# Direction of Arrival Estimation Based on Received Signal Strength Using Two-Row Electronically Steerable Parasitic Array Radiator Antenna

^{*}

## Abstract

**:**

## 1. Introduction

- In-depth analysis of the antenna from the connectivity perspective with respect to possible beam steering in horizontal and elevation directions;
- Presentation of an approach for DoA estimation relying solely on RSS values gathered at the antenna output, which is a prerequisite for energy-efficient WSN nodes having DoA functionality [9,10], that is suitable for the antenna and can provide acceptable DoA estimation results also for low θ angles and are free from ambiguities for lower SNR values;
- Proposal of a detailed DoA algorithm performance testing method for more accurate DoA estimation accuracy assessment that involves all θ angles to address strong error variation at low θ angles.

## 2. Two-Row ESPAR Antenna

#### 2.1. Antenna Design

#### 2.2. Realized Antenna

#### 2.3. Antenna Radiation Performance Analysis

## 3. RSS-Based DoA Estimation for Two-Row ESPAR Antenna

_{1}= 10°, θ

_{2}= 20°, …, θ

_{9}= 90°}, provides 6° 1D DoA precision for RF signals impinging from 9 test vertical angles spanning equally between θ = 10° and θ = 90°. However, it has been shown that PPCC-MCP algorithm accuracy is sensitive to correct placement of calibration planes positions [24], while obtained results depend on testing setup [28] parameters, especially the choice of testing directions in horizontal and vertical planes as well as SNR values set for testing signals [24,28]. Moreover, the existing PPCC formulation was created to provide DoA results based on a number of directional radiation patterns, while new ESPAR antennas can have a number of possible radiation patterns that can be used in DoA estimation [32,33] having different performance, especially when testing signals may come from multiple horizontal and vertical directions. Therefore, to be used for DoA estimation together with new ESPAR antennas, including the two-row ESPAR antenna proposed in [31], PPCC-MCP algorithm and associated DoA testing methods have to be generalized.

#### 3.1. PPCC-MCP Algorithm

^{T}is the vector transpose operator, contains $I=360$ measured discreet values of $P\left({V}_{max}^{n},\phi \right)$ and ‘∘’ denotes the element-wise product of vectors. In result, the cross-correlation coefficient $g={\left[\mathsf{\Gamma}\left({\phi}_{1}\right),\mathsf{\Gamma}\left({\phi}_{2}\right),\dots ,\mathsf{\Gamma}\left({\phi}_{I}\right)\right]}^{T}$ is also a vector with $I=360$ entries being discretized values of the correlation coefficient $\mathsf{\Gamma}\left(\phi \right)$ for every considered value of $\phi $ in $\phi ={\left[{\phi}_{1},{\phi}_{2},\dots ,{\phi}_{I}\right]}^{T}={\left[0\xb0,1\xb0,\dots ,359\xb0\right]}^{T}$ and $\widehat{\phi}$ corresponds now to the maximum value of $g$. One should note, however, that as only a single calibration plane at θ = 90° is used to measure directional ESPAR antenna radiation patterns in an anechoic chamber during the calibration phase, cross-correlation operation Equation (2) will produce the most accurate results when RF signals impinging on the antenna arrive from θ = 90° vertical angle, which is aligned with the calibration plane. The results will significantly deteriorate for lower θ angles as the shape of ESPAR antenna radiation patterns gradually changes for θ > 90° [23,24].

#### 3.2. Generalized PPCC-MCP Algorithm for Two-Row ESPAR Antenna

## 4. Results and Discussion

#### 4.1. Mesurement Setup

#### 4.2. Deatiled DoA Testing Method

#### 4.3. DoA Estimation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Simulated and measured antenna radiation patterns at 2.44 GHz in the elevation plane (for φ = 90°) and in the horizontal plane for three configurations (see text for explanations): (

**a**) ${V}_{UP}^{90}$ (maximum at ${\theta}_{max\_up}=46\xb0$ ), (

**b**) ${V}_{MID}^{90}$ (maximum at ${\theta}_{max\_mid}=52\xb0$ ), and (

**c**)${V}_{DOWN}^{90}$ (maximum at ${\theta}_{max\_down}=56\xb0$).

**Figure 4.**Measured 3D radiation patterns for each considered configuration with different inclination angles: ${\theta}_{max\_up}$, ${\theta}_{max\_mid}$, ${\theta}_{max\_down}$ (from left to right).

