- Research
- Open Access
Cross-layer design for reducing delay and maximizing lifetime in industrial wireless sensor networks
- Jiawei Tan^{1},
- Anfeng Liu^{1}Email authorView ORCID ID profile,
- Ming Zhao^{2},
- Hailan Shen^{1} and
- Ming Ma^{3}
https://doi.org/10.1186/s13638-018-1057-x
© The Author(s). 2018
- Received: 27 December 2017
- Accepted: 9 February 2018
- Published: 1 March 2018
Abstract
Low delay and long lifetime are a very important issue for industrial wireless sensor networks (IWSNs) in which it require long-time monitoring of industrial sites and respond quickly to events that is monitored; therefore, high delay communications can cause serious damage to property and personnel at industrial field. Due to delay, lifetime, and other performance involved to multiple layers, it is difficult to optimize from a single layer. Therefore, a cross-layer design optimal scheme for reducing delay and maximizing lifetime (RDML) scheme is proposed for IWSNs which is from several layers such as transmitted power, duty cycle, and node deployment positions to optimize the network performance of delay and lifetime etc. Firstly, due to the node which sends a packet within a cycle, different duty cycle leads to different selection of the modulation level, resulting in different power consumption efficiency of transmitting data. Through careful analysis, the optimal value of the duty cycle is given which has the lowest energy consumption per bit. In fact, the energy consumption of the node is not balanced. Therefore, an optimization method of changing the duty cycle is proposed. In this paper, larger duty cycle is chosen for nodes with residual energy to improve the reliability of data transmission, reducing the probability of data retransmission, so that the network delay can be reduced in IWSNs. Third, based on the previous analysis, a network optimization deployment algorithm is proposed, which not only maximizes the energy efficiency of a single node but also maximizes the network lifetime and the total network energy efficiency. Both our comprehensive theoretical analysis results indicate that the performance of RDML scheme is better than the previous studies. Relative to equal distance and optimal duty cycle scheme, the RDML scheme can reduce the delay by 19–30% and increase the lifetime by more than 43%.
Keywords
- Industrial wireless sensor networks
- Duty cycle optimal
- Network performance optimization
- Transmitted power
- Low delay
- Lifetime
1 Introduction
Industrial wireless sensor networks (IWSNs) are important components of Internet of things (IoT) [1–9] which leverage the ubiquity of sensor-equipped devices to collect information at low cost and provide a new paradigm for solving the complex sensing applications from the significant demands of industrial applications such as [2, 4] surveillance systems [10–15], intelligent traffic management [16, 17], and automated vehicles in environmental transportation [18–20]. The wireless sensor networks have been developed for a long time [21–26]; with the development of wireless portable devices and sensor technology, the application of wireless sensor network in the industrial field becomes the focus of attention [2, 4]. Industrial wireless sensor networks (IWSNs) is emerging in this background; it does not require wiring to be deployed at any time and has simple requirements for complex industrial sites; the device is small and easy to deploy and has powerful functions that can be used to detect and monitor a variety of visible and invisible physical phenomena in close range and high precision; and the strong practicality makes it to have broad application prospects in various fields of industrial production [1, 2, 9, 10], especially with the rise of cloud computing [27] and fog computing [28–30], to make its development face greater opportunities.
Industrial wireless sensor networks also face similar problems with wireless sensor networks, and because of the different application situations, there are some differences between IWSNs and WSNs [2]. Firstly, high energy efficiency is urgently required for IWSNs [2]. In IWSNs, sensors are powered by battery; therefore, the energy is limited [31, 32]. But what is more troublesome is that the sensors are placed in a variety of industrial equipment or production workshop. These industrial equipment and workshops were not designed to provide space for these sensors; thus, these sensing nodes can only be required to adapt to the industrial production environment. Therefore, it is required to be smaller in size than other application to adapt to industrial production. But reducing the size of the sensors means that the battery size also decreases [31], and the battery size determines the energy stored in the battery; therefore, in IWSNs, it is very important to design a more efficient energy system [31–33]. The same as wireless sensor networks, the energy consumed by data communications is the most of the energy consumed by the entire system [34, 35]. Thus, the key to reduce energy consumption and increasing network lifetime is how to maintain efficient communications [36–40, 42]. In IWSNs, sensor nodes can send perceived data to a hub in a one-hop method and can also use multi-hop routing to the control center (CC) [36–39, 41, 42]. Therefore, how to reduce the energy consumption of routing is the key to improving lifetime [43–45].
