Mutual coupling is an important source of error in antenna arrays that should be compensated for super resolution direction-of-arrival (DOA) algorithms, such as Multiple Signal Classification (MUSIC) algorithm. A crucial step in array calibration is the determination of the mutual coupling coefficients for the antenna array. In this paper, a system theoretic approach is presented for the mutual coupling characterization of antenna arrays. The comprehension and implementation of this approach is simple leading to further advantages in calibration measurement reduction. In this context, a measurement reduction method for antenna arrays with omni-directional and identical elements is proposed which is based on the symmetry planes in the array geometry. The proposed method significantly decreases the number of measurements during the calibration process. This method is evaluated using different array types whose responses and the mutual coupling characteristics are obtained through numerical electromagnetic simulations. It is shown that a single calibration measurement is sufficient for uniform circular arrays. Certain important and interesting characteristics observed during the experiments are outlined.