Distributed topology construction algorithm to improve link quality and energy efficiency for wireless sensor networks

Author’s Accepted Manuscript Distributed topology construction algorithm to improve link quality and energy efficiency for wireless sensor networks Xiaochen Hao, Weijing Liu, Ning Yao, Dehua Geng, Xida Li www.elsevier.com/locate/jnca

PII: DOI: Reference:

S1084-8045(16)30068-6 http://dx.doi.org/10.1016/j.jnca.2016.04.017 YJNCA1631

To appear in: Journal of Network and Computer Applications Received date: 21 October 2015 Revised date: 30 March 2016 Accepted date: 20 April 2016 Cite this article as: Xiaochen Hao, Weijing Liu, Ning Yao, Dehua Geng and Xida Li, Distributed topology construction algorithm to improve link quality and energy efficiency for wireless sensor networks, Journal of Network and Computer Applications, http://dx.doi.org/10.1016/j.jnca.2016.04.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Distributed Topology Construction Algorithm to Improve Link Quality and Energy Efficiency for Wireless Sensor Networks a*

a

a

a

b

Xiaochen Hao , Weijing Liu , Ning Yao , Dehua Geng , Xida Li a

School of electrical engineering, Yanshan University, Qinhuangdao 066004, China

b

Institute of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China

[email protected] [email protected] [email protected] [email protected] [email protected] *

Corresponding author.

Abstract The evaluation of link quality plays a vital role in designing the upper level protocol in wireless sensor networks. The high rate of packet loss occurs when data is transmitting on the poor quality link, thus resulting in data retransmission and energy waste. Motivated with the aforementioned problem, we present the link weight model to address the problem of poor link quality and high energy consumption. This model regards the node’s transmitting power as an adjustment factor. It fuses the link quality parameter and nodes’ energy parameter to mathematically formulate the above problem for decreasing the interference and making the network energy balanced. Then exploiting the method of function derivation, we validate the analytical solution of the link weight. On the basis of this model, a distributed topology construction algorithm to improve link quality and energy efficiency is proposed. Finally several simulation experiments are conducted to evaluate the performance of this algorithm and validate its theoretical properties. Theoretical analyses and simulation results show that this algorithm can enhance the link steadiness, decrease the interference and prolong the network’s lifetime. Key words: wireless sensor networks; link quality; energy consumption; link weight

1. Introduction In wireless sensor networks (WSNs), considerable research has gone into topology control algorithms (Bahi et al., 2014; Chu and Sethu, 2014). The goal of topology control is to dynamically change the nodes’ transmitting range in order to maintain the network connectivity (Paolo S, 2005). Thus the topology control algorithms can decrease energy consumption and prolong the time of network connectivity. In topology control, the quality of the links used decides many higher layer protocols’ performance. The poor link quality may cause high energy consumption and the dynamic change of packet loss. If we choose these poor quality links to communicate, the accuracy of packet reception will decrease, and the node energy consumption will increase. Maybe it will happen that the low energy nodes can’t undertake more transmission task or will prematurely die because of the increasing energy consumption. Or even, these nodes will lead to energy holes in the surrounding area(Salarian et al., 2014; Olariu and Stojmenovic, 2006; Watfa et al., 2014), thus causing network disconnection or network collapse. For this reason, it is an indispensable content on how to improve the link quality and effectively exploit the sensor nodes’ energy in WSNs. Adjacent figure can describe the network topology structure, and it has decisive effect on network

performance. Most current topology control algorithms collect node information based on the geographical position of sensor nodes. However, it becomes the particularly difficult matter to achieve the precise geographical position information due to the existing of interference and obstacles. Thus, decreasing communication interference becomes significant in WSNs. Luo and Bao (2013) have presented an algorithm which adjusts the node’s transmitting power to gain its appropriate node degree. However this algorithm can not be applied to the area in which the nodes are deployed unevenly, because these nodes need a very large transmitting power for reaching their appropriate node degrees. So Gong has presented an algorithm to decrease the interference from the angle of graph theory(Gong at al., 2011). This algorithm has created a spanning tree by minimizing the shortest path’s interference. But it can not be applied in the network with few nodes. Because if the distribution of nodes is too sparse, the node’s transmitting power will be very big, easily causing unbalanced energy consumption. Hence in order to lower the energy waste, Bajaj (2014) puts forward a new energy-efficient heuristic to prolong the time of network connectivity. Younis et al. (2014) have provided a thorough analysis and comparison of the recent topology management techniques. However these two papers ignore that the poor link quality in network could cause the poor network performance, such as low throughput, high energy consumption and high transmission delay. Even the poor link quality will greatly increase receiving nodes’ interference when multiple sending nodes’ signals are stacked, disturbing nodes’ accurate signal reception. The better quality links can decrease this interference, guarantee the higher success rate of communication and the lesser retransmission. Therefore, an interesting question might arise, which is how to decrease the interference by enhancing the link quality. To improve the link quality, Sahoo has proposed a distributed power control protocol in use of Received Signal Strength Indicator (RSSI) (Sahoo et al., 2007). But this protocol has the limited application range, namely it can’t be applied in a homogeneous network. Moreover it ignores the physical barriers in real environment, and uses the distance and link quality in the ideal environment to construct the algorithm. The signal-to-noise ratio (SINR) is associated with the real distance between nodes. It considers the distance and the degree of attenuation in the transmission process, reflects the interference nature in wireless network. So Alfieri et al. (2007) has established a linear model about the Packet Reception Ratio (PRR) and SINR. Nevertheless in this model there is a problem which is if the change of SINR increases, the error of PRR also raises. So Qin et al. (2011) propose a novel approach concerned directly with SINR, thus avoiding the error brought by the change of SINR. In this algorithm, the greater the signal strength is, the better the link quality is. However the greater signal strength can bring more energy waste, hence causing node death even the network disconnection. Lee et al. (2011) have proposed another algorithm by considering the limited energy of sensor nodes. It uses the nodes’ low power which could lessen energy consumption to measure the link quality. But the low power can not guarantee that the node receives packets accurately. Besides, the low-power node is easy to cause the packet retransmission. Thus it not only decreases the real time of data transmission, but also lowers down the probability of receiving node’s correct reception of packets. An effective link quality prediction mechanism can prevent data exchange, and makes the node receive more data packets, lower the interference which the receiving node suffered by adjusting the node transmitting power. While the above research has the weakness in predicting the link quality, they can not achieve the high link quality, the low interference and energy consumption simultaneously. Therefore, we present the link weight model which joints the link quality and node energy. What’s more, based on the link weight model, we propose a distributed topology construction algorithm ILQEE (improve link quality and energy efficiency). The theoretical analyses and simulation results show that this algorithm can make the network’s energy balanced, achieve high link quality and low interference. The work in this paper is different from the above mentioned algorithms, and the differences lie in the following three aspects.

