A Delay-Aware Data Collection Network Structure for ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. IEEE SENSORS JOURNAL, VOL. XX, NO. Y, MONTH 2010

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A Delay-Aware Data Collection Network Structure for Wireless Sensor Networks Chi-Tsun Cheng, Member, IEEE, Chi K. Tse, Fellow, IEEE, and Francis C. M. Lau, Senior Member, IEEE

Abstract— Wireless sensor networks utilize large numbers of wireless sensor nodes to collect information from their sensing terrain. Wireless sensor nodes are battery-powered devices. Energy saving is always crucial to the lifetime of a wireless sensor network. Recently, many algorithms are proposed to tackle the energy saving problem in wireless sensor networks. In these algorithms, however, data collection efficiency is usually compromised in return for gaining longer network lifetime. There are strong needs to develop wireless sensor networks algorithms with optimization priorities biased to aspects besides energy saving. In this paper, a delay-aware data collection network structure for wireless sensor networks is proposed. The objective of the proposed network structure is to minimize delays in the data collection processes of wireless sensor networks. Two network formation algorithms are designed to construct the proposed network structure in a centralized and a decentralized approach. Performances of the proposed network structure are evaluated using computer simulations. Simulation results show that, when comparing with other common network structures in wireless sensor networks, the proposed network structure is able to shorten the delays in the data collection process significantly. Index Terms— Networks, topology, optimization methods, centralized control, distributed control.

I. I NTRODUCTION TRONG adaptability, comprehensive sensing coverage, and high fault tolerance are some of the unique advantages of wireless sensor networks. Wireless sensor networks consist of large amounts of wireless sensor nodes, which are compact, light-weighted, and battery-powered devices that can be used in virtually any environment. Because of these special characteristics, sensor nodes are usually deployed near the targets of interest in order to do close-range sensing. The data collected will undergo in-network processes and then return to the user who is usually located in a remote site. Most of the time, wireless sensor nodes are located in extreme environments, where are too hostile for maintenance. Sensor nodes must conserve their scarce energy by all means and stay active in order to maintain the required sensing coverage of the environment. Much prior work has focused on conserving energy by clustering. A network with clustering is divided into several clusters. Within each cluster, one of the sensor nodes is

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Manuscript received July 26, 2010. This work was supported by The Hong Kong Polytechnic University under internal grant G-YF51. C. T. Cheng is with the Department of Electrical and Computer Engineering, The University of Calgary, Canada. (Email: [email protected]) C. K. Tse and F. C. M. Lau are with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong. (Email: [encktse,encmlau]@polyu.edu.hk) Digital Object Identifier xx.xxxx/xxx.2010.xxxxxx

elected as a cluster head (CH) and with the rest being cluster members (CM). The cluster head will collect data from its cluster members directly or in a multi-hop manner. By organizing wireless sensor nodes into clusters, energy dissipation is reduced by decreasing the number of nodes involved in long distance transmission [1]. The number of data transmissions and energy consumption can be further reduced by performing data/decision fusion on nodes along the data aggregation path. Clustering provides a significant improvement in energy saving. In sensor networks with cluster, it is common for a cluster head to collect data from its cluster members one by one. Let T be the average transmission delay among nodes. Data packets generated by sensor nodes are considered as highly correlated, and thus a node is always capable of fusing all received packets into a single packet by means of data/decision fusion techniques [2], [3]. Referring to the situation shown in Fig. 1 (a), a base station will take 4 × T to collect a complete set of data from the network. By transforming the network into a multi-hop network as shown in Fig. 1 (b), it can be shown that the time needed by the base station to collect a full set of data from the network can be reduced to 3×T . In the modified network, apart from requiring a shorter delay in data collection, cluster members will need smaller buffers to handle the incoming data while waiting for the belonging cluster head to become available. The aim of this paper is to investigate the characteristics of a delay-aware data collection network structure in wireless sensor networks. Two algorithms for forming such a network structure are proposed for different scenarios. The proposed algorithms are operating between the data link layer and the network layer. The algorithms will form networks with minimum delays in the data collection process. At the same time, the algorithms will try to keep the transmission distance among wireless sensor nodes at low values in order to limit the amount of energy consumed in communications. The rest of the paper is organized as follows. Section II briefly reviews related work.

BS

T=4

CH

T=1 CM

(a)

T=3

CM

T=2

BS

T=3

CH

T=1 CM

CM

T=2

CM

T=1 CM

(b)

Fig. 1. (a) Data collection in a 2-hop network and (b) data collection in an improved multi-hop network. Circles with CM represent the cluster members. Circles with CH represent the cluster heads. Filled circles with BS represent the base stations. A dashed arrow represents the existence of a data link and the direction of the arrow shows the direction of data flow.

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Section III defines the proposed network structure. Section IV explains the algorithm for forming the proposed network structure in different scenarios. A numerical analysis is given in Section V to show how different network structures perform in terms of delays in data collection processes. Simulation results and their analysis will be given in Sections VI and VII, respectively. Finally, the paper is concluded in Section VIII. II. R ELATED W ORK Due to the energy constraint of individual sensor nodes, energy conservation becomes one of the major issues in sensor networks. In wireless sensor networks, a large portion of the energy in a node is consumed in wireless communications. The amount of energy consumed in a transmission is proportional to the corresponding communication distance. Therefore, long distance communications between nodes and the base station are usually not encouraged. One way to reduce energy consumption in sensor networks is to adopt a clustering algorithm [1]. A clustering algorithm tries to organize sensor nodes into clusters. Within each cluster, one node is elected as the cluster head. The cluster head is responsible for 1) collecting data from its cluster members, 2) fusing the data by means of data/decision fusion techniques, and 3) reporting the fused data to the remote base station. In each cluster, the cluster head is the only node involved in long distance communications. Energy consumption of the whole network is therefore reduced. Intensive research [2], [3], [4], [5] has been conducted on reducing energy consumption by forming clusters with appropriate network structures. Heinzelman et al. proposed a clustering algorithm called LEACH [2]. In networks using LEACH, sensor nodes are organized in multiple-cluster 2-hop (MC2H) networks (i.e., cluster members → cluster head → base station). Using the idea of clustering, the amount of long distance transmissions can be greatly reduced. Lindsey and Raghavendra proposed another clustering algorithm called PEGASIS [3], which is a completely different idea by organizing sensor nodes into a single-chain (SC) network. In such networks, a single node on the chain is selected as the cluster head. By minimizing the number of cluster heads, the energy consumed in long distance transmission is further minimized. Tan and Körpeoˆ glu developed PEDAP [4], which is based on the idea of a minimum spanning tree (MST). Besides minimizing the amount of long distance transmission, the communication distances among sensor nodes are minimized. Fonseca et al. proposed the collection tree protocol (CTP) [5]. The CTP is a kind of gradient based routing protocol which uses expected transmissions (ETX) as its routing gradient. ETX is the number of expected transmissions of a packet necessary for it to be received without error [6]. Paths with low ETX are expected to have high throughput. Nodes in a network using CTP will always pick a route with the lowest ETX. In general, the ETX of a path is proportional to the corresponding path length [7]. Thus, CTP can greatly reduce the communication distances among sensor nodes. All these algorithms show promising results in energy saving. However, a network formed by an energy efficient clustering

