Summary
Based on
Umehira, 2025: Umehira, M. and Takeuchi, Y.. DFTs-OFDM Radar using Zadoff-Chu Sequence for Radar-Communication Integration. In 2025 International Conference on Computing, Networking and Communications (ICNC) (pp. 33-37). IEEE, 2025, February.
1. Introduction
The integration of radar and communication is vital in 5G NR, WLAN, and 6G. DFTs-OFDM radar using Zadoff-Chu (ZC) sequences offers:
- Low PAPR
- Excellent autocorrelation
- Compatibility with communication frameworks
Resource sharing (e.g., OFDMA, CSMA-CA) enables flexible and efficient spectrum use.
2. Zadoff-Chu Sequence Fundamentals
\[
Z_C^u(n) =
\begin{cases}
\exp\left(-j\pi \frac{u n^2}{N}\right), & \text{if } N \text{ is even} \\
\exp\left(-j\pi \frac{u n(n+1)}{N}\right), & \text{if } N \text{ is odd}
\end{cases}
\]
- N: sequence length
- u: root index (coprime with N)
- 0 ≤ n < N
These CAZAC sequences have ideal cyclic autocorrelation and constant envelope.
3. DFTs-OFDM Radar Signal Generation
Step 1: DFT Spreading
\[
Z_C^v(m) = \sum_{n=0}^{N-1} Z_C^u(n) \cdot \exp\left(-j \frac{2\pi m n}{N}\right)
\]
Step 2: Zero Padding
\[
Z_C^w(k) = \begin{cases}
Z_C^v(k), & 0 \leq k < \frac{N}{2} \\
0, & \frac{N}{2} \leq k < K - \frac{N}{2} \\
Z_C^v(k - (K - N)), & K - \frac{N}{2} \leq k < K
\end{cases}
\]
Step 3: IFFT
\[
S(k) = \sum_{m=0}^{K-1} Z_C^w(m) \cdot \exp\left(j \frac{2\pi m k}{K}\right)
\]
After filtering, this gives radar signal \( s(t) \) of duration \( T_s = N T_c \).
4. Radar Frame Structure
\[
r(t) = s(t+T_s) + \sum_{m=0}^{M-1} s(t - mT_s) + s(t - MT_s)
\]
This structure preserves cyclic properties and supports Doppler estimation.
5. Correlation-Based Detection
\[
X(k) = \frac{1}{N} \sum_{n=0}^{N-1} r(nT_c - \tau) \cdot Z_C^{u*}(n - k)
\]
Peak in \( |X(k)| \) implies target presence; delay \( \tau \) relates to range.
6. Radar Performance Metrics
6.1 Ranging Resolution
\[ \Delta R = \frac{c T_c}{2} \]
6.2 Max Detection Range
\[ R_{\text{max}} < \frac{c N T_c}{2} = \frac{c T_s}{2} \]
\[ R_{\text{max, practical}} \approx \frac{c T_s}{4} \]
6.3 Velocity Resolution and Maximum
\[ \Delta v = \frac{\lambda}{2 M T_s} \]
\[ v_{\text{max}} = \frac{\lambda}{4 T_s} \]
7. Simulation Insights
- Narrower main lobe and reduced sidelobes with larger N
- Doppler shifts impact only off-sample delays
\[ X(\tau) = \frac{\sin(\pi \tau / T_c)}{\pi \tau / T_c} \]
8. Conclusion
- Supports 5G/6G compatibility
- Low PAPR, configurable performance
- Efficient spectrum and hardware use
Summary Table
| Parameter | Expression | Improved By |
|---|---|---|
| Range Resolution | \( \Delta R = \frac{c T_c}{2} \) | ↓ Tc (↑ Bandwidth) |
| Max Detection Range | \( R_{\text{max}} < \frac{c N T_c}{2} \) | ↑ N |
| Velocity Resolution | \( \Delta v = \frac{\lambda}{2 M T_s} \) | ↑ M |
| Max Velocity | \( v_{\text{max}} = \frac{\lambda}{4 T_s} \) | ↓ Ts |