Interpolation or coupling matrices in the calibration of antenna arrays

Various approaches are available for correcting errors in antenna arrays through calibration. In this context, the concept of coupling matrices is a popular approach since it allows the prediction of the array port voltages for an arbitrary excitation and, for some array geometries, the estimation of the incident electromagnetic fields through the inversion of the matrices. Another popular approach consists in measuring the array port voltages for signals arriving from a set of incident angles, and interpolating between the data points to predict the voltages for intervening angles. Unfortunately, it is not possible to estimate the incident electromagnetic fields using this approach, but in many applications this is not required. Currently, the advantages of coupling matrices over interpolation in these applications are unclear. This paper compares the accuracy of array calibration performed using coupling matrices and interpolation in typical applications and array geometries, and determines the conditions where one approach should be preferred over the other.