# Continuous and Stable Cross-Eye Jamming via a Circular Retrodirective Array

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## Abstract

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## 1. Introduction

- MRCJ with a circular antenna array is proposed which has the potential to deal with the radar threat in any likely direction.
- The modulation direction of the jammer loop is defined which makes the jammer have the ability to provide continuous jamming performance.
- The array configuration with uniform-spacing angular separation is proved to be the optimal configuration for modified C-MRCJ to achieve stable jamming performance.
- Six antenna elements are advised for modified C-MRCJ in consideration of considerable jamming performance and moderate hardware cost.

## 2. Theoretical Analysis of C-MRCJ

#### 2.1. Jamming Scenario

#### 2.2. Cross-Eye Gain of C-MRCJ

#### 2.3. Continuous Jamming by Modifying MD

## 3. Results and Discussion

- the radar carrier frequency is 9 GHz,
- the radar antenna aperture is $2.54\lambda $,
- the jammer range is 1 km,
- the jammer base-length is 10 m.

#### 3.1. Angular Error Induced by C-MRCJ

#### 3.2. Continuous Jamming Provided by Modified C-MRCJ

#### 3.3. Stable Jamming Provided by Modified C-MRCJ

- Symmetrical case: ${\alpha}_{1}={\alpha}_{3}$, ${\alpha}_{2}={180}^{\circ}-{\alpha}_{1}-{\alpha}_{3}$, ${\alpha}_{1}$ and ${\alpha}_{3}$ vary from ${0}^{\circ}$ to ${90}^{\circ}$ with the step of ${10}^{\circ}$;
- Asymmetrical case: ${\alpha}_{1}\ne {\alpha}_{3}$, ${\alpha}_{2}={180}^{\circ}-{\alpha}_{1}-{\alpha}_{3}$, ${\alpha}_{1}={60}^{\circ}$, ${\alpha}_{3}$ varies from ${0}^{\circ}$ to ${90}^{\circ}$ with the step of ${10}^{\circ}$.

#### 3.4. Choice of the Number of Antenna Elements

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MRCJ | Multiple-element Retrodirective Cross-eye Jamming |

C-MRCJ | MRCJ employing a Circular array |

JSR | Jammer-to-Signal Ratio |

TRCJ | Two-element Retrodirective Cross-eye Jamming |

MCJ | Multiple-element Cross-eye Jamming |

L-MRCJ | MRCJ employing a Linear array |

DOA | Direction Of Arrival |

MD | Modulation Direction |

MAW | Missile Approach Warner |

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**Figure 6.**Two different configurations of C-MRCJ with six antenna elements. The platform is denoted by a black square. (

**a**) Configuration 1 where ${\alpha}_{1}={\alpha}_{3}={15}^{\circ}$, ${\alpha}_{2}={150}^{\circ}$. (

**b**) Configuration 2 where ${\alpha}_{1}={\alpha}_{2}={\alpha}_{3}={60}^{\circ}$.

**Figure 7.**Configuration of L-MRCJ with six antenna elements. The base-lengths of the three jammer loops are ${d}_{c}$, $4{d}_{c}/5$ and $3{d}_{c}/5$, respectively.

**Figure 8.**Monopulse-indicated angles of different jammer array configurations when the radar antennas rotate. The system parameters of TRCJ are $-0.5$ dB and ${180}^{\circ}$, and the system parameters of L-MRCJ and C-MRCJ which are ${a}_{1}={a}_{3}=-0.5$ dB, ${a}_{2}=0.5$ dB, ${\varphi}_{1}={\varphi}_{2}={\varphi}_{3}={180}^{\circ}$.

**Figure 9.**Monopulse-indicated angles of L-MRCJ and C-MRCJ when the jammer antennas rotate. (

**a**) The system parameters are ${a}_{1}={a}_{2}={a}_{3}=-0.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${\varphi}_{1}={\varphi}_{2}={\varphi}_{3}={180}^{\circ}$. (

**b**) The system parameters are ${a}_{1}=-0.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${a}_{2}=-1.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${a}_{3}=-2.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${\varphi}_{1}={170}^{\circ}$, ${\varphi}_{2}={175}^{\circ}$, ${\varphi}_{3}={180}^{\circ}$.

**Figure 10.**Monopulse-indicated angles of L-MRCJ and modified C-MRCJ when the jammer antennas rotate. (

**a**) The system parameters are ${a}_{1}={a}_{2}={a}_{3}=-0.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${\varphi}_{1}={\varphi}_{2}={\varphi}_{3}={180}^{\circ}$. (

**b**) The system parameters are ${a}_{1}=-0.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${a}_{2}=-1.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${a}_{3}=-2.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$, ${\varphi}_{1}={170}^{\circ}$, ${\varphi}_{2}={175}^{\circ}$, ${\varphi}_{3}={180}^{\circ}$.

**Figure 11.**Monopulse-indicated angles for different configurations when the jammer antennas rotate. The system parameters are ${a}_{1}={a}_{2}={a}_{3}=-0.5$ dB, ${\varphi}_{1}={\varphi}_{2}={\varphi}_{3}={180}^{\circ}$. (

**a**) Symmetrical case. (

**b**) Asymmetrical case.

**Figure 12.**The arithmetic mean and variance of monopulse-indicated angle. (

**a**) Arithmetic mean for the symmetrical case. (

**b**) Arithmetic mean for the asymmetrical case. (

**c**) Variance for the symmetrical case. (

**d**) Variance for the asymmetrical case.

**Figure 13.**Monopulse-indicated angles of modified C-MRCJ with the optimal configuration for a range of antenna numbers when the jammer antennas rotate. The system parameters are ${a}_{1}={a}_{2}={a}_{3}=-0.5$ dB, ${\varphi}_{1}={\varphi}_{2}={\varphi}_{3}={180}^{\circ}$.

**Figure 14.**The arithmetic mean and variance of monopulse-indicated angle for different jammer antenna numbers. (

**a**) Arithmetic mean. (

**b**) Variance.

DOA Information | ${\mathit{I}}_{1}$ | ${\mathit{I}}_{2}$ | ${\mathit{I}}_{3}$ |
---|---|---|---|

Direction in the region between antenna 1 and 2 | −1 | 1 | 1 |

Direction in the region between antenna 2 and 3 | −1 | −1 | 1 |

Direction in the region between antenna 3 and 4 | −1 | −1 | −1 |

Direction in the region between antenna 4 and 5 | 1 | −1 | −1 |

Direction in the region between antenna 5 and 6 | 1 | 1 | −1 |

Direction in the region between antenna 6 and 1 | 1 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Liu, T.; Wei, X.; Liu, Z.; Guan, Z.
Continuous and Stable Cross-Eye Jamming via a Circular Retrodirective Array. *Electronics* **2019**, *8*, 806.
https://doi.org/10.3390/electronics8070806

**AMA Style**

Liu T, Wei X, Liu Z, Guan Z.
Continuous and Stable Cross-Eye Jamming via a Circular Retrodirective Array. *Electronics*. 2019; 8(7):806.
https://doi.org/10.3390/electronics8070806

**Chicago/Turabian Style**

Liu, Tianpeng, Xizhang Wei, Zhen Liu, and Zhiqiang Guan.
2019. "Continuous and Stable Cross-Eye Jamming via a Circular Retrodirective Array" *Electronics* 8, no. 7: 806.
https://doi.org/10.3390/electronics8070806