Deployment method of multi-chain wireless sensor network nodes

Abstract

In order to overcome the energy “hole” problem caused by uneven energy consumption of nodes in equidistant deployment, an unequal spacing optimization deployment method is adopted to deploy a chain type wireless sensor network to balance node energy consumption and extend the network life-cycle. Furthermore, a star-chain structure multi-chain wireless sensor network node optimization deployment method is adopted to deploy a two-dimensional monitoring network; Taking into account inter chain interference, network connectivity, and node energy consumption, the optimal node spacing and hop count for each chain, as well as the optimal number of chains in circular areas, are obtained. Through MATLAB simulation, it is proven that this deployment method can effectively reduce and balance node energy consumption, and maximize the network’s life-cycle.

Keywords

multi chain WSN node deployment optimal spacing optimal number of chains

Introduction

Wireless sensor network can be flexibly deployed to specific areas to monitor and collect some environmental data, has been widely used in many fields, some scholars have conducted applied research in environmental monitoring,^1–3 bridge monitoring,^4–6 underwater monitoring,^7,8 smart grid monitoring,^9,10 smart agriculture,^11,12 and other aspects. How to improve the performance of the network and meet the actual engineering application needs is the focus of researchers.

As a basic problem of wireless sensor network, node deployment is an important research direction to improve the network coverage, reduce and balance the node energy consumption, extend the network life cycle, and improve the network performance, which is particularly important for engineering applications. Many scholars have conducted research on the deployment of nodes in underwater WSN,^13,14 intelligent agricultural WSN,^15,16 and smart grid WSN.¹⁷ These results mainly through the research node deployment algorithm, to achieve the purpose of improving network coverage, further network performance.

At present, from the perspective of extending the network life cycle to study the wireless sensor network node deployment is not much, most of the work assumes that the sensor node is uniform deployment, this will bring energy “empty” problem, because the closer to the sink node, to forward the more data, because of the energy depletion and the earlier “death,” thus greatly reducing the life cycle of the network.

By studying the energy consumption of wireless sensor network nodes, the sensor nodes on each chain to synchronize and balance the energy consumption and extend the linear network structure to two-dimensional network plane for multi-chain wireless sensor network nodes, analyze the energy consumption and connectivity to obtain the optimal spacing of deployed nodes, the optimal number of jumps of each chain and the optimal number of chains deployed in the plane area, so as to realize the balanced energy consumption of nodes and further extend the network life cycle.

Optimization deployment model of multi-chain wireless sensor network

Multi-chain network has the characteristics of multi-jump routing and unbalanced energy consumption, so the following network model is adopted:

(1) Nodes are deployed in a flat circular area. The sink node is located in the center of the monitoring area, with no energy limit and a fixed location, and its communication signal covers the whole network.

(2) The sensor node has a unique ID, fixed position and the same initial energy, and the optimal deployment along the line with unequal spacing; Data can be routed through multiple hops along the local or neighboring chains, and the transmission power is adjustable.

(3) The sink node and sensor node form a multi-chain structure, and the number of sensor nodes on each chain is equal, and the distance between the sink node and the sensor nodes on the same layer of each chain is equal; On each chain, the closer to the sink node, the smaller the spacing between adjacent sensor nodes; the sensor node periodically collect data, and transmit the data to the sink node through multi-hop, and transmit the data between the chain. The data is transmitted between chains by time-division multiplexing.

For monitoring areas such as greenhouse agriculture, the sensor nodes are usually deployed by optimal deployment of multi-chain unequal spacing, which combines star structure and linear structure and has a distinct hierarchical structure. The topology of the deployment method is shown in Figure 1:

Figure 1.

Optimize the deployment of the topology with unequal spacing.

Let the radius of the two-dimensional circular monitoring area is r, and the whole network has l chains, and n sensor nodes are deployed with unequal spacing in each chain. The deployment diagram of the monitoring area nodes of one chain is shown in Figure 2:

Figure 2.

Schematic diagram of single-chain deployment.

Among, d_i represents the spacing between node i+1 and node i, t_i represents the coverage radius at node i when the power is at a minimum, that is P_min, d_i = t_i+t_i+1.

