# Indoor Large-Scale MIMO-Based RSSI Localization with Low-Complexity RFID Infrastructure

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## Abstract

**:**

## 1. Introduction

- We propose large-scale MIMO-based RSSI localization at mm-wave band using the extremely simple dielectric resonator (DR) tags as the anchor node infrastructure in order to improve the self-localization accuracy of smart objects. Unlike UHF and UWB, mm-wave band offers the advantage of equipping large-scale MIMO structure at the reader and tag sides. The reader is equipped with a large-scale antenna in order to benefit from the channel hardening, making the small-scale quickly diminish with the increase of the array size. Furthermore, each reference DR tag is designed to have its unique resonance frequency and to have an array of DR elements in order to extend the ranging coverage. The validation of the DR tag is presented using measurements.
- We apply the weighted linear least-squares (WLLS) estimator combined with the optimal large-scale MIMO-based ranging technique in order to estimate the position of the object.
- We derive the Cramér–Rao Lower Bound (CRLB) for the variance of the position estimator for the proposed framework.
- Two sub-optimal algorithms are proposed, which can approach the performance of the optimal large-scale MIMO-based ranging with low computational complexity.
- Simulations are performed using analytical and deterministic channels to demonstrate the performance of the proposed algorithms considering various topologies of the infrastructure. These results show that the proposed method significantly improves the localization accuracy with simple hardware and computational complexity.

## 2. Related Work

## 3. System Model

#### 3.1. Tag Setup

#### 3.2. System Configuration

#### 3.3. RSSI Modeling

## 4. Large-Scale MIMO-Based RSSI Localization

#### 4.1. Ranging

#### 4.2. Location Estimation Methods

#### 4.3. Cramér–Rao Lower Bound Derivation

**Theorem**

**1.**

**Proof.**

## 5. The Sub-Optimal Algorithms

#### 5.1. Distance-Based Averaging (Dis-Avg) Algorithm

#### 5.2. Power-Based Averaging (Power-Avg) Algorithm

## 6. Measurements and Simulation Setup

#### 6.1. Measurements

#### 6.2. Localization Coverage Area

#### 6.3. Path Loss Model Using 3D Ray-Tracing

## 7. Results and Discussion

#### 7.1. Analytical Channels

#### 7.2. Deterministic Channels

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**2D radio frequency identification (RFID) localization system with monostatic configuration.

**Figure 2.**(

**A**) The monostatic radar cross-section (RCS) for a single dielectric resonator (DR) tag. (

**B**) The bi-static scattering cross-section (${\mathrm{m}}^{2}$) for a plane wave incident along the z-axis at 60.24 GHz (resonance frequency) on the plane $\varphi $ = 0 and $\pi $/2.

**Figure 4.**The measurement setup. (

**A**) Double ridge horn. (

**B**) $5\times 5$ and $5\times 1$ DR array configurations.

**Figure 5.**Measured RCS magnitudes compared to simulated RCS for $5\times 5$ and $5\times 1$ DR array structures.

**Figure 7.**3D layout of simulated real environment of the office room modeled in Wireless InSite (WI).

**Figure 8.**The cumulative distribution function (CDF) of localization root-mean-square error (RMSE) for the proposed algorithms for the line-of-sight (LOS) environment and the co-polarized antenna configuration.

**Figure 9.**Localization errors change with respect to different random object positions for the LOS environment and the co-polarized antenna configuration.

**Figure 10.**The CDF of ranging RMSE for the proposed algorithm for the LOS environment and the co-polarized antenna configuration.

**Figure 11.**The CDF of localization RMSE for the proposed algorithm for the LOS environment and the cross- and combined polarized antenna configurations.

**Figure 12.**The CDF of localization RMSE for different position estimation algorithms for the NLOS environment and the co-, cross- and combined-polarized antenna configurations.

**Figure 13.**The CDF of localization RMSE for different position estimation algorithms for the LOS environment and the co-polarized antenna configuration.

**Figure 14.**The localization RMSE for the proposed algorithms for different number of antennas on the reader for the LOS environment and the co-polarized antenna configuration.

**Figure 15.**The CDF of the RMSE for different numbers of nested reference tags for the LOS environment and the co-polarized antenna configuration.

**Figure 16.**The RMSE for the proposed algorithms for different path loss exponent values. M = 50, N = 8, $\sigma $ = 3.

**Figure 17.**The RMSE for the proposed algorithms for different standard deviation values of shadowing. M = 50, N = 8, $\alpha $ = 1.62.

**Figure 18.**The RMSE for the proposed algorithms for different indoor area dimensions ${w}_{1}={w}_{2}=w$. M = 50, N = 8, $\sigma $ = 3, $\alpha $ = 1.62.

**Figure 19.**Cramér–Rao Lower Bound (CRLB) for different path loss exponent and shadowing standard deviation values.

**Figure 20.**The CDF of the RMSE for the proposed algorithms for different spatial correlation values $\rho $ for the LOS environment and the co-polarized antenna configuration.

**Figure 21.**Estimated positions of the reader using deterministic channels, where the L-MIMO-RSSI algorithm is used.

Parameter | Value |
---|---|

Frequency Range | 57–63 GHz |

Operating Bandwidth | 100 MHz |

Transmit Power ${P}_{\mathrm{T}}$ | 10 dBm |

Reader Antenna Element Gain ${G}_{\mathrm{T}}$ | 2.15 dBi |

Room Width and Length | $10\times 10$${\mathrm{m}}^{2}$ |

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## Share and Cite

**MDPI and ACS Style**

El-Absi, M.; Zheng, F.; Abuelhaija, A.; Al-haj Abbas, A.; Solbach, K.; Kaiser, T.
Indoor Large-Scale MIMO-Based RSSI Localization with Low-Complexity RFID Infrastructure. *Sensors* **2020**, *20*, 3933.
https://doi.org/10.3390/s20143933

**AMA Style**

El-Absi M, Zheng F, Abuelhaija A, Al-haj Abbas A, Solbach K, Kaiser T.
Indoor Large-Scale MIMO-Based RSSI Localization with Low-Complexity RFID Infrastructure. *Sensors*. 2020; 20(14):3933.
https://doi.org/10.3390/s20143933

**Chicago/Turabian Style**

El-Absi, Mohammed, Feng Zheng, Ashraf Abuelhaija, Ali Al-haj Abbas, Klaus Solbach, and Thomas Kaiser.
2020. "Indoor Large-Scale MIMO-Based RSSI Localization with Low-Complexity RFID Infrastructure" *Sensors* 20, no. 14: 3933.
https://doi.org/10.3390/s20143933