication and others. <...> The beamforming technique is one of the most popular methods to form digital antenna directional diagram. <...> This technique allows one to form maximum in the antenna diagram in the direction of useful signal and to form null in the antenna diagram in the direction of interference. <...> We consider theoretical foundations of digital beamforming algorithms such as the recursive Kalman filtering algorithm and the recursive least squares algorithm based on the QR decomposition (QR-RLS)[2]. <...> On the basis of these two algorithms we propose an algorithm that minimizes the noise at the output of an antenna array and allows one to maintain a constant level of the desired signal. ∗tyapkin58@mail.ru †dmitriev121074@mail.ru ‡fateev_yury@inbox.ru §Nkremez@sfu-kras.ru ⃝ Siberian Federal University. <...> All rights reserved c – 258 – Valeriy N.Tyapkin, Dmitry D. Dmitriev, Yuri L.Fateev, Nikolay S.Kremez The Synthesis Algorithm . . . 1. <...> Kalman filtering algorithm The Kalman filtering algorithm is an important adaptive digital <...>