First, we build the link quality model based on bidirectional PRR, while many algorithms use the unidirectional one to construct topology. The bidirectional PRR avoids that only one end of a link receives the data accurately, while the other end can not receive the data. Then the data can be transmitted smoothly for reaching any destination node. Hence the number of retransmission, the transmission delay of data and network congestion are decreased. So we use the bidirectional PRR to construct the link quality model for decreasing the network congestion, increasing the real time of data transmission and guarantying the link’s high steadiness. Second, we construct the link weight model by combining with the node energy. This model can be adjusted for the purpose of achieving good quality link. It guarantees the node’s successful receiving data, and improves the network’s throughput. Furthermore, this model combines the link stability with nodes’ lower energy consumption. It makes the nodes with high residual energy participate in more data transmission, and the nodes with low residual energy rest, thus preventing the node from premature death. So the link weight model can not only lessen the energy consumption and the delay of data transmission, but also increase the network’s throughput. Third, different from the traditional EG (Enclosure Graph) model, ILQEE uses a new link weight model to construct topology. The traditional EG model usually uses the distance between nodes as its weight, while the distance can not be measured accurately because of the interference in reality. So ILQEE can not only balance the energy consumption, decrease the interference, but also improve the link quality. Moreover this algorithm can construct the optimized topology in the real environment, laying the foundation for the packets to transmit. In this paper, the rest parts are organized as follows. In Section 2, the link weight model is built. Section 3 describes ILQEE algorithm, and provides the theoretical analyses of this algorithm. Section 4 proves the validity of this algorithm by simulations and we summarize the full text in Section 5.

2. Overview of link weight model In this section, we give an overview of the link weight model. Firstly this section is started by the key issues of the low communication quality and unnecessary energy consumption. Then the link quality index and the bidirectional link energy consumption rate are constructed. In the last subsection, we build the link weight model. 2.1. Problem description The link quality has significant effect on data transmission. The good quality links can guarantee the stability of data transmission. But the poor quality links will cause the packets retransmission, resulting in the transmitting nodes’ energy waste and the network’s low throughput. So the nodes should choose steady links to transmit data for increasing the network’s throughput and decreasing the energy waste. For the other angle, the node energy is limited and can’t be supplemented, so the node energy should be made full use of. Therefore, we better take into account both the link quality and the node energy to construct topology. Fig. 1 is used as an example to show the influence exerted by the link quality and the energy on topology. There are ten nodes which are v1, v2, v3  v10 in Fig. 1. The numbers beside the nodes indicate their serial number and surplus energy. The red line represents a poor quality link (Here the poor quality link means the PRR of both ends of a link is less than 0.9); the black line indicates a good quality link (Here the good quality link means the PRR of both ends of a link is more than 0.9). The topology in Fig. 1(a) has the good and poor quality links at the same time. It will increase the node transmission energy consumption on the poor quality link, consequently the low energy nodes will prematurely die. In general, this topology has the poor performance. In the following description we take the purple node v1 and the blue node v2 as an example to show their choice of the link in different conditions. In Fig. 1(b), v1 and v2 choose their connected nodes according to which node’s PRR is larger than 0.9. From Fig. 1(b), we can know there is an isolated node v3 which can’t

participate in the data transmission. Then there will be more data to be transmitted by v1. Accordingly v1 will increase its communication load, and is easy to bring about fast death. Additionally, the topology has cross links which can produce vast interference, thus destroying the network normal transmission. Fig. 1(c) has the similar problem. In this figure, v1 and v2 choose their neighbors on the principle that the node energy is larger than the threshold (here we define that the threshold is 10J). Then v5 and v8 are isolated from the topology. This case will increase v1 and v2’s communication load, and waste their energy. In addition, the topology has the poor quality links as shown by the red lines. These poor quality links will lower down the link’s steadiness and the real time of data transmission. In summary, the above two methods can not get the topology with better performance. Therefore, it is essential for us to establish a topology in which the data can be transmitted smoothly as shown in Fig. 1(d). v3(29J) v1(30J)

v10(21J)

v3(29J) v1(30J)

v9(28J)

v5(6J) v4(27J)

v10(21J) v9(28J)

v5(6J) v4(27J)

v2(28J) v6(29J)

v8(9J)

v7(24J)

(a)

v3(29J) v1(30J)

v10(21J) v9(28J)

v5(6J) v4(27J)

v2(28J) v6(29J)

v7(24J)

(b)

v8(9J)

v3(29J) v1(30J)

v10(21J) v9(28J)

v5(6J) v4(27J)

v2(28J) v6(29J)

v7(24J)

(c)

v8(9J)

v2(28J) v6(29J)

v8(9J)

v7(24J)

(d)

Fig. 1. Topology figure (a) Topology with the maximal power; (b) Topology constructed according to the link quality; (c) Topology constructed according to the surplus energy; (d) Topology synthesizing the link quality and the surplus energy.

