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Abstract

Simultaneous data gathering is an application that exploits the unique advantages of wireless sensor networks. Because many sensor nodes access a channel, co-channel interference limits the number of nodes who can access it. To suppress co-channel interference, a frequency spectrum (or channel) is required to obtain large diversity and spreading gains. Cognitive radio with transmit power control exploits available channels because, in this approach, the co-channel interference on the primary system is suppressed and spectrum sharing between the primary system and a secondary system is possible. Prolonging a node’s life is also important in wireless sensor networks. However, in simultaneous data gathering, the power consumed by the relay station (cluster head) is quite high. In this article, a method for constructing a cluster head selection and rotation that is optimal for increasing the number of available channels and prolonging the life of the node is proposed. In simultaneous data gathering, the link with the minimum number of available channels is the bottleneck. Our proposed technique achieves the maximum number of available channels and extends the life of the nodes because of the cluster head rotation. In addition, the optimal number of clusters is also determined.

Keywords

Wireless sensor networks cognitive radio resource management for Internet of Things multiple access for simultaneous data gathering cluster head selection

Introduction

The task of gathering the sensing results of machine monitoring such as in the Internet of Things (IoT)¹ or machine-to-machine (M2M) communications² is attracting a large amount of attention. An IoT connected cloud server makes it possible to collect a huge and wide sensing data. The analysis results of IoT data are counted on the application of health care, agriculture, and industry.³ As the applications of IoT are widely spread, the diversity of data quality is also required. A cross-layer technique among the application layer, the network layer, and medium access control (MAC) or physical layer for accommodating the various user end quality is considered.⁴ In order to compensate the network delay of cloud server, the cooperation between cloud server and a fog computing is also considered and the fog computing achieves the real-time capability of IoT.⁵

As the novel network and server are considered for real-time processing and huge data gathering, the wireless access techniques from a lot of sensors to data center (fusion center (FC)) more significantly demand the small accessing delay and the accommodation of huge sensor accesses. In delay sensitive systems such as robotics and automated driving systems⁶ as well as a wide range of event-driven sensor systems such as seismograph and tide-gauge systems,⁷ many sensors send sensing results to a data center over a short period of time. This type of data gathering is called simultaneous or semi-simultaneous data gathering. The distributed wireless access techniques, such as ALOHA and carrier sense multiple access with collision avoidance (CSMA/CA), cause the large delay and the significant drop of throughput due to packet collision and automatic request.⁸ To support simultaneous data gathering, multiple access technology for massive number of data accesses is desired.

Recently, wireless access technologies have been considered for simultaneous data gathering. The non-orthogonal multiple access (NOMA) method, which is based on transmit power control and interference cancelation, can increase the number of simultaneous accessing terminals.⁹ Spread spectrum technologies, such as frequency hopping¹⁰ and ultra wide band,¹¹ enable massive numbers of sensor accesses thanks to their large spreading gains. In addition, physical wireless parameter conversion sensor network (PhyC-SN) can recognize the median and outliers of all the sensing results because they project all the sensing results onto the frequency spectrum of the carrier signal.¹²

In these wireless access technologies, the number of accessing terminals is restricted by co-channel interference (CCI). Wireless sensor networks (WSNs) should secure wider frequency bandwidth in order to obtain a larger spreading gain and frequency diversity gain as well as to suppress CCI.

Cognitive radio (CR) exploits the available channels from the frequency resources licensed by the primary system (PS), where the CR system is referred to as the secondary system (SS).¹³ In frequency sharing between a PS and SS, there are two spectrum divisions, space division, and frequency division.^14,15 In space division, the SS suppresses the CCI to the PS by transmit power control (TPC) or antenna beam forming, and thus, the simultaneous access of both the PS and SS is possible. If the signal power is smaller than the level desired by the SS, the SS gives up the accessing channel and switches to another one. This strategy is called frequency division. An SS can secure more channels by adaptively selecting channels using space division and frequency division.¹⁴