IWSNs not only require high energy efficiency but also have special needs for network performance [46]. As IWSNs are mainly used in industrial production monitoring and control process, there are many industrial processes in high-temperature and high-pressure environment, and the control process requires extremely sensitive monitoring physical phenomena, and sending out control information requires that time interval is less than industrial milliseconds, that is, the perception of information to the control center and the feedback control information to the control equipment delay is very strict. Because of the large delay which may lead to serious disasters [8, 11, 18, 24, 36, 47], such as monitoring of industrial boiler temperature and industrial furnace metallurgy, if the control is not timely, may lead to explosion of the boiler, the product quality does not meet the requirements and results in waste. It affects production schedule, wastes production material, destroys industrial production equipment, and seriously causes death to people. Thus, in addition to energy efficiency [9, 22, 36, 37], in IWSNs, the performance metrics such as lifetime and delay are referred to as quality of services (QoS) requirements which is actually important for IWSNs [44, 46, 48].
- (1)
Firstly, the optimal duty cycle of the nodes is obtained from the theoretical analysis when the energy consumption of per bit data successfully received is smallest. Because the data transmitted by a node in a cycle is constant, so the duty cycle is larger and the required modulation level is lower; conversely, the smaller the duty cycle, the higher the modulation level required. And the duty cycle and modulation level is related to energy consumption. Therefore, in this paper, the optimized duty cycle is obtained theoretically which can make the lowest energy consumption per bit transmission.
- (2)
Secondly, a cross-layer design optimal scheme is proposed to optimize the delay of network and energy efficiency for IWSNs. RDML scheme first selects the optimized duty cycle for each node to maximize the energy efficiency of the data transmission. Then, according to nodes in the network at different locations, the energy consumption of nodes is unbalanced. Greater duty cycle for nodes with residual energy is needed to improve data transfer reliability and reduce delay. Because the node has residual energy, the duty cycle is not to minimize the energy consumption of the sending unit bit at this time. Therefore, increasing the node duty cycle, although more energy is consumed and no effect on network lifetime, can effectively reduce the number of data retransmissions, which can effectively reduce the delay.
- (3)
Thirdly, a strategy of network deployment is proposed. By unequal deployed nodes, the energy consumption of the network is optimized.
- (4)
Through our extensive simulation study, the delay and energy efficiency can be enhanced simultaneously using the proposed RDML scheme. RDML scheme selects the optimized parameters for multiple layers and takes full advantage of the residual energy to improve network performance. Comparing with the previous method, the energy utilization rate has reached more than 43%. The delay can be reduced by 19–30%. More importantly, the performance is enhanced without reducing the network lifetime, which is difficult to be achieved in the previous studies.
The rest of this paper is organized as follows: a simple description of the method is presented in Section 2. In Section 3, the related works are reviewed. The system model and problem statement are described in Section 4. In Section 5, the RDML scheme is presented to cross-layer optimization. The performance analysis of RDML scheme is provided in Section 6. We present our conclusions in Section 7.
2 Methods
In IWSNs, the energy consumption of sensor nodes is unbalanced, causing the low energy efficiency, and it requires lower delay. Therefore, a method of reducing delay and maximizing network lifetime is proposed. In a typical network, the nodes near sink forward more data packets, so these nodes will consume more energy and thus determine the network lifetime. Therefore, reducing the distance of these nodes to the sink node reduces the energy consumption of these nodes and improves the network lifetime. However, it is difficult to balance the energy consumption of each node through node deployment, so there will still be some nodes that have residual energy; therefore, by mathematically analyzing, adjusting the duty cycle of node can affect the energy consumption and also affect the delay. In the previous strategy, the duty cycle of nodes is of optimal value, so increasing the duty cycle of nodes can increase the energy consumption and will reduce the delay. So, increasing the duty cycle of nodes that have residual energy cannot reduce the network lifetime and can reduce the delay. The background and related work on this method can be found in Section 3.
