## 3 RSS-Based DoA Estimation for Two-Row ESPAR Antenna  
Power-pattern cross-correlation algorithm is one of the most practical methods to determine unknown directions of RF signals impinging on an ESPAR antenna [10; 18; 19; 20]. It relies solely on RSS measurements gathered at the antenna output port and uses simple correlation coefficient calculation [18]. When written as matrix-vector operations, they can easily be integrated with a simple microcontroller and provide DoA estimation functionality to the WSN node [10]. In its original implementation, the algorithm relies on ESPAR antenna radiation patterns measured in an anechoic chamber only in the horizontal direction [18]. In consequence, it makes DoA estimation results accurate in the \(\theta\) = 90\({}^{\circ}\) direction (i.e., the horizontal plane) with 2-4\({}^{\circ}\) precision being the maximum DoA estimation error [18; 19; 20]. When the directions of RF signals impinging on an ESPAR antenna are different, one may expect an accuracy drop. It has been reported that for low values of \(\theta\) angle of RF signals impinging on the antenna the maximal error, referred to as precision, of 1D DoA estimation performed in the horizontal direction can easily reach 13\({}^{\circ}\) due to the fact that the shape of ESPAR antenna radiation patterns with respect to \(\varphi\) angles gradually changes for \(\theta>\) 90\({}^{\circ}\)[23]. To improve the overall accuracy for the \(\theta\) angles different than 90\({}^{\circ}\), one can employ multiple calibration planes (MCP) [23; 24] in the original PPCC formulation, which relies on a single \(\theta\) = 90\({}^{\circ}\) calibration plane [18].  
PPCC-MCP algorithm uses ESPAR antenna radiation patterns measured in chosen vertical directions. In the first implementation, all ESPAR antenna radiation patterns were measured in an anechoic chamber at \(\theta\) = 90\({}^{\circ}\) and \(\theta\) = 45\({}^{\circ}\) and, based on such two calibration planes, it was possible to maintain 4\({}^{\circ}\) precision for RF signals impinging from angles between \(\theta\) = 50\({}^{\circ}\) and \(\theta\) = 90\({}^{\circ}\)[23]. Involvement of 9 calibration planes, namely \(\{\theta_{1}=10^{\circ}\), \(\theta_{2}=20^{\circ}\), \(\dots\), \(\theta_{9}=90^{\circ}\)}, provides 6\({}^{\circ}\) 1D DoA precision for RF signals impinging from 9 test vertical angles spanning equally between \(\theta\) = 10\({}^{\circ}\) and \(\theta\) = 90\({}^{\circ}\). However, it has been shown that PPCC-MCP algorithm accuracy is sensitive to correct placement of calibration planes positions [24], while obtained results depend on testing setup [28] parameters, especially the choice of testing directions in horizontal and vertical planes as well as SNR values set for testing signals [24; 28]. Moreover, the existing PPCC formulation was created to provide DoA results based on a number of directional radiation patterns, while new  
Figure 9: Cumulative Distribution Function of the aggregated gain for different sets of characteristics.  
ESPAR antennas can have a number of possible radiation patterns that can be used in DoA estimation [32; 33] having different performance, especially when testing signals may come from multiple horizontal and vertical directions. Therefore, to be used for DoA estimation together with new ESPAR antennas, including the two-row ESPAR antenna proposed in [31], PPCC-MCP algorithm and associated DoA testing methods have to be generalized.