# Energy-Aware Control of Error Correction Rate for Solar-Powered Wireless Sensor Networks

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## Abstract

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## 1. Introduction

- Energy-neutral operation (ENO): The energy input during a harvesting period should not be less than the amount consumed during the same period. Because the energy harvested in one day can vary owing to environmental conditions, a node should adapt its power consumption rate to match the harvested energy for eternal operations.
- Minimizing the waste of harvested energy: In order to satisfy ENO, it is important to control the energy consumption such that it is below the energy input. This means that the less energy a node consumes, the better for satisfying the ENO conditions. However, in this case, a different problem can occur. Assuming that there is continuous sunny weather over several days, there may be a surplus of energy in excess of that required for a node’s general operation; thus, overcharged energy would inevitably be discarded owing to the capacity constraints of a rechargeable battery. Therefore, it is important to not only satisfy the ENO conditions, but also keep the remaining energy from exceeding the battery capacity.
- Reserving energy for the non-harvesting time: There is no energy to be harvested when the Sun has set. However, in many applications, the user wants to collect data at all times. Therefore, a node should reserve a certain amount of energy for the non-harvesting time. This requirement allows a node to operate regardless of the time of day.

- Energy-adaptive operation: A node running EA-RS adjusts the energy consumption rate according to the energy collection rate by controlling the parity length used in the RS code. Thus, it can satisfy the ENO condition, minimize the waste of harvested energy and reserve energy for non-harvesting times, which leads to the best utilization of harvested energy.
- Enhancing the throughput of a WSN: Because the EA-RS utilizes surplus energy to increase data reliability (i.e., the error-correction rate), the amount of data collected at the sink during a time period can be increased.
- Fully-localized algorithm: A node running EA-RS only uses information for itself and its one-hop neighbors. This localized approach is crucially important for the scalability of a WSN.

## 2. Related Work

#### 2.1. Solar Energy as a Power Source for WSNs

- Periodicity: The Sun rises and sets once a day. This is the duration of a charging or harvesting cycle. A new supply of solar energy can be expected during every harvesting cycle.
- Dynamics: Solar energy varies throughout the day. Commonly, it increases in the morning, decreases in the afternoon and is absent during the night. In addition, it varies from day to day depending on the weather and season.

#### 2.2. Energy Optimization for Solar-Powered WSNs

#### 2.3. ARQ and FEC in WSN Environments

#### 2.4. Reed–Solomon Block in the FEC Scheme

## 3. Energy-Aware Reed–Solomon Scheme

#### 3.1. Overview of Node Operation with EA-RS

- Energy prediction (explained in Section 3.2)
- Prediction of harvested energy: Predict the energy harvested in the next period ${p}_{\mathrm{tx}}$ using the given solar-energy harvesting model [18]
- Prediction of consumed energy: Predict the energy consumed in the next period ${p}_{\mathrm{tx}}$ with a varying parity length:

- Determination of the parity length (explained in Section 3.3)
- Determination of the parity length for the node itself: Calculate the appropriate parity length for ${p}_{\mathrm{tx}}$, considering its energy prediction
- Finalization of the parity length: Finalize the appropriate parity length for ${p}_{\mathrm{tx}}$, considering the parity length of the target node

- Data processing (explained in Section 3.4)
- Sensing the data: Gather the data that the application requires
- Encoding the data: Encode the sensory data to the RS block with the determined parity length
- Transferring the data: Send the encoded RS block to the RF module at the physical layer for transferring

#### 3.2. Energy Prediction

#### 3.2.1. Energy Harvesting Model

#### 3.2.2. Energy Consuming Model

#### 3.3. Determining the Parity Length for the Next Period

#### 3.3.1. Determining the Parity Length for a Node Itself

- (1) The parity length that allows the amount of residual energy after the end of the next period not to exceed the maximum capacity of the battery: these parity lengths can minimize the amount of energy dissipated owing to the limited battery capacity. By using these parity lengths, the node consumes more energy than must be wasted in order to prevent the remaining energy from exceeding the battery capacity.
- (2) The smallest parity length among those of (1): by using this parity length, the node can use the minimal required energy for data reliability, except for energy that must be wasted. That is, it allows the node to store as much energy as possible while minimizing the blackout time.

