# A Robust Design for Aperture-Level Simultaneous Transmit and Receive with Digital Phased Array

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- According to the demands of the ALSTAR array, the weight ${w}_{f}$ is put forward to trade EII, EIRP, and EIS. Its significance is to enable the performance of the ALSTAR array to meet the needs of EII, EIRP, and EIS in various scenarios.
- (2)
- The proposed ARGQBSO algorithm aims to achieve digital self-interference cancellation and adaptive beamforming. By proposing preset initial values and improving random grouping, dynamic probability functions, and quantum updates, the algorithm is a better balance in solving accuracy, solution time, and robustness.
- (3)
- The beamformer optimized by ARGQBSO is independent of an angle and can be applied to any scanning angle. Its advantage is that the resources of the digital chip are greatly saved.

## 2. System Model

#### 2.1. Signal Model

#### 2.2. Metrics and Optimization Problems

## 3. Our Proposed Algorithm

#### 3.1. Preset Initial Value

#### 3.2. Random Grouping

#### 3.3. Dynamic Probability Function

#### 3.4. Quantum Update

## 4. Simulation Results

#### 4.1. Phased Array with High Isolation

#### 4.2. Algorithm Performance Analysis

#### 4.2.1. Analysis of the Role of Improved Operations

#### 4.2.2. Comparison of ARGQBSO with Other Algorithms

#### 4.3. Design of ALSTAR Array by ARGQBSO

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**a**) E-Pattern of the second element. (

**b**) H-Pattern of the second element. (

**c**) E-Pattern of the third element. (

**d**) H-Pattern of the third element. (

**e**) E-Pattern of the fourth element. (

**f**) H-Pattern of the fourth element.

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**Figure 4.**Broadband antenna model: (

**a**) 3D view; (

**b**) gap structure; (

**c**) feed-network; (

**d**) metal reflector.

**Figure 6.**(

**a**) The port reflection parameters of the array. (

**b**) Port isolation parameters of the array. (

**c**) E-plane pattern of the first element. (

**d**) H-plane pattern of the first element.

**Figure 7.**(

**a**) Comparison of the fitness value with/without preset initial value. (

**b**) The influence curve of grouping method on algorithm running time. (

**c**) Comparison of the fitness value of fixed probability and dynamic probability density function and quantum update.

**Figure 8.**(

**a**) Box plot of the three algorithms for EII, EIRP, EIS, and noise floor ${P}_{n}$. (

**b**) Iterative curve and operation time of the four algorithms.

**Figure 10.**(

**a**) EII with different transmit power. (

**b**) EIRP with different transmit power. (

**c**) EIS with different transmit power.

**Figure 11.**(

**a**) EII with different ${w}_{f}$. (

**b**) EIRP with different ${w}_{f}$. (

**c**) EIS with different ${w}_{f}$.

Algorithm Types | Parameter Setting | Reference |
---|---|---|

BSO | ${p}_{r00}=0.2;$${p}_{r0}=0.8;$${p}_{r01}=0.4$ | [15] |

${p}_{r02}=0.5;$$M=10;$$N=60$ | ||

PSO | $w:0.9\u20130.4.4;$${c}_{1}={c}_{2}=2;$$N=60;$ | [22] |

AO | error accuracy = 0.001; Itern = 200 | [11] |

GA | ${p}_{c}=1;$${p}_{m}=0.05;$$N=60$ | [23] |

DE | $F=0.5;$$CR=0.5;$$N=60$ | [24] |

Proposed | $\begin{array}{ll}{p}_{0}:0.9\u20130.4;& {p}_{3}:0.4\u20130.8;\\ & {p}_{1}=0.7;\\ {p}_{2}=0.5;& M=10;& N=60\end{array}$ | This work |

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**MDPI and ACS Style**

Xie, M.; Wei, X.; Tang, Y.; Hu, D.
A Robust Design for Aperture-Level Simultaneous Transmit and Receive with Digital Phased Array. *Sensors* **2022**, *22*, 109.
https://doi.org/10.3390/s22010109

**AMA Style**

Xie M, Wei X, Tang Y, Hu D.
A Robust Design for Aperture-Level Simultaneous Transmit and Receive with Digital Phased Array. *Sensors*. 2022; 22(1):109.
https://doi.org/10.3390/s22010109

**Chicago/Turabian Style**

Xie, Mingcong, Xizhang Wei, Yanqun Tang, and Dujuan Hu.
2022. "A Robust Design for Aperture-Level Simultaneous Transmit and Receive with Digital Phased Array" *Sensors* 22, no. 1: 109.
https://doi.org/10.3390/s22010109