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algorithm may not necessarily be desirable for data collection. An analysis on how these network structures perform in terms of data collection efficiency will be given in Section V. The focus of this paper is on investigating the data collection efficiency of networks formed by different clustering algorithms. Therefore, event triggering algorithms such as TEEN [8] and APTEEN [9] will not be considered in this paper. A related work on data collection efficiency was done by Florens et al. [10]. In their work, lower bounds on data collection time are derived for various network structures. However, the effect of data fusion, which is believed as one of the major features of sensor networks, was not considered. Wang et al. [11] proposed link scheduling algorithms for wireless sensor networks which can raise network throughput considerably. In their work, however, it is assumed that data links among wireless sensor nodes are predefined. In contrast, the objective of this paper is to form data links among wireless sensor nodes and thus to shorten the delays in the data collection processes. Another related work was done by Solis and Obraczka [12] who studied the impact of timing in data aggregation for sensor networks. Chen et al. [13] investigated the effects of network capacity under different network structures and routing strategies. A similar work was done by Song and He [14]. In their work, the term capacity is defined as the maximum end-to-end traffic that a network can handle. The delay in a data collection process is not their major concern. III. T HE P ROPOSED N ETWORK S TRUCTURE The proposed network structure is a tree structure. To deliver the maximum data collection efficiency, the number of nodes N in the proposed network structure has to be restricted to N = 2p , where p = 1, 2, · · · . It will be shown in a later part that such restriction can be relaxed by giving up some performance. Each cluster member will be given a rank, which is an integer between 1 and p. A node with rank k will form k − 1 data links with k − 1 nodes, while these k − 1 nodes are with different ranks starting from 1, 2, · · · up to k − 1. All these k − 1 nodes will become the child nodes of the node with rank k. The node with rank k will form a data link with a node with a higher rank. This higher rank node will become the parent node of the node with rank k. The cluster head will be considered as a special case. The cluster head is the one with the highest rank in the network. Instead of forming a data link with a node of higher rank, the cluster head will form data link with the base station. By following this logic, the distribution of the rank will follow an inverse exponential base-2 function, as shown in Table I. An example of the proposed network with N = 16 is shown in Fig. 2. In this example, it takes 5 × T for the base station to collect all data from 16 nodes. By dividing the time domain TABLE I C LUSTER MEMBERS ’ RANK DISTRIBUTION IN THE PROPOSED NETWORK STRUCTURE WITH NETWORK SIZE

Rank No. of nodes

1

2

N 21

N 22

··· ···

N = 2p , WHERE p = 1, 2, · · · . log2 N − 1

log2 N

N

N 2(log2 N )

2(log2 N −1)



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1, 2, · · · . Through adopting the proposed network structure, the cluster head is the only node with the highest ranking which is

BS

T=5 CH k=5

kmax = log2 N + 1

T=3 CM k=1

CM k=2

CM k=3

CM k=1

CM k=1

CM k=2

CM k=4

T=3

T=2 CM k=1

CM k=2

T=1 CM k 1 k=1

From Lemma 1, the number of time slots t(N ) required for a cluster head, with rank kmax , to collect data from all its child nodes is

CM k=3

T=2 CM k 1 k=1

CM k 1 k=1

CM k 2 k=2

T=1 CM k=1

Fig. 2. Proposed network structure with network size N = 16. Circles with CM represent the cluster members. Circle with CH represents the cluster head. Filled circle with BS represents the base station. Rank of each node is represented by the variable k. A dashed arrow represents the existence of a data link and the direction of the arrow shows the direction of data flow.

into time slots of durations T , the above process will last for 5 time slots. Lemma 1: Consider a network with N = 2p , where p = 1, 2, · · · . Data packets generated by sensor nodes are considered as highly correlated, and thus a node is always capable of fusing all received packets into a single packet by means of data/decision fusion techniques. Through adopting the proposed network structure, a node i of rank k ≥ 2 (where k ∈ Z) requires k − 1 time slots to collect data from all its child nodes. Proof: Consider a network with N = 2p , where p = 1, 2, · · · . For a node of rank k = 2, the time slots required for it to collect data from all its child nodes is equal to the number of child nodes it has, which is 1. Thus the case for k = 2 is true. Now let us assume that any node of connection k = n requires n − 1 time slots to collect all data from its child nodes. For node i of rank k = n + 1, it has n directly connected child nodes. Each of these directly connected child nodes has different ranks ranging from 1 to n. Thus, they need 0 to n − 1 time slots to collect data from all their sub-child nodes plus one extra time slot to report their aggregated data to node i. Therefore, the maximum time slots required for node i to collect data from all its child nodes is k − 1 = n. By induction, the Lemma is proved. Theorem 1: Consider a network with N = 2p , where p = 1, 2, · · · . Data packets generated by sensor nodes are considered as highly correlated, and thus a node is always capable of fusing all received packets into a single packet by means of data/decision fusion techniques. By adopting the proposed network structure, the number of time slots t(N ) required for the base station to collect data from the whole network is given by t(N ) = log2 N + 1 (1) Proof: Consider a network with N = 2p , where p =

t(N )

= kmax − 1 = log2 N

Thus, the number of time slots t(N ) required for the base station to collect data from the whole network is the time slots required by the cluster head to collect data from all its child nodes plus one, i.e., t(N ) = log2 N + 1

IV. N ETWORK F ORMATION A LGORITHM It has been proven in the last section that the delay in the data collection process of a wireless sensor network can be greatly reduced by adopting the proposed network structure. Since energy consumption is always a major issue in the study of wireless sensor networks, the objective of the proposed network formation algorithms is, therefore, to achieve the proposed network structure while keeping the energy consumption in the data collection process at low value. A wireless sensor node can be considered as a device built up of three major units, namely the micro-controller unit (MCU), the transceiver unit (TCR), and the sensor board (SB). Each of these units will consume a certain amount of energy while operating. The energy consumed by a wireless sensor node i can be expressed as Ei SN = Ei MCU + Ei TCR + Ei SB

