Antenna Arrays Calibration Using Recursive Least Squares Adaptive Filtering Algorithms Based on Inverse QR Decomposition

摘要

This paper considers the antenna arrays calibration by the using of the Recursive Least Squares (RLS) adaptive filtering algorithms. An algorithm, based on the inverse QR decomposition, has been selected among the diversity of the RLS algorithms. This is caused by its stable operation. Because the algorithm contains the computationally heavy square root operations, a square root free version of the algorithm is also presented. Both versions of the QR RLS algorithms are mathematically identical to each other if they operate in float point arithmetic. The proposed calibration can be used in the antenna arrays with digital beamforming, because the algorithms usage requires the access to the array channel signals. The calibration requires a known training signal, which can be easily provided not only in a laboratory environment, but also in a field operation, if an array is used as a directional antenna of the digital communication system equipment. In the second case, the calibration can be also conducted even in the presence of the interference signal sources. Simulation validates the proposed calibration algorithm, using linear antenna arrays with 4, 8 and 16 antennas with a half wavelength distance between the neighbor antennas. In this simulation, the array channel noise has been varied in 0 … 30 dB range of the Signal-to-Noise Ratio. Two interference sources with the –30 dB Signal-to-Interference Ratio each have been simulated. These sources were located symmetrically relatively the required main lobe direction of the array radiation pattern. A training signal has been simulated as a random one with no specific autocorrelation properties. The signal has been modulated by the Phase Shift Keying (PSK) and the Quadrature Amplitude Modulation.