# Systematic Random Deployment for Wireless Sensor Network in Agricultural Sampling-Interpolation Applications

Hui Liu, Zhijun Meng, Hua Wang, Min Xu

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Hui Liu, Zhijun Meng, Hua Wang, Min Xu. Systematic Random Deployment for Wireless Sensor Network in Agricultural Sampling-Interpolation Applications. 6th Computer and Computing Technologies in Agriculture (CCTA), Oct 2012, Zhangjiajie, China. pp.53-59, 10.1007/978-3-642-36137-1_7.hal-01348214

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Systematic Random Deployment for Wireless Sensor
Network in Agricultural Sampling-Interpolation
Applications

Hui Liu<fnref n="1" />,², Zhijun Meng<fnref n="1" />, Hua Wang² and Min Xu²

¹National Engineering Research Center for Information Technology in Agriculture, Beijing Nongke Mansion Room A-516,No 11, ShuGuangHuaYuan Middle Road, Banjing, Haidian District, Beijing, 100097, P.R. China
{Hui Liu, Zhijun Meng, mengzj@nercita.org.cn}

²Information Engineering College, Capital Normal University, No.56 North Road of Western 3rd-Ring P.O.Box 801, Beijing, 100048, P.R. China
{Hui Liu, Hua Wang, Min Xu}

**Abstract.** Wireless sensor network can act as a distributed sampling system in precision farming applications which aim at estimating the spatiotemporal variability. Sensor nodes should be deployed referring to the communication range $r_c$ and the sampling range $r_s$ instead of the sensing range. In this paper, a kind of systematic random deployment based on three popular regular patterns-equilateral triangle, square and hexagon is explored to achieve both coverage and connectivity. The efficiency of different regular patterns of systematic random deployment is also compared, thus enabling to make a better deployment decision for different values of $r_c/r_s$.

**Keywords:** Precision farming, Wireless sensor network, Sensor nodes deployment

# 1 Introduction

Precision farming demands soil, microclimate, crop and other field data for spatial and temporal variability analysis [1]. But limited samples could not explain exactly the variability and support farming decision. The application of Wireless Sensor Network (WSN) technology could provide the optimal and integrated solution for real-time data acquisition, reliable transport, aggregation, in-network processing and statistics [2]. The potential benefits of using the WSN technology resulted in the appearance of a large number of academic and industrial R&D projects in agriculture. Lofar Agro project resulted in an experimental WSN installation in a potato field. The purpose of the WSN is to measure the microclimate factors essential to resist the phytophthora disease [3]. Camalie vineyard currently had an advanced soil moisture monitoring system named Camalie Net. It used twenty Mica2dot motes of Crossbow Inc. to

<footnote n="1">¹ Corresponding Author: Zhijun Meng</footnote>
establish the network. These motes sent data of temperature, soil moisture and soil
temperature to a central computer once every 10 minutes [4]. It is obvious that wireless
sensor networks could act as a distributed sampling system in precision farming
applications, which aim at estimating the spatiotemporal variability.

Sensor nodes deployment is one of the primary issues for any WSN application.
Most researches on deployment concentrate on event detection applications, which
aim to detect when and where particular event takes place such as the start of a fire.
The communication range and the sensing range are introduced to design the
deployment in such applications. However, WSNs in precision farming are mostly
kind of continuous sampling-interpolation applications different from event detection.
The goal of the network is to carry out continuous spatiotemporal sampling and build
field data distribution map by interpolating the values of the field where no sensor
reading exist. The sensing range is largely meaningless in this case unlike in the event
detection class of sensor networks. In this paper, the sampling range is proposed for
WSN deployment instead of the sensing range. A kind of systematic random
deployment based on regular patterns to achieve both coverage and connectivity is
discussed.

## 2 Systematic Random Deployment

Wireless sensor nodes could be generally placed in three methods including random
deployment, regular deployment and customized deployment [5]. Taking the
agricultural scenario, sensors could be mostly possible installed during terrain
preparation. It is a good choice for sensor node deployment referring to traditional
sampling methods.

The most commonly used sampling design for spatial data is systematic sampling
in agricultural experiments because it is easy to implement. A Square grid, an
equilateral triangle grid or a regular hexagonal grid is commonly chosen in systematic
sampling. Liu et al. show how to deploy sensor nodes in regular patterns in farmland
environmental monitoring applications[6] But Systematic sampling does have a few
disadvantages for spatial correlation analysis. There is a danger that the systematic
grid might coincide with a systematic feature of the landscape, especially in man
made landscapes. Systematic random sampling is another type of sampling spreading
the data in space in a similar fashion as systematic sampling. One sampling unit is
selected at random in each grid cell. It is more efficient for spatially correlated data
than systematic sampling and simple random sampling.

Consequently we present systematic random deployment approach for wireless
sensor network in agricultural sampling-interpolation applications. However, it is
different from pure sampling that the network connectivity has to be maintained in the
sensor nodes deployment at the same time.

