# Exponential Interpolation (EXP) Algorithm

An alternative algorithm for the extrapolation of 3D antenna radiation patterns based on the given horizontal and vertical patterns is the exponential interpolation. In this method the horizontal diagram is corrected according to the difference between the front-to-back ratio at elevation angle 0° and the front-to-back ratio at the elevation angle theta by using the following equation:

$$G(\phi ,\vartheta )={G}_{V}(\vartheta )+\left[\frac{{G}_{V}({\vartheta}^{\prime})-{G}_{V}(\vartheta )}{{G}_{V}(270\xb0)-{G}_{V}(90\xb0)}\right]\cdot {G}_{H}(\phi )-{G}_{VMax}\text{with}{\vartheta}^{\prime}=360\xb0-\vartheta $$

This exponential interpolation provides accurate predictions especially for antennas with electrical down tilt.