3 Background and related work
4 The system model and problem statement
4.1 The energy consumption model
P_{Tx} is the power of data transmission. P_{circuit} is the circuit power for transmitter and receiver block without considering the amplifier. Because the T_{start} is very small, it only needs to compute the frequency synthesizer with the higher power in the circuit.
where η represents the drain efficiency of the amplifier and ξ is the peak to average ratio which is expressed as a function of constellation size M as \( \xi =3\left(\frac{\sqrt{M}-1}{\sqrt{M}+1}\right) \) for MQAM and MPSK modulation technique [53].
G_{ d } = G_{1}d^{ k }M_{1}, where d is the distance between two communicating nodes, the exponent order k is between 2 and 4, G_{1} is the gain factor, and M_{1} is the link margin.
- (1)
For M-ary QAM
- (2)
For M-ary PSK
where the number of bit per symbol \( b=\frac{L}{B\tau T} \) and the constellation size M = 2^{ b }.
Thus, the signal-to-noise ratio can be obtained from the duty cycle. Then, according to Eqs. (6) and (7), the relationship between the duty cycle and the transmitter power can be obtained. So through the duty cycle, get the total energy consumption E_{total}.
4.2 Realistic unreliable link model
The unreliable link models are approximated for AWGN channels. Therefore, the BER (bit error rate) under MQAM modulation technique or MPSK modulation technique can be obtained from Eq. (8) or (9).
4.3 Problem statement
- (1)
The first goal of this paper is to maximize the network lifetime. The network lifetime is defined as l and the energy consumption of sensor nodes as E_{ i }. It is clear to maximize the network lifetime is to minimize the energy consumption of the node with the largest energy consumption, which can be expressed as min{max(E_{ i })}. When the energy consumption of the nodes is balanced, the system performance is maximized. Therefore, the goal of this paper is to make the energy consumption of the nodes equal, which is E_{ i } = E_{ j } ∣∀i ≠ j, i, j ∈ N (N={1, 2, …m} consists of all nodes in the network). At the same time, the network lifetime is maximized by adjusting the node duty cycle τ, that is, choosing the optimized duty cycle maximizes the network lifetime.
- (2)
The equidistant deployment of the network, due to each node in network forwarding different amount of data, will result in each node having different energy consumption. However, the network lifetime only related to the largest energy consumption node. Therefore, a strategy is considered in which the duty cycle of nodes in a network is different, ∃τ_{ i } ≠ τ_{ j } ∣∀i ≠ j, i, j ∈ N. We define ϖ(τ_{ i }) as the delay of node i. Then, Eqs. (8) and (9) combined with Eqs. (10) and (11) can deduce the delay. So, our second goal is as much as possible to improve the duty cycle τ_{ i } of each node without affecting the network lifetime, thus reducing the network delay δ.
5 The design of the RDML scheme
5.1 The RDML scheme for linear network
Network parameters
Parameter | Value | Value |
---|---|---|
T | Transmission period | 100 ms |
T _{start} | The time of transient mode | 5 10^{−6}s |
η | The power of amplifier | 0.35 |
k | The exponent order | 3 |
G _{1} | The gain factor | 10^{3} |
M _{1} | The link margin | 10^{4} |
P _{circuit} | The power of circuit | 140.7 mW |
P _{syn} | The power of frequency synthesizer | 50 mW |
σ ^{2} | The AWGN power spectral density | 3.981 10^{−21} |
B | The channel bandwidth | 10^{4} |
L | The number of bits in a packet | 10^{3} |
N _{ f } | The receiver noise figure | 10 |
The energy consumed to transmit a packet using MQAM or MPSK is defined as E_{total}. The energy consumption of nodes in linear network is shown in Theorem 1.
E_{total} is the energy consumption to transmit a data packet using MQAM or MPSK, which is equal to (14) or (15).
The following gives optimization methods for linear network under different modulation techniques.
5.1.1 The RDML scheme in MQAM technique
This part focuses on the optimization for sensor network using the MQAM modulation technique. First, the network lifetime at a certain duty cycle is optimized by non-equidistant deployment of nodes, and the distance between nodes is as Theorem 2.
Proof If the energy consumption of all nodes is balanced, the maximum energy consumption in network is minimum. So the E_{ i } = E_{ j }, i ≠ j is required.
Proof From Eq. (18), if the length of the linear network is unchanged, the distance between the first node and the sink becomes smaller as the duty cycle increases.