Firstly, some definitions and the model description in this paper are as follows.

**Definition 1:** Let {$x_0, \cdots, x_{n-1}$} be the locations of *n* sensor nodes spread over a 2-D monitoring area.

**Definition 2:** Let there be *m* environmental variables to be sampled by each sensor node in the monitoring network.
**Definition 3:** Each environmental variable has the spatial correlation. It has a sampling range $r_s^i$, which could be determined according to historical data, experience results or some literature. $r_s$ is defined as the sampling range for the whole network. Then

$$r_s = \min(r_s^i) \quad i = 1, \dots, m \qquad (1)$$

**Definition 4:** Each active node has a communication range of $r_c$, and two active nodes can communicate reliably at a distance of $r_c$ or less. In addition, all nodes have the same communication ranges.

Systematic random deployment is designed based on three popular regular patterns including an equilateral triangle pattern, a square pattern and a regular hexagonal pattern (shown in Fig.1). We need to address the following two questions. (1) How to determine the optimal grid size for these systematic random deployment patterns? (2) Which is the best pattern on the efficiency among these systematic random deployment patterns? We explained the first question in Section 3 and the second in Section 4.

<figure><img src="image_2.png" /><figcaption>Fig. 1 Systematic random deployment</figcaption></figure>

## 3 Optimal Grid Size of Different Deployment Patterns

Let $l^T$, $l^S$, $l^H$ denote the grid side length of regular deployment patterns-triangular, square and hexagon. In terms of sampling requirements, the feasible grid size could be determined by the criterion of system sampling patterns-equilateral triangle, square and hexagon. Then,

$$l^T \le \sqrt{3}r_s \qquad (2)$$

$$l^S \le r_s \qquad (3)$$

$$l^H \le \frac{\sqrt{3}}{3}r_s \qquad (4)$$
To achieve connectivity, the communication range $r_c$ must be also considered. In Fig.1a, $x_0$ is the sensor node with three neighboring nodes $x_1, x_2, x_3$. Let $x_0$ locate in $\triangle ABC$. Considering connectivity requirement, at least one of the respective distances from $x_0$ to $x_1, x_2, x_3$ is less than $r_c$. Hence, we must have

$$ egin{cases} \frac{\sqrt{3}}{3} r_c < l^T \le \frac{\sqrt{3}}{2} r_c & \text{at least 1 - connectivity} \\ l^T \le \frac{\sqrt{3}}{3} r_c & \text{at least 3 - connectivity} \end{cases} \qquad (5) $$

Let $l_{max}^T$ denote the maximum grid side length of the equilateral triangle pattern. Using (2) and (5), then

$$ l_{max}^T = \begin{cases} \sqrt{3} \min \left( r_s, \frac{1}{2} r_c \right) & \text{at least 1 - connectivity} \\ \sqrt{3} \min \left( r_s, \frac{1}{3} r_c \right) & \text{at least 3 - connectivity} \end{cases} \qquad (6) $$

Similar calculation could be used for the other two patterns. Let $l_{max}^S$, $l_{max}^H$ denote the maximum grid side length of the square and hexagon pattern respectively. Hence, we obtain

$$ l_{max}^S = \begin{cases} \min \left( r_s, \frac{\sqrt{10}}{5} r_c \right) & \text{at least 1 - connectivity} \\ \min \left( r_s, \frac{\sqrt{5}}{5} r_c \right) & \text{at least 4 - connectivity} \end{cases} \qquad (7) $$

$$ l_{max}^H = \begin{cases} \min \left( \frac{\sqrt{3}}{3} r_s, \frac{\sqrt{7}}{7} r_c \right) & \text{at least 1 - connectivity} \\ \frac{1}{3} \min \left( \sqrt{3} r_s, r_c \right) & \text{at least 3 - connectivity} \\ \min \left( \frac{\sqrt{3}}{3} r_s, \frac{\sqrt{13}}{13} r_c \right) & \text{at least 6 - connectivity} \end{cases} \qquad (8) $$

## 4 Efficiency Comparison of Different Deployment Patterns

Which is the best pattern on the efficiency among these systematic random deployment patterns? For the same field, the number of sensor nodes could be calculated using the area of grid cell. The bigger the grid cell area, the fewer required
nodes. $A_{max}^T$, $A_{max}^S$, $A_{max}^H$ are denoted the maximum area of grid cell in equilateral triangle, square and hexagonal patterns respectively. Then

$$A_{max}^T = \frac{\sqrt{3}}{4} (l_{max}^T)^2 \qquad (9)$$

$$A_{max}^S = (l_{max}^S)^2 \qquad (10)$$

$$A_{max}^H = \frac{3\sqrt{3}}{2} (l_{max}^H)^2 \qquad (11)$$

Using (6) and (9), then

$$A_{max}^T = \begin{cases} \frac{3\sqrt{3}}{16} (r_s)^2 \left[ \min(2, \frac{r_c}{r_s}) \right]^2 & \text{at least 1 - connectivity} \\ \frac{\sqrt{3}}{12} (r_s)^2 \left[ \min(3, \frac{r_c}{r_s}) \right]^2 & \text{at least 3 - connectivity} \end{cases} \qquad (12)$$

