# First SIMO Harmonic Radar Based on the SFCW Concept and the HR Transfer Function
## 6 Verification of the HR Transfer Function  
In order to verify the HR transfer function in a free-space environment in a scientifically sound manner, a large anechoic measurement room is necessary to exclude the unknowns and uncertainties associated with multi-path propagation effects. Since this equipment and space is not readily available to the authors, the verification measurement was instead carried out in a coaxial line system, which allows a comparatively much higher amount of repeatability, lower uncertainty, and ease of traceability by allowing the independent fundamental and harmonic transfer function measurements to be performed by a VNA using a precision calibration kit. For the verification measurement, the HR system presented and explained in [19], which contains the same VNA modules as the SIMO device presented here, was used to build a harmonic reflectometer to perform the same normalized harmonic \(S^{II,f}_{11,M}\) reflection measurements as the system presented previously, although in a slightly different frequency range (2900...2940 MHz fundamental signal, 5800...5880 MHz harmonic signal) due to the required filters and diplexers, as well as the narrow-band power amplifier, for its intended application in the maritime S-band. A schematic block diagram of the setup is shown in Figure 16 and an annotated picture of the verficiation setup is shown in Figure 17.  
A suitable coaxial harmonic reflection tag equivalent was constructed by combining a passive transmission doubler circuit based upon the HSMS-286F zero-bias Schottky diode (see [19] for characterization and explanation) with a diplexer and a harmonic band reject filter for the fundamental frequency input of the doubler into a one-port nonlinear device. Figure 15: Ray-casting visualization of a complex measurement scenario using multiple mixed frequency switched reflection matrices (MFSRM) in a massive SIMO scenario to analyze a visually opaque box with dielectric and metal contents. A 40 dB coaxial attenuator is placed between the harmonic reflectometer and the surrogate harmonic radar tag at the normalization reference plane to fulfill three different important tasks: First, this attenuator acts as a stand-in for the free-space attenuation normally experienced by the stimulus and harmonic return signals. Second, this attenuator allows the operation of the doubler in its optimized square law transfer function region without the onset of harmonic compression at stimulus power levels below \(-21\) dBm, despite the fairly high (+15 dBm) minimum output power signal provided by the setup. Finally, this attenuator also provides a good hardware source match at the reference plane to reduce the influence of matching errors without full (mathematical) system error correction  
Figure 16: Components of the realized HR system, the harmonic reflectometer setup, including relevant power levels and frequency ranges, and the one-port coaxial nonlinear element used for the verification measurements, the position of the \(S_{11}^{II,I}\) normalization reference plane highlighted. Figure 17: Picture of the verification setup with components and normalization reference plane highlighted. Letter A: VNA HR-receiver module, B: VNA stimulus generator module, C: S-Band 150 W SSPA, D: High-power diplexer, E: High-power HZ termination, F: Coaxial low-pass filter, G: High-power diplexer, H: Low-power diplexer with termination, I: Harmonic LNA, J: UT-250 cable 1 m, K: 30 dB 20 W 18 GHz attenuator, L: 10 dB attenuator, M: Low-power diplexer, N: Harmonic rejection filter, O: HSMS-282F frequency doubler, P: SMA attenuators inserted at the normalization reference plane, left to right: 3 dB, 6 dB, 10 dB and 20 dB nominal attenuation. to hold up the assumptions made when deriving the normalized HR transfer function shown in Equation (11).