In multi-hop WSNs based on cluster heads (CHs), a CH relays the sensing results from each node to the data center (or FC).¹⁶ Since the distance from each node to the FC is smaller on average than that from each node to the CH, the transmit signal power of each node is reduced and hence, the propagation of harmful CCI emitted by a node is also suppressed. If the PS and nodes of the SS are geographically widely spread, each node should care about the different PSs. When the accessing channels of each PS are diversified, the available channels of each node are also diversified.¹⁷ In simultaneous data gathering, the access technologies are limited by CCI. The minimum frequency bandwidth among the links from all the nodes to the CH and from all CHs to the FC decides the throughput of a sensor because the size of sensor data is common for all the sensors and the minimum throughput from a node to FC decides the throughput of all the sensors. Therefore, the minimum frequency bandwidth is the bottleneck for the simultaneous data gathering. If the node of the CH is changed to another node, the communication link is changed and the available channels of each node are also changed. Therefore, a WSN based on CR for simultaneous data gathering should select a suitable CH such that the minimum channels of all the links are maximized.

However, a CH consumes more power than a node,¹⁸ resulting a short lifetime. Especially, in simultaneous data gathering, the power consumed by the CH is significant. There are three reasons for this fact. First, the CH requires a complicated data separation calculation to suppress CCI in the receiving process, and thus, the power consumed for signal processing is large. Second, relaying a large amount of data consumes a lot of power. Third, the power efficiency of the transmit power amplifier is significantly reduced due to the highly fluctuating envelop of a multiplexed signal, similarly to the peak-to-average power problem of a multicarrier system.¹⁹

To prolong the lifetime of a sensor network, the role of the CH is rotated among the nodes. This process is called CH rotation.¹⁶ The protocol for CH selection and rotation is referred to as the low-energy adaptive clustering hierarchy (LEACH).¹⁶ A power consumption-aware CH selection technique for energy harvesting has been considered.²⁰ A LEACH protocol that exploits the frequency spectrum using the CR concept has also been considered.²¹ To our best knowledge, a CH selection method for maximizing the channels in the bottleneck link and prolonging the lifetime of a WSN for simultaneous data gathering has not yet been investigated.

This article proposes a method for the construction of a CH rotation that is optimal for maximizing the minimum channel in a bottleneck link and prolonging the lifetime of a WSN for simultaneous data gathering. The construction of the CH rotation is treated as a min-max problem of the available channels in the bottleneck link subject to the constant number of CHs available for CH rotation. We propose an algorithm for this min-max problem. As Takyu et al.²² exploit available frequency resource, the TPC controls the interference area which is also considered as the area of frequency sharing with PS. When the transmit power is reduced in maintaining the required level of link quality, the interference area becomes narrow and hence, the available channels are additionally secured. The stable securement of available channels is achieved even under the high traffic load of PS.

Computer simulations show that the proposed CH rotation obtains large number of available channels in the bottleneck link than random selection¹⁶ and a method using criterion of maximum available channels. When we set the number of CHs for rotation as the constraint for optimization, the optimal divisions for clustering are also determined. We also evaluate the lifetime of WSN system by counting the successful data gathering, where it is referred to as round time. As a result, our proposed method achieves the better trade-off between the round time and the available channels than any other method.

Mathematical notations

We apply the following notation in the rest of the paper. Let $N$ be the set of all positive integers. For $i, j \in N$ such that $i < j$ , we let the integer interval including both $i$ and $j$ be denoted by $[[i, j]]$ . For two sets $A$ and $B$ , the product set $A \times B$ is the set of tuples $(a, b)$ of all possible combination of $a \in A$ and $b \in B$ . If $A = B$ , we simply write $A^{2} = A \times A$ . Analogously, by $A^{K}$ we denote the set of K-tuples $(a_{1}, \dots, a_{K})$ of all possible combination of $a_{k} \in A$ for all $k = 1, \dots, K$ .