Similar calculation could be used for the other two patterns. Then, we obtain

$$A_{max}^S = \begin{cases} \frac{2}{5} (r_s)^2 \left[ \min(\frac{\sqrt{10}}{2}, \frac{r_c}{r_s}) \right]^2 & \text{at least 1 - connectivity} \\ \frac{1}{5} (r_s)^2 \left[ \min(\sqrt{5}, \frac{r_c}{r_s}) \right]^2 & \text{at least 4 - connectivity} \end{cases} \qquad (13)$$

$$A_{max}^H = \begin{cases} \frac{3\sqrt{3}}{14} (r_s)^2 \left[ \min(\frac{\sqrt{21}}{3}, \frac{r_c}{r_s}) \right]^2 & \text{at least 1 - connectivity} \\ \frac{\sqrt{3}}{6} (r_s)^2 \left[ \min(\sqrt{3}, \frac{r_c}{r_s}) \right]^2 & \text{at least 3 - connectivity} \\ \frac{3\sqrt{3}}{26} (r_s)^2 \left[ \min(\frac{\sqrt{39}}{3}, \frac{r_c}{r_s}) \right]^2 & \text{at least 6 - connectivity} \end{cases} \qquad (14)$$

Comparing (12), (13) and (14), the maximum area $A_{max}$ of the corresponding patterns is computed for all values of $r_c/r_s$. Fig.2 shows the results from which we make the following observations.
<figure><img src="image_3.png" /><figcaption>Fig. 2 Efficiency Comparison of different deployment patterns</figcaption></figure>

1. When $r_c/r_s \le 1.755$, the square based pattern to achieve both coverage and 1-connectivity is optimal because it has the maximum grid area to ensure the best efficiency. While requiring more connectivity, the hexagon pattern which provides coverage and 3-connectivity should be chosen for this range of $r_c/r_s$.

2. When $1.755 \le r_c/r_s \le 2.081$, the triangle based pattern to achieve both coverage and 1-connectivity is optimal because it has the maximum grid area to ensure the best efficiency. If requiring more connectivity, the hexagon pattern which provides coverage and 3-connectivity should be chosen for this range of $r_c/r_s$.

3. When $2.081 \le r_c/r_s \le 2.632$, the triangle based pattern to achieve both coverage and 1-connectivity is optimal because it has the maximum grid area to ensure the best efficiency. If requiring more connectivity, the square pattern which provides coverage and 4-connectivity should be chosen for this range of $r_c/r_s$.

4. For $r_c/r_s \ge 3$, the triangle based pattern to achieve both coverage and 3-connectivity is optimal because it has the maximum grid area to ensure the best efficiency.

# 5 Conclusion

In this paper we discussed the problem on the sensor nodes deployment in agricultural sampling-interpolation applications. We proposed systematic random deployment approach to achieve coverage and k-connectivity based on three popular regular
patterns-equilateral triangle, square and hexagon. We also compared the efficiency of different regular patterns of systematic random deployment, which enabling to make a better deployment decision for different values of $r_c/r_s$.

## Acknowledgement

This project is supported by National Nature Science Foundation (31101078), Beijing Natural Science Foundation (Connectivity and coverage for wireless sensor network in agricultural applications, 4112013) and Scientific Research Common Program of Beijing Municipal Commission of Education (KM201110028018).

## References

1. Niaqian Zhang, Maohua Wang, Ning Wang. 2002. Precision Agriculture-a worldwide overview. Computer and Electronics in Agriculture. 36(2002): 113-132

2. Ning Wang, Niaqian Zhang, Maohao Wang. 2006. Wireless sensors in agriculture and food industry-Resent development and future perspective. Computer and Electronics in Agriculture. 50(2006). pp.1-14.

3. A. Baggio, "Wireless sensor networks in precision agriculture", In Proc. Workshop on Real-World Wireless Sensor Networks (REALWSN'05), Stockholm, Sweden, Jun. 2005

4. Camalie Net: Wireless sensor network at Camalie Vineyard. http://www.camalie.com: Camalie Vineyards. 2006

5. Tilak S, Abu-Ghazaleh N, Heinzelman W. 2002. Infrastructure tradeoffs for sensor networks. In: Proc. of 1st Int'l Workshop on Wireless Sensor Networks and Applications (WSNA 2002). 49-57.

6. Hui Liu, Zhijun Meng, Yuanyuan Shang. Sensor Nodes Placement for Farmland Envionment Monitoring Applications. The 5th Interational Conference Wireless Communications, Networking and Mobile Computing. September 24-26, 2009. Beijing, China.