The optimal spacing of nodes in the topology of multiple chains

In wireless sensor networks, the energy consumption of sensor nodes mainly includes the energy consumption for data reception, transmission, and the startup energy consumption when transitioning from sleep state to reception/transmission state. The transmission energy consumption is mainly composed of the energy consumption of the signal transmitting circuit and the energy consumption of the amplifier circuit. Therefore, the energy consumption for transmitting k bits of data is as shown in equations (3-1).

E_{T X} (k, d) = {\begin{cases} (E_{t x} + ξ_{a m p 1} \cdot d^{β}) \cdot k, d < d_{0} \\ (E_{t x} + ξ_{a m p 2} \cdot d^{β}) \cdot k, d \geq d_{0} \end{cases}

(3-1)

Among them, d is the distance between the transmitting node and the receiving node. E_tx is the energy consumption required to receive 1 bit. β is the path loss constant. When d > d₀, the multi-path attenuation model is adopted, and at this time β = 4. When d < d₀, the free space model is adopted, and at this time β = 2. ε_amp1 = 10 × 10⁻¹² J/bit, ε_amp2 = 0.001×10⁻¹² J/bit.

For the receiving node, the total energy consumption of the received Kbit packet is:

E_{R X} (k, d) = E_{r x} \cdot d

(3-2)

For any node i, the energy consumption of the sending kbit packet is:

E_{net (i)} = E_{T X} (i) + E_{R X} (i)

(3-3)

According to the energy consumption model, the energy needed for the node to send and receive the data can be calculated.

Assuming that there are a total of n jump nodes on each chain, then node i needs (n-i+1)data sending and (n-i) data receiving during the data uploading process, so the energy consumption of node i can be expressed as:

E_{net (i)} = {\begin{cases} (E_{t x} + ξ_{a m p 1} \cdot {d_{i}}^{β}) \cdot k \cdot (n - i + 1) + E_{r x} \cdot k \cdot (n - i), d < d_{0} \\ (E_{t x} + ξ_{a m p 2} \cdot {d_{i}}^{β}) \cdot k \cdot (n - i + 1) + E_{r x} \cdot k \cdot (n - i), d \geq d_{0} \end{cases}

(3-4)

To facilitate the discussion, the formula is expressed as:

E_{net (i)} = (E_{t x} + ξ_{a m p} \cdot {d_{i}}^{β}) \cdot k \cdot (n - i + 1) + E_{r x} \cdot k \cdot (n - i)

(3-5)

To ensure that each layer of sensor nodes centered around the sink node consumes energy evenly, there must be:

E_{net (i)} = E_{net (i + 1)}

(3-6)

Assuming that the initial energy of each node is Einit, the life cycle of the entire network can be expressed as:

T = \frac{E_{i n i t}}{E_{i}} (1 \leq i \leq n)

(3-7)

Substitute (3-5) into (3-6), and set Etx = Erx = E , then:

2 E + ξ_{a m p} \cdot {d_{i}}^{β} = (2 E + ξ_{a m p} \cdot {d_{i}}^{β}) \cdot (n - i - 1) + ξ_{a m p} \cdot {d_{i}}^{β}

(3-8)

Each chain has a total of n nodes, each node covers 2ti under Pmin, so the whole chain should meet:

\sum_{i = 1}^{n} 2 \cdot t_{i} = r

(3-9)

\sum_{i = 1}^{n} d_{i} = r

(3-10)

The relationship between the distance di between two adjacent nodes i and i+1 and ti is:

d_{i} = t_{i} + t_{i + 1} (1 \leq i \leq n - 1)

(3-11)

Using $\max T$ as the objective function, (3-8)–(3-11) as constraints, we can obtain the value of the optimal node spacing di and the value of the number of nodes n.

In conclusion, the network life cycle model is obtained as follows:

\begin{array}{l} \max T \\ s . t E_{net (i)} = E_{net (i + 1)} \\ \sum_{i = 1}^{n} 2 \cdot t_{i} = r \\ \sum_{i = 1}^{n} d_{i} = r \\ d_{i} = t_{i} + t_{i + 1} (1 \leq i \leq n - 1) \end{array}

Using the data in Table 1, the node spacing is obtained through MATLAB simulation.

