On the Effects of Calibration Errors and Mutual Coupling on the Beam Pattern of an Antenna Array

The beam pattern of an antenna array is one of the most important characteristics of classical phased arrays and of more modern smart antenna, digital beamforming and multiple-input multiple-output array systems. Most approaches to designing such systems are based on an ideal mathematical model, which leads to an ideal beam pattern. However calibration errors and mutual coupling are real-world effects that often deteriorate the beam pattern and thus the array performance. In this paper we present worst-case boundaries and a statistical analysis of the beam pattern deviation for linear, angle-independent calibration error and mutual coupling models. We provide general results as well as specialized results for calibration errors and coupling between adjacent channels of linear arrays. The results provide an understanding of the influence of different array design parameters. They are also meant as tools for specifying tolerance and channel coupling requirements as well as for the analysis of the probabilities to achieve a beam pattern within certain boundaries.