Related works

This article considers WSNs with CR for achieving simultaneous data gathering, exploitation of available channel, and prolonging lifetime of sensor. The conventional works related to this article are given as follows.

The channel assignment for maximizing residual energy is considered in the WSN with clustering.²³ It can prolong the lifetime of sensor but it does not consider how to exploit available channels for securing them enough.

A node clustering for constructing cooperative spectrum sensing in CR is proposed.^24,25 The operations of spectrum sensing are decreased with exploiting the space-correlation of sensing results for prolonging the lifetime of sensor. Securing channel for transferring the sensing results to data center is not considered.

In Salameh et al.²⁶ and Xu et al.,²⁷ the sensor with the function of CR dynamically selects a channel among multiple channels for transferring the sensing result to data center. Since the packet collision is reduced due to selecting the vacant channel, the retransmission of packets is reduced. As a result, the sensor activity is prolonged. However, this work limits single channel access but does not extend multichannel access.

In multi-hop WSNs, a lot of forwarding data are concentrated to the nodes around FC. Therefore, these nodes are more quickly dead. It is referred to as hotspot problem.²⁸ In Helal et al.,²⁸ the more clusters with peculiar channel are constructed in the nodes near FC for off-loading effect. It does not consider the space distribution of PS but the common available channels for all the nodes within a sensor system are used. In wide area sensor networks, the common available channels are limited because PS occupies various partial channels.²⁹ The spectrum sharing of common channels by code division multiple access is considered³⁰ but it meets a serious interference limitation.

A collaboration between LEACH and a function of CR is proposed as cogLEACH.^21,31 Since each node can autonomously access to available channels, local available channels based on the space distribution of PS are actively exploited. In other words, the special reuse of available channels is achieved. However, in autonomous access control, an access channel mismatch, which the mismatch of accessing channel between transmitter and receiver occurs, is a serious problem.²⁷ In addition, the link connection is broken under a high loading environment of PS because the available channels cannot be found.

In Shah et al.,³² the CH selection based on the criterion of minimum energy consumption in the subject to the satisfaction of acceptable distortion in movie is considered. Although the special reuse of available channels is achieved due to the space distribution of PS, the outage of link is not avoided under the high loading environment of PS.

The protection of interference to PS and the extension of parallel transmissions are achieved due to an effect of special multiplexing with multiple-input multiple-output (MIMO).^33,34 The collaborate transmission among sensor nodes within a cluster makes MIMO multiplexing possible. A stable securement of available channels is expected if the collaboration between MIMO and multichannel extension is considered.

The purpose of this article is a stable securement of large available channels for the scheme of simultaneous data gathering, such as NOMA with MIMO multiplexing,⁹ spread spectrum technique,¹⁰ and PhyC-SN.¹² An effect of incrementing available channels due to controlling the interference to PS with TPC²² is applied to the considered wireless sensor system. Therefore, the divisions of available channels are frequency plus special domains. Although the limitation of latency for real-time application is severe, available channels are secured in both frequency and special domains even under large loading environment of PS. The multi-dimensional securement of available channels for the cognitive WSN with prolonging the lifetime of sensor has not been considered, yet but it is considered by this article.

System model

PS and SS

Figure 1 shows the system model of the cognitive WSN used in this article. The PS is composed of a transmitter terminal and receiver terminal. A PS has higher channel access priority than an SS. The PSs, which include the transmitter and receiver, are uniformly spread over the geographical field. We model the offered load of the PS using full buffering. Therefore, a PS always has access to the channels. In an SS, there is one data center, which is referred to as the FC, and multiple sensor nodes (nodes). The network topology is star type. All the nodes send the sensing results to the FC. When some sensor nodes become CHs, they receive the sensing results from the accessing nodes and then relay them to the FC.

Figure 1.

System model of a cognitive WSN.