As the duty cycle of the sensor node increased, the modulation level will be reduced. Therefore, the energy consumption of transmission will gradually decrease and the energy consumption of circuit increases linearly with the duty cycle. Therefore, it is possible that the energy consumption of transmission is same as that of circuit. If the above two parts are same, there must be a minimum total energy consumption. Therefore, the problem translates into whether two function images can be equal in a same duty cycle.
Obviously, b is a large number. Thus, when \( \tau \to \frac{L{P}_e}{4 BT} \), f(τ) is bound to infinity.
Obviously, f(τ) > g(τ).
Because T_{2} is a small number (<10^{−10}), we usually can get g(1) > f(1).
Then, tiding up the above, when \( \tau \to \frac{L{P}_e}{4 BT} \), f(τ) > g(τ), and when τ = 1, g(τ) > f(τ), and the above two functions in the interval (0,1) is a continuous function. Thus, there are intersections between the two functions. So the maximum energy consumption have a minimized value.
Theorem 2 shows that the network lifetime can be maximized by non-equidistant deployment of nodes in a certain duty cycle. Theorem 3 shows that the network lifetime can be further increased by finding an optimal duty cycle so our goal min{max(E_{ i }(τ))} can be reached.
But it is impossible to completely balance the energy consumption in the network. Therefore, the nodes in the linear network have residual energy, so we can use the residual energy to increase the duty cycle of nodes (see in Theorem 4) and reduce the node’s BER (see in Theorem 5). Therefore, this strategy can achieve the purpose of reducing the delay.
Proof It is clear that the node which is closest to the sink has the maximum energy consumption in linear network. Assume E_{ total }(τ_{ i }) is the energy consumption of transmitting a data packet. Because we hope the network lifetime to be as long as possible, the node with the largest energy consumption uses the optimal duty cycle, and the energy consumption of other nodes does not exceed the maximum energy consumption, so the network lifetime will not be reduced. So, according to (19), we can calculate the duty cycle of each node.
The delay can be obtained from the BER by Eqs. (10) and (11). Obviously, as the BER decreases, the delay will also decrease, and in Theorem 5, the BER decreases as the duty cycle increases. So, the larger the duty cycle of the nodes, the smaller the delay. Therefore, this paper can reduce the delay by increasing the duty cycle of the node that is away from the sink. The following in Theorem 6 give the formula for the delay calculation under the optimization strategy of this paper.
5.1.2 The RDML scheme in MPSK technique
Similar to the previous analysis, when the modulation technique is MPSK, the non-equidistant strategy is used to optimize the network lifetime and the distance between nodes is as Theorem 7.
Proof According to Eq. (22), the distance between the first node and the sink decreases as the duty cycle increases.
Then, the problem is whether the two functions of the duty cycle have an intersection.
The β, d(τ) is a constant which can be obtained from b equals to \( \frac{2}{P_e} \); M = 2^{ b } is a big number, and it is close to ∞. So the formula is converted into a type of \( \frac{0}{0} \).
Obviously, b is a big number, so when \( \tau \to \frac{L{P}_e}{2 BT} \), the f(τ) → + ∞.
It is clear that f(τ) > g(τ).
Because T_{2} is a small number (<10^{−10}), we usually can get g(1) > f(1).
Then, tiding up the above formula, when \( \tau \to \frac{L{P}_e}{2 BT} \), f(τ) > g(τ), and when τ = 1, g(τ) > f(τ), and the above two functions in the interval (0,1) is a continuous function. Thus, there is an intersection between the two functions. So the maximum energy consumption has a minimum value.
For MPSK modulation technique, the same as the above formula, some nodes have residual energy. Because the difference of MQAM and MPSK is the calculation of the signal-to-noise ratio, according to Eq. (23), we also can compute the duty cycle.
From Eqs. (10) and (11), the delay will decrease with the duty cycle increase. Theorem 9 gives the relationship between the BER and the duty cycle in MPSK modulation technique, and the BER will decrease with the duty cycle increase. Therefore, the delay will decrease with the duty cycle increase. Therefore, the delay of network can be reduced by increasing the duty cycle of node which is far away from sink. Theorem 10 gives the calculation formula as follows.