(2)

where Ei MCU represents the energy consumed by the MCU, Ei TCR represents the energy consumed by the TCR, and Ei SB represents the energy consumed by the SB. Here, Ei TCR can be further expressed as Ei TCR = Ei TCR RX + Ei TCR TX (di )

(3)

where Ei TCR RX denotes the energy consumed by the TCR in receiving mode, while Ei TCR TX (di ) denotes the energy consumed by the TCR to transmit for a distance of di . The total energy consumed by a network of N sensor nodes is expressed as ETOT (N ) =

PN

i=1 Ei MCU + Ei TCRRX +Ei TCR TX (di ) + Ei SB

(4)

Normally, Ei MCU , Ei TCR , and Ei TCR RX are constants. On the other hand, Ei TCR TX (di ) is a function of di which is heavily depending on the network structure. Therefore, (4) can be simplified as follow ETOT (N ) = C1 +

N X

Ei TCR TX (di )

(5)

i=1



4

where C1 is a constant. Assume that the path loss exponent is equal to 2, Ei TCR TX (di ) can be further expressed as Ei TCR TX (di ) = Ei TCR EC + Ei TCR PA d2i

(6)

where Ei TCR EC is the energy consumed by the TCR’s electronic circuitry, while Ei TCR PA denotes the energy consumed by the power amplifier of the TCR. Both Ei TCR EC and Ei TCR PA are constants and therefore, (5) can be expressed as

A fully connected network of N node (N4). These N nodes form a set ƨs=1. Set b=N/2. Select b nodes from set ƨs to form set Hs+1 such that the total edge weight within set Hs+1 is maximized. The rest in ƨs form ƨs+1 . Cut all connections among nodes in set Hs+1 . Set b=b/2 and s=s+1 b N-r form set U. Reduce connections among nodes between set L and U until each node in set L is only connected to a single node in set U. Set r=r×2. r=N?

No

Fig. 3. Network formation of the proposed network structure using centralized top-down approach (N ≥ 4).

4) Nodes with degree N −r form set L. Nodes with degree greater than N − r form set U such that set L and set U are of the same number of nodes. Connections among nodes in the two sets are reduced until each node in set L is only connected to a single node in set U . Here, data links are removed according to their distance. Details of the optimization method are given in the later part of this section. After reducing the number of connections, set r←r × 2. 5) Repeat step 4 until r = N . The 2 nodes belonging to the last set U of step 4 are having the highest connection degree among the nodes in the network. ˆs These 2 nodes are in fact the nodes belonging to the set H in step 2, when b = 1 < 2. Since these nodes are from ˆ s generated from step 2, they have not gone the last set H through the intra-connection removal process. Therefore, these 2 nodes are inter-connected with each other. Because of this, the connection degrees of these 2 nodes are always higher than the others. As a result, these two nodes are always included in the set U in step 4. By the end of step 4, each of these 2 nodes will have directly connected child nodes with unique rankings, provided that the rankings of the child nodes are lower than the 2 nodes. These 2 nodes are, therefore, with connection degrees equal to log2 (N ). Among these 2 nodes, the one which is located closer to the base station will be selected as the cluster head and be connected directly to the base station. Therefore the cluster head will have a degree of log2 N + 1 which is the highest within the cluster. Notice that the connection degree of a node is in fact denoting its rank. By substituting “connection degree” with “rank”, the proposed network structure is achieved. According to the definition of the proposed network structure, half of the sensor nodes (i.e. N/2) in the network will have connection degrees equal to 1. In addition, a quarter of the sensor nodes (i.e. N/4) will have connection degrees equal



to 2. The pattern goes on and follows the trend as shown in Table I. Except for the nodes with degree log2 (N ), no node in the proposed network structure will connect to another node with the same connection degree. Therefore, if a set of nodes are selected to have the same connection degree, all edges among these nodes must be removed. Nevertheless, in order to reduce the total communication distance in the final network structure, the length of the edges to be removed should be maximized. In the proposed top-down approach, the selection of nodes to have the same connection degree is done by the procedures in step 1 and the removal of edges among those selected nodes is done by the procedures in step 2. The procedure in step 2 is in fact the heaviest k-subgraph problem defined in [15]. The heaviest k-subgraph problem is to find the k-vertex subgraph out of a given graph, such that the total weight of edges among these k vertexes is maximized. In this paper, the weight of an edge (data link) connecting any two vertexes (nodes) i and j (wireless sensor nodes) is defined as d2ij , where dij is the geographical distance between nodes i and j. The proposed algorithm can always be modified to accommodate different cost metrics by redefining the edge weights. The problem is a kind of combinatorial problem which is defined as NP-complete. Dynamic programming is commonly used to solve combinatorial problem [16] and thus it is used to solve the heaviest k-subgraph problem in this paper. ˆs For each iteration of step 2, half of the nodes from set H are selected to form set Hs+1 . The remaining nodes will form ˆ s+1 . After the selection, all connections among the nodes set H in set Hs+1 will be removed. Therefore, in step 2, a larger set of Hs+1 will yield nodes with lower connection degrees, and ˆ s are selected vice versa. As half of the nodes from set H in each iterations of step 2, the number of nodes with degree N −r and the number of nodes with degree greater than N −r are always equal in step 4. Note that the proposed network structure is a tree-based network. In a tree-based network, a child node will connect itself to one parent node only (i.e. a node with higher rank in our case). Step 1 and step 2 of the proposed top-down approach will only remove edges among nodes which are selected to have the same connection degree. Therefore, from the outcomes of step 2, a child node will be connected with more than one parent node. In the proposed top-down approach, step 3 and step 4 are designed to remove excess edges from the child nodes, provided that the total weight of the remaining edges are minimized. By the end of step 4, each child node will be connected to one parent node only. The nodes involved in the optimization in step 4 will form a distance matrix with each entry storing the distance between two nodes. The x-axis is representing the nodes from set L while the y-axis is representing the nodes from set U . The two sets of nodes therefore form a bipartite graph and the optimization problem becomes a weighted matching problem. This problem can be optimized by applying matching techniques such as Hungarian Method [17], [18] or Munkres’ Assignment Algorithm [19]. In this paper, Munkres’ Assignment Algorithm is used to solve the weighted matching problem.

