The measurement of far-field radiation patterns is time consuming and expensive. Therefore, a novel technique that reduces the samples required to measure radiation patterns is proposed where random far-field samples are measured to reconstruct two-dimensional (2D) or three-dimensional (3D) far-field radiation patterns. The proposed technique uses a compressive sensing algorithm to reconstruct radiation patterns. The discrete Fourier transform (DFT) or the discrete cosine transform (DCT) are used as the sparsity transforms. The algorithm was evaluated by using 3 antennas modeled with the High-Frequency Structural Simulator (HFSS) --- a half-wave dipole, a Vivaldi, and a pyramidal horn. The root mean square error (RMSE) and the number of measurements required to reconstruct the antenna pattern were used to evaluate the performance of the algorithm. An empirical test case was performed that validates the use of compressive sensing in 2D and 3D radiation pattern reconstruction. Numerical simulations and empirical tests verify that the compressive sensing algorithm can be used to reconstruct radiation patterns, reducing the time and number of measurements required for good antenna pattern measurements.
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