5.2 The RDML scheme for Grid network
Another network studied in this paper is the Grid network. The Grid network has applications in many scenarios [41, 62]. The Grid network is a two-dimensional network. The deployment of nodes in the network is at the intersection of rows and columns, the sink is deployed at the intersection of the bottom leftmost row and column, and the sink is only connected with S_{1, 1}. The network model is as follows:
Theorem 12 For Grid network, the node that is forwarding the most data packets must be in the first row or in the first column.
So, we require D_{n, 3} < 2.
So the number must be less than 2. Thus, D_{n, 1} > D_{n, 2}.
Then, by the nth row derived to the (n − 1)th row, it is easy to know D_{n − 1, 1} > D_{n − 1, 2}.
And so on, get D_{i, 1} > D_{i, 2}.
Therefore, the nodes in the first row have the largest forwarding number of data packets. The same can also prove for the nodes in the first column.
5.2.1 The RDML scheme in MQAM technique
This section focuses on optimization for Grid network using MQAM modulation technique. From Theorem 12, the first column node has the most data packets to forward, so the first column node has the highest energy consumption. Because the network lifetime is determined by the nodes with the largest energy consumption, the first column is needed to be considered. Theorem 13 gives the energy consumption of the first column nodes.
where T_{1} is the same as Theorem 11.
Proof In the Grid network, when the row (column) length is unchanged, according to (33), the length of d_{1} will decrease with the duty cycle increase.
Because the energy consumption of these two parts and that of Theorem 3 has only the number of data packets different, and has the number of data packets constant, so similar with Theorem 3, we can prove that there are two curves intersecting and there is an optimal duty cycle to maximize the network.
Theorem 14 shows that there exists a set of d_{1}, d_{2}, d_{3}, …, d_{ n } to ensure the energy consumption is balanced at the first row (column) nodes. Theorem 15 shows that there is an optimal duty cycle to minimize the maximum energy consumption.
The same as the linear network, because the energy consumption of nodes is completely balanced which is very difficult, a strategy is used to increase the duty cycle of nodes with lower energy consumption in an equidistant deployed network, thereby reducing the delay. Theorem 16 gives the calculation method of the duty cycle of each node in the Grid network.
Proof According to Theorem 12, the node S_{1, 1} forwarded the largest data packet, so the maximum energy consumption is in this node. Therefore, node S_{1, 1} uses the optimal duty cycle to guarantee the maximum network lifetime. At the same time, the energy consumption of the other nodes in the network does not exceed that of node S_{1, 1} to guarantee the network lifetime. So according to Eq. (33), we can calculate the duty cycle of each node.
Theorem 17 gives the delay formula in the Grid network, so the delay can be calculated in the Grid network under MQAM modulation technique.
5.2.2 The RDML scheme in MPSK technique
This section focuses on optimization for Grid network using MPSK modulation technique. First, Theorem 18 gives the energy consumption of the first column nodes under the MPSK modulation technique.
where T_{3} is similar to Theorem 15.
Proof In Grid network, when the row (column) length is unchanged; according to (36), the length of d_{1} will decrease with the duty cycle increase.
Similar with Theorem 7, we can prove that there are two curves intersecting and there is an optimal duty cycle to maximize the network.
Theorem 19 shows that there exists a set of d_{1}, d_{2}, d_{3}, …, d_{ n } to ensure the energy consumption is balanced at the first row (column) nodes, and Theorem 20 shows that there is an optimal duty cycle to maximize the network lifetime.
Theorem 16 also can get the calculation method of the duty cycle of each node in Grid network using the MPSK modulation technique. Theorem 21 gives the delay formula in the Grid network as follows:
6 The experimental results and analysis
This section provides some simulation examples to study the RDML scheme proposed in this paper. In the following simulation experiments, the total length of the linear network and Grid network rows (columns) are all 500 m and at optimal duty cycle the delay for each node is taken as 1.5. We define the unequal distance of nodes policy as UDNP, the equal distance of nodes policy as EDNP [49], the unequal duty cycle of nodes policy as UDCNP, and the optimal duty cycle of nodes policy as ODCNP [55].
6.1 Linear network
6.1.1 Performance in MQAM technique
For EDNP, the energy consumption of nodes is unbalanced due to the different data packets of each node. Therefore, UDNP strategy is proposed. The following will verify our strategy by some simulation examples.