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For networks with number of nodes other than N = 2p , where p = 1, 2 · · · , dummy nodes are virtually added in the calculation process to expand the network in order to fulfill the network size requirement of the algorithm. These dummy nodes will have infinite separations with the real nodes and have infinite separations among themselves. The number of dummy nodes will always be smaller than N/2. At the end of the optimization process, these dummy nodes will all have degree (rank) of 1 which can be ignored and removed without partitioning the network. Since the condition N = 2p , where p = 1, 2 · · · is fulfilled during the network formation, Lemma 1 and Theorem 1 still applied. Thus, the time slots required for complete data collection will still be governed by equation (1), provided that the number of nodes N in equation (1) is replaced by the number of real nodes Nr plus the number of dummy nodes Nd . In general, equation (1) can be written as t(N )

= log2 (Nr + Nd ) + 1 = ⌈log2 Nr ⌉ + 1

(8)

where ⌈u⌉ denotes the nearest integer larger than u. Note that the top-down approach is mainly designed for sensor nodes with communication distance long enough to cover the whole sensing terrain. For scenarios where the diagonal of the sensing terrain is larger than the maximum communication distance of a node, the top-down approach can still be applied by arranging the terrain into multiple sub-regions and performing the top-down approach to each sub-region. Example 1: The following example will show how the proposed network structure can be constructed by using the top-down approach. 1) Consider a network with N = 8 (see Fig. 4(i)). The topdown approach begins with a fully connected network with N ≥ 4. In the current example, N is equal to 8. Therefore, all nodes are with connection degree equal to ˆ s , where s = 1 (i.e. 7. These 8 nodes will form a set H ˆ 1 ). Now define parameter b = N = 4. H 2 ˆ s (i.e. H ˆ 1 ) to form set 2) Select b = 4 nodes from set H Hs+1 (i.e. H2 ) such that the total edge weight within set H2 is maximized. This combinational problem is solved using dynamic programming. In this example, the total edge weight among nodes C, D, E, and F is the highest. Therefore nodes C, D, E, and F will form the set H2 . The rest of the nodes, i.e. nodes A, B, G, and H will form ˆ s+1 (i.e. H ˆ 2 ). Cut all connections among nodes in set H set H2 (see Fig. 4(ii)). Set b to 2b (i.e. b = 2) and set s to s + 1 (i.e. s = 2). 3) Since b = 2 ≥ 2, the previous step is repeated. Select ˆ s (i.e. H ˆ 2 ) to form set Hs+1 b = 2 nodes from set H (i.e. H3 ) such that the total edge weight within set H3 is maximized. Since the total edge weight between nodes A, H, and that between nodes B, G are the highest, one out of the 2 pairs is randomly selected to be the set H3 . In this example, nodes A and H are selected as the set H3 . The rest of the nodes, nodes B and G, will form set ˆ s+1 (i.e. H ˆ 3 ). Cut all connections among nodes in set H H3 (see Fig. 4(iii)). Set b to 2b (i.e. b = 1) and set s to s + 1 (i.e. s = 3).



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B.S.

A(7)

B.S.

B(7)

A(7)

B.S.

B(7)

A(6)

B(7)

C(7)

D(7)

C(4)

D(4)

C(4)

D(4)

E(7)

F(7)

E(4)

F(4)

E(4)

F(4)

G(7)

H(7)

G(7)

H(7)

G(7)

(i)

B.S.

A(5)

H(6)

(ii)

(iii)

B.S.

B(6)

A(2)

B.S.

B(3)

A(2)

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C(4)

D(4)

C(1)

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F(1)

E(1)

F(1)

G(6)

H(5)

G(3) (iv)

H(2)

G(3) (v)

H(2) (vi)

Fig. 4. An example of the top-down approach with N =8. Sensor nodes are represented by circles and the base station (B.S.) is represented by a rectangle. Each node is assigned with a unique letter for identification purpose. The numbers in the brackets represent the connection degrees of the nodes.

4) With b = 1 < 2, the algorithm proceeds and defines parameter r = 2. Nodes with degree equal to N − r = 6 (i.e. nodes A and H) form set L. Nodes with degree > N − r (i.e. nodes B and G) form set U . Reduce connections among nodes between set L and U until each node in set L is only connected to a single node in set U , provided that the total edge weight is minimized (see Fig. 4(iv)). The weighted matching problem is solved by Munkres’ Assignment Algorithm. Set parameter r to 2r (i.e. r = 4). 5) Since r = 4 < N , the previous step is repeated. Nodes with degree equal N − r = 4 (i.e. nodes C, D, E, and F) form set L. Nodes with degree > N − r (i.e. nodes A, B, G, and H) form set U . Reduce connections among nodes between set L and U until each node in set L is only connected to a single node in set U , provided that the total edge weight is minimized (see Fig. 4(v)). Set parameter r to 2r (i.e. r = 8). 6) When r = 8 = N , the basic operation of the proposed top-down approach is completed. The resultant network will now consist of 2 nodes with degree log2 (N ) = 3 (i.e. nodes B and G) which are connected together. Among these 2 nodes, the one which is located closer to the base station (i.e. node B) will be selected as the cluster head and be connected directly to the base station. Including the connection with the base station, the cluster head (i.e. node B) will now have a connection degree of log2 (N ) + 1 = 4 (see Fig. 4(vi)).

B. Bottom-Up Approach Basically, the operation of the bottom-up approach is to join clusters of the same size together. The bottom-up approach is, when comparing with the top-down approach, more scalable. It can be implemented in either centralized or decentralized fashion. Specifically, a decentralized bottom-up approach can be described as follows. 1) Each node is labeled with a unique identity and marked as level w. The unique identity will only serve as an identification which has no relation with sensor nodes’ locations and connections. Here, w is a function which represents the number of nodes in a cluster. For a cluster of i nodes, its w value is equal to log2 i. Since nodes are disconnected initially (i.e. no data link exists among wireless sensor nodes), these N nodes can be considered as N level–0 clusters. Within each cluster, one node will be elected as the sub-cluster head. We denote SCH(w) as a sub-cluster head of a level–w cluster. In the bottom-up approach, a SCH can only make connection (i.e. setup a data link) with another SCH of the same level. Because there is only 1 node in each cluster, all nodes begin as SCH(0). The dimensions of the terrain (tx , ty ) are provided to the sensor nodes before deployment. 2) Each SCH performs random back-off and then broadcasts a density probing packet (DPP) to its neighboring 1 SCHs which are within a distance of rdp = (t2x +t2y ) 2 m. Note that the size of a DPP is much smaller than that of a data packet. A SCH can use the number of received DPP, together with the dimensions of the terrain, to estimate the total number of nodes (Nest ) in the network. A SCH will use the Nest to adjust its communication distance