There are some simultaneous access protocols such as NOMA,⁹ Spread Spectrum,^10,11 and PhyC-SN.¹² Since the target of this article is how to exploit the available channels by the frequency and space reuse, the secured available channels can be used for any simultaneous access protocol. Therefore, this article does not specify simultaneous access protocol. We consider one-hop wireless communication. Figure 2 shows the WSN access flow in the SS. In the first step, the FC broadcasts the data gathering trigger signal to all the nodes, including the CH. In the second step, all the nodes send the sensing results to each CH, and in the third step, all the CHs send the sensing results to the FC. We assume that the applications of sensor networks allow the delay of time consumed by three steps.

Figure 2.

Access flow of simultaneous data gathering.

Multichannel access environment

Figure 3 shows the definition of a channel in the frequency domain. The frequency bandwidth of each channel is equivalent. Various rules for channel selection by the PS can be considered, such as the largest throughput based on channel state information and the suppression of mutual interference between PSs. We assume simple random channel selection by the PS in this article. Note that our proposed method for constructing a CH rotation can be used even if any other channel selection rule is assumed.

Figure 3.

Definition of a channel in a multichannel environment.

Space and frequency division for spectrum sharing

We consider two divisions for spectrum sharing between the PS and SS space division²² and frequency division.¹⁵ We assume the acceptable level of CCI in the PS is decided. The SS controls transmit power to send the sensing results to the receiver without error. The transmit power is set at the minimum level needed to satisfy the required received signal power. As the distance between the transmitter and receiver increases, the transmit power increases to compensate the propagation loss.

Once the SS emits the signal for channel access, the CCI area is defined. Figure 4 shows an example of the CCI area. The border of the area is defined by the acceptable CCI level. If the PS is within the CCI area, the CCI from the node degrades the quality of the channel for the PS. This is because the CCI is larger than the acceptable CCI level. If the PS is outside the CCI area, the CCI from the node is acceptable. This is because it is smaller than the acceptable CCI level. In a practical environment, the border of this area is not smooth because of fading and shadowing effects. We assume the border of CCI area includes an interference margin,³⁵ and thus, its shape becomes circular. This article assumes that the position information of the PS is known because of a location system like global positioning system. The channel accessed by the PS outside of the CCI area can be accessed by the SS. Therefore, a space division is constructed. In contrast, if it is accessed by the PS within the CCI area, it cannot be accessed by the SS. As a result, each node has an available channel list. Figure 5 shows the channel list in each node. Using this channel list, the number of channels in each link can be determined. If multiple SSs access a channel, the interference power increases and this is called cumulative interference.³⁶ This article assumes that the acceptable CCI level includes an interference margin for the cumulative interference.

Figure 4.

CCI area and spectrum sharing with the PS and SS.

Figure 5.

Available channel list in the SS nodes.

Optimal selection of CHs for rotation

Figure 6 shows the WSN of an SS that has been clustered. Here, the nth node $(n \in [[1, N_{i}]])$ in the ith cluster ( $i \in 1, 2, \dots, I$ ) is denoted as $[n]_{i}$ , where $N_{i} (\in N)$ is the total number of nodes in the ith cluster and $I (\in N)$ is the number of clusters. Let $X = [[1, N_{1}]] \times \dots \times [[1, N_{I}]]$ be the set of all possible combination of node indices from each cluster. Let $K$ be the total number of nodes becoming CH in per one cluster. We choose $K$ combinations of nodes denoted as $x_{1}, \dots, x_{K}$ . Let $[x_{k}]_{i}$ be the node index for the ith cluster in $x_{k} (k \in [[1, N_{i}]])$ . Then $x_{k} = ([x_{k}]_{1}, \dots, [x_{k}]_{I})$ and $[x_{k}]_{i} \in [[1, N_{i}]]$ for all $i \in [[1, I]]$ . When the nodes included in kth combination, $x_{k}$ , become CH, the numbers of available channels for $[n]_{i}$ node in accessing to nearest CH or FC and that for $[x_{k}]_{i}$ node in accessing to FC are defined as $C_{{[n]}_{i}} (x_{k})$ and $C_{{[x_{k}]}_{i}} (x_{k})$ , respectively.

