# A Low Energy Consumption DOA Estimation Approach for Conformal Array in Ultra-Wideband

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## Abstract

**:**

## 1. Introduction

## 2. The Application of LDPA

## 3. The Principle of Arbitrary Baseline Algorithm

#### 3.1. The Model of the Incident Signal

#### 3.2. The 2D Arbitrary Baseline Algorithm

## 4. The 3D Arbitrary Baseline Algorithm

#### 4.1. The Principle of 3D Arbitrary Baseline Algorithm

#### 4.2. The Virtual Elements Based on Virtual Baseline

**Figure 7.**Positions of the virtual elements. The black points represent the actual element (E, F and M); and the shadow points represent the virtual elements(G, H and N).

#### 4.3. The Solving Ambiguous Method Based on Rotation Comparison

## 5. The Algorithm Based on Conformal Antenna

#### 5.1. The Pre-Processing of Sub-Array Divided Technique

**Figure 8.**Positions of the expanded virtual elements. The black points represent the actual elements (1–4); and the shadow points represent the virtual elements (a−l).

#### 5.2. The Algorithm Step

- The array antennas mounted on aircraft are arranged reasonably. Two combinations are selected in each sub-array for direction finding, the four antenna elements (including the virtual elements) constitute a combination;
- The azimuth α and the elevation β can be obtained by solving Equations (16) or (17) of one combination. By checking whether ${\gamma}_{1}$ and ${\gamma}_{2}$ are positive or negative, the mirrored ambiguous problem can be solved. All values including ambiguous values are obtained, which will be recorded as the first solution;
- Apply the same procedure for another combination as step 2;
- According to Equation (20), the 2D-DOA of the incident signal can be obtained;
- Comparing the 2D-DOA of each sub-array (There is a greater difference between the error angle and the real angle due to the “shadow effect”), the closest value of each sub-array’s 2D-DOA is regarded as the real value, and the average value is calculated. Using transformation Equations (2) and (3), the course angle θ and pitching angle $\phi $ can be obtained finally.

## 6. The Analysis of Direction Finding Error

## 7. Simulation Results

#### 7.1. The Antenna Model

**Figure 10.**Antenna placement. (

**a**) 2D array of the planar spiral antenna; (

**b**) 3D array of LPDA conformal antenna.

#### 7.2. Simulation Results

**Figure 11.**Comparison of solving ambiguous probability at different frequencies. (

**a**) $\beta ={80}^{\circ}$; (

**b**) $\beta ={60}^{\circ}$.

**Figure 12.**Comparison of RMSE of 2D array with respect to different frequency and SNR. (

**a**) $\beta ={80}^{\circ}$; (

**b**) $\beta ={60}^{\circ}$.

**Figure 13.**Comparison of RMSE of 3D array with respect to different frequency and SNR. (

**a**) $\beta ={80}^{\circ}$; (

**b**) $\beta ={60}^{\circ}$.

**Figure 14.**Comparison of RMSE with respect to different frequency and azimuth. (

**a**) 2D array; (

**b**) 3D array.

Algorithm | 100 | 200 | 500 |
---|---|---|---|

2D array | 0.54 s | 0.94 s | 2.22 s |

3D array | 4.53 s | 9.05 s | 22.29 s |

MUSIC | 20.06 s | 41.79 s | 108.10 s |

## 8. Conclusions

## Acknowledgements

## Conflicts of Interest

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**MDPI and ACS Style**

Wan, L.; Liu, L.; Han, G.; Rodrigues, J.J.P.C. A Low Energy Consumption DOA Estimation Approach for Conformal Array in Ultra-Wideband. *Future Internet* **2013**, *5*, 611-630.
https://doi.org/10.3390/fi5040611

**AMA Style**

Wan L, Liu L, Han G, Rodrigues JJPC. A Low Energy Consumption DOA Estimation Approach for Conformal Array in Ultra-Wideband. *Future Internet*. 2013; 5(4):611-630.
https://doi.org/10.3390/fi5040611

**Chicago/Turabian Style**

Wan, Liangtian, Lutao Liu, Guangjie Han, and Joel J. P. C. Rodrigues. 2013. "A Low Energy Consumption DOA Estimation Approach for Conformal Array in Ultra-Wideband" *Future Internet* 5, no. 4: 611-630.
https://doi.org/10.3390/fi5040611