3)

4)

5)

6)

7) In rcom

7

rcom . Definition of rcom will be explained in the later part of this section. Each SCH will do a random back off and then broadcast an invitation packet (IVP) to its neighbors within rcom m. The IVP contains the level w and the identity of the issuing SCH. A SCH will estimate the distances to its neighboring SCHs using the received signal strength of the IVPs received. A SCH will also count the number of IVPs received. If the number of IVPs received has exceeded a predefined threshold or a maximum duration has been reached, a SCH will send a connection request (CR) to this nearest neighbor. If both SCHs are the nearest neighbor of each other, a connection will be formed between these 2 SCHs. Once they are connected, the two SCHs and their belonging level-w clusters will form a composite levelw+1 cluster. One of the two involved SCHs will become the chief SCH of the composite cluster. The chief SCH will listen to the communication channel and reply any CR from lower levels with a rejecting packet (RP). When no more CR from lower levels can be heard, the chief SCH will start to make connection with other SCHs of the same level. If a RP is received, a SCH will send a CR to its next nearest neighbor in its database. If such neighbor does not exist, the SCH will increase its rcom . The SCH will then broadcast a CR using the new rcom . Upon receiving the CR, a SCH of the same level will grant the request if it is still waiting for a CR. If no connection can be made within a period of time, either all neighbors of the same level are unavailable or all CRs have been rejected, the SCH will increase its rcom and broadcast q the CR again. This process repeats q 2 2 2 as long as rcom < tx + ty . If rcom = tx + t2y , the SCH will make connection with the base station directly. The above processes continue until no more connection can be formed. the bottom-up approach, the communication distance is defined as √2 2 tx +ty (9) rcom = α−β−w , β+w 0|N ∈ Z, the minimum number of time slots required for a base station to collect data from N nodes is t(N )min = ⌈log2 N ⌉ + 1

(14)

From Theorem 1 and equation (8), it can be shown that the proposed network structure is an optimum network structure in terms of data collection efficiency provided that 1) each sensor node can only communicate with one sensor node at a time, 2) data fusion can be carried out at every sensor node, and 3) sensor nodes are belonging to a single cluster with a single cluster head. The same idea can be applied to multiple-cluster network by considering the base station as the root of the network structure. Therefore, in multiple-cluster networks, the minimum number of time slots required for a base station to collect data from N nodes is t(N )min = ⌈log2 (N + 1)⌉

(15)

Using equation (12), it can be shown that the proposed network structure is again an optimum network structure in terms of data collection efficiency provided that 1) each sensor node can only communicate with one sensor node at a time, 2) data fusion can be carried out at every sensor node, and 3) the network consists of multiple clusters. In a MC2HP network with N nodes organized in g clusters, g where N ≥ m=1 m, the time slots required by the base station to collect data from all sensor nodes is minimized when all clusters have different numbers of nodes. Therefore, each cluster can communicate with the base station interleavingly. Meanwhile, the number of nodes in the largest cluster should be minimized such that the total number of time slots required by the base station is also minimized. An example for g = 2 is shown below. Example 2: For a MC2H network of N nodes organized in 2 clusters (where N ≥ 3), in order to achieve the maximum data collection efficiency, the number of nodes in these 2 clusters should be equal to N 2

N +1 2

and N 2−1 , + 1 and N2 − 1,

for N odd for N even

(16)

The minimum number of time slots t(N )min required by the base station to collect data from all sensor nodes is equal to

the number of nodes in the largest cluster. Therefore, N +1 2 , N is odd (17) t(N )min = N + 1, N is even 2 In general, for a MC2H Pgnetwork of N nodes organized in g clusters, where N ≥ m=1 m, the number of nodes in the j th cluster can be written as N − Sg + (j − 1)(g + 1) + 1, j = 1, 2, 3, · · · , g (18) g where ⌊u⌋ denotes the nearest integer smaller than u and Sg = P g m=1 m. Thus, the minimum number of time slots t(N )min required by the base station to collect data from all sensor nodes is equal to N − Sg + (g − 1)(g + 1) t(N )min = + 1. (19) g Based on (18), the optimum number of clusters gopt for a MC2H network in terms of data collection efficiency can be obtained from the following inequality: (1 + g)g 2

≥

⇒

g

≥

⇒

gopt

=

N

√ 12 + 8N 2 & ' √ −1 + 12 + 8N 2 −1 +

(20) (21)

where N is the number of nodes in the network, and g is the number of clusters. Theorem 3: For a MC2H network of N nodes organized in g clusters of completely different sizes, where g ≤ N < Sg . The minimum number of time slots t(N )min required by the base station to collect data from all sensor nodes is equal to the number of clusters in the system, i.e., g. Proof: Consider the extreme case, which a MC2H network of N nodes is organized in g clusters of completely different sizes, where N = Sg . These g clusters will all have different numbers of nodes ranging from 1 to g. The minimum number of time slots t(N )min required by the base station to collect data from all sensor nodes is equal to the number of nodes in the largest cluster, which is g. Suppose one node has to be removed from the network such that N is reduced to N − 1. To maintain the number of clusters in the network, this particular node must be removed from one of the clusters except the one with a single node. Removing a node from any of the clusters will cause two clusters to have the same number of nodes. During a data collection process, the 2 clusters of the same size will have to do interleaving, which will not affect t(N )min . Therefore, the minimum number of time slots t(N )min required by the base station is always equal to the number of clusters in the system. In contrast, for a MC2H network with N nodes organized in g clusters, where N ≥ g, the number of time slots required by the base station to collect data from all sensor nodes is maximized when N − (g − 1) nodes are belonging to the same cluster. The remaining g − 1 clusters will all have a cluster



size of 1, and we have  N − (g − 1),  N − (g − 1) + 1, t(N )max =  g,

9

Averaged data collecting time (lower the better) 70

N > 2(g − 1) N = 2(g − 1) otherwise

Proposed (Top−Down) Proposed (Bottom−Up) Single Cluster 2−Hop Single Chain Minimum Spanning Tree Collection Tree

60

(22)

50

where N is the number of nodes in the network. On the contrary, in a SC network, the number of time slots required by the base station to collect data from all sensor nodes is maximized when the cluster head is at the end of the chain, i.e., t(N )max = N (24)

time slots

In a SC network, the number of time slots required by the base station to collect data from all sensor nodes is minimized when the cluster head is at the middle of the chain, i.e., N +1 2 + 1, N is odd (23) t(N )min = N 2 , N is even

40 30 20 10 0 0

10

20

30 40 50 number of sensor nodes ( N )

60

70

Fig. 5. Averaged data collection time of different single tree structures. Note that results obtained from the proposed algorithm using the top-down approach are overlapping with those obtained from the bottom-up approach.

where N is the number of nodes in the network. In networks using MST and CTP, the number of time slots required by the base station to collect data from all sensor nodes is lower bounded by equations (13) and (14). On the other hand, the number of time slots required by the base station to collect data from all sensor nodes is maximized when the resultant networks of MST and CTP are in single cluster 2-hop structure which is upper bounded by t(N )max = N .

