# Enhanced Message-Passing Based LEACH Protocol for Wireless Sensor Networks

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## Abstract

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## 1. Introduction

- Generalized energy consumption model: This paper adopts a realistic energy consumption model of a sensor node. The model considers the transmission power dissipation and digital-processing power related to data decoding and aggregation. We capture the impact of the dynamic cluster size on the digital-processing power of a CH node which has been unaddressed in the previous studies. In addition, the data compression rate based on the correlation of the collected data is considered. It influences the transmission power dissipation of a CH node since an inaccurate energy consumption model of CH nodes incurs a suboptimal cluster formation. None of the previous works have properly addressed this issue to the best of the authors’ knowledge.
- Distributed algorithm: The new energy consumption model renders the optimization formulation highly nonlinear. We propose a message-passing approach that can tackle this nonlinearity very efficiently. We construct a graphical model that corresponds to the WSN of interest and develop an efficient distributed algorithm based on it. The advantages of the proposed algorithm include that (i) the algorithm is distributed by nature; (ii) computational load for each node is minimal; and (iii) the algorithm converges rapidly with only a small number of message-passing iteration. The advantages characterize the usefulness of the proposed algorithm for practical implementations.
- Performance: The performance of the proposed algorithm is verified with extensive simulation results. The proposed algorithm outperforms all the previous approaches in terms of energy consumption rate, total delivered data, and network lifetime. In particular, the proposed algorithm improves the network lifetime up to $28.5\%$ compared to existing LEACH protocols in the network lifetime. Based on the realistic energy consumption model, the proposed algorithm provides an efficient solution for different network sizes. As the network size grows, the improvement also increases. This is one of the prominent main benefits of the proposed algorithm.

## 2. System Model

## 3. Proposed LEACH-XMP Protocol

#### 3.1. Formulation

#### 3.2. Message Updates

#### 3.3. Cluster Head Selection

Algorithm 1 Cluster formation algorithm |

For each $(i,j)$, initialize $t\leftarrow 0$, ${\rho}_{ij}^{\left(t\right)}\leftarrow 0$, and ${\alpha}_{ij}^{\left(t\right)}\leftarrow 0$. repeat Update ${\alpha}_{ij}^{\left(t\right)}$ using (21) and send to neighbors. Update ${\rho}_{ij}^{(t+1)}$ using (22) and send to neighbors. Increment $t\leftarrow t+1$ until$|{\mathcal{U}}_{i}^{(t+1)}-{\mathcal{U}}_{i}^{\left(t\right)}|<\sigma $ for all i or $t>{t}_{max}$. |

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

LEACH | Low-Energy Adaptive Clustering Hierarchy |

WSN | Wireless Sensor Network |

PEGASIS | Power-Efficient Gathering in Sensor Information Systems |

HEED | Hybrid Energy-Efficient Distributed clustering |

EEUC | Energy-Efficient Uneven Clustering |

LEACH-XMP | LEACH-eXtended Message-Passing |

LEACH-AP | LEACH-Affinity Propagation |

LEACH-C | LEACH-Centralized |

LEACH-CE | LEACH-Centralized Efficient |

LEACH-CKM | LEACH-C with K-Means and Minimum Transmission Energy routing protocol |

CH | Cluster Head |

BS | Base Station |

## References

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**Figure 1.**A battery-powered wireless sensor network (WSN) with low-energy adaptive clustering hierarchy (LEACH).

**Figure 3.**Graphical models. (

**a**) Graphical model of 3-node WSN; (

**b**) Message definition around a single variable; (

**c**) Example of message-passing operation for 3-node WSN.

Description | Value |
---|---|

Radio circuitry energy dissipation, ${E}_{elec}$ | 50 nJ/bit |

Energy dissipation of amplifier in free-space, ${\u03f5}_{fs}$ | 10 pJ/bit/m${}^{2}$ |

Energy dissipation of amplifier in multipath, ${\u03f5}_{mp}$ | $0.0013$ pJ/bit/m${}^{4}$ |

Energy consumption for data aggregation, ${E}_{da}$ | 5 nJ/bit/signal |

Initial energy of each sensors, ${\mathcal{E}}_{0}$ | 2 J |

Initial number of sensors | 100 |

Reporting interval | 1 h |

Cluster reformation interval | 7 days |

Packet size (/node/report) | 200 bytes |

Maximum value of allowed iterations, ${t}_{max}$ | 50 |

Stopping threshold, $\sigma $ | $0.001$ |

Protocol | Complexity |
---|---|

LEACH-C | $O\left(tKN\right)$ |

LEACH-CE | $O\left(tKN\right)$ |

LEACH-CKM | $O\left(tKN\right)$ |

LEACH-AP | $O\left(t{N}^{2}\right)$ |

LEACH-XMP | $O(t{N}^{2}logN)$ |

Case | Scenario Description |
---|---|

A | BS = (50, 175), ${\mathcal{E}}_{0}$ = 2 J |

B | BS = (50, 125), ${\mathcal{E}}_{0}$ = 2 J |

C | BS = (50, 150), ${\mathcal{E}}_{0}$ = 2 J |

D | BS = (50, 200), ${\mathcal{E}}_{0}$ = 2 J |

E | BS = (50, 175), ${\mathcal{E}}_{0}$ = unif(1,3) J |

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**MDPI and ACS Style**

Kang, J.; Sohn, I.; Lee, S.H.
Enhanced Message-Passing Based LEACH Protocol for Wireless Sensor Networks. *Sensors* **2019**, *19*, 75.
https://doi.org/10.3390/s19010075

**AMA Style**

Kang J, Sohn I, Lee SH.
Enhanced Message-Passing Based LEACH Protocol for Wireless Sensor Networks. *Sensors*. 2019; 19(1):75.
https://doi.org/10.3390/s19010075

**Chicago/Turabian Style**

Kang, Jaeyoung, Illsoo Sohn, and Sang Hyun Lee.
2019. "Enhanced Message-Passing Based LEACH Protocol for Wireless Sensor Networks" *Sensors* 19, no. 1: 75.
https://doi.org/10.3390/s19010075