Figure 6.

WSN with clustering.

In simultaneous data gathering, the FC collects the sensing results from all the nodes without dropping any data. The link with the least number of channels is considered to be the bottleneck. When the nodes included in kth combination, $x_{k}$ , become CH, the number of channels in the bottleneck link is defined as

$\begin{array}{l} f_{C} (x_{k}) = \min {C_{{[1]}_{1}} (x_{k}), \dots, C_{{[N_{1}]}_{1}} (x_{k}), C_{{[1]}_{2}} (x_{k}) \dots, \\ C_{{[N_{I}]}_{I}} (x_{k}), C_{{[x_{k}]}_{1}} (x_{k}), \dots, C_{{[x_{k}]}_{I}} (x_{k})} \end{array}$ (1)

For example, in Figure 5, there are two nodes and one CH. The number of minimum channels in channel list among two nodes and one CH is three. Therefore, the number of channels in bottleneck link is three.

Since bottleneck link depends on the combination of nodes for CH, $x_{k}$ , the available channels in the considered WSN are decided as minimum of $C (x_{k})$ for all the $k$ and it is defined as

$F_{C} (x_{1}, \dots, x_{K}) = min {f_{C} (x_{1}), \dots, f_{C} (x_{K})}$ (2)

Optimal CH selection

Let $f_{C} : X \to R$ be a real valued function defined for each combination $x_{k} \in X$ . Our objective function to be maximized is defined as follows

$\begin{matrix} \underset{(x_{1}, \dots, x_{K}) \in X^{K}}{arg max} F_{C} (x_{1}, \dots, x_{K}) = \\ \underset{(x_{1}, \dots, x_{K}) \in X^{K}}{arg max} min {f_{C} (x_{1}), \dots, f_{C} (x_{K})} \end{matrix}$ (3)

subject to

$\begin{matrix} [x_{k}]_{i} \neq [x_{l}]_{i} \\ for all 1 \leq i \leq I, for all 1 \leq k < l \leq K \end{matrix}$ (4)

As $K$ increases, the lifetime of the WSN is prolonged because the opportunities for a node to be assigned the role of CH decrease. However, not only the largest $f_{C} (x_{k})$ but also the second and third largest $f_{C} (x_{k})$ are selected. The number of available channels decreases. Therefore, the trade-off between the WSN lifetime and available channels is controlled by $K$ .

The algorithm for the proposed optimal CH selection is as follows:

For each $x \in X$ , we compute $f_{C} (x)$ and store it to a list $L_{f}$ for a later use.

Sort the elements of $X$ so that $f_{C} (x_{1}) \geq \dots \geq f_{C} (x_{X})$ , where $X$ is the number of elements in $X$ .

Let $n = K$ .

For each combination $c = (c_{1}, \dots, c_{K}) \in 1, n$ without replacement, check whether $[x_{c_{i}}]_{t} \neq [x_{c_{j}}]_{t}$ for all $1 \leq t \leq I$ for all $1 \leq i < j \leq K$ .

If there exists one or more than one ( $c$ ) such that satisfies the condition in the above step, return $(x_{c_{1}}, \dots, x_{c_{K}})$ for one of such $c$ . Otherwise, increment $n$ and go back to the previous step.

It is guaranteed that the algorithm returns one of the optimal solutions as long as $N_{i} \geq K$ for all $i = 1, \dots, I$ . The proof of optimality is given in Appendix 1.

The motivation for our proposed selection technique is to ensure that the CH combinations of the lowest rank are as large as possible. As the minimum ranking $n$ drops one by one, finding $K$ CH combinations is the maximization of the minimum number of available channels in the bottleneck link.