Table 1.

Simulation-related parameters.

The parameter name	Parameter values
Energy consumption of the transmission unit bit	50×10⁻⁹ J/bit
Amplification circuit coefficient ε_amp1	10×10⁻¹² J/bit
Amplification circuit coefficient ε_amp2	0.001×10⁻¹² J/bit
Node initial energy	50 J
Maximum node transmission distance	200 m
Database length k	72 bits

When the radius of the monitoring area is 500 m, 1000 m, 1500 m, 2000 m, and 2500 m, respectively, the relationship between the number of nodes in each chain and the network life cycle is shown in Figure 3.

Figure 3.

The network life cycle under the radii of different regions.

It can be seen from Figure 3 that the optimal monitoring radii are 500 m, 1000 m, 1500 m, 2000 m, and 2500 m, respectively. The number of nodes is 7, 13, 18, 24, 30, when the optimal number of nodes, the life of the network tends to stabilize.

The optimal spacing of the sensor nodes at 500 m, 1000 m, 1500 m, 2000 m, and 2500 m is shown in Figure 4.

Figure 4.

Optimal spacing of the sensor nodes under the radii.

Figure 4 shows that in the spacing between each node under the optimal number of nodes, when the monitoring radius is 1000 m, the optimal distance between nodes is shown in Table 2.

Table 2.

Optimal spacing of nodes when the radius of the monitoring area is 1000 m.

Node number	Node spacing/m
1	24.4183
2	35.9423
3	44.2215
4	49.7045
5	54.8792
6	58.5531
7	68.3476
8	75.2519
9	89.6777
10	100.9306
11	114.0545
12	129.3110
13	154.7330

The optimal number of chains in the topological structure of unequal spacing

When multiple chains are deployed in a circular region, interference occurs between chains in data transmission, and reasonable power control is used to avoid the interference between chains.

Generally, the formula of the receiving terminal power during data communication is:

P_{r} = \frac{G_{t} G_{r} P_{t} λ^{2}}{{(4 π)}^{2} d^{2} β}

(4-1)

where β is the loss coefficient, d is the distance between the transmitting node and the receiving node, Gt is the transmitting antenna gain, Gr is the receiving antenna gain, and Pt is the transmitting power of the antenna.

Assuming that Plimit is the threshold of the receiving node and Pmin is the minimum transmission power of the transmitting node, then:

P_{\min} = \frac{{(4 π)}^{2} d^{2} P_{\lim i t} β}{G_{t} G_{r} λ^{2}}

(4-2)

The powers available from (4-1) and (4-2) are as follows:

P_{\min} = \frac{P_{\lim i t} P_{t}}{P_{r}}

(4-3)

According to this formula, we can get the optimal transmission power between any two jumps. In order to avoid interference between chains, the distance of the sensor nodes and the sensor nodes in the adjacent chain should be less than the distance between the adjacent sensor nodes on the same chain, and the corresponding optimal power value should be set by the node spacing.

Suppose in the coverage situation shown in Figure 5, the initial power of each sensor node is all the minimum power Pmin. The distance of dAD is the optimal distance when the power of A is Pmin. The distance of dDG is the optimal distance when the power of node D is Pmin. In order to avoid interference to node C when node A on chain lAD sends data to node D, node D must ensure that dDG<dAD<dED. This can ensure that neighboring chain nodes are not interfered when the previous-hop node receives the data frame.

Figure 5.

Sensor node coverage.

Obtained from Figure 5:

\sin θ = \frac{d_{E D}}{2 (r - d_{A D})}

(4-4)

Then,

θ = \arcsin \frac{d_{ED}}{2 (r - d_{AD})} > \arcsin \frac{d_{A D}}{2 (r - d_{A D})}

(4-5)

Then the number of chains in the entire monitored region:

l < \frac{180 °}{\arcsin \frac{d_{A D}}{2 (r - d_{A D})}}

(4-6)

At the same time, the power must be guaranteed within a reasonable range, so: $P_{\min} \leq P (R_{t}) \leq P_{\max}$ (4-7)

Assuming semi-circular radius r = 500 m and perceptual radius Rs = 15 m , MATLAB simulation, the connectivity probability of node communication radius 32 m and 26 m when the number of chains increases from 3 to 20 is shown in Tables 3 and 4.

