**Authors:** Ngoy Mutonkole and Dirk I.L. de Villiers

**Source:** FERMAT, Volume 13, Communication 22, Jan.-Feb., 2016

**Abstract:**
A simple and effective method to extend the characteristic basis function pattern (CBFP) method to multiple frequencies is presented. Transformation matrices are generated from simulated basis functions at each frequency of interest. By computing model coefficients, by means of a singular value decomposition (SVD) to enhance accuracy over a wide bandwidth, using a few directional measurements of any given pattern at a single frequency, linear algebra is applied to extract expansion coefficients at any other frequency within the model's range by utilising the transformation matrices. For cases where a large number of basis functions is required, k sparse approximation of the expansion coefficients is used to improve accuracy. The full radiation pattern at all frequencies is then recovered from a single frequency measurement using the extracted expansion coefficients. Simulation results show a maximum pattern recovery error below 40 dB across a bandwidth ratio of up to 10 : 1.

**Index Terms:** calibration, characteristic basis function patterns, radio astronomy.

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