Auto-calibration of Uniform Linear Array Antennas

Calibration is instrumental to realize the full performance of a measurement system. In this contribution we consider the calibration of a uniformly linear array antenna where we assume each antenna element has an unknown complex gain. We present an algorithm which can be used to calibrate the array without full knowledge of the environment. Particularly, if the number of signal sources are known we show that we can determine the individual unknown antenna gains up to an ambiguity parametrized by a single complex scalar. If the ratio of the complex gains between two consecutive elements is also known, this ambiguity is resolved. The method is based on determining the antenna calibration parameters such that the Hankel matrix of the array snapshots has a given rank. A numerical example illustrates the performance of the method. The numerical results suggest that the method is consistent in SNR.