Forward Transformation from Reactive Near-Field to Near- and Far-Field at Millimeter-Wave Frequencies

Serge Pfeifer, Arya Fallahi, Jingtian Xi, Esra Neufeld, and Niels Kuster, Applied Sciences 2020, Volume 10, Issue 14, 4780, online 11 July 2020; doi: 10.3390/app10144780

With the advent of 5G mobile communications at millimeter-wave frequencies, the assessment of the maximum averaged power density on numerous surfaces close to the transmitter will become a requirement. This makes phasor knowledge about the electric and magnetic fields an inevitable requirement. To avoid the burdensome measurement of these field quantities in the entire volume of interest, phase reconstruction algorithms from measurements over a plane in the far-field region are being extensively developed. In this paper, we extended the previously developed method of phase reconstruction to evaluate the near and far-field of sources with bounded uncertainty, which is robust with respect to noisy data and optimized for a minimal number of measurement points at a distance as close as λ/5 from the source. The proposed procedure takes advantage of field integral equations and electric field measurements with the EUmmWVx probe to evaluate the field phasors close to the radiation source and subsequently obtain the field values in the whole region of interest with minimal computation and measurement costs. The main constraints are the maximal noise level regarding the peak electric field and measurement plane size with respect to the percentage of transmitted power content. The measurement of a third plane overcomes some of the noise issues. The method was evaluated by simulations of a wide range of antennas at different noise levels and at different distances and by measurements of four different antennas. A successful reconstruction in the near- and far-field was achieved both qualitatively and quantitatively for distances between 2.5–150 mm from the antenna and noise levels of -24 dB from the peak. The deviation of reconstruction from the simulation reference for the peak spatial-average power density with an averaging area of 1 cm2 was, in all cases, well within the uncertainty budget of 0.6 dB, if the reconstruction planes captured >95% of the total radiated power. The proposed new method is very promising for compliance assessment and can reduce test time considerably.

The scientific and technical impact of the study can be summarized as:

  • A new forward transformation method for measured data in the reactive near-field is proposed
  • The new method can be applied to evaluate the radiation pattern and the mmWave exposure anywhere above the measured plane
  • The results demonstrate that the accuracy of the method is sufficient for demonstration of compliance of wireless devices operating above 6 GHz
  • The number of measurements required for the full evaluation of transmitters is dramatically reduced with this method which leads to substantial time savings and provides fast demonstration of safety for devices operating close to the human head