Figure 7 shows an example of constructing the optimal CH selection. For comparison, as the total number of available channels is larger, the selection rule of using the CH group with the highest ranking is also shown in Figure 8, where this construction rule is referred to as max available channel selection. These figures show that CH selection using the proposed method has a larger number of channels in the bottleneck link than that using max available channel selection. This is because our proposed CH selection method avoids selecting the CH combination with the first ranking, and thus, the CH combination with the minimum ranking has a higher rank.

Figure 7.

Example of CH selection and rotation in the proposed construction method.

Figure 8.

Example of CH selection and rotation using max available channel selection.

In the ranking construction, the CH combinations explosively increase as the number of nodes increases. To reduce the computational complexity, this random node selection is used to construct the CH combination. This selection is repeated until $G$ CH combinations are constructed. Therefore, the best CH combinations are selected by the proposed algorithm among $G$ CH combinations.

Simulation results

The performance of the proposed CH rotation selection method is evaluated using computer simulation. Table 1 shows the simulation parameters. In simulation, the minimum transmit power of node for achieving the required quality of receiver is ideally controlled and we assume that the twice distance between transmitter and receiver is required for suppressing the interference to be acceptable level in PS. Therefore, the CCI area is modeled by a circle with a radius that is twice as large as the distance between the SS transmitter and receiver. Note that the interference margin is decided by the radio propagation and the acceptable level of interference power in PS. Therefore, the assumed CCI area is one of control parameters depending on the situation. Note the margin for cumulative interference is included for the construction of CCI area. Whenever the node density is significantly large, the power of cumulative interference is large. Therefore, the CCI area becomes wider range in order to buffer the cumulative interference. In this simulation, we assume that the number of nodes is not so large that the increment of cumulative interference is not negligible. The nodes of the SS are uniformly spread over the geographical field. We partition the area into $I$ clusters in a radial pattern and there is an FC at the center of the radial pattern. As the number of nodes is equivalent in each cluster, the partition of clusters is slightly shifted for every computer simulation. We assume that the PSs are indicated by their receiver and are uniformly spread over the geographical area. Furthermore, the locations of the PSs are ideally known by the SS.

Table 1.

Simulation parameters.

Number of channels	512
Number of selected channels per PS	10
PS geolocation area	4000 m²
SS geolocation area	1000 m²
Number of PSs	150
Number of SSs (sensor nodes)	30, 35, 40, 50
PS and SS positioning model	Poisson point process
Number of clusters $I$	3, 4, 5
Number of CHs for rotation $K$	4, 6, 10
Number of CH combinations for searching $G$	1000

PS: primary system; SS: secondary system; CH: cluster head.

We consider two conventional methods for constructing a CH rotation. The first one is random selection.¹⁶ Some nodes in each cluster are selected as CHs. The second one is max available channel selection, as shown in Figure 8.

Available channels

Figure 9 shows the cumulative distribution function (CDF) performance with respect to the number of available channels in the bottleneck link, where $K$ is 4 and the number of SSs (nodes) is 30. In these figures, “CH” indicates the number of clusters, where it is equal to $I$ . This figure shows that our proposed construction method obtains a larger number of channels than the conventional methods. When CDF = 0.1, the minimum number of channels in the CH rotation of our proposed construction is 40 channels larger than that of the max available channel selection and is 100 channels larger than that of random selection. Therefore, our proposed technique can increase the number of channels in the bottleneck link. As the number of clusters, CH, increases, the number of channels in the bottleneck link increases because as the number of clusters increases, the area per cluster narrows. As a result, the average distance between each node and the CH decreases. Because the transmit power of the node is reduced, the CCI area shrinks. As the number of PSs within the CCI area decreases, the number of available channel in each node increases.

Figure 9.

CDF versus available channels for rotation number $K = 4$ .

Figure 10 shows the CDF performance with respect to the number of available channels in the bottleneck link, where $K$ is 6 and the number of SSs (nodes) is 30. Compared to the results with $K = 4$ , the number of channels in the bottleneck link is less. This is because in Figure 8, the CH groups of lower rank are required for the $K = 6$ . Note that for CH = 5, zero channels in the bottleneck link occurs in the results of random and max available channel selection, where we defines the condition of securing zero channels as WSN outage. On the other hand, our proposed construction obtains at least 20 channels. Therefore, our proposed technique completely avoids WSN outage.

