## 1 Introduction
### Contribution of This Work  
Motivated by the limitations of the existing methods, we propose a novel signal reconstruction-based peak detection technique called Learned Thresholded Subspace Projection (LTSP). The LTSP method projects the beat signal into a lower-dimensional subspace via singular value decomposition, reconstructs the dominant signal mode, and applies spectral peak detection to the reconstructed signal. This technique is designed to balance robustness and complexity, improving detection performance under low SNR conditions without the need for large training datasets or deep networks. The LTSP is not a machine learning-based approach but rather a model-based adaptive subspace projection technique.  
The key contributions of this paper are as follows:  
* A comparative study of five peak detection methods for an FMCW radar: FFT thresholding, CA-CFAR, MPM (simplified), SVD-based detection, and the proposed LTSP.
* A derivation of the mathematical models for each technique, highlighting their assumptions and operational trade-offs.
* A comprehensive Monte Carlo-based evaluation framework assessing detection performance across a wide SNR range.
* Experimental evidence that LTSP offers a favorable trade-off between computational complexity and detection robustness, particularly in noisy environments.  
It is important to note that the goal of the proposed LTSP method is not to achieve the highest detection performance across all scenarios but to provide a balanced solution that combines robustness under moderate SNR and phase noise with feasible implementation complexity for real-time deployment on hardware platforms such as FPGAs or embedded processors.  
As shown in recent works [13; 14; 15; 16; 17], advanced detection algorithms and efficient hardware implementations are critical for modern FMCW radar systems.  
As recent studies demonstrate the importance of phase noise-aware and hardware-efficient detection methods in FMCW radar systems, significant progress has been made in addressing both signal processing and implementation challenges. Comprehensivesurveys such as [18] highlight the growing complexity of automotive FMCW radar systems. Several works have focused on enhancing peak detection in the presence of noise and clutter [19; 20; 21], while others have introduced robust subspace-based algorithms tailored to low-SNR conditions [22; 23]. On the implementation side, real-time FPGA and ASIC architectures have been proposed to meet the computational demands of embedded radar systems [24; 25; 26]. In parallel, advances in harmonic radar and nonlinear tag design [27; 28] have enabled new applications in passive sensing. Finally, recent studies emphasize the critical impact of oscillator phase noise on range accuracy and peak observability [29; 30; 31; 32], reinforcing the need for detection algorithms that are robust to spectral distortion.  
Table 1 provides a comparative summary of recent works in FMCW radar peak detection, highlighting differences in algorithmic approach, phase noise resilience, hardware feasibility, and validation strategy. In contrast to prior studies that either focus on detection accuracy in idealized scenarios or omit hardware considerations, the proposed LTSP-based framework offers a balanced trade-off between robustness and implementation practicality, supported by both simulation and real-world measurement results.  
The remainder of this paper is structured as follows. Section 2 presents the mathematical formulation of the five detection techniques. Section 3 describes the simulation setup and performance evaluation. Section 4 illustrates the measurements depicted in a real environment using the realized harmonic FMCW radar system. Section 5 concludes this paper and outlines future research directions.