Table 3.

Connectivity probabilities with a communication radius of 32 m.

Chain number	Connectivity probability	Square deviation
3	0.054	0.003
4	0.160	0.005
5	0.311	0.006
6	0.556	0.009
7	0.727	0.012
8	0.831	0.011
9	0.895	0.007
10	0.934	0.011
11	0.958	0.014
12	0.973	0.008
13	0.983	0.009
14	0.989	0.012
15	0.993	0.016
16	0.995	0.005
17	0.997	0.005
18	0.998	0.008
19	0.999	0.007
20	0.999	0.008

Table 4.

Connectivity probabilities with a communication radius of 26 m.

Chain number	Connectivity probability	Square deviation
3	0.002	0.001
4	0.010	0.002
5	0.046	0.004
6	0.105	0.008
7	0.219	0.010
8	0.369	0.009
9	0.519	0.009
10	0.671	0.010
11	0.769	0.010
12	0.838	0.003
13	0.880	0.005
14	0.921	0.007
15	0.945	0.006
16	0.960	0.005
16	0.974	0.007
18	0.981	0.013
19	0.986	0.003
20	0.990	0.004

The data in the table shows that the simulation results are relatively stable without much deviation. Through the above experimental data, the relationship between the number of semi-circular region chains and the connectivity probability can be obtained as shown in Figure 6.

Figure 6.

Plot of the number of chains and the connectivity probability.

In the Figure 6, when the communication radius is 32 m, the connectivity probability has stabilized when the number of chains is greater than 15. When the optimal number of chains in the semicircular monitoring area is 15, the connectivity probability of the whole network is close to 1, and the optimal number of chains in the whole circular monitoring area is 30; similarly, when the communication radius is 26 m, the optimal number of chains in the whole circular monitoring area is 38.

Network energy consumption of multi-chain WSN with optimal deployment

In the existing research, the deployment method of equal spacing nodes is usually used, and the optimal deployment method of unequal spacing and the deployment method of equal spacing nodes are compared with the network energy consumption.

For the chain structure shown in Figure 2, when d1 = d2 = ···· = dn = d, that is, when n nodes are deployed at equal intervals, the energy consumption of each data bit reaching the sink node through n hops is:

e_{b m} = {(n (e_{t e} + e_{t a} (r / n)}^{β}) + (n - 1) e_{r x}) (1 + \frac{α}{l}) + \frac{n E_{s t} + (n - 1) E_{s r}}{l + α}

(5-1)

Among them, α is the packet header length of the data packet, l is the data length of the data packet, and r is the distance from the data source to the node (sink).

Assuming that only node n has one data packet that needs to pass through a hop to reach the sink node, and the communication distance of each hop is equal to d, for n nodes, a total of n times are sent and n-1 times are received. Assuming the length of the data packet is k, the energy consumption of the entire system is:

E_{M H} = k (n (e_{t e} + e {}_{t a}d^{β}) + (n - 1) e_{r x}) + n E_{s t} + (n - 1) E_{s r} = n (k (e_{t e} + e_{t a} d^{β}) + E_{s t}) + (n - 1) (k e_{r x} + E_{s r})

(5-2)

To find the optimal single hop distance, let the single hop distance be dlhop, and the energy consumption of the entire system is:

E_{M H} = c e i l (\frac{r}{d_{l h o p}}) (k (e_{t e} + e_{t a} {d_{l h o p}}^{β}) + E_{s t}) + (c e i l (\frac{r}{d_{l h o p}}) - 1) (k e_{r x} + E_{s r})

(5-3)

Among them, ceil () is the rounding function. To find the optimal dlhop, take the derivative of the above equation with dlhop and let: $\frac{\partial E_{M H}}{\partial d_{l h o p}} = 0$ , the optimal spacing d_opt for equidistant deployment is obtained:

d_{o p t} = \sqrt[β]{\frac{k E_{t x} + E_{s t} + E_{s r} + k * E_{r x}}{(β - 1) k ξ_{a m p 1}}}

(5-4)

Among, E_st and E_sr represent the sending start energy and the receiving start energy, consider the case where d<d0, take β = 2. By substituting the simulation parameters in Table 2 into (5-4) to calculate: d_opt = 62.53 m.

