Frequency Interpolation of LOFAR Embedded Element Patterns Using Spherical Wave Expansion

Abstract

This paper describes the use of spherical wave expansion (SWE) to model the embedded element patterns of the LOFAR low-band array. The goal is to reduce the amount of data needed to store the embedded element patterns. The coefficients are calculated using the Moore–Penrose pseudoinverse. The Fast Fourier Transform (FFT) is used to interpolate the coefficients in the frequency domain. It turned out that the embedded element patterns can be described by only 41.8% of the data needed to describe them directly if sampled at the Nyquist rate. The presented results show that a frequency resolution of 1 MHz is needed for proper interpolation of the spherical wave coefficients over the 80 MHz operating frequency band of the LOFAR low-band array. It is also shown that the error due to interpolation using the FFT is less than the error due to linear interpolation or cubic spline interpolation.