Determining Electromagnetic Exposure Compliance of Multi-Antenna Devices in Linear Time

Electromagnetic exposure metrics such as specific absorption rate (SAR) are used to assess the user safety of portable wireless devices under all transmitting conditions. When there are multiple transmitter chains operating at a single frequency, the process of determining compliance is complicated by the fact that testing needs to cover all possible combinations of transmissions from all antennas. For <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> antennas, the number of possible distinct transmitted signals can grow quickly with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>. We propose a compliance test whose measurement time burden is linear in <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>, independently of the number or type of transmitted signals. For <inline-formula> <tex-math notation="LaTeX">$N\geq 3$ </tex-math></inline-formula> antennas, the proposed test requires <inline-formula> <tex-math notation="LaTeX">$7N-12$ </tex-math></inline-formula> excitations and corresponding measurements per probe location. Using analysis, simulations, and measurements with SAR compliance tools, we establish the accuracy of the method as compared with exhaustive measurements over all possible transmitted signals. The method is useful in evaluating the compliance of portable devices that use codebooks or beamforming as part of their transmission capabilities.