#### 3.3.2. Finalizing the Parity Length Considering a Target Node’s Status

Algorithm 1: EA-RS(i) | |

1 | ${D}_{\mathrm{parity}}^{i}$⟵ 1; |

2 | ${D}_{\mathrm{parity}}^{j}$⟵ size of parity bits of node i’s target node; |

3 | while${E}_{\mathrm{residual}}^{i}(t+{p}_{\mathrm{tx}})>{B}_{\mathrm{full}}^{i}$do |

4 | | ${D}_{\mathrm{parity}}^{i}\u27f5{D}_{\mathrm{parity}}^{i}+\gamma $; |

5 | end |

6 | Broadcast the ${D}_{\mathrm{parity}}^{i}$ to neighbor nodes using ACK packet; |

7 | if${D}_{\mathrm{parity}}^{i}<{D}_{\mathrm{parity}}^{j}$then |

8 | | Encoding with parity ${D}_{\mathrm{parity}}^{i}$; |

9 | else |

10 | | Encoding with parity ${D}_{\mathrm{parity}}^{j}$; |

11 | end |

12 | sleep($period$); |

#### 3.4. Architecture of EA-RS in a Sensor Node

## 4. Experimental Results and Discussion

#### 4.1. Experimental Environment

#### 4.2. Blackout Time Analysis

#### 4.3. Received Data Analysis

#### 4.4. Performance in Various Error Environments

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Sudevalayam, S.; Kulkarni, P. Energy harvesting sensor nodes: Survey and implications. IEEE Commun. Surv. Tutor.
**2011**, 13, 443–461. [Google Scholar] [CrossRef] - Lee, S.; Park, W.; Kwon, G.I. Overlapped channels interference between IEEE 802.15.4 and IEEE 802.11 g/n. J. Korean Inst. Next Gener. Comput.
**2011**, 7, 9–16. [Google Scholar] - LAN/MAN Standards Committee. Part 15.4: Wireless medium access control (MAC) and physical layer (PHY) specifications for low-rate wireless personal area networks (LR-WPANs). IEEE Comput. Soc.
**2003**. [Google Scholar] - Akyildiz, I.F.; Su, W.; Sankarasubramaniam, Y.; Cayirci, E. Wireless sensor networks: A survey. Comput. Netw.
**2002**, 38, 393–422. [Google Scholar] [CrossRef] - Reed, I.S.; Solomon, G. Polynomial codes over certain finite fields. J. Soc. Ind. Appl. Math.
**1960**, 8, 300–304. [Google Scholar] [CrossRef] - Kansal, A.; Potter, D.; Srivastava, M.B. Performance Aware Tasking for Environmentally Powered Sensor Networks. SIGMETRICS Perform. Eval. Rev.
**2004**, 32, 223–234. [Google Scholar] [CrossRef] - Melodia, T.; Pompili, D.; Akyildiz, I.F. Optimal Local Topology Knowledge for Energy Efficient Geographical Routing in Sensor Networks. In Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), Hong Kong, China, 7–11 March 2004; pp. 1705–1716. [Google Scholar]
- Kansal, A.; Hsu, J.; Zahedi, S.; Srivastava, M.B. Power Management in Energy Harvesting Sensor Networks. Trans. Embed. Comput. Syst.
**2007**, 6, 32. [Google Scholar] [CrossRef] - Piorno, J.R.; Bergonzini, C.; Atienza, D.; Rosing, T.S. Prediction and Management in Energy Harvested Wireless Sensor Nodes. In Proceedings of the IEEE International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Technology, Aalborg, Denmark, 17–20 May 2009; pp. 6–10. [Google Scholar]
- Cammarano, A.; Petrioli, C.; Spenza, D. Pro-Energy: A Novel Energy Prediction Model for Solar and Wind Energy-Harvesting Wireless Sensor Networks. In Proceedings of the IEEE International Conference on Mobile Adhoc and Sensor Systems, Las Vegas, NV, USA, 8–11 October 2012; pp. 75–83. [Google Scholar]
- Noh, D.K.; Abdelzaher, F.T. Efficient flow-control algorithm cooperating with energy allocation scheme for solar-powered WSNs. Wirel. Commun. Mob. Comput.
**2012**, 12, 379–392. [Google Scholar] [CrossRef] - Zhang, Y.; He, S.; Chen, J. Data Gathering Optimization by Dynamic Sensing and Routing in Rechargeable Sensor Networks. Trans. Netw.
**2016**, 24, 1632–1646. [Google Scholar] [CrossRef] - Yoon, I.; Kim, H.; Noh, D.K. Adaptive Data Aggregation and Compression to Improve Energy Utilization in Solar-Powered Wireless Sensor Networks. Sensors
**2017**, 17, 1226. [Google Scholar] [CrossRef] [PubMed] - Shim, Y.; Park, T.; Kwon, G.I. Reliable and efficient data transmission in congested wireless sensor networks. J. Korean Inst. Next Gener. Comput.
**2012**, 8, 15–23. [Google Scholar] - Ahn, J.S.; Yoon, J.H.; Lee, K.W. Performance and energy consumption analysis of 802.11 with FEC codes over wireless sensor networks. J. Commun. Netw.
**2007**, 9, 265–273. [Google Scholar] [CrossRef] - Jung, K.K.; Choi, W.S. Performance Analysis of RS codes for Low Power Wireless Sensor Networks. J. Korea Soc. Comput. Inf.
**2010**, 15, 83–90. [Google Scholar] [CrossRef] [Green Version] - Wicker, S.B.; Bhargava, V.K. Reed-Solomon Codes and Their Applications; John Wiley & Sons: Hoboken, NJ, USA, 1999. [Google Scholar]
- Noh, D.K.; Wang, L.; Yang, Y.; Le, H.K.; Abdelzaher, T. Minimum variance energy allocation for a solar-powered sensor system. In Proceedings of the International Conference on Distributed Computing in Sensor Systems, Marina del Rey, CA, USA, 8–10 June 2009; pp. 44–57. [Google Scholar]
- Jung, J.; Kang, M.; Yoon, I.; Noh, D.K. Adaptive Forward Error Correction Scheme to Improve Data Reliability in Solar-Powered Wireless Sensor Networks. In Proceedings of the IEEE International Conference on Information Science and Security (ICISS), Jaipur, India, 16–20 December 2016; pp. 1–4. [Google Scholar]
- Yi, J.M.; Kang, M.J.; Noh, D.K. SolarCastalia: Solar energy harvesting wireless sensor network simulator. Int. J. Distrib. Sens. Netw.
**2015**. [Google Scholar] [CrossRef] - Kang, M.J.; Jeong, S.; Noh, D.K. Energy-aware transmission power control for solar energy harvesting wireless sensor system and its effects on network-wide performance. J. KIISE
**2015**, 42, 1495–1502. [Google Scholar] [CrossRef]