2.2. Link weight model In accordance with above analyses, this paper constructs the link weight model which considers both node energy and link quality. This model mainly includes the link quality index and the bidirectional link energy consumption rate. Its specific description is described below. (i) The link quality index: In the real communication environment, the sensor nodes easily suffer from the interference of surrounding noise, causing the signal distortion and the fluctuation of communication link. Therefore if the data is transmitted on the link with poor quality, it can easily lead to the data’s transmission failure. Then the nodes will receive the less data packets, and decrease its packet reception rate. Gong et al. (2011) defines the probability of successfully delivering a packet as PRR. It can describe the link quality more directly than other metrics, like RSSI, LQI (Link Quality Indicator). The links with higher PRR make the nodes resist the environmental interference to successfully receive the data packet. It can improve the throughput of entire network, and lower the node energy consumption. So based upon PRR we define the link quality index. On the ground communication, the mode of the radio module with low power usually shows the asymmetry of the link. The asymmetry of the link manifests itself in that both ends of the link have different PRR. It can cause a series of problems. For example, we can not construct the route in the network layer because of the unidirectional link communication. So the bidirectional PRR is introduced to build the link quality index. Definition 1 (The link quality index). The link quality index between any node pair i and j can be

expressed as: (1) line(i, j )  (1  PRRij )  (1  PRR ji ) Here, line(i,j) is an index measuring the link quality. PRRij represents the packet reception ratio when i is a transmitting node and j is a receiving node. PRRji represents the packet reception ratio when j is a transmitting node and i is a receiving node. Eq. (1) models that the larger PRRij and PRRji are, the smaller line(i,j) is, then the link is more reliable for the data to be transmitted on. In other words, line(i,j) is a communication index reflecting the link’s stability. We expatiate on the derivation process of line(i,j) next. There will be conflicts when multiple node pairs use the same channel to transmit data at the same time. The node cannot receive the data correctly. Then the energy is waste and the network throughput is greatly cut down. So Yu et al. (2014) uses SINR as shown in Eq. (2) to formulize the interference caused by nodes’ using the same channel. Definition 2 (The SINR). When the signal is transmitted on the link lij, the SINR at the receiving end j can be expressed as: pi g (i, j ) SINR j  (2)  pk g (k , j )  N j kG , k i , j

Here, pi is node i’s transmitting power. g(i,j) indicates the link gain between nodes i and j. G is the set of node j’s neighbors. Nj is the background noise node j suffers. The threshold of signal-to-noise ratio (defined as SINRth) is the minimum requirement for the packets to be received successfully. So in order to ensure that the node can accurately receive packets, the SINR at node j should meet the requirement of SINRth as below. SINR j  SINRth (3) min According to Eq. (2) and Eq. (3), node i’s minimum transmitting power pi should satisfy the requirement: SINRth  ( min i





kG , k  i , j

pk g (k , j )  N j )

(4) g (i, j ) The PRR-SINR model is closer to the actual situation of the transmission performance. So based on the SINR constructed above, we achieve the formula of PRR. By modeling the mechanism of wireless sensor network link as Li and Carmen (2007), the relation between PRR and SINR is shown as follows. 1 PRR  (1  e  SINR )8 f (5) 2 Here, f is the length of a packet, and f > 0. PRR is positively related to SINR. So we get the higher PRR by getting higher SINR. And then, the network interference is low. When i is a transmitting node and j is a receiving node, the PRR between them is shown below. p

8f

 pi g ( i , j )   pk g ( k , j )  N j    1  SINR j 8 f 1  (6) PRRij  (1  e )  1  e kG ,k i , j 2  2    Eq. (6) shows when the nodes’ transmitting power changes, the PRR floats between 0~1. If PRRij is very small, it’s easy to cause that the nodes inaccurately receive information, and easy to bring about the incremental numbers of retransmission. Therefore the nodes’ power in the network needs to be adjusted to an appropriate value to achieve the higher PRR. If PRRij is greater than 0.9, it can be made sure that the nodes are capable of receiving information accurately (Mamun et al., 2010). Then

the energy consumption brought by packets retransmission is reduced. So we define the threshold of PRR as 0.9. According to Eq. (6) and the PRR threshold, when PRRij is greater than 0.9 we can get that node i’s minimum transmitting power meets Eq. (7).  ln(2  2  min i

p



8f

0.9)  (



kG , k i , j

pk g (k , j )  N j )

g (i, j ) Combining Eqs. (4) and (7), i’s minimum transmitting power can be determined:

