## 4 Measurement Setup and Results
### Measurement Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criterion** & **FFT Thresholding** & **CA-CFAR** & **MPM (Simplified)** &
\begin{tabular}{c} **SVD-Based** \\ **Detection** \\ \end{tabular} & **LTSP (Proposed)** \\ \hline
**Detection** & Max magnitude in & \begin{tabular}{c} Adaptive \\ thresholding based \\ FFT spectrum \\ \end{tabular} & \begin{tabular}{c} Local peak \\ on local noise \\ estimate \\ \end{tabular} & \begin{tabular}{c} Ratio of dominant \\ detection with \\ dynamic threshold \\ \end{tabular} & \
\begin{tabular}{c} Reconstruct signal \\ to median singular \\ values from \\ Hankel SVD \\ \end{tabular} &
\begin{tabular}{c} from rank-1 SVD \\ mode, then detect \\ FFT peak \\ \end{tabular} \\ \hline
**Processing Flow** & FFT \(\rightarrow\) argmax & \begin{tabular}{c} FFT \(\rightarrow\) sliding \\ window noise \\ estimation \(\rightarrow\) \\ threshold test \\ \end{tabular} & \begin{tabular}{c} FFT \(\rightarrow\) find \\ prominent local \\ peaks \\ \end{tabular} & \
\begin{tabular}{c} Hankel matrix \(\rightarrow\) \\ full SVD \(\rightarrow\) energy \\ ratio test \\ \end{tabular} &
\begin{tabular}{c} Hankel matrix \(\rightarrow\) \\ rank-1 SVD \(\rightarrow\) \\ diagonal averaging \\ \(\rightarrow\) FFT \(\rightarrow\) peak \\ detection \\ \end{tabular} \\ \hline
**Phase Noise** & Low (sensitive to \\ **Resilience** & \begin{tabular}{c} Low (sensitive to \\ spectral distortion) \\ \end{tabular} & \begin{tabular}{c} High (robust \\ against clutter and \\ phase noise) \\ \end{tabular} & \begin{tabular}{c} Moderate (better \\ than FFT due to \\ local peak \\ constraint) \\ \end{tabular} & \
\begin{tabular}{c} Poor under phase \\ noise and SNR \\ mismatch \\ \end{tabular} &
\begin{tabular}{c} Moderate to high \\ (robust in \\ mid-SNR and \\ phase noise \\ environments) \\ \end{tabular} \\ \hline
**SNR Range of** & High SNR only & \begin{tabular}{c} Wide range \\ (especially low to \\ mid SNR) \\ \end{tabular} & \
\begin{tabular}{c} Mid SNR \\ High SNR only \\ \end{tabular} &
\begin{tabular}{c} Mid SNR (5-15 dB) \\ with moderate \\ phase noise \\ \end{tabular} \\ \hline
**Computational** & \(\mathcal{O}(N\log N)\) & \(\mathcal{O}(N)\) & \(\mathcal{O}(N^{3})\) & \(\mathcal{O}(N^{3})\) (rank-1) \\
**Complexity** & Very high (FFT IP \\ cores available) & \begin{tabular}{c} High (simple \\ arithmetic \\ operations) \\ \end{tabular} & \begin{tabular}{c} High (simple peak \\ and threshold \\ logic) \\ \end{tabular} & \
\begin{tabular}{c} Low (full SVD is \\ computationally \\ intensive) \\ \end{tabular} &
\begin{tabular}{c} Moderate (rank-1 \\ SVD with FFT, \\ suitable for HLS or \\ co-design) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative summary of evaluated peak detection techniques. Figure 15: Probability of detection versus SNR from measurement data at a distance of 2.0 m. The increased distance led to a noticeable rightward shift in detection curves across all methods due to reduced received power and increased propagation loss. CA-CFAR continued to provide the most consistent detection, while LTSP maintained strong mid-SNR performance. MPM and FFT exhibited slower convergence toward high detection probability, and SVD-based detection became viable only beyond 14 dB. This trend reinforces the importance of robustness to range-dependent attenuation in practical radar systems. to provide a step-up in subspace reconstruction without incurring the full complexity of classical SVD, while achieving detection performance comparable to FFT, which remains a widely adopted technique in FMCW radar range estimation. Table 3 summarizes the computational complexity and estimated hardware resource requirements for implementing the five evaluated peak detection techniques on a Xilinx SoC FPGA platform. Techniques such as FFT thresholding, CA-CFAR, and simplified MPM are well suited for real-time FPGA implementation due to their low-to-moderate complexity and resource demands.