On the Minimum Number of Samples for Sparse Recovery in Spherical Antenna Near-Field Measurements

A thorough picture is presented on the capability of compressed sensing to reduce the number of measurement samples that are required for a near-field to far-field transformation (NFFFT), based on the spherical vector wave expansion of the radiated field of an antenna under test. To this end, the minimum number of samples for a sparse recovery is determined such that a predefined far-field accuracy can be achieved. As no suitable sampling theorem exists, this is done by performing extensive numerical simulations, considering possible deviations from exact sparsity, the influence of measurement noise, the sampling scheme, and the probe correction. Particularly, the influences are determined not only qualitatively but also quantitatively. The resulting modified phase transition diagrams (PTDs) show that a reconstruction by the quadratically constraint basis pursuit strategy is sufficiently stable and robust for practical purposes. The simulation and measurement results of NFFFTs show that the predictions for the required number of samples hold true. Consequently, the presented approach using modified PTDs allows to reduce the number of measurement samples with predictable accuracy, when the sparsity level is known.