**Figure 6.**Measured radiation patterns for each configuration in all directions for steering vectors: (

**a**) ${V}_{UP}^{{\phi}_{max}}$, (

**b**) ${V}_{MID}^{{\phi}_{max}}$, and (

**c**)${V}_{DOWN}^{{\phi}_{max}}$.

**Figure 9.**Cumulative Distribution Function of the aggregated gain for different sets of characteristics.

**Figure 10.**Anechoic chamber measurement setup used for the calibration phase of the proposed generalized PPCC-MCP algorithm for two-row ESPAR antenna.

**Figure 11.**RMSE and precision values calculated using the proposed detailed DoA testing method, which involves all elevation angles during testing process, for the generalized PPCC-MCP algorithm relying on combinations of specific steering vector sets: (

**a**) $\left\{{V}^{{n}_{up}}\right\}$; (

**b**) $\left\{{V}^{{n}_{mid}}\right\}$; (

**c**) $\left\{{V}^{{n}_{down}}\right\}$; (

**d**) $\left\{{V}^{{n}_{up}},{V}^{{n}_{mid}}\right\}$; (

**e**) $\left\{{V}^{{n}_{up}},{V}^{{n}_{down}}\right\}$; (

**f**) $\left\{{V}^{{n}_{mid}},{V}^{{n}_{down}}\right\}$.

**Figure 12.**RMSE and precision values calculated using the proposed detailed DoA testing method, which involves all elevation angles during testing process, for the generalized PPCC-MCP algorithm relying on all possible steering vectors $\left\{{V}^{{n}_{up}},{V}^{{n}_{mid}},{V}^{{n}_{down}}\right\}$ (

**a**) together with precision value comparison for combinations of sets giving the most accurate results (

**b**).

**Figure 13.**Comparison of precision values obtained using the proposed detailed DoA testing method and the combinations of steering vector sets giving the most accurate results for different SNR levels: (

**a**) SNR = 5 dB (

**b**) SNR = 0 dB.

Configuration | ${\mathit{\theta}}_{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{G}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\mathit{H}\mathit{P}\mathit{B}{\mathit{W}}_{\mathit{\theta}}$ | $\mathit{H}\mathit{P}\mathit{B}{\mathit{W}}_{\mathit{\phi}}$ | $\mathit{S}\mathit{L}{\mathit{L}}_{\mathit{\theta}}$ | $\mathit{S}\mathit{L}{\mathit{L}}_{\mathit{\phi}}$ | |S11| |
---|---|---|---|---|---|---|---|

UP | 46° | 7.7 dB | 45° | 88° | 10 dB | 14 dB | −20.9 dB |

MID | 52° | 7.8 dB | 43° | 100° | 10 dB | 28 dB | −10.5 dB |

DOWN | 56° | 8.1 dB | 46° | 93° | 12 dB | 25 dB | −8.8 dB |

$\mathit{n}$ | ${\mathit{V}}^{\mathit{n}}$ | Steering Vector Short Name | ${\mathit{\phi}}_{\mathit{m}\mathit{a}\mathit{x}}$ | ${\mathit{\theta}}_{\mathit{m}\mathit{a}\mathit{x}}$ |
---|---|---|---|---|

