  In this article, we address the problem of reducing the number of required
samples for Spherical Near-Field Antenna Measurements (SNF) by using Compressed
Sensing (CS). A condition to ensure the numerical performance of sparse
recovery algorithms is the design of a sensing matrix with low mutual
coherence. Without fixing any part of the sampling pattern, we propose sampling
points that minimize the mutual coherence of the respective sensing matrix by
using augmented Lagrangian method. Numerical experiments show that the proposed
sampling scheme yields a higher recovery success in terms of phase transition
diagram when compared to other known sampling patterns, such as the spiral and
Hammersley sampling schemes. Furthermore, we also demonstrate that the
application of CS with an optimized sensing matrix requires fewer samples than
classical approaches to reconstruct the Spherical Mode Coefficients (SMCs) and
far-field pattern.