Averaged ψ (lower the better)

4

3.5

x 10

3

ψ (m2)

2.5

Proposed (Top−Down) Proposed (Bottom−Up) Single Cluster 2−Hop Single Chain Minimum Spanning Tree Collection Tree

2 1.5 1

VI. S IMULATIONS

0.5

ψ=

N X i=1

ui dhi B +

N −1 X

N X

cij dhij

(25)

i=1 j=i+1

where ui is an indicator to indicate cluster heads (ui =1) and cluster members (ui =0). Parameter di B is the distance between a cluster head and the base station. Here, cij is an indicator to indicate the presence (cij =1) or absence (cij =0)

0 0

Fig. 6.

10

20


60

70

Averaged ψ of different single tree structures. Averaged lifetime (higher the better) 400 number of data collection processes (rounds)

In this section, the proposed network structure will be compared with a MC2H network, a SC network, a MST network, and a CTP network. Networks having N nodes with N varying from 4 to 64, with a step size of 4, will be distributed randomly and evenly on a sensing field of 50 × 50 m2 . The center of the sensing field is located at (x, y) = (25 m, 25 m). In the simulations, synchronization among wireless sensor nodes are maintained by the physical layer and the data link layer. Wireless sensor nodes are assumed to be equipped with CDMA-based transceivers [20]. Interference due to parallel transmissions can be alleviated by utilizing different spreading sequences in different data links. Media access control during network formation is handled by the MAC sub-layer and is assumed to be satisfactory. A node can either receive or transmit at any time. In the simulation, a wireless sensor node is always capable of fusing all received packets into a single packet by means of data/decision fusion techniques and the size of an aggregated packet is independent to the number of packets received. For each network, the averaged data collection time (DCT) will be used to indicate its data collection efficiency. The communication distance of a network is represented by the following function:

300 250 200 150 100 50 0 0

Fig. 7.

Proposed (Top−down) Proposed (Bottom−up) Single Cluster 2−Hop Single Chain Minimun Spanning Tree Collection Tree

350

10

20


60

70

Averaged lifetime of different single tree structures.

of a data link between node i and node j. Furthermore, dij is the geographical distance between nodes i and j. In the simulations, the path loss exponent h is assumed to be 2. The base station is assumed to be at the center of the sensing field (i.e., x = 25 m, y = 25 m). For the simulations on network lifetime, each node is given 50 J of energy. The energy model of the wireless sensor nodes is the same as the one introduced in Section IV. A network will perform the data collection process periodically. The lifetime

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10

TABLE II VALUES OF PARAMETERS USED IN THE SIMULATIONS Values Parameters Ei TCR RX 50 × 10−6 J/bit Ei TCR EC 50 × 10−6 J/bit Ei TCR PA 100 × 10−9 J/bit/m2 Ei MCU 5 × 10−6 J/bit Ei SB 50 × 10−6 J/bit pdata 1024 bits pctrl 64 bits

Averaged data collecting time (lower the better) 14

Proposed (Bottom−Up) Multiple Clusters 2−hop

12

time slots

10

8

6

4

2 0

10

20


60

70

Fig. 8. Averaged data collection time of different multiple-cluster structures. Averaged ψ (lower the better) 10000 9000


8000

ψ (m2)

7000 6000 5000 4000 3000 2000 1000 0

Fig. 9.

10

20


60

70

Averaged ψ of different multiple-cluster structures. Averaged lifetime (higher the better) 400 number of data collection processes (rounds)

of a network is defined as the number of data collection processes (in terms of rounds) that a network can accomplish before any of its nodes runs out of energy. Each data packet is pdata bits long. Other packets are all regarded as control packets. Each control packet is pctrl bits long. Values of the parameters used in the energy model are shown in Table II. The network structures under test are classified into two types: Type I) single-cluster network structure; Type II) multiple-cluster network structure. Under this classification, all structures under test belong to Type I, whereas MC2H and the proposed network structure belong to both types. Note that as the number of clusters in Type I and Type II network structures are different, results obtained by different types of network structures should not be compared directly. For the proposed network structure to work as a Type I structure, either the top-down or the bottom-up approach can be applied provided that sufficient dummy nodes are added. To work as a Type II structure, the proposed network structure can only be constructed by the bottom-up approach without adding any dummy node. The cluster number of the MC2H network is fixed to 1 when it works as a Type I structure. Here, ψ of the MC2H network is minimized by selecting the node with minimum separations from its fellow nodes as the cluster head. To work as a Type II structure, cluster heads in the MC2H networks are selected in a random manner as given in [2], while the optimum number of cluster heads is selected according to equation (21). In both configurations, cluster members are connected to their nearest cluster head. The SC network can only work as a Type I structure, and the chain is formed by using a greedy algorithm as given in [3]. To minimize DCT, the node closest to the middle of the chain (in terms of hops) will be selected as the cluster head. Similar to the SC network, the MST network can only work as a Type I structure. Networks will be formed by using the Prim’s algorithm as given in [4]. To minimize DCT, the node with the smallest separation (in terms of hops) to all leaf nodes will be selected as the cluster head. In networks using CTP, the node closest to the center of the sensing terrain is regarded as the root of the collection tree. The ETX of a path is expressed as the squared value of the path length [6]. The root of the tree will have an ETX of 0. The ETX of an arbitrary node is the cumulated ETX from it, through its parent nodes, to the root [5]. Each node will choose its best route by selecting the path with the minimum cumulated ETX. Simulation results are shown in Figs. 5–10. All results presented in this paper are averaged over 100 simulations.

300 250 200 150 100 50 0

Fig. 10.


350

10

20


60

70

Averaged lifetime of different multiple-cluster structures.