pk g (k , j )  N j )  ln(2  2  0.9)  (  pk g (k , j )  N j ) kG , k  i , j kG , k  i , j max{ , }  pimin  pmax (8) g (i, j ) g (i, j ) When the node power meets Eq. (8), the receiving node can smoothly receive the signal from the transmitting node i. After the range of i’s minimum transmitting power is achieved, we synthesize Eqs. (1) and (6) to determine the link quality index as follows. 8f 8f  p j g ( j ,i )  pi g ( i , j )              1 k 1Gj,k 1i , j pk 1g ( k1, j )  N j     1 k 2Gi,k 2i , j pk 2 g ( k 2,i )  Ni       1  1  e line(i, j )  1  1  e (9)        2   2               The smaller line(i,j) is, the better the link quality is. However the link quality index can't reflect the energy consumption of both ends of a link. When the energy of the nodes on a certain link is little but the data packet is transmitted on this link for many times, these nodes’ energy will be used up rapidly. Consequently the data transmission is broken off, even the network is unconnected. Therefore we introduce the following bidirectional link energy consumption rate to measure the energy of the nodes on one link. (ii) Bidirectional link energy consumption rate: This section is mainly adopted to build a model in order to reflect the size of nodes’ energy consumption. To facilitate the description and analyses, the following assumptions are: Every node’s maximum transmitting power is the same, and the radius of its coverage area is dmax. In the model of wireless communication energy consumption, if the distance between the transmitting node and the receiving node is d, the total energy consumption of sending and receiving l bit data is shown in Eq. (10) (Liu et al., 2014). Ecos t  2l  Eelect   amp  l  d 2 (10) Here, Eelect is transmitting / receiving circuit loss, εamp is amplifying circuit loss, the relationship between the sending data’s length l and the packet's length f is l = 8f. Additionally, when node i transmits data to node j, its minimum transmitting power pi meets pi = α  d2(i,j). Here, the constant α represents a parameter concerning the distance d(i,j). Then we can get that when any node i emits its power pi, its energy consumption can be rewritten as p Ecos t (i)  2l  Eelect   amp  l  i (11) SINRth  (



(7)

8f



Therefore we can get the bidirectional link energy consumption rate between nodes i and j as Eq. (12). p p 4l  Eelect   amp  l  i   amp  l  j Ecos t (i)  Ecos t ( j )   (12) Eloss (i, j )   E0 (i)  E0 ( j ) E0 (i)  E0 ( j ) Here, E0(i) and E0(j) are node i and node j’s initial energy respectively. In the actual environment,

because the volume of nodes and the surrounding environment are diverse, every node’s initial energy is different. So we allocate different initial energy toward each node. If the residual energy of i and j is greater, Eloss(i,j) is smaller. On the contrary, if the residual energy of i and j is smaller, Eloss(i,j) is greater. The bidirectional link energy consumption rate is simplified as shown in Eq. (13). p p 4l  Eelect   amp  l  i   amp  l  j   (13) Ec(i, j )  E0 (i)  E0 ( j ) Any node’s residual energy and its transmitting power are different owing to the effect of actual environment, so the node’s residual energy is not the same after data transmission over a period of time. When the transmitting power is larger, PRR is greater in accordance with Eq. (6). But energy consumption produced by the large transmitting power is greater as well. On the contrary when the transmitting power is less, PRR and the energy consumption is less, too. So we need to construct the link weight to adjust the relation between PRR and node’s energy. Below is the description of the link weight model. (iii) The link weight model: The link weight model weight(i,j) is a standard measuring both PRR and the link energy. And this model is built based on the link between any node pairs i and j, as shown below. weight (i, j ) line(i, j ) Ec(i, j )   Er (i ) Er ( j ) PRRij  PRR ji  E0 (i ) E0 ( j ) 8f 8f  p j g ( j ,i )  pi g ( i , j )              1 k 1G,k 1i , j pk 1g ( k1, j )  N j     1 k 2G,k 2i , j pk 2 g ( k 2,i )  Ni       1  1  e  1  1  e        2   2              

/((1 

2l  Eelect   amp  l  E0 (i )

pi

 )  (1 

2l  Eelect   amp  l  E0 ( j )

(14)

pj

 )) 8f

 p j g ( j ,i )  pi g ( i , j )     4l  Eelect   amp  l    amp  l   1  pk 1g ( k1, j )  N j   1  pk 2 g ( k 2,i )  Ni    / ( 1  e k 1Gj ,k 1i , j  )   1  e k 2Gi ,k 2i , j  E0 (i )  E0 ( j ) 2 2           From Eq. (14), we can know when both ends of one link have the balanced energy and PRR, the weight(i,j) will be small. And if weight(i,j) is smaller, the numbers of data retransmission and the superfluous energy consumption are cut down efficaciously. Namely, the possibility of data’s successful transmission on the good quality link is larger, and the nodes can decrease the energy consumption caused by the poor quality link. According to above equation, we get that weight(i,j) can adjust the link quality and the node energy consumption by adjusting nodes’ transmitting power to get the better network performance.

pi

pj

8f

3. Distributed topology construction algorithm ILQEE In this section, we start ILQEE algorithm by gathering the node’s neighbor information, and describe the stage of node power’s determination. Then a detailed description about the process of

link’s connection is given. In the last subsection we will show some analytic results, including the key properties of ILQEE. 3.1. Stage of neighbor list’s establishment First of all, each node collects the information of its neighbors by means of information exchange. Its neighbors are in the scope of its maximum transmitting power. In particular, all the nodes in network send Hello1 message by their maximum transmitting power. The message includes the node’s serial number ID, maximum power pmax and current energy Er. When node j receives the Hello1 message from node i, it calculates the Euclidean distance d(i,j) between node i and node j, calculates its minimum power pij when communicating with node i. All the nodes are statically distributed in the region with total area of A. So the Euclidean distance between nodes is fixed. Node j packs its ID(j), current energy Er(j), the Euclidean distance d(i,j) and its minimum power pij to “ACK” message. Then it sends this message to node i. After i receives the “ACK” message, it decodes this message, and adds node j’s information into its neighbor information list. The header of node i’s neighbor information list is shown in TABLE I. TABLE I. Neighbor information list of node i.

