Adaptive sampling for compressed spherical near-field measurements

Spherical Near-Field (SNF) measurements typically require a long acquisition time. This is due to the need of sampling a whole sphere around the Antenna Under Test (AUT) to perform the Near-Field-to-Far-Field Transformation (NFFFT). A step of the NFFFT is to decompose the measured signal in each one of the spherical waves it consists of, thus retrieving the Spherical Mode Coefficients (SMCs) associated to the AUT. Under typical measurement conditions, the SMCs of most physical AUTs prove sparse, i.e., most of their terms are zero or neglectable. This assumption is used to reconstruct the SMCs using an l1 -minimization algorithm. To improve the probability of the acquired samples resulting in linearly independent equations while allowing for a fast acquisition, a compressed sampling scheme based on the minimum mutual coherence of the sampling matrix for an equidistant distribution on elevation is chosen. The number of samples M required for reconstruction for a given error is difficult to determine, however, since non-preventable factors, such as aliasing, affect it. A method for the adaptive choice of M based on an on-line estimation of the error curve is suggested. The division of a large compressed sampling scheme into partial schemes is proposed. A correlation between the error of a reconstruction with sampling schemes of increasing size and the difference between the SMCs reconstructed from is found. To exploit this correlation, the SMCs are estimated during a measurement with few iterations of a quick l1 -minimization algorithm, SPGL1, and an error-estimation curve is derived. The technique is particularized for exemplary antennas with numerical experiments, performed using measurement data.