VII. A NALYSIS As expected in Section V, the DCT of networks with the proposed network structure is the lowest among Type I structures. In simulations among the six Type I structures, DCT of networks with the proposed network structure is the lowest, followed by networks with CTP. Since the aim of the MST is to minimize the total weight of edges, it does not perform well in reducing bottleneck and therefore it ranks fourth. In a SC network, it takes a very long time for data to propagate from both ends of the chain to the cluster head at

Copyright (c) 2010 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs−[email protected].


the middle. This explains why SC networks have much higher DCT than networks with the proposed network structure. With the single cluster 2-hop structure, the networks with MC2H structure do not have any advantage in reducing DCT. The MC2H network is the one with the highest DCT among Type I structures. In terms of minimizing ψ, the MST network no doubt ranks first. The ETX used in network with CTP can greatly reduce the communication distances among sensor nodes and make it ranks second. Nodes in networks with SC structure try to reduce the total communication distance by connecting to their nearest neighbors only. The strategy is effective for network with small number of nodes. However, to maintain a single-chain structure, it is unavoidable for the SC network to increase its ψ as the number of nodes increases. The SC network therefore ranks third. Using the optimization techniques employed in Section IV, the ψ of networks constructed using the proposed top-down or bottom-up approach does not increase drastically as N increases and they ranks fourth and fifth. When N ≤ 56, the performance of the top-down approach in terms of ψ is better than that of the bottomup approach. However, as N further increases, the top-down approach is outperformed by the bottom-up approach. This is because all the optimization techniques employed in the top-down approach are carried out individually. Although all the optimization techniques will provide optimum solutions, there is lack of a global optimization method. This makes the top-down approach more effective for small-scale networks, but at the same time, it is more prone to be trapped in local optimum points as the network density increases. Therefore, the top-down and the bottom-up approaches are recommended for low density and high density networks, respectively. With all sensor nodes connected to a single cluster head, the MC2H network is the structure with the highest ψ without question. In a data collection process, a node with connection degree k is required to receive k − 1 data packets, perform k − 1 times of data fusion, and transmit 1 data packet. A node with a high connection degree will certainly consume more energy that one with a low connection degree. Therefore, a network which has a uniform connection degree distribution is more likely to yield a longer network lifetime than one with a non-uniform connection degree distribution. The minimum spanning property of a MST network can make the connection degree evenly distributed among nodes. Therefore, the MST network can achieve the highest network lifetime for networks with N > 4. In a SC network, as most of the nodes are having connection degrees equal to 2, the energy consumed by each node in receiving and fusing data is relatively low. Therefore, the SC network ranks second. Similar to the simulations on the ψ, network lifetime of networks with CTP, the proposed topdown approach, and the proposed bottom-up approach rank third, fourth, and fifth, respectively. In a SC2H network, all cluster members are connected to a single cluster head. The cluster head is heavily loaded and has a very high energy consumption, which explain why a SC2H network has the lowest network lifetime among all network structures under test. In simulations of the two Type II structures, networks

11

formed by the proposed algorithm are shown to have the lowest DCT. Although the networks with MC2H structure have been tuned to give the optimum number of clusters, there is no control on the distribution of sensor nodes in each cluster. The DCT of networks with MC2H structure therefore greatly increases as N increases. For the same reason, network lifetime of networks with MC2H structure decreases gradually as N increases.In terms of ψ, both the proposed and the MC2H network structures give similar results when N ≤ 12. For N > 12, networks constructed by the proposed algorithm have lower ψ than those constructed in MC2H structure. The gap increases further as N increases. According to (21), a MC2H network is most efficient if there are gopt clusters, where gopt is proportional to N . As N increases, gopt increases and thus more nodes are involved in long distance transmissions. The same thing happens to networks constructed by the proposed algorithm. Nevertheless, due to the special topology of the proposed network structure, the number of clusters increases at a lower rate. This explains why ψ of networks formed by the proposed algorithm is lower than those constructed in MC2H structure. This also explains why networks formed by the proposed algorithm can obtain a longer network lifetime than those constructed with the MC2H structure. VIII. C ONCLUSIONS In this paper, a delay-aware data collection network structure and its formation algorithms are proposed. To cater for different applications, network formation can be implemented in either centralized or decentralized manner. Two network formation approaches are derived to provide optimized results for networks with different sizes. The performance of the proposed network structure is compared with a multiple-cluster 2-hop network structure, a single-chain network structure, a minimum spanning tree network structure, and a collection tree network structure. The proposed network structure is shown to be the most efficient in terms of data collection time among all the network structures mentioned above. The proposed network structure can greatly reduce the data collection time while keeping the total communication distance and the network lifetime at acceptable values. R EFERENCES [1] J. N. Al-karaki and A. E. Kamal, “Routing techniques in wireless sensor networks: a survey,” IEEE Wireless Communications Mag., vol. 11, no. 6, pp. 6–28, December 2004. [2] W. B. Heinzelman, A. P. Chandrakasan, and H. Balakrishnan, “An application-specific protocol architecture for wireless microsensor networks,” IEEE Trans. Wireless Communications, vol. 1, no. 4, pp. 660– 670, October 2002. [3] S. Lindsey and C. S. Raghavendra, “PEGASIS: Power-efficient gathering in sensor information systems,” in Proc. IEEE Conf. Aerospace, vol. 3, Big Sky, Montana, USA, March 2002, pp. 1125–1130. ¨ Tan and Í. Körpeoˆglu, “Power efficient data gathering and ag[4] H. O. gregation in wireless sensor networks,” ACM SIGMOD Record, vol. 32, no. 4, pp. 66–71, December 2003. [5] R. Fonseca, O. Gnawali, K. Jamieson, S. Kim, P. Levis, and A. Woo, “The collection tree protocol,” TinyOS Enhancement Proposals (TEP) 123, December 2007. [6] D. S. J. D. Couto, “High-throughput routing for multi-hop wireless networks,” Ph.D. dissertation, Dept. Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Massachusetts, USA, June 2004.