ID( j )

pij

d (i, j )

g (i, j )

Er ( j )

Finally we array node i’s neighbor information list according to its power’s descending order. There is the method to calculate the minimal transmitting power between nodes. According to Friis formula(Li et al., 2009), we have the relationship between the signal strength p r at 2 PG t t Gr l propagation distance d and the sender power pt : pr  . Here, Gt is the antenna gain on 16 2 d 2 L transmitting terminal; Gr is the antenna gain on receiving terminal; l is the wavelength of electromagnetic wave, L is the system loss parameters. If the signal strength p r monitored by one node in channel is greater than threshold Rth , there must be data which is transmitted. Therefore, the

minimal transmitting power of transmitter is pmin  Rth formulas, pmin 

16 2 d 2 L . Synthesizing the above two Gt Gr l 2

Pt  Rth is achieved. pr

3.2. Stage of node power’s determination In this stage each node completes the determination of its power, preparing for the next phase of the links’ connection. In this topology control algorithm, we assume that each link is assigned the same channel, and the channel doesn’t change. Step1 i=1 (here i is the serial number of each node in the network, the total number of nodes within the scope of network’s coverage is N). Step2 Node i firstly sends message with the minimum power p1 in the neighbor information list, here p1 ≤ pmax. Step3 After j (j represents the serial number of the farthest neighbor node which is in the scope of i’s current transmitting power. It changes with i’s transmitting power) receives the message, it calculates PRRij between node i and node j in accordance with Eq. (6). Step4 Judge if PRRij is equal to or greater than 0.9. If it is, node i keeps the current power, and records its current power as its final transmitting power. If the transmitting power of the nodes in i’s neighbor information list is larger than i’s current power, delete these nodes’ information from the list.

Then we enter Step 7. Otherwise, node i updates its transmitting power to the next-hop power in the neighbor information list, then we enter Step 5. Step5 Node i’s transmitting power is updated to the power pn (pn is the power in the neighbor information list), judge if pn is smaller than pmax. If it is, node i sends message with its current power, return Step 3; otherwise we enter Step 6. Step6 Node i keeps its maximum power fixed, and doesn’t update its neighbor information list. Step7 i=i+1, judge if i≥N. If it is, we end the stage of node power’s determination; otherwise we return Step 2. After the above steps, every node has determined its final transmitting power and its updated neighbor information list. 3.3. Stage of links’ connection At this stage, node i sends out Hello2 message to its neighbors which are in the updated neighbor information list. If node j receives Hello2 message from i, it judges if i is in its neighbor information list. If i is, j packets its neighbor information list to ACK message, and transmits the message to i. When i receives ACK message, it parses this message, and judges if j is in its neighbor information list. If j is, i adds j’s information, such as ID(j), sign(i,j) (sign(i,j) indicates the mark of the link’s connectivity. At first it is marked as 0 which means that the link is disconnected), to its bidirectional neighbor list. Node i calculates the weight(i,j) according to its current transmitting power and j’s current transmitting power, and adds the weight(i,j) to its bidirectional neighbor list. Then i constructs its bidirectional neighbor list as TABLE Ⅱshown. TABLE Ⅱ. Bidirectional neighbor list of node i.

ID( j )

weight (i, j )

sign(i, j )

After all the nodes construct their bidirectional neighbor lists, i sends out Hello3 message, which includes its bidirectional neighbor list, to the neighbors which are in its bidirectional neighbor list. The node j which receives Hello3 message judges if there is a public node g in node j and node i’s bidirectional neighbor list. If there are no public nodes, node j directly connects node i, and the link between them is marked as 1. If there are public nodes, we give an example to explain how to mark the links. Assuming that g is one public node, we mark the links according to the relationship of the link weights among nodes i,j,g. We divide the relationship into two parts. Case (a): If weight(i,g)+weight(g,j) < weight(i,j), then the link between node i and node g is marked as 1. Case (b): If weight(i,g)+weight(g,j) ≥ weight(i,j),then the link between node i and node g is marked as 0, the link between node i and node j is marked as 1. Based on the above process of links’ establishment, each node firstly builds the local topology within the scope of its transmitting power. After connecting all the links marked 1, the global topology is constructed. 3.4. Theoretical analysis To verify the correctness and effectiveness of ILQEE, this part analyzes the algorithm’s property from two aspects, which are network’s connectivity and link’s bi-direction. Then we prove that PRR can get its threshold by Theorem 3. Among this part, the topology when all the nodes in network transmit their maximum power to construct is Gmax. The topology that ILQEE algorithm constructs is G’(V,E’). Theorem 1: If Gmax is connected, G’(V,E’) is also of connectivity. Proof: If G’(V,E’) is connected, there must be a path path(u→w1→  →wn→v) between node u and node v in network. Node u and node v are any pair of nodes in network, wm and wm+1 (m=1  n-1) is each other’s neighbor node. So if we prove that G’(V,E’) is connected, we just prove the

existence of the path path(u→w1→  →wn→v), namely we should prove there must be a communication link between two neighbor nodes wm and wm+1. In ILQEE algorithm, each node sets up its own neighbor information list. If node wm and node wm+1 exist in each other’s neighbor information list, the forms of communication between wm and wm+1 have the following situations in accordance with the process of establishing topology. Case (a): If there are no public neighbor nodes between wm and wm+1, then the two nodes can communicate with each other directly. And there must be a single hop link wm  wm+1 between them. Case (b): If there is a public neighbor node wi between wm and wm+1, if weight(wm,wi)+ weight(wi,wm+1) ≥ weight(wm,wm+1), wm and wm+1 can communicate with each other directly, and the link wm  wm+1 must exist. If weight(wm,wi)+weight(wi,wm+1) < weight(wm,wm+1), wm and wm+1 will be connected by wi, namely there is a path wm  wi  wm+1 between wm and wm+1. After running ILQEE, there must be a communication path between two neighbor nodes wm and wm+1. Then any two nodes u and v can be connected by the path path(u→w1→  →wn→v). So the topology G’(V,E’) is connected. Theorem 2: Node i and node j can communicate with each other if all the nodes in G’(V,E’) transmit their optimal power. Proof: After running ILQEE, any node uses the optimal power as its final power. We assume that node i’s optimal power is piop, its neighbor node j’s optimal power is pjop. There are two cases to prove the bidirectional path’s existence between any pair of nodes: Case (a): If node i and node j are in each other’s bidirectional neighbor list, then i can transmit data to j with the power piop. In like manner, j can transmit data to i with the power pjop. So the path between i and j is bidirectional. Case (b): If node i and node j can not be directly connected, there must be nodes w(w=w1,w2…wn) that connect the two nodes, here n is the number of the nodes on one path between i and j. According to ILQEE, w and i are in each other’s bidirectional neighbor list, besides w and j are also in each other’s bidirectional neighbor list. Then w and i can be bilaterally connected; w and j can be bilaterally connected. So we can prove that path(i→w1→  →wn→j) is bidirectional. Above all, any path in G’(V,E’) is bidirectional. Theorem 3: If G’(V,E’) is connected and the transmitting power satisfies Eq. (8), there is an appropriate power for PRR to get its threshold. Proof: PRRij is a function about the variable pi, we discuss if it can be larger than 0.9 under the g (i, j ) condition of Eq. (8). Firstly we assume a  , here a > 0, then PRRij is:  pk g (k , j )  N j kG , k  i , j

