# First SIMO Harmonic Radar Based on the SFCW Concept and the HR Transfer Function
## 1 Introduction  
The combination of a stepped frequency continuous wave (SFCW) radar and a multiple input multiple output (MIMO) system topology has only recently been explored, with the basic theory being published in [1]. A follow-on paper demonstrating the first measurements performed by such a radar system followed shortly after [2]. A comparison of the single input multiple output (SIMO) radar with the MIMO and interpolated interferometric radar was made in [3], which especially elaborated upon the clutter problems associated with SFCW radar. These issues can, however, be mitigated to a degree, when the harmonic radar (HR) principle is combined with SFCW MIMO radar. While HR can certainly currently be considered a niche radar application, it has found its practical applications in cooperative insect tracking [4, 5, 6, 7, 8, 9] and the non-cooperative remote detection and location of (RF) electronics in the form of nonlinear junction detectors (NLJD, [10, 11]). In this paper, the first SIMO harmonic radar is presented, which generates a MIMO like setup without the associated multitude of antennas, switches, or receivers and RF cables scattered through the radar scene by providing a wide-beam scenario illumination and selecting specific harmonic propagation paths by activating individual HR tags organized in an array. It is based upon the harmonic SFCW concept, of which details and in-depth descriptions are found in the references [12, 13, 14]. An extensive overview ofdifferent harmonic radar system principles and their performance measures can be found in [15; 16]. The system's signal generation and reception hardware is built around the house-made vector network analyzer (VNA) modules from [17] (based upon the work of [18]), to perform repeatable complex-valued mixed-frequency or HR transfer function measurements in an arbitrary frequency grid. This HR transfer function is also presented in this paper and introduced for material and object measurements. The very important verification of this transfer function is done with coaxial devices in reference to VNA measurements. However, despite the same internal modules from [17], this application presented here differs considerably from the work in [18] (including [19]) in the circuitry using filters and amplifiers. The outstanding feature of an HR system for indoor applications its inherent clutter rejection ability, as the receiver only detects the second harmonic generated from the transmitter's fundamental frequency illumination signal by the nonlinear response of the tag and strongly rejects the otherwise dominant linear reflections, or clutter, on the fundamental frequency caused by walls or large obstacles. This feature makes such a system especially attractive for in-line radar measurements in production environments, which generally encompass a dynamic environment with a lot of moving reflective metal parts. Thus far, material surveys in free space have only been performed for coarse discrimination using radar systems and for more detailed investigations using VNAs. For measurements where the dielectrics only have to be measured to an accuracy of a few tenths, a normalized VNA measurement is sufficient. For more precise measurements, one uses a calibration procedure and several calibration measurements. The LNN method is particularly suitable here [20]. Most VNA measurements in free space are performed using a two-port configuration [21; 22]. However, it is shown in [23] that it is also possible to perform a single-port or reflectometer measurement calibrated in free space. This article is structured as follows: first, the well-known harmonic radar equation is presented, which is followed by the derivation of the important transfer function of an HR measurement. In the next section, the hardware used for the prototype of the SIMO system is presented. Afterwards, simple measurements are shown to demonstrate the basic functionality of the setup.