On the Influence of the Transformation Matrix in Compressed Spherical Near-Field Measurements

The radiation characteristics of an object are represented by the coefficients vector of a Wigner-D expansion. For most physical antennas and with appropriate choice of the expansion's center, the coefficients vector, also called the Spherical Mode Coefficients (SMCs) vector, is proven sparse. The sparsity of the vector allows the undersampling of the system and the reconstruction of the SMCs vector by application of 11-minimization methods. However, the reconstructed results, for equivalent analytical formulations of the problem, change depending on the used transformation matrix. In this work, the SMCs of two antennas calculated from measurement data are used to simulate compressed spherical near-field measurements. The sampling schemes used for the compressed measurements are calculated based on the minimum coherence of the sampling matrix for the basis functions. The reconstruction error is assessed for a different formulation of the problem, using a different transformation matrix and highlighting the performance difference.