Novel Application of Compressed Sensing in Cylindrical Mode Filtering for Far-Field Antenna Measurements

Mode filtering has been shown to be very effective in suppressing spurious reflections in antenna measurements. Specifically, it has been well documented that in the quasi-far-field, the two polarizations are decoupled, making it possible to apply standard cylindrical near-field theory on the amplitude and phase data acquired from a single polarization measurement on a great circle cut [1]. The method was further extended to allow data collected from an unequally spaced angular abscissa by formulating the solution as a pseudo-inversion of the Fourier matrix [2]. This formulation, however, can be prone to spectral leakage because of nonorthogonality of the Fourier basis on an irregularly sampled grid, especially when the positions deviate significantly from the regular grid [2]. In this paper, we propose to use Compressed Sensing (CS) to compute the Cylindrical Mode Coefficients (CMCs), which improves the signal to noise ratio, allowing more accurate recovery of the prominent modes. The CS recovery is tenable because with the coordinate translation of the measurement pattern to the rotation center, the Maximum Radial Extent (MRE) of the antenna under test is greatly reduced, making CMCs quite sparse in the mode domain. The novel application of CS presented in this paper further expands the generality of the mode filtering method, which is now applicable to under-sampled data (at below the Nyquist rate) acquired on positions that grossly deviate from the equally-spaced regular grid.