1 PRRij  (1  e api )8 f 2 PRRij’s first-order derivative PRRij ' about the variable pi is:

(13)

4af 1 (1  e api )8 f 1 (14) api e 2 4af 1 From the above analysis, we know api  0 and (1  e api )8 f 1  0 . So PRRij '  0 . Then we e 2 can get that PRRij is a monotone-increasing function. When PRRij=0.9, we achieve 1 8f pi  ln(2(1  0.9)) . When we adjust the node transmitting power until it is equal to or larger a 1 8f ln(2(1  0.9)) , PRRij is larger than 0.9. than a PRRij ' 

4. Performance evaluation In this section, we evaluate the performance of ILQEE through simulations. The evaluation metrics include: ① topology; ② link quality; ③ energy; ④ network lifetime; ⑤ local paths’ average hop; ⑥ average node degree. Both the POA (path optimization algorithm) and PLBD (path-loss based distributed topology control algorithm) use the path quality to construct topology (Hao et al., 2015; Hao et al., 2009). Different from ILQEE, POA uses the nodes distance to calculate the PRR of receiving nodes, and PLBD uses the nodes distance to reflect the path loss of its algorithm. In order to make this study more objective and comparable, we use the PRR and SINR under the condition of NCFSK modulation to afresh calculate the weight in POA. Then POA and PLBD are useful when contrasted with ILQEE. It is assumed that the sensing field of WSN is 500m×500m. And the node communication power is 110m. The other specific simulation parameters used by the model are shown in TABLE Ⅲ. TABLE Ⅲ.

Framework of topology control algorithm

Parameter

Denotation

Value

Eelect

Energy consumed by transmitting/receiving circuit per bit

50×10-4 J/bit

εamp

Energy consuming by transmitting amplifier spreading in unit area per bit under free space model

100×10-7 J/bit/m2

g

Path Loss

1/d2.5

l

Bits of a data packet

5 bit

Ni

Noise Intensity

e-8 w

pmax

Maximum Transmitting Power

4w

4.1. Comparison of topology 500

500

500

450

450

450

400

400

400

350

350

350

300

300

300

250

250

250

200

200

200

150

150

150

100

100

100

50

50

0 0

100

200

300

400

500

0 0

50 100

200

300

400

500

0 0

100

200

300

400

500

(a) (b) (c) Fig. 2. Comparison of topologies (a) Topology derived by POA (b) Topology derived by PLBD (c) Topology derived by ILQEE

In the first simulation, we run the three algorithms to get their topologies in Fig. 2 where 150 nodes are randomly distributed in the 500m×500m area. The cross links cause the increment of the whole network’s average node degree, hence giving rise to the death of nodes with a little energy. Moreover, the cross links may result in the interference’s increment. Then the nodes can not receive information accurately. Compared with ILQEE, there are many cross links in the topology constructed by POA and PLBD. So ILQEE can decrease the energy consumption and protect the nodes from using up their energy prematurely. In addition, the topology built by ILQEE has less number of links. It can effectively reduce the competition and conflict in MAC layer, and overcome the drawback of large redundancy. In summary, ILQEE can guarantee that the network is

energy-balanced and the interference is decreased. 4.2. Comparison of link quality In the second simulation, when the total number of sensor nodes varies from 100 to 300, we run the three algorithms for twenty times under the different node number. So we achieve the average SINR and the average PRR when the node density varies from fewer to larger as shown in Fig. 3. SINR reflects the change of the whole network’s interference. The greater the SINR is, the less the interference is. From Fig. 3(a) we can know ILQEE can make sure its average SINR is higher. Hence the node interference of ILQEE is less than that of the other two algorithms. PRR reflects the quality of a link. The high link quality can make the nodes receive information smoothly, and increase the network’s throughput. In Fig. 3(b), the straight line represents that the PRR threshold is equal to 0.9. The greater PRR is, the higher the link quality is. From this figure, we know the PRR of ILQEE is larger than 0.9. That is, ILQEE ensures that data can be transferred accurately between nodes. While the PRR of the others is smaller than 0.9, then the information can’t be received smoothly. So Fig. 3(b) proves the link quality of ILQEE is much better than that of the others. 1

25

The PRR of total topology

The average SINR of total topology

30

20 15 10 5 0 100

ILQEE POA PLBD

0.8 0.6 0.4 ILQEE 0.2

POA PLBD

150 200 250 Total number of nodes

(a)

300

0 100

150 200 250 Total number of nodes

300

(b)

Fig. 3. Change of SINR and PRR as the node number increases (a) Change of SINR as the node number increases (b) Change of PRR as the node number increases

4.3. Comparison of energy In the real situation, due to the existence of network’s interference and obstacles, sensor node’s initial energy is different from others. Because nodes’ energy is consumed in the process of executing the algorithm, their residual energy has the difference. This simulation realizes the contrast of this difference. Fig. 4 shows the ratio of the link residual energy to the link initial energy. Fig. 5 describes the standard deviation of the ratio of the link residual energy to the link initial energy. And the link residual energy is the sum of the residual energy of both ends on one link; the link initial energy is the sum of the initial energy of both ends on one link.

