Improved Asymptotic Friis Formula with Higher-Order Terms: Calculating Antenna Coupling in Close Proximity

The emergence of near-field communication as a part of sixth-generation (6G) communication necessitates accurate estimation of the link budget between two antennas operating in the near-field region. In this paper, we present an asymptotic expression for the gain reduction factor that includes higher-order terms to evaluate the accuracy of predicting antenna coupling at short distances in the near-field region. Asymptotic Friis formulas with gain reduction factors for both circular and rectangular apertures are examined, and we show that asymptotic formulas including higher-order terms yield a 22–25% shorter minimum prediction distance than those with lower-order terms. The validity of the formula is evaluated through the full-wave simulation and measurement.