Monostatic to Bistatic Equivalence Theorem for 2-Dimensional Reflection Pattern Measurements of Reconfigurable Intelligent Surfaces

One of the most important key performance indicators of Reconfigurable Intelligent Surfaces (RISs) represents the RIS reflection or bistatic RIS Radar Cross Section (RCS) pattern, which needs to be evaluated under Far-Field (FF) conditions. Since a bistatic setup that fulfills FF conditions is mechanically complex, expensive and results in a large setup footprint, the measurement of RIS reflection patterns within a monostatic setup is proposed. Subsequently, the monostatic pattern results are transformed into bistatic patterns using a Monostatic to Bistatic Equivalence Theorem (MBET). This approach reduces the total measurement time tremendously. However, the state-of-the-art MBET proposed for RIS measurements, is limited to 1-D pattern application, where the illumination-/transmit- and the probing-/measurement- antennas are located in the same plane. As RIS can also be configured to reflect off-the-plane, the evaluation of 2-D scenarios is crucial. With the state-ofthe-art 1-D MBET such scenarios cannot be investigated. To close this gap, this paper derives a novel 2-D MBET well suited for RIS measurements. The novel MBET is validated with an analytical metal plate reflection model, by comparing the resulting 2-D MBET transformed monostatic pattern with the bistatic reference pattern. This procedure is repeated for measurement and simulation data of two different RIS prototypes designed for the mmWave frequency range. The deviation of the resulting patterns after applying the novel derived MBET from the bistatic reference patterns is analyzed based on the pattern difference metric. This difference metric evaluated in the main cuts exhibits a worst case mean value of – 24 dB which proves the suitability of this novel MBET for 2-D RIS measurements.