# Signal Subspace Reconstruction for DOA Detection Using Quantum-Behaved Particle Swarm Optimization

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

#### 2.1. Array Signal Model

#### 2.2. Introduction of MUSIC Algorithm

## 3. DOA Detection Approach Using QPSO through Signal Subspace Reconstruction

- (1)
- Initialize particle position vector ${\mathit{\Theta}}_{n}$ and the best previous position ${\mathit{\Theta}}_{n}^{{}_{pbest}}$ of each particle.
- (2)
- Calculate the mean best position $\mathit{m}\mathit{b}\mathit{e}\mathit{s}\mathit{t}\left(t\right)$ using Equation (15).
- (3)
- Determine the current fitness value by substituting ${\mathit{\Theta}}_{n}$ into the cost function $\mathrm{min}f\left(\tilde{\mathit{\Theta}}\right)$ and compare it with the particle’s previous best value. If the current fitness value is smaller than the previous best value, replace the previous best value with the current value.
- (4)
- Similarly, calculate the current global best position and compare it with the previous global position. If the current global best position is smaller, set the global position to the current global.
- (5)
- Determine the local attractor ${\mathit{\Theta}}^{la}$ through Equation (16) and update the particle position according to Equation (17).
- (6)
- Repeat the iteration from step (2) to step (5) until the termination condition or the optimal solution of particle position vector ${\mathit{\Theta}}_{n}^{opt}$ is reached, such as taking iterative 100 times as an end.

## 4. Experimental Studies

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Root mean square errors (RMSE) versus number of snapshots (signals with the same signal-to-noise ratio (SNR)). (

**b**) The cost function and the RMSE versus the number of iterations.

**Figure 4.**(

**a**) RMSE versus number of snapshots (signals with different SNRs). (

**b**) The cost function and the RMSE versus the number of iterations.

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**MDPI and ACS Style**

Zhang, R.; Xu, K.; Quan, Y.; Zhu, S.; Xing, M.
Signal Subspace Reconstruction for DOA Detection Using Quantum-Behaved Particle Swarm Optimization. *Remote Sens.* **2021**, *13*, 2560.
https://doi.org/10.3390/rs13132560

**AMA Style**

Zhang R, Xu K, Quan Y, Zhu S, Xing M.
Signal Subspace Reconstruction for DOA Detection Using Quantum-Behaved Particle Swarm Optimization. *Remote Sensing*. 2021; 13(13):2560.
https://doi.org/10.3390/rs13132560

**Chicago/Turabian Style**

Zhang, Rui, Kaijie Xu, Yinghui Quan, Shengqi Zhu, and Mengdao Xing.
2021. "Signal Subspace Reconstruction for DOA Detection Using Quantum-Behaved Particle Swarm Optimization" *Remote Sensing* 13, no. 13: 2560.
https://doi.org/10.3390/rs13132560