**Figure 1.**Total amount of data in the network required for the sink node to gather 80 KB of data. ARQ, automatic repeat request; FEC, forward error correction.

**Table 1.**Types and characteristics of harvesting sources (Data from [1]).

Energy Source | Characteristics | Amount of Energy Available | Harvesting Technology | Conversing Efficiency | Amount of Energy Harvested |
---|---|---|---|---|---|

Solar | Ambient, Uncontrollable, Predictable | 100 mW/cm^{2} | Solar Cells | 15% | 15 mW/cm^{2} |

Wind | Ambient, Uncontrollable, Predictable | - | Anemometer | - | 1200 mWh/day |

Finger motion | Active Human power, Fully controllable | 19 mW | Piezoelectric | 11% | 2.1 mW |

Vibrations in indoor environments | Ambient, Uncontrollable, Predictable | - | Electromagnetic Induction | - | 0.2 mW/cm^{2} |

**Table 2.**Energy consumption of RS encoding and decoding (Data from [15]).

RS Code | Encoding Energy (mJ) | Decoding Energy (mJ) |
---|---|---|

(15, 13) | 0.1844 | 0.2352 |

(31, 27) | 0.3499 | 0.4281 |

(63, 55) | 0.5631 | 0.6872 |

(127, 115) | 0.8798 | 1.0354 |

Parameter | Description |
---|---|

Time unit | round (1 round = 1 min) |

Experimental time | 43,200 round (30 days) |

RF module | CC2420 |

Number of nodes | 100, 150, 200, 250, 300 |

Size of field | 3600∼6100 m${}^{2}$ |

Transmission range | 10 m |

Channel status (BER) | 0.05, 0.10, 0.15, 0.20, 0.25, 0.30 |

Sensing rate | 256 bits/round/node |

Weather | Random |

$\theta $ in moving average | 0.5 |

Update period of moving average | 1 h |

Avg. harvesting energy per day | 33.5 J |

Energy consumption rate for transferring data | 52.2 mJ/s |

Energy consumption rate for receiving data | 59.1 mJ/s |

RS(36, 32) encoding energy | 0.860 mJ/s |

RS(36, 32) decoding energy | 1.477 mJ/s |

RS(68, 32) encoding energy | 6.612 mJ/s |

RS(68, 32) decoding energy | 22.515 mJ/s |

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**MDPI and ACS Style**

Kang, M.; Noh, D.K.; Yoon, I.
Energy-Aware Control of Error Correction Rate for Solar-Powered Wireless Sensor Networks. *Sensors* **2018**, *18*, 2599.
https://doi.org/10.3390/s18082599

**AMA Style**

Kang M, Noh DK, Yoon I.
Energy-Aware Control of Error Correction Rate for Solar-Powered Wireless Sensor Networks. *Sensors*. 2018; 18(8):2599.
https://doi.org/10.3390/s18082599

**Chicago/Turabian Style**

Kang, Minjae, Dong Kun Noh, and Ikjune Yoon.
2018. "Energy-Aware Control of Error Correction Rate for Solar-Powered Wireless Sensor Networks" *Sensors* 18, no. 8: 2599.
https://doi.org/10.3390/s18082599