1 | $\left[001101010100\right]$ | ${V}_{UP}^{30}$ | 30° | 46° |

2 | $\left[100110001010\right]$ | ${V}_{UP}^{90}$ | 90° | 46° |

3 | $\left[010011000101\right]$ | ${V}_{UP}^{150}$ | 150° | 46° |

4 | $\left[101001100010\right]$ | ${V}_{UP}^{210}$ | 210° | 46° |

5 | [$110100010001]$ | ${V}_{UP}^{270}$ | 270° | 46° |

6 | [$011010101000]$ | ${V}_{UP}^{330}$ | 330° | 46° |

7 | $\left[001010100100\right]$ | ${V}_{DOWN}^{30}$ | 30° | 56° |

8 | $\left[000101010010\right]$ | ${V}_{DOWN}^{90}$ | 90° | 56° |

9 | $\left[100010001001\right]$ | ${V}_{DOWN}^{150}$ | 150° | 56° |

10 | $\left[010001100100\right]$ | ${V}_{DOWN}^{210}$ | 210° | 56° |

11 | $\left[101000010010\right]$ | ${V}_{DOWN}^{270}$ | 270° | 56° |

12 | $\left[010100001001\right]$ | ${V}_{DOWN}^{330}$ | 330° | 56° |

13 | $\left[000100001000\right]$ | ${V}_{MID}^{30}$ | 30° | 52° |

14 | $\left[000010000100\right]$ | ${V}_{MID}^{90}$ | 90° | 52° |

15 | $\left[000001000010\right]$ | ${V}_{MID}^{150}$ | 150° | 52° |

16 | $\left[100000000001\right]$ | ${V}_{MID}^{210}$ | 210° | 52° |

17 | $\left[010000100000\right]$ | ${V}_{MID}^{270}$ | 270° | 52° |

18 | $\left[001000010000\right]$ | ${V}_{MID}^{330}$ | 330° | 52° |

**Table 3.**Combinations of steering vector sets used in verification of DoA estimation performance using generalized PPCC-MCP algorithm (see text for explanations).

Combination of Steering Vector Sets | Steering Vectors Numbers | Total Number of Steering Vectors |
---|---|---|

$\left\{{V}^{{n}_{up}}\right\}$ | $\left\{1,2,3,4,5,6\right\}$ | 6 |

$\left\{{V}^{{n}_{mid}}\right\}$ | $\left\{13,14,15,16,17,18\right\}$ | 6 |

$\left\{{V}^{{n}_{down}}\right\}$ | $\left\{7,8,9,10,11,12\right\}$ | 6 |

$\left\{{V}^{{n}_{up}},{V}^{{n}_{mid}}\right\}$ | $\{1,2,3,4,5,6,$ $13,14,15,16,17,18\}$ | 12 |

$\left\{{V}^{{n}_{up}},{V}^{{n}_{down}}\right\}$ | $\{1,2,3,4,5,6,$ $7,8,9,10,11,12\}$ | 12 |

$\left\{{V}^{{n}_{mid}},{V}^{{n}_{down}}\right\}$ | $\{13,14,15,16,17,18,$ $7,8,9,10,11,12\}$ | 12 |

$\left\{{V}^{{n}_{up}},{V}^{{n}_{mid}},{V}^{{n}_{down}}\right\}$ | $\{1,2,3,4,5,6,$ $13,14,15,16,17,18,$ $7,8,9,10,11,12\}$ | 18 |

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**MDPI and ACS Style**

Rzymowski, M.; Nyka, K.; Kulas, L. Direction of Arrival Estimation Based on Received Signal Strength Using Two-Row Electronically Steerable Parasitic Array Radiator Antenna. *Sensors* **2022**, *22*, 2034.
https://doi.org/10.3390/s22052034

**AMA Style**

Rzymowski M, Nyka K, Kulas L. Direction of Arrival Estimation Based on Received Signal Strength Using Two-Row Electronically Steerable Parasitic Array Radiator Antenna. *Sensors*. 2022; 22(5):2034.
https://doi.org/10.3390/s22052034

**Chicago/Turabian Style**

Rzymowski, Mateusz, Krzysztof Nyka, and Lukasz Kulas. 2022. "Direction of Arrival Estimation Based on Received Signal Strength Using Two-Row Electronically Steerable Parasitic Array Radiator Antenna" *Sensors* 22, no. 5: 2034.
https://doi.org/10.3390/s22052034