The unequal distance of nodes
d | d _{1} | d _{2} | d _{3} | d _{4} | d _{5} | d _{6} |
---|---|---|---|---|---|---|
τ | ||||||
0.2 | 63.98 | 68.27 | 73.83 | 81.59 | 93.76 | 118.6 |
0.25 | 62.95 | 67.57 | 73.50 | 81.66 | 94.34 | 119.9 |
0.3 | 61.36 | 66.52 | 73.03 | 81.83 | 95.27 | 122.0 |
0.35 | 59.09 | 65.09 | 72.42 | 82.10 | 96.56 | 124.7 |
0.4 | 56.03 | 63.26 | 71.73 | 82.54 | 98.26 | 128.2 |
0.45 | 51.96 | 61.04 | 71.02 | 83.21 | 100.4 | 132.4 |
0.5 | 46.55 | 58.50 | 70.42 | 84.24 | 103.1 | 137.2 |
0.55 | 39.05 | 55.81 | 70.16 | 85.77 | 106.3 | 142.9 |
0.6 | 27.54 | 53.58 | 70.68 | 88.17 | 110.5 | 149.5 |
0.65 | 5.33 | 54.10 | 73.41 | 92.49 | 116.5 | 158.1 |
Next, we will consider the maximum energy consumption of UDNP and EDNP in networks with different number of nodes when both strategies adopt an optimal duty cycle.
We used to deploy the nodes into a non-equidistant method to optimize the network lifetime. In addition, when the nodes are deployed equidistantly, we can use a strategy of unequal duty cycle, near the sink nodes using the optimal duty cycle to ensure the network lifetime and away from the sink node appropriate to increase the duty cycle to reduce the delay.
6.1.2 Performance in MPSK technique
For MPSK modulation technique, we can also use UDNP to optimize the network lifetime.
The unequal distance of nodes under MPSK
d | d _{1} | d _{2} | d _{3} | d _{4} | d _{5} | d _{6} |
---|---|---|---|---|---|---|
τ | ||||||
0.2 | 64.55 | 68.65 | 74.02 | 81.53 | 93.41 | 117.79 |
0.25 | 64.01 | 68.28 | 73.84 | 81.58 | 93.73 | 118.54 |
0.3 | 62.74 | 67.43 | 73.43 | 81.68 | 94.46 | 120.20 |
0.35 | 60.51 | 65.98 | 72.79 | 81.91 | 95.75 | 123.03 |
0.4 | 57.16 | 63.92 | 71.97 | 82.36 | 97.63 | 126.96 |
0.45 | 52.56 | 61.35 | 71.11 | 83.10 | 100.08 | 131.78 |
0.5 | 46.54 | 58.50 | 70.42 | 84.23 | 103.05 | 137.24 |
0.55 | 38.68 | 55.70 | 70.16 | 85.85 | 106.49 | 143.13 |
0.6 | 27.80 | 53.60 | 70.66 | 88.11 | 110.43 | 149.40 |
0.65 | 10.53 | 53.62 | 72.67 | 91.51 | 115.26 | 156.41 |
6.2 Grid network
The data packet forwarded of node in Grid network
j | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
i | ||||||
6 | 1.969 | 1.938 | 1.875 | 1.750 | 1.500 | 1.000 |
5 | 3.844 | 3.719 | 3.500 | 3.125 | 2.500 | 1.500 |
4 | 5.555 | 5.266 | 4.813 | 4.125 | 3.125 | 1.750 |
3 | 7.047 | 6.539 | 5.813 | 4.813 | 3.500 | 1.875 |
2 | 8.293 | 7.539 | 6.539 | 5.266 | 3.719 | 1.938 |
1 | 9.293 | 8.293 | 7.047 | 5.555 | 3.844 | 1.969 |
6.2.1 Performance in MQAM technique
The unequal distance of nodes (MQAM)
d | d _{1} | d _{2} | d _{3} | d _{4} | d _{5} | d _{6} |
---|---|---|---|---|---|---|
τ | ||||||
0.3 | 48.43 | 71.82 | 76.69 | 84.12 | 96.49 | 122.4 |
0.35 | 47.29 | 70.62 | 76.02 | 84.11 | 97.35 | 124.6 |
0.4 | 45.79 | 69.08 | 75.19 | 84.15 | 98.47 | 127.3 |
0.45 | 43.87 | 67.18 | 74.23 | 84.27 | 99.87 | 130.6 |
0.5 | 41.46 | 64.92 | 73.19 | 84.51 | 101.6 | 134.3 |
0.55 | 38.43 | 62.28 | 72.10 | 84.95 | 103.7 | 138.6 |
0.6 | 34.55 | 59.28 | 71.07 | 85.64 | 106.1 | 143.3 |
0.65 | 29.39 | 56.02 | 70.25 | 86.72 | 109.0 | 148.6 |
0.7 | 21.80 | 52.88 | 69.97 | 88.40 | 112.5 | 154.5 |
0.75 | 6.98 | 51.63 | 71.28 | 91.40 | 117.1 | 161.6 |
