$K$ -Order Estimation Technique for Determining the Maximum Electric Fields of Multiple-Antenna Transmitters in Compliance Tests

This paper presents a new estimation technique with K-order expressions for evaluating the maximum electric fields radiated from multiple-antenna transmitters such as those in mobile phones, WiFi access points, and cellphone base stations. The need for K-order estimation to provide precisely estimated electric fields, then develop useful expressions for the estimation and validate the estimation model numerically and experimentally is explained. Fundamental concepts of estimation and detailed electric field formulas, applied to various measurement systems using vector or scalar E-field probes, are presented. Several validations are also illustrated. As a result, it is verified that K-order estimations significantly reduce the differences between the estimated and simulated/measured E-fields [or specific absorption rates (SARs)]. Investigations on the maximum electric fields of two antennas operating at 2.5 GHz in an ordinary room show that the maximum difference between the electric fields obtained by conventional estimations and calculations can be 8.5%, which is suppressed to below 0.24% and 0.02% by 2- and 3-order estimations, respectively. Similarly, in evaluations of the SAR of a three-antenna configuration, the maximum difference between the estimated and calculated SARs of about 5% obtained by conventional estimations is reduced to 0.1% or 0.01% by 2- and 3-order estimations, respectively.