[7] O. Tekdas, J. H. Lim, A. Terzis, and V. Isler, “Using mobile robots to harvest data from sensor fields,” IEEE Wireless Communications Mag., vol. 16, no. 1, pp. 22–28, February 2009. [8] A. Manjeshwar and D. P. Agrawal, “TEEN: a routing protocol for enhanced efficiency in wireless sensor networks,” in Proc. 15th Int. Symp. Parallel and Distributed Processing, (IPDPS 2001), San Francisco, California, USA, April 2001, pp. 2009–2015. [9] A. Manjeshwar and D. P. Agrawal, “APTEEN: a hybird protocol for efficient routing and comprehensive information retrieval in wireless sensor networks,” in Proc. 16th Int. Symp. Parallel and Distributed Processing, (IPDPS 2002), Fort Lauderdale, Florida, USA, April 2002, pp. 195–202. [10] C. Florens, M. Franceschetti, and R. J. McEliece, “Lower bounds on data collection time in sensory networks,” IEEE Jour. Selected Areas in Communications, vol. 22, no. 6, pp. 1110–1120, August 2004. [11] W. Wang, Y. Wang, X.-Y. Li, W.-Z. Song, and O. Frieder, “Efficient interference-aware TDMA link scheduling for static wireless networks,” in Proc. 12th Annual Int. Conf. Mobile Computing and Networking, (MobiCom’06), Los Angeles, California, USA, September 2006, pp. 262–273. [12] I. Solis and K. Obraczka, “The impact of timing in data aggregation for sensor networks,” in Proc. IEEE Int. Conf. Communications, vol. 6, Paris, France, June 2004, pp. 3640–3645. [13] Z. Y. Chen and X. F. Wang, “Effects of network structure and routing strategy on network capacity,” Phys. Rev. E, vol. 73, no. 3, pp. (036 107) 1–5, March 2006. [14] M. Song and B. He, “Capacity analysis for flat and clustered wireless sensor networks,” in Proc. Int. Conf. Wireless Algorithms, Systems and Applications, (WASA 2007), Chicago, Illinois, USA, August 2007, pp. 249–253. [15] A. Billionnet, “Different formulations for solving the heaviest ksubgraph problem,” Information Systems and Operational Research, vol. 43, no. 3, pp. 171–186, August 2005. [16] S. M. Roberts and B. Flores, “Solution of a combinatorial problem by dynamic programming,” Operations Research, vol. 13, no. 1, pp. 146– 157, January 1965. [17] H. W. Kuhn, “The Hungarian method for the assignment problem,” Naval Research Logistics, vol. 52, no. 1, pp. 7–21, February 2005. [18] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. New York: Dover Publications INC., 1998. [19] J. Munkres, “Algorithms for assignment and transportation problems,” Jour. Society for Industrial and Applied Mathematics, vol. 5, no. 1, pp. 32–38, March 1957. [20] CC2520. Texas Instruments Incorporated. [Online]. Available: http://focus.ti.com/lit/ds/symlink/cc2520.pdf

Chi-Tsun Cheng (S’07–M’09) received the BEng and MSc degrees from the University of Hong Kong, Hong Kong, China, in 2004 and 2005, respectively. He received the PhD degree from the Hong Kong Polytechnic University, Hong Kong, China, in 2009. During his studies, he was the recipient of the Sir Edward Youde Memorial Fellowship. From January 2010, Dr. Cheng is a Postdoctoral Fellow with the Department of Electrical and Computer Engineering, the University of Calgary, Alberta, Canada. He is involved in a GEOIDE project, which is supported by the Government of Canada through the Networks of Centres of Excellence programs. His research interests include wireless sensor networks, bio-inspired computing, and meta-heuristic algorithms.

12

Chi K. Tse (M’90–SM’97–F’06) received the BEng (Hons) degree with first class honors in electrical engineering and the PhD degree from the University of Melbourne, Australia, in 1987 and 1991, respectively. He is presently Chair Professor and Head of Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong. His research interests include power electronics, complex networks and nonlinear systems. He is the author of Linear Circuit Analysis (London, U.K.: Addison-Wesley 1998) and Complex Behavior of Switching Power Converters (Boca Raton: CRC Press, 2003), co-author of Chaos-Based Digital Communication Systems (Heidelberg, Germany: Springer-Verlag, 2003), Chaotic Signal Reconstruction with Applications to Chaos-Based Communications (Singapore: World Scientific, 2007) and Sliding Mode Control of Switching Power Converters: Techniques and Implementation (Roca Raton: CRC Press, 2010), and co-holder of 2 US patents and 2 other pending patents. Dr. Tse was awarded the L.R. East Prize by the Institution of Engineers, Australia, in 1987, the IEEE T RANSACTIONS ON P OWER E LECTRONICS Prize Paper Award in 2001, and the International Journal of Circuit Theory and Applications Best Paper Award in 2003. In 2007, he was awarded the Distinguished International Research Fellowship by the University of Calgary, Canada. In 2009, he and his co-inventors won the Gold Medal with Jury’s Commendation at the International Exhibition of Inventions of Geneva, Switzerland, for a novel driving technique for LEDs. In 2010, he was appointed the Chang Jiang Scholar Chair Professorship by the Ministry of Education of China and the appointment is hosted by Huazhong University of Science and Technology, Wuhan, China. Currently, Dr. Tse serves as Deputy Editor-in-Chief for the IEEE Circuits and Systems Magazine and Editor-in-Chief of IEEE Circuits and Systems Society Newsletter. He was/is an Associate Editor for the IEEE T RANSACTIONS ON C IRCUITS AND S YSTEMS PART I from 1999 to 2001 and again from 2007 to 2009. He has also been an Associate Editor for IEEE T RANSACTIONS ON P OWER E LECTRONICS since 1999. He is an Associate Editor of the International Journal of Systems Science, and also on the Editorial Boards of the International Journal of Circuit Theory and Applications and International Journal and Bifurcation and Chaos. He also served as Guest Editor and Guest Associate Editor for a number of special issues in various journals.

Francis C.M. Lau (M’93–SM’03) received the BEng (Hons) degree with first class honors in electrical and electronic engineering and the PhD degree from King’s College London, University of London, UK, in 1989 and 1993, respectively. He is an Associate Professor and Associate Head at the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong. He is the co-author of ChaosBased Digital Communication Systems (Heidelberg: Springer-Verlag, 2003) and Digital Communications with Chaos: Multiple Access Techniques and Performance Evaluation (Oxford: Elsevier, 2007). He is also a co-holder of one US patent and two pending US patents. His main research interests include channel coding, cooperative networks, wireless sensor networks, chaos-based digital communications, applications of complex-network theories, and wireless communications. He served as an associate editor for IEEE Transactions on Circuits and Systems II in 2004–2005 and IEEE Transactions on Circuits and Systems I in 2006–2007. He was also an associate editor of Dynamics of Continuous, Discrete and Impulsive Systems, Series B from 2004 to 2007 and was a coguest editor of Circuits, Systems and Signal Processing for the special issue “Applications of Chaos in Communications” in 2005. He is currently a guest associate editor of International Journal and Bifurcation and Chaos.