The duty cycle used at each node (MQAM)
j | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
i | ||||||
6 | 1 | 1 | 1 | 1 | 1 | 1 |
5 | 1 | 1 | 1 | 1 | 1 | 1 |
4 | 1 | 1 | 1 | 1 | 1 | 1 |
3 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 0.8 | 0.9 | 1 | 1 | 1 | 1 |
1 | 0.7 | 0.8 | 1 | 1 | 1 | 1 |
6.2.2 Performance in MPSK technique
The unequal distance of nodes (MPSK)
d | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
τ | ||||||
0.35 | 48.00 | 71.36 | 76.43 | 84.11 | 96.81 | 123.26 |
0.4 | 46.34 | 69.64 | 75.49 | 84.13 | 98.06 | 126.35 |
0.45 | 44.15 | 67.46 | 74.37 | 84.25 | 99.67 | 130.12 |
0.5 | 41.46 | 64.92 | 73.19 | 84.51 | 101.59 | 134.33 |
0.55 | 38.29 | 62.17 | 72.06 | 84.97 | 103.75 | 138.77 |
0.6 | 34.63 | 59.34 | 71.09 | 85.63 | 106.05 | 143.24 |
0.65 | 30.42 | 56.60 | 70.37 | 86.50 | 108.45 | 147.63 |
0.7 | 25.49 | 54.16 | 69.99 | 87.59 | 110.89 | 151.86 |
0.75 | 19.41 | 52.29 | 70.06 | 88.92 | 113.39 | 155.94 |
0.8 | 11.10 | 51.49 | 70.77 | 90.61 | 116.05 | 159.99 |
The duty cycle used at each node (MPSK)
j | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
i | ||||||
6 | 1 | 1 | 1 | 1 | 1 | 1 |
5 | 1 | 1 | 1 | 1 | 1 | 1 |
4 | 1 | 1 | 1 | 1 | 1 | 1 |
3 | 0.9 | 1 | 1 | 1 | 1 | 1 |
2 | 0.7 | 0.8 | 1 | 1 | 1 | 1 |
1 | 0.6 | 0.7 | 0.9 | 1 | 1 | 1 |
7 Conclusions
In this paper, we propose a cross-layer design scheme for IWSNs which is from duty cycle and node deployment and other layers to optimize the network lifetime and delay. This paper discusses the linear network and Grid network that use two modulation techniques which are the MQAM technique and the MPSK technique to optimize the performance of network under additive white Gaussian noise channels.
Different from the previous research, the previous optimization strategies choose to increase the energy efficiency of the node and optimize the network lifetime under a certain duty cycle. The strategy of this paper is to further optimize the network lifetime by adjusting the duty cycle when the energy efficiency has reached an optimal value.
However, in reality, the node deployment difficulty and deviation are considered, and the energy consumption of the node cannot be completely balanced, so we put forward a strategy of unequal duty cycle. For energy-intensive nodes, the duty cycle uses the optimal value to optimize the network lifetime; for those nodes with low energy consumption, the duty cycle is appropriately increased to reduce the transmission delay. This strategy can be applied to industrial wireless sensor networks, can increase the lifetime of IWSNs, and can speed up the response of the network to events. Therefore, this strategy has a good meaning.
Declarations
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (61772554, 61379110, 61572526, 61572528) and the National Basic Research Program of China (973 Program) (2014CB046305).
Funding
Not applicable.
Availability of data and materials
Not applicable.
Authors’ contributions
JT is the main author of the current paper. AL contributed to the conception and design of the study. MZ, HS, and MM commented the work. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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