# An Efficient Approach for Sidelobe Level Reduction Based on Recursive Sequential Damping

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Paper Contribution

#### 1.3. Paper Organization

## 2. Modelling of the Proposed SSD Technique

## 3. SSD Performance Analysis

#### 3.1. SSD Damping Behavior

#### 3.2. SSD Behavior at Different Angular Step Sizes

#### 3.3. Impact of SSD on the Beamwidth

#### 3.4. SSD Performance with Interelement Spacing

#### 3.5. SSD Performance with the Mainlobe Direction

## 4. SSD Performance Comparisons and Discussions

#### 4.1. Comparisons with Conventional Tapering Windows

#### 4.2. Comparisons with Optimization Techniques

## 5. Mutual Coupling Effects on the SSD Performance

## 6. SSD for Two-Dimensional Planar Arrays

## 7. SSD Operational Constraints and Limitations Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Uniform array configurations for (

**a**) a one-dimensional array and (

**b**) a two-dimensional array.

**Figure 2.**Flowchart representation for the recursive sidelobe sequential damping (SSD) sidelobe level (SLL) reduction algorithm.

**Figure 3.**SLL reduction by SSD at different damping cycles. (

**a**) $K=2$ with (

**b**) the weighting profile at $K=2$, (

**c**) $K=50$ with (

**d**) the weighting profile at $K=50$, and (

**e**) $K=\mathrm{10,000}$ with (

**f**) the weighting profile at $K=\mathrm{10,000}$.

**Figure 12.**SLL comparison between the proposed SSD technique (blue curves) and conventional windows (red curves) at the same beamwidth. (

**a**) A comparison with the Dolph-Chebyshev window. (

**b**) A comparison with the Gaussian window.

**Figure 13.**SLL comparison between the proposed SSD technique (black curves) and different optimization techniques in a 16 element uniform linear array (ULA) at (

**a**) $K=50$, (

**b**) $K=100$, (

**c**) $K=150$, and (

**d**) $K=200$.

**Figure 14.**Maximum and average SLL comparison between the proposed SSD technique (black curves) and different optimization techniques for a 16 element ULA at $K=50$, $100$, $150$, and $200$.

**Figure 15.**Mainlobe beamwidth comparison between the proposed SSD technique and different optimization techniques for a 16 element ULA at $K=50$, $100$, $150$, and $200$.

**Figure 16.**Normalized antenna coefficients for a 16 element ULA. (

**a**) Optimization benchmarking techniques and (

**b**) the SSD algorithm at different values for $K$.

**Figure 17.**SLL comparison between the proposed SSD technique (black curves) and different efficient optimization techniques for a 32 element ULA at (

**a**) $K=50$, (

**b**) $K=100$, (

**c**) $K=150$, and (

**d**) $K=200$.

**Figure 18.**Maximum and average SLL comparison between the proposed SSD technique (black curves) and different optimization techniques for a 32 element ULA at $K=50$, $100$, $150$, and $200$.

**Figure 19.**Mainlobe beamwidth comparison between the proposed SSD technique and different optimization techniques for a 32 element ULA at $K=50$, $100$, $150$, and $200$.

**Figure 20.**Impact of mutual coupling on the SSD performance for a 16 element ULA at (

**a**) $K=100$ and (

**b**) $K=1000$.

**Figure 21.**Impact of mutual coupling on the SSD performance for a 16 element ULA at (

**a**) $K=100$ and (

**b**) $K=1000$.

**Figure 22.**Two-dimensional planar array configuration formed by $20\times 20$ dipole antennas with mutual coupling effects. (

**a**) Array configuration. (

**b**) Normalized power pattern with uniform feeding. (

**c**) Normalized power pattern with SSD feeding at $K=100$. (

**d**) Normalized power pattern with SSD feeding at $K=1000$.

**Figure 23.**The impact of one antenna element failure on the SDD performance at different locations in a 16 element ULA.

**Figure 24.**The impact of multiple antenna element failures on the SDD performance at different locations in a 16 element ULA.

**Table 1.**SLL level comparison between conventional windows and the SSD algorithm at the same beamwidth.

Benchmarking Window | Window SLL (dB) | SSD SLL (dB) | Relative Reduction in the Maximum SLL (dB) | Beamwidth (Degrees) |
---|---|---|---|---|

Triangular window | −26.39 | −32.32 | 6.32 | 7.12° |

Hamming | −27.89 | −30.5 | 2.61 | 7.14° |

Hanning | −27.6 | −30.6 | 3 | 7.14° |

Blackman | −37.74 | −44.83 | 7.09 | 8.06° |

Dolph-Chebyshev | −50 | −52 | 2 | 8.38° |

Kaiser | −35.96 | −46.55 | 10.59 | 8.2° |

Gaussian | −37.19 | −40.02 | 2.83 | 7.74° |

Cosine square | −28 | −40 | 12 | 7.74° |

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**MDPI and ACS Style**

Albagory, Y.; Alraddady, F.
An Efficient Approach for Sidelobe Level Reduction Based on Recursive Sequential Damping. *Symmetry* **2021**, *13*, 480.
https://doi.org/10.3390/sym13030480

**AMA Style**

Albagory Y, Alraddady F.
An Efficient Approach for Sidelobe Level Reduction Based on Recursive Sequential Damping. *Symmetry*. 2021; 13(3):480.
https://doi.org/10.3390/sym13030480

**Chicago/Turabian Style**

Albagory, Yasser, and Fahad Alraddady.
2021. "An Efficient Approach for Sidelobe Level Reduction Based on Recursive Sequential Damping" *Symmetry* 13, no. 3: 480.
https://doi.org/10.3390/sym13030480