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Multi-Frequency Phase Retrieval for Antenna Measurements

Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be successful. Larger amounts of independent data may improve the reconstruction of the phase information from magnitude-only measurements. We show how the knowledge of relative phases among the spectral components of a modulated signal at the individual measurement locations may be employed to reconstruct the relative phases between different measurement locations at all frequencies. Projection matrices map the estimated phases onto the space of fields possibly generated by equivalent antenna under test (AUT) sources at all frequencies. In this way, the phase of the reconstructed solution is not only restricted by the measurement samples at one frequency, but by the samples at allfrequencies simultaneously. The proposed method can increase the amount of independent phase information even if all probes are located in the far field of the AUT.