Figure 10.

CDF versus available channels for rotation number $K = 6$ .

In proposed technique, the number of available channels in the bottleneck link for CH = 4 is larger than that for CH = 5. This is because as we described, the number of available channels in each node is larger because of the short average distance between the transmitter and receiver in the SS. However, the number of nodes per cluster decreases. The nodes causing the small number of available channels are required for the CH, and the number of available channels in the bottleneck link hence decreases. Therefore, there is a trade-off between minimizing the distance between the transmitter and receiver and reducing the density of the nodes per cluster. As a result, CH = 4 obtains the largest number of available channels in the bottleneck link.

Figure 11 shows the performance between the number of clusters, $I$ , and the number of channels in CDF = 0.1, where the number of SSs (nodes) is 30. In $K = 4$ , CHs = 6 and 7, the conventional techniques cannot achieve CDF = 0.1. Therefore, WSN outage occurs. The performance of proposed selection is convex tendency for CHs. The available channels are maximal in $K = 4$ and CHs = 5 and CHs = 6 and $K = 6$ and CHs = 4, respectively. Therefore, it is important to select the best number of clusters for achieving largest channels.

Figure 11.

Number of clusters versus number of channels in CDF = 0.1.

Figure 12 shows the performance between the number of SSs (nodes) and the number of channels at the CDF = 0.1, where the number of clusters, $I$ , is three, and the number of CHs per one cluster, $K$ , is 6 and 10 ( $K = 6, 10$ ). It can be seen that the difference between “Conventional MAX” and “Proposed” becomes smaller as the number of nodes becomes larger in $K = 6$ . This reason is as follows. The distance among nodes becomes small, the available channels for each node are not different, and the different of available channels by switching CH is not large. As a result, the semi-optimal CH rotation achieves the large available channels near to that of optimal one.

Figure 12.

Number of nodes versus number of channels in CDF = 0.1.

On the other hand, in $K = 10$ , the difference between “Conventional MAX” and “Proposed” is larger than that in $K = 6$ . Since the larger number of nodes is required for constructing the larger size of CH rotation, constructing the CH rotation takes the more number of nodes into consideration. Therefore, the various distance among nodes causes the various available channels by changing the selection of CH, where it is considered as obtaining the selectivity of CH. The proposed optimal construction of CH rotation achieves larger available channel due to the selectivity of CH. Therefore, the proposed construction is especially effective in fewer nodes per one cluster and/or larger nodes to become CH in CH rotation for prolonging sensor lifetime.

Performance between lifetime and available channels

We introduce the energy consumption model of sensor node for evaluating lifetime of WSN system. In accordance with Heinzelman et al.,¹⁶ the energy consumption required for data transmission, $E_{TX}$ , is given as follows

$E_{TX} (k) = E_{bi t_{t}} \times m + ε \times m \times d^{2}$ (5)

where $E_{bi t_{t}}$ is the energy consumption required for transmitting one bit information in baseband process, $m$ is the number of transmitting bits, $ε$ is the energy consumption per unit distance of power amplifier for attaining the required received signal power, and $d$ is the distance between transmitter and receiver. In this model, the model of propagation loss follows square law.

The energy consumption required for receive process, $E_{RX}$ , is modeled as follows¹⁶

$E_{RX} (k) = E_{bi t_{r}} \times k$ (6)

where $E_{bi t_{r}}$ is the power consumption required for receiving one bit information.

