# Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms

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## Abstract

**:**

## 1. Introduction

## 2. Golay Complementary Waveforms and Pointwise Processors

#### 2.1. Golay Pairs

#### 2.2. Pointwise Minimization Procedure

#### 2.3. Pointwise Thresholding Procedure

## 3. Simulation and Further Discussion

- ${f}_{\mathrm{c}}$, carrier frequency: 1 GHz;
- B, bandwidth: 50 MHz;
- ${f}_{\mathrm{ts}}$, time sampling rate: 2 B;
- ${f}_{\mathrm{ds}}$, Doppler sampling rate: 0.01 rad;
- T, PRI: 50 μs;
- N, pulse number: 32;
- L, chip number of Golay pair: 64;
- ${T}_{\mathrm{c}}$, chip interval: 0.1 μs;
- E∼$\mathcal{CN}(0,1)$, complex Gaussian zero-mean white noise: −10 dB (i.e., $SNR$ = 10 dB).

#### 3.1. Fixed Scenario

#### 3.2. Further Filtering for the PTP

#### 3.3. Randomized Scenario

- (1)
- Target number: 2 (one strong and one weak);
- (2)
- Target number: 3 (one strong and two weak);
- (3)
- Target number: 4 (two strong and two weak);
- (4)
- Target number: 5 (three strong and two weak).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Delay-Doppler maps: (

**a**) standard order; (

**b**) PTM design; (

**c**) BD algorithm (the unit of the colorbar is dB, $N=32$).

**Figure 4.**The results (in dB) of (

**a**) the BD algorithm; (

**b**) the WD algorithm; (

**c**) the PMP; (

**d**) the PTP.

**Figure 5.**The delay cross-section of (

**a**) target 1; (

**b**) target 2; (

**c**) target 3 using the PMP and PTP.

**Figure 6.**The Doppler cross-section of (

**a**) target 1 and target 2 and (

**b**) target 3 using the PMP and PTP.

**Figure 7.**Delay-Doppler maps of the PTP when (

**a**) $thr$ = 1 dB; (

**b**) $thr$ = 2 dB; (

**c**) $thr$ = 4 dB; (

**d**) $thr$ = 8 dB (the unit of the colorbar is dB).

**Figure 8.**The outputs of further filtering of the PTP when (

**a**) $thr=1\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=32$; (

**b**) $thr=2\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=32$; (

**c**) $thr=4\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=32$; (

**d**) $thr=8\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=32$; (

**e**) $thr=1\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=64$; (

**f**) $thr=2\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=64$; (

**g**) $thr=4\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=64$; (

**h**) $thr=8\phantom{\rule{4.pt}{0ex}}\mathrm{dB}$, $N=64$ (the unit of the colorbar is dB).

Target | Delay | Doppler | Magnitude |
---|---|---|---|

Target No. 1 | ${\tau}_{1}=16.6\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{4.pt}{0ex}}\mathsf{\mu}\mathrm{s}$ | ${f}_{{\mathrm{d}}_{1}}=-0.4\phantom{\rule{3.33333pt}{0ex}}\mathrm{rad}$ | 0 dB |

Target No. 2 | ${\tau}_{2}=16.6\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{4.pt}{0ex}}\mathsf{\mu}\mathrm{s}$ | ${f}_{{\mathrm{d}}_{2}}=-0.9\phantom{\rule{3.33333pt}{0ex}}\mathrm{rad}$ | 0 dB |

Target No. 3 | ${\tau}_{3}=22\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{4.pt}{0ex}}\mathsf{\mu}\mathrm{s}$ | ${f}_{{\mathrm{d}}_{3}}=2.4\phantom{\rule{3.33333pt}{0ex}}\mathrm{rad}$ | −20 dB |

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## Share and Cite

**MDPI and ACS Style**

Zhu, J.; Song, Y.; Jiang, N.; Xie, Z.; Fan, C.; Huang, X.
Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms. *Remote Sens.* **2023**, *15*, 2452.
https://doi.org/10.3390/rs15092452

**AMA Style**

Zhu J, Song Y, Jiang N, Xie Z, Fan C, Huang X.
Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms. *Remote Sensing*. 2023; 15(9):2452.
https://doi.org/10.3390/rs15092452

**Chicago/Turabian Style**

Zhu, Jiahua, Yongping Song, Nan Jiang, Zhuang Xie, Chongyi Fan, and Xiaotao Huang.
2023. "Enhanced Doppler Resolution and Sidelobe Suppression Performance for Golay Complementary Waveforms" *Remote Sensing* 15, no. 9: 2452.
https://doi.org/10.3390/rs15092452