# Horizontal Projection Interpolation (HPI) Algorithm

If the main radiation is not in the horizontal plane (for example, if the antenna has an electrical or mechanical down tilt), the pattern computed with the bilinear interpolation (BI) and weighted bilinear interpolation (WBI) algorithms becomes less accurate. Especially in these cases, the HPI algorithm should be used.

The HPI algorithm takes the gain of the horizontal pattern ${G}_{H}\left(\phi \right)$ as a basis and considers a correction term for the influence of the vertical pattern ${G}_{V}\left(\vartheta \right)$ . Therefore, the gains ${G}_{H}\left(\phi \right)$ and ${G}_{V}\left(\vartheta \right)$ in the horizontal and vertical pattern, respectively, are taken and processed by using the following equation:

(1) $G\left(\phi ,\vartheta \right)={G}_{H}\left(\phi \right)-\left[\frac{\pi -|\phi |}{\pi }\cdot \left({G}_{H}\left(0\right)-{G}_{V}\left(\vartheta \right)\right)+\frac{|\phi |}{\pi }\cdot \left({G}_{H}\left(\pi \right)-{G}_{V}\left(\pi -\vartheta \right)\right)\right]$

Hereby it is assumed that the horizontal and vertical patterns are two sections of the 3D antenna pattern. This means that the two following conditions are fulfilled:
• ${G}_{H}\left(0\right)={G}_{V}\left(0\right)$ and ${G}_{H}\left(\pi \right)={G}_{V}\left(\pi \right)$ and in the case without electrical tilt
• ${G}_{H}\left(0\right)={G}_{V}\left(\alpha \right)$ and ${G}_{H}\left(\pi \right)={G}_{V}\left(\pi -\alpha \right)$ in the case of electrical tilt $\alpha$ .