When we assume the energy of battery in sensor node is $B$ and a node sends a bit to receiver, the residual energy of battery is

$B - E_{Tx} (k)$ (7)

If a node becomes CH and it performs the three processes, which are receiving, regenerating, and retransmitting, the residual energy of battery in the node is

$B - E_{RX} (k) - γ E_{Tx} (k)$ (8)

where $γ$ is the extension indicator of energy consumption caused by large peak-to-average power ratio (PAPR).¹⁹ When we use the PhyC-SN, the reconstructed signal of CH is composed of the multiple tone signals transmitted from some nodes. Therefore, the amplitude of it is significantly fluctuated, where it looks like the amplitude of an orthogonal frequency division multiple (OFDM) access.³⁷ For simplicity, we assume that $γ$ is constant value. Table 2 shows the simulation parameters for evaluating the lifetime of WSN system.

Table 2.

Simulation parameters for evaluating lifetime of WSN systems.

Battery of node, $B$	1 J
Energy for transmitting a bit, $E_{bi t_{t}}$	50 nJ/bit
Energy consumption per unit distance of Power amplifier $ε$	100 pJ/bit/m²
Extension coefficient of power consumption by PAPR, $γ$	4
Energy for receiving a bit, $E_{bi t_{r}}$	50 nJ/bit
Information bits per round, $m$	1

PAPR: peak-to-average power ratio.

Figure 13 shows the performance between the available channels and the round times, where the round times are defined as the number of data gathering from all the nodes to FC until any one sensor becomes out of battery. The number of SSs (nodes) is 30. The available channels are given in CDF = 10%. In this figure, the initial number of clusters, CH, is 3 and it is increased until the available channels are kept over zero.

Figure 13.

Number of available channels versus number of round times.

From Figure 13, we can see the convex tendency of available channels and the increment tendency of round times, respectively in increasing the number of CH. We also confirm the convex tendency of available channels in Figure 11 and the reason given in Figure 13 is the same as that given in Figure 11. As CH increases, the average distance between transmitter and receiver becomes shorter and the power consumption of sensor for data transmission is reduced. As a result, the WSN achieves long lifetime. As the number of nodes in the CH rotation, $K$ , becomes 4 to 5, the round times increase but the available channels decrease for all the performances. This is because although the more nodes share the huge power consumption caused by CH processing, the node having the fewer available channels in bottleneck link is additionally used for CH.

From this figure, the proposed method achieves the more available channels and the more round times than the conventional methods except for $K = 4$ and CH = 4. The reason why proposed technique achieves the long life and the large available channels is as follows. The selection policy of proposed method is the smaller required transmit signal power of nodes and CH because the CCI is suppressed and the available channels are enlarged. It can also save the power consumption of node. Therefore, the proposed method achieves the long life of WSN system. In Figure 13, the results in $K = 4$ , CH = 5, 6, and 7, and $K = 5$ , CH = 5 are located in the upper right side in compared to any other results. Therefore, the proposed technique achieves the good trade-off between the available channels and the long life of WSN system.

Conclusion

This article proposed a method to determine the optimal CH selection and rotation for simultaneous data gathering in cognitive WSNs. In simultaneous data gathering using WSNs, the nodes simultaneously accessing the network are limited by CCI. Therefore, the link with the minimum number of available channels is the bottleneck. In our proposed construction method, the minimum number of available channels in the bottleneck link is maximized. The computer simulation shows that the proposed construction method obtains a larger number of available channels in the bottleneck link while prolonging the life of the sensor node because of CH rotation. Therefore, the proposed method achieves the good trade-off between the available channels and the lifetime of wireless sensor system. Even if the available channels are secured for SS, SS suffers from the CCI from not only SS but also PS accesses. Therefore, the spectrum efficiency derived by the throughput normalized by the available channels decides the more exact bottleneck link, but the evaluation of it is important future works. In addition, the theoretical analysis for evaluating the available channels by proposed construction of CH rotation is also important future works.

Footnotes

Handling Editor: Won-Yong Shin

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: A part of this research project is sponsored by Ministry of Internal Affairs and Communications in Japan under the project name of Strategic Information and Communications R&D Promotion Programme (SCOPE 135003005 and 165003007) and JSPS KAKENHI (17H03264).

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