0.9

Rsidual energy of link

0.8

ILQEE POA PLBD

0.7 0.6 0.5 0.4 0.3 0.2 100

150

200 250 The number of nodes

300

Fig. 4. Comparison of residual energy

Standard deviation of residual energy

0.35 0.3 ILQEE POA PLBD

0.25 0.2 0.15 0.1 0.05 0 100

150 200 250 Total number of nodes

300

Fig. 5. Standard deviation of residual energy

As can be seen from Fig. 4, the residual energy of ILQEE is greater than that of the other two algorithms. This suggests that the energy consumption speed of ILQEE is obviously lower than POA’s and PLBD’s energy consumption speed. Fig. 5 shows that the standard deviation of nodes’ residual energy of ILQEE is lower. It indicates that the nodes’ residual energy in ILQEE is closer to the average value, namely this algorithm can make the energy balanced. Therefore, ILQEE extends the lifetime of nodes and makes the nodes complete more transmission task. 4.4. Comparison of lifetime In the forth simulation, 200 nodes are randomly distributed in the area, and the nodes are given initial energy by the way of Poisson distribution. We run the three algorithms to record the number of dead nodes for twenty times. In this part, the number of dead nodes is used to reflect network lifetime. The less the number of dead nodes are, the longer the network lifetime is.

Number of dead nodes

200

150

100

50

0 0

ILQEE POA PLBD 50 100 150 Number of network running round

200

Fig. 6. Network lifetime

Fig. 6 can reflect that the topology built by PLBD appears the earliest dead node. And with the increasing of running time, the number of ILQEE’s dead nodes is significantly lower. Additionally, in the 200 round, ILQEE algorithm has the less dead nodes than POA and PLBD. It means ILQEE effectively prolongs the network lifetime by improving the link quality and cutting down the energy consumption. It shows the better performance comparing with POA and PLBD. Therefore, we know ILQEE will provide the foundation to construct the topology. 4.5. Comparison of local paths’ average hop When the node number is fixed, we collect the hop between one node and the neighbors within its covering range, then average the hop of all nodes in network. Then the local paths’ average hop under the condition of different node number is showed in Fig. 7. The local paths’ average hop count of ILQEE is larger than that of the other two algorithms. This is because ILQEE algorithm simultaneously considers the link quality and the communication nodes’ surplus energy (Both are related to the distance between nodes). This situation results in that it’s not the shortest path from the transmitting node to receiving node, then the hop count of ILQEE increases as shown in Fig. 7. The larger local paths’ average hop can reduce the interference each node suffers from others, and reduce the energy each node consumes. Obviously, ILQEE gets the appropriate local paths’ average hop. It can decrease the interference, and save the node energy. 4.6. Comparison of average node degree The node degree means the number of one node’s neighbors. The average node degree means the average of all the node degrees in network which is used to evaluate the network’s sparseness and robustness. The low average node degree decreases the interference and conflict in signal’s propagation path, and save the energy of nodes. The high average node degree can enhance the network’s robustness. But the higher the degree is, the greater the interference is. What’s more, the average node degree is concerned with node transmitting power. The smaller transmitting power can decrease the average node degree and energy consumption. Hence, we better get the smaller transmitting power for the node to get the smaller average node degree. In this part we average the twenty times’ average node degree with the different node number as shown in Fig. 8.

Local paths’ average hop count

2.4 2.3 2.2

ILQEE POA PLBD

2.1 2 1.9 1.8 1.7 1.6 100

150 200 250 Total number of nodes

300

Fig. 7. Comparison of local paths’ average hop count 8

Average node degree

7

ILQEE POA PLBD

6 5 4 3 2 100

150 200 250 Total number of nodes

300

Fig. 8. Comparison of average node degree

On the premise that node’s transmitting power meets the requirement of Eq. (8), we choose the smaller power to build topology in ILQEE. So in Fig. 8, ILQEE’s average node degree is obviously lower. The smaller the node degrees are, the more effectively the interference can be reduced. Then the information cannot be retransmitted, and the receiving node can achieve the information smoothly. Therefore ILQEE can decrease the energy consumption by data retransmission, and extend the network’s lifetime.

5. Conclusion Based on the low link quality and the high energy consumption, we propose the link weight model to optimize the network link quality and decrease the node energy waste. This model fuses the link quality index and bidirectional link energy consumption rate, can be used to get the best network performance by adjusting nodes’ transmitting power. According to the demand of high link quality and balanced energy consumption, we tinker up nodes’ transmitting power to achieve the minimum link weight. Moreover this paper proposes a distributed topology construction algorithm ILQEE. It ensures the data is transmitted unfailingly, avoids the energy consumption of redundant transmission, and refrains from the premature death of nodes. Finally the simulation results show that ILQEE can decrease the network’s interference, heighten the link quality and balance the network’s energy consumption. Acknowledgments

