## 4 Measurement Setup and Results
### Measurement Results  
This subsection presents the detection performance of the five evaluated algorithms using measurement data acquired from the harmonic FMCW radar system described in [33,34]. The measurements were conducted at target distances of 1.2 m, 1.6 m, and 2.0 m, using a passive harmonic tag in an indoor environment. The system operated in the 2.4-2.5 GHz transmission band and 4.8-5.0 GHz harmonic reception band, with a chirp duration of 200 us and a sweep bandwidth of 100 MHz. Beat signals were recorded using a 16 bit ADC at 744 ksps and the beat frequency was extracted using the aforementioned detection techniques. To further clarify the signal processing chain and demonstrate that peak detection was performed after range compression, Figure 11 presents the received intermediate frequency (IF) signal in both time and frequency domains for a measurement conducted at a distance of 1.6 m. In Figure 11a, the sampled time-domain signal \(y_{\mathrm{norm}}[n]\) corresponds to the beat signal prior to range compression. This signal exhibited a quasi-sinusoidal waveform modulated by amplitude fluctuations due to multipath and noise. Figure 11b shows the result of applying a Fast Fourier Transform (FFT), which acted as a range compression operation. The spectrum \(Y_{\mathrm{norm}}[k]\) reveals a well-localized spectral peak, corresponding to the target's beat frequency, clearly distinguishable above the noise floor. This transformation improved the signal-to-noise ratio and facilitated reliable peak detection. The figure confirms that all detection algorithms in this work operated on the FFT-compressed (i.e., range-compressed) signal, not on the raw time-domain waveform. Figure 10: Realized measurement setup for beat frequency analysis with and without reflectors in an indoor scenario. The setup included the harmonic radar system with a TX antenna (2.4–2.5 GHz) and an RX antenna (4.8–5.0 GHz), a passive harmonic tag, and two reflectors. The left image shows a top view of the setup with reflectors, the middle image provides a front view highlighting the antennas and reflectors, and the right image shows a zoomed-in image of the reflectors and passive harmonic tag [34]. To illustrate the performance of the system under low-SNR and long-range conditions, Figure 12 presents the received intermediate frequency (IF) signal measured at a target distance of \(2.1\,\mathrm{m}\), which was considered a challenging case due to increased path loss and the diode's conversion loss. Figure 12a shows the normalized time-domain beat signal \(y_{\mathrm{norm}}[n]\), where the sinusoidal pattern was visibly distorted by noise and amplitude fluctuations. In Figure 12b, the corresponding FFT magnitude spectrum \(Y_{\mathrm{norm}}[k]\) is plotted, demonstrating the range-compressed signal. Although the peak appeared more broadened and accompanied by spurious sidelobes compared to shorter ranges, the main lobe remained sufficiently pronounced to enable correct peak detection. This result highlights the effectiveness of the FFT-based range compression stage in preserving peak observability even under reduced SNR conditions. Figure 11: Sampled time-domain and frequency-domain representations of the received IF signal measured at a target distance of \(1.6\,\mathrm{m}\). (**a**) Time-domain beat signal \(y_{\mathrm{norm}}[n]\) prior to range compression. (**b**) Frequency-domain magnitude spectrum \(Y_{\mathrm{norm}}[k]\) obtained via FFT, illustrating range compression and revealing a dominant spectral peak corresponding to the target range. This figure highlights the effect of range compression and confirms that peak detection was performed on the range-compressed signal. Figures 13-15 show the probability of detection versus SNR for the considered distances. Across all scenarios, CA-CFAR consistently demonstrated the most robust performance, achieving near-perfect detection even at low SNR values.