According to formula (3-5), the energy consumption of node i under the equally spaced deployment is:

E_{n e t} (i) = (E_{t x} + ξ_{a m p} \cdot d_{β}^{o p t}) \cdot k \cdot (n - i + 1) + E_{r x} \cdot k \cdot (n - i)

(5-5)

Under the deployment of equal spacing, the closer the energy to the convergence node, the node closest to the sink node first “dies” and determines the life cycle of the entire network. Therefore, the life cycle of the entire network T should be the same as that of the sensor node closest to the sink node, so, T = E_init/E_net(1).

In the case of unequal spacing optimization deployment, the last residual energy of each node is basically the same. With MATLAB simulation, the life cycle of each hop node of the two methods is obtained as shown in Figure 7:

Figure 7.

The lifecycle of each hop node.

In Figure 7, the life cycle of the optimized spacing deployment is basically the same, and the life cycle of the network farther away from the sink node is greater than the optimized spacing deployment. However, in the process of data routing, with the increase of the data amount, the node network life cycle drops sharply.

Comparing the life cycle trends at the same monitoring radius, when r = 1000 m, the network lifetime of the two deployment methods is shown in Figure 8.

Figure 8.

Network lifetime at r = 1000.

In the Figure 8, the network life-cycle is maximum at n = 13 when using optimized spacing deployment, and is maximum at n = 16 when using equidistant deployment, and the life cycle of the optimized spacing deployment is always greater than that of the equally spaced deployment. Thus, the optimized spacing deployment can achieve better network performance.

The network life cycle of the two deployment methods at several different monitoring region radii is shown in Figure 9.

Figure 9.

Network life cycle under different monitoring area radii.

In Figure 9, the life cycle of optimized spacing deployment is always greater than that of equal spacing, and the whole network life increases by 35%–55%; When the radius of the monitoring area increases, the network life cycle tends to decline.

Due to the unequal spacing between adjacent hop nodes, the distance between sensor nodes further away from the sink node increases, resulting in a lower density of sensors. The number of sensor nodes is significantly less than the number of nodes deployed at equal intervals, which may lead to the inability to monitor certain local areas. For this purpose, heterogeneous nodes can be uniformly deployed in wireless sensor networks. The farther away the sensor nodes are from the sink node, the more initial energy they have. This can improve the density of nodes and effectively enhance the performance of the network while balancing the energy consumption of nodes.

Conclusion

Life cycle of wireless sensor network is an important performance, and the network life must meet the user needs before it can be put into application. The optimal deployment of nodes can effectively solve the problem of energy “hole,”, balance the energy consumption of each node, make all sensor nodes synchronously exhaust energy as much as possible, maximize the network life cycle, and greatly reduce the maintenance workload.

Based on the energy consumption model of the sensor nodes, and the energy calculated by the analysis for each node on each chain to receive and send the entire data, make the nodes consume energy evenly, get the optimal spacing for each jump; then according to the monitoring radius, calculate the optimal number of jumps for each chain; single chains deployed with optimal spacing are then deployed to a two-dimensional plane, according to the network data transmission mechanism, and considering the inter-chain interference, to obtain the optimal number of chains deployed in the circular region, to form the optimal deployment method of multi-chain wireless sensor network nodes. MATLAB Simulation has been proved that, this method can effectively improve the network performance and greatly extend the network life cycle.

Footnotes

ORCID iD

Cheng Xiaoling

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge Science and Technology Project of Jiangxi Provincial Department of Education (GJJ2402614).

Conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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