## 1 Introduction

[2] In antenna arrays, mutual coupling between the array elements is an important problem. An extensive review on array mutual coupling analysis is presented in *Craeye and Gonzalez-Ovejero* [2011] where the relationship between array impedance matrix and embedded element patterns is considered. An antenna array cannot function properly without a proper mutual coupling calibration. In *Camps et al*. [1998], this is shown for the case of interferometric radiometers through a detailed theoretical analysis of mutual coupling effect which is also supported with experimental results.

[3] In the literature, there are several methods for mutual coupling calibration which consider omnidirectional antenna elements. In *Hui* [2007], a review of the mutual coupling modeling methods is presented. The open-circuit method presented by *Gupta and Ksienski* [1983] is one of the earliest methods for mutual coupling modeling. In this method, the N-element antenna array is treated as an N-port network, and the antenna terminal voltages are related to the so-called open-circuit voltages through an impedance matrix consisting of mutual impedances. However, it is insufficient to model the mutual coupling effect completely since the scattering effect due to the presence of other antenna elements is not considered. In *Hui* [2003; 2004], the receiving mutual impedance concept is proposed to overcome the problems of the open-circuit method. The receiving mutual impedances are calculated by considering the antenna elements in pairs. The calculation method is further developed in *Lui and Hui* [2010] where all the array elements are considered simultaneously.

[4] Previous works usually use dipole and monopole antenna arrays since mutual coupling characterization is relatively easier. In practice, many antennas are non-omnidirectional (NOD) or at least their patterns change with frequency destroying the omnidirectional pattern. In *Mir* [2008], multiple calibration matrices are used using a series-like expansion in order to account for directional dependency of array manifold calibration.

[5] In this paper, a new method for mutual coupling calibration of arrays composed of identical NOD antennas is proposed. The proposed approach takes into account the directional dependency of mutual coupling matrix and presents a systematic approach for its treatment. It also presents a way for reducing the number of calibration measurements by introducing the symmetry plane definition which depends on the symmetry of the array radiation patterns for the symmetric array elements.

[6] Mutual coupling matrix for an NOD antenna array has azimuth, elevation, and frequency dependency in general. Therefore, a single mutual coupling matrix cannot characterize the mutual coupling effect adequately. In this paper, a sectorized approach is proposed for mutual coupling calibration of NOD antenna arrays. Azimuth and elevation planes are divided into uniform angular sectors, and a different mutual coupling matrix is found for each sector using a transformation matrix. The size of the angular sectors should be selected appropriately in order to decrease the calibration complexity as well as to avoid ill-conditioned matrices.

[7] The manual labor required for mutual coupling calibration measurements is an important factor for practical implementations. In *Aksoy and Tuncer* [2012], a measurement reduction method (MRM) is proposed for omnidirectional antennas where the number of calibration measurements are reduced by using the symmetry in the array geometry. In this paper, the definition of symmetry plane is presented, and it is shown that MRM is also valid for NOD antenna arrays. MRM is based on the symmetry planes which are determined by the symmetry of the array radiation patterns for the symmetric array elements. This symmetry depends on the array and antenna geometries as well as the antenna radiation patterns and alignments. The amount of measurement reduction for NOD antennas is usually less than the omnidirectional antennas. However, it is still significant and reduces the cost and complexity of the array calibration process.

[8] The sectorized approach combined with MRM is evaluated through direction-of-arrival (DOA) estimation experiments using Multiple Signal Classification (MUSIC) algorithm [*Schmidt*,1986]. Calibration measurements are obtained using the numerical electromagnetic simulation tool FEKO [*User's Manual*,2008]. Several simulations are provided to show that the proposed approach is an effective way of mutual coupling calibration of NOD antenna arrays.