The proliferation of surveying drones and UAVs has revolutionized industries from infrastructure inspection to precision agriculture. These surveying UAVs operate as quintessential low-slow-small (LSS) targets – characterized by altitudes below 200m, velocities under 55m/s, and radar cross-sections (RCS) smaller than 0.1m². Traditional detection methods struggle in urban environments where ground clutter and terrain occlusion mask these surveying drones. Current approaches like radar, electro-optical, and acoustic systems face scalability limitations. This study introduces a curve fitting-based peak separation technique leveraging 5G-A integrated sensing and communication (ISAC) base stations, capitalizing on their dense low-altitude coverage to detect surveying UAVs in cluttered environments.
Echo Characteristics in 5G-A Low-Altitude Scenarios
5G-A ISAC base stations operating at 3.74GHz with 100MHz bandwidth exhibit distinct clutter properties compared to conventional radar. Key parameters include:
| Parameter | Value |
|---|---|
| Carrier Frequency | 3.74 GHz |
| Signal Bandwidth | 100 MHz |
| Pulse Repetition Interval | 5 ms |
| Sampling Rate | 122.88 MHz |
Ground clutter in 5G-A systems demonstrates narrow spectral width centered at zero-Doppler with smooth Gaussian-like distribution, expressed as:
$$C(f) = A \exp\left(-\frac{(f – f_0)^2}{2\sigma_f^2}\right)$$
where $A$ is clutter amplitude, $f_0$ is Doppler center (≈0 Hz), and $\sigma_f$ is spectral width (typically 5-10Hz). This contrasts sharply with conventional radar clutter showing wider spectra (20-50Hz) and irregular fluctuations at zero-Doppler. The smoothness enables precise spectral decomposition for surveying drone detection.
Curve Fitting and Peak Separation Technique
The detection framework processes range-Doppler (RD) maps through four stages:
1. Peak Detection via Smoothing Derivative Method
For each range bin $r_i$, the Doppler spectrum $S_i(f)$ undergoes 5-point moving average smoothing:
$$S_{\text{smooth}}[k] = \frac{1}{5} \sum_{j=-2}^{2} S_i[k+j]$$
Peak candidates satisfy the first-derivative zero-crossing condition:
$$\frac{dS_{\text{smooth}}}{df} \bigg|_{f=f_p} = 0 \quad \text{and} \quad \frac{d^2S_{\text{smooth}}}{df^2} \bigg|_{f=f_p} < 0$$
2. Peak Filtering with 2D CA-CFAR
Candidate peaks are validated against adaptive threshold $T_{\text{CA}}$ computed from reference cells (4 cells) and guard cells (2 cells):
$$T_{\text{CA}} = \alpha \cdot \frac{1}{N} \sum_{j \in \Omega} S_i[f_j]$$
where $\alpha$ scales for $P_{fa} = 10^{-3}$, and $\Omega$ denotes reference regions. Noise peaks below $T_{\text{CA}}$ are discarded.
3. Lorentzian Peak Decomposition
Valid peaks are modeled as Lorentzian functions:
$$L(f; h,f_p,w) = h \exp\left(-\frac{(f – f_p)^2}{w^2}\right)$$
Parameters are initialized using Caruana’s algorithm:
| Parameter | Estimation |
|---|---|
| Peak height $h$ | $\exp\left(a – \frac{b^2}{4c}\right)$ |
| Peak center $f_p$ | $-\frac{b}{2c}$ |
| Peak width $w$ | $\frac{2.35482}{\sqrt{-2c}}$ |
where $a,b,c$ are quadratic coefficients from fitting $\ln(S_i(f))$. Final parameters are optimized via Levenberg-Marquardt algorithm minimizing residual:
$$\min_{h,f_p,w} \sum_k \left| S_i(f_k) – \sum_m L_m(f_k) \right|^2$$
4. Target Declaration
Surveying UAVs are detected when non-zero Doppler peaks satisfy:
$$|f_p| > f_{\text{min}} \quad \text{and} \quad \frac{h}{h_{\text{clutter}}} > \gamma$$
where $f_{\text{min}} = 2$Hz (0.06m/s velocity resolution) and $\gamma = 3$dB SNR threshold.
Field Experiments and Performance Analysis
Experimental validation used DJI Mavic 3 Pro surveying UAVs under three scenarios:
| Scenario | Altitude | Velocity | Range |
|---|---|---|---|
| A (Target present) | 1.5m | 0.6m/s | 36.6m |
| B (Clutter only) | – | – | – |
| C (Target present) | 2.0m | 0.3m/s | 36.6m |
The algorithm achieved detection probabilities ($P_d$) of 0.83 and 0.73 for Scenarios A and C respectively, outperforming conventional techniques:
| Detection Method | $P_d$ (Scenario A) | Improvement |
|---|---|---|
| Proposed Technique | 0.83 | Baseline |
| MTI + 2D-CA-CFAR | 0.70 | +18.6% |
| 2D-CA-CFAR | 0.49 | +69.4% |
Critical performance factors include:
- Peak separation accuracy: 94.2% correct component identification
- Velocity estimation error: < 0.05m/s RMS
- Processing latency: 28ms per frame (256 Doppler bins)
Conclusion and Future Directions
The curve fitting-based peak separation technique enables reliable surveying UAV detection in 5G-A networks by exploiting unique low-altitude clutter characteristics. By decomposing Doppler spectra into Lorentzian components, the method achieves 69.4% higher $P_d$ than conventional CA-CFAR in cluttered environments. Future work will investigate deep learning-enhanced peak modeling and multi-node fusion for swarm detection. Integration with 5G-A base stations provides a scalable framework for nationwide surveying drone monitoring, addressing critical security challenges in the low-altitude economy.