The authors would like to thank the reviewers for their constructive comments on the Manuscript. This work is supported by the National Natural Science Foundation of China under Grant No. 61403336, the Natural Science Foundation of Hebei province, China under Grant No. F2015203342, and the Independent Research Project Topics A Category for Young Teacher of Yanshan University of China under Grant No. 13LGA008 and Grant No. 15LGB007. References Alfieri A, Bianco A, Brandimarte P, Chiasserini CF. Maximizing system lifetime in wireless sensor networks. Eur. J. Oper. Res. 2007; 181(1):390-402. Bahi JM, Guyeux C, Hakem M, Makhoul A. Epidemiological approach for data survivability in unattended wireless sensor networks. J Netw Comput Appl, 2014; 46: 374-383. Bajaj D. Maximum coverage heuristics (MCH) for target coverage problem in Wireless Sensor Network. In Proceedings of 2014 IEEE International Advance Computing Conference (IACC); 2014; p. 300-305. Chu XY, Sethu H. An Energy Balanced dynamic Topology Control algorithm for improved network lifetime. In: IEEE 10th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob); 2014; p. 556-561. Gong DW, Zhao M, Yang YY. Topology Control and Channel Assignment in Lossy Wireless Sensor Networks. In Proceedings of the 23th International Teletraffic Congress; 2011; p. 222-229. Hao XC, Dou JJ, Liu B. Path-Loss Based Distributed Topology Control Algorithm for Wireless Sensor Networks. Journal of Software, 2009; 20(12):3213-3222. Hao XC, Liu WJ, Xin MJ, Yao N, Ru XY. Energy balance and robustness adjustable topology control algorithm for wireless sensor networks. Acta Phys. Sin. 2015; 64(8):080101. Lee YD, Jeong DU, Hwang GH, Lee HJ. Wireless link quality based measurement for wireless sensor networks. In Proceedings of 2011 6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT); 2011; p. 558-561. Li FM, Liu XH, Kuang HL, Fang YL. Research on a stable clustering algorithm based on the optimal connectivity power for wireless sensor networks. J Commun, 2009, 30(3): 75-83. Li RE, Carmen B. System level performance metrics in mobile wireless communication networks considering both resource insufficiency and link unreliability. In Proceedings of 50th Annual IEEE Global Telecommunications Conference; 2007; p. 2612-2616. Liu B, Dong MR, Liu HR, Yin RR, Han L. A scale-free fault tolerant topology model in wireless sensor network for toleration of comprehensive fault. Acta Phys. Sin 2014; 63(17):170506. Luo NX, Bao J. A Topology Control Algorithm Based on Pass Loss for Wireless Sensor Network. Applied Mechanics and Materials 2013; 347: 677-681. Mamun IM, Hasan-Al-Mahmud T, Debnath SK, Islam MZ. Analyzing the Low Power Wireless Links for Wireless Sensor Networks. J Telecommun, 2010; 1(1):123-127. Olariu S, Stojmenovic I. Design Guidelines for Maximizing Lifetime and Avoiding Energy Holes in Sensor Networks with Uniform Distribution and Uniform Reporting. INFOCOM; 2006. p. 1-12. Paolo S. Topology Control in Wireless Ad Hoc and Sensor Networks. ACM Computing Surveys. 2015;

37(2):164-194. Qin Y, He Z, Voigt T. Towards accurate and agile link quality estimation in wireless sensor networks. In Proceedings of The 10th IFIP Annual Mediterranean Ad Hoc Networking Workshop (Med-Hoc-Net); 2011; p. 179-185. Sahoo PK, Sheu JP, Hsieh KY. Power control based topology construction for the distributed wireless sensor networks. Comput. Commun. 2007; 30(14):2774-2785. Salarian H, Chin KW, Naghdy F. An energy-efficient mobile-sink path selection strategy for wireless sensor networks. IEEE T Veh. Technol. 2014; 63(5): 2407-2419. Watfa MK, Al-Hassanieh H, Salmen S. A novel solution to the energy hole problem in sensor networks. J Netw Comput Appl, 2013; 36(2): 949-958. Younis M, Senturk IF, Akkaya K, Lee S, Sensl F. Topology management techniques for tolerating node failures in wireless sensor networks: A survey. Computer Networks, 2014; 58:254-283. Yu DX, Hua QS, Wang YX, Tan HS Lau FCM. Distributed multiple-message broadcast in wireless ad hoc networks under the SINR model. Theor Comput Sci. 2014.

Highlights   

A model that represents bi-directional link communication quality is proposed. The link weight can lessen energy waste, and increase the network throughput. The algorithm relies on high quality of all the links in network.

Graphical abstract

Distributed Topology Construction Algorithm to Improve Link Quality and Energy Efficiency for Wireless Sensor Networks Xiaochen Hao *, v3(29J) v1(30J)

v10(21J)

v5(6J) v4(27J)

v6(29J)

(a)

v3(29J) v1(30J)

v9(28J)

v2(28J)

v4(27J) v8(9J)

v7(24J)

Weijing Liu , Ning Yao , Dehua Geng , Xida Li

v10(21J)

v5(6J) v2(28J)

v6(29J)

v7(24J)

v3(29J) v1(30J) v10(21J)

v4(27J)

v2(28J)

v6(29J)

(c)

v10(21J)

v5(6J)

v5(6J)

v9(28J)

v8(9J)

(b)

v3(29J) v1(30J)

v9(28J)

v8(9J) v7(24J)

v4(27J)

v9(28J)

v2(28J)

v6(29J)

v8(9J) v7(24J)

(d)

Figure. 1 The different topology (a) The topology with the maximal power; (b) The topology constructed according to the link quality; (c) The topology constructed according to the surplus energy; (d) The topology synthesizing the link quality and the surplus energy

The above figures show the problem of the poor link quality and energy consumption. We provide a new valuable model, called the link weight model, to address the problem of the poor link quality and energy consumption. The link weight model combines the link quality with nodes’ energy to reduce the interference and make the network energy balanced. Then exploiting the method of function derivation, we validate the analytical solution of this model. On the basis of this forwarding model, a distributed topology construction algorithm to improve link quality and energy efficiency (ILQEE) is proposed.