A collaborative multi-hop routing algorithm for maximum achievable rate

A collaborative multi-hop routing algorithm for maximum achievable rate

Author's Accepted Manuscript A Collaborative Multi-hop Routing Algorithm for Maximum Achievable Rate Dingde Jiang, Zhengzheng Xu, Wenqin Wang, Yuanti...

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Author's Accepted Manuscript

A Collaborative Multi-hop Routing Algorithm for Maximum Achievable Rate Dingde Jiang, Zhengzheng Xu, Wenqin Wang, Yuanting Wang, Yang Han

www.elsevier.com/locate/jnca

PII: DOI: Reference:

S1084-8045(15)00135-6 http://dx.doi.org/10.1016/j.jnca.2015.06.010 YJNCA1417

To appear in:

Journal of Network and Computer Applications

Received date: 27 May 2014 Revised date: 29 March 2015 Accepted date: 1 June 2015 Cite this article as: Dingde Jiang, Zhengzheng Xu, Wenqin Wang, Yuanting Wang, Yang Han, A Collaborative Multi-hop Routing Algorithm for Maximum Achievable Rate, Journal of Network and Computer Applications, http://dx.doi.org/ 10.1016/j.jnca.2015.06.010 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.

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A Collaborative Multi-hop Routing Algorithm for Maximum Achievable Rate Dingde Jiang, Zhengzheng Xu, Wenqin Wang, Yuanting Wang, and Yang Han, Abstract—This paper studies collaborative multi-hop communication technology in next generation wireless communications. We propose a collaborative multi-hop routing algorithm combined with clustering to improve network performance. To build the multi-hop routing with maximum achievable rate, a relation matrix is exploited to describe the possible coverage of network nodes. Clustering-based path strategy is presented to create the effective next-hop link. Collaboration strategy is proposed to construct collaborative matrix. And then by clustering and collaboration, a multi-hop routing with maximum achievable rate is successfully built. The effectiveness and feasibility of the proposed methods are verified by simulation results. Index Terms—achievable rate; collaborative routing; optimal path; multi-hop networks; collaborative communication



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I NTRODUCTION

Collaborative multi-hop routing has received much attention due to its importance for performance improvement. Mathematical modeling and branch-andcut framework are often used to jointly optimize relay node assignment and flow routing for cooperative communications in multi-hop networks [1,2]. In [3], the routing and scheduling methods of optimal throughputs in multi-hop wireless networks are investigated, and some routing policies of optimal throughputs are proposed. Collaborative relaying schemes are presented in [4] to achieve the cooperative diversity of the physical layer. A hybrid multi-hop routing algorithm via mixing flat multi-hop routing and hierarchical multi-hop routing is studied [5]. Additionally, the feasibility and impacts of the multi-hop routing on sensor networks are analyzed in [6]. Therefore, to achieve better performance improvement, it is necessary to introduce collaboration to the multi-hop routing, but how to build effectively collaborative multi-hop routing is an open problem. To solve this problem, Jung et al. used linear programming to optimize a cooperative routing in multihop wireless sensor networks [7]. They found out some important factors and behaviors for achieving the optimal cooperative routing [8]. Kwon et al. studied the energy-efficient routing problem in multi-hop wireless networks, and proposed an energy-efficient routing scheme by considering transmission power, interference, remaining energy, and energy replen• D. Jiang, Y. Wang, and Y. Han are with the College of Information Science and Engineering, Northeastern University, Shenyang, China, 110819 . Corresponding author: D. Jiang, E-mail: [email protected] • Z. Xu is with the School of Economics and Management, Anqing Normal University, Anqing, China, 246011. • W. Wang is with the Department of Electronic Engineering, City University of Hong Kong.

ishment [9]. Tang et al. investigated the availability and stability of links in multi-hop and multi-flow mobile ad hoc cognitive networks, and proposed a cross-layer distributed approach to improve network throughput using mobility prediction [10]. Liang et al. studied how to choose candidate nodes and how to determine the prioritization metric about them for the opportunistic routing in multi-hop wireless mesh networks, and then presented the cooperative opportunistic routing [11]. Gohari et al. studied the endto-end delay estimation in mobile multi-hop wireless networks [12]. Liu et al. proposed a second-order distributed Newton’s method to design the joint multipath routing and perform flow control [13]. Yue et al. studied the coding-aware routing metric in multi-hop wireless networks [14]. Bhattacharjee et al. proposed an energy efficient routing algorithm to balance data traffic among network nodes and improve network lifetime [15]. Additionally, Tao et al. presented a flow-balanced routing protocol for multi-hop clustered wireless sensor networks to achieve power efficiency and coverage preservation [16]. Ong et al. studied the routing in cooperative multiple- terminal wireless networks and proposed an algorithm to construct optimal routes [17]. Rondinone et al. exploited a multihop connectivity metric to estimate the capability of forwarding paths and proposed a contention-based broadcast forwarding protocol to select forwarding paths [18]. Wong et al. proposed a distributed greedy algorithm to attain maximum gain cost ratio for each node [19]. Kuo et al. proposed a multi-hop multicast routing scheme for wireless multi-hop relay networks [20]. Ranjitkar et al. presented a collaborative routing protocol to help relaying nodes without employing forward data packets [21]. Zhang et al. proposed an analytical model of network throughput to consider traffic demands of clients [22]. Chen et al. analyzed the energy balance problem of cooperative routing

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and proposed a routing scheme to balance the energy among nodes and attain the maximum network lifetime [23]. James et al. proposed an adaptive rate transmission scheme to optimize network throughput [24]. Lakshmanan et al. proposed an adaptive diversity routing protocol to determine the cooperating node number for each link and the corresponding cooperation strategy [25]. Nordio et al. presented several analytical bounds to the achievable data rate for nodes’ full-duplex and half-duplex radios [26]. Dynamic spectrum access problem for multi-hop networks [27] and networks’ energy efficiency [28-29] were also researched. This paper proposes a collaborative multi-hop routing algorithm with maximum achievable rate to raise the performance of next generation wireless networks. Firstly, we analyze the system model including transmission model of nodes and multi-hop transmission model with collaboration. Our problem can be mathematically modeled as as an optimization problem. Next, a relation matrix is defined to describe the possible coverage of network nodes. We cluster network nodes to include possible collaborative nodes, and then build possible paths from source node to destination node. A clustering-based path strategy is presented to build the neighbor node matrix and create the effective next-hop link. A clustering path algorithm is proposed to create the multi-hop path set from source node to destination node. Next, a collaborative strategy is proposed to create the collaborative matrix, where the optimal object is to maximize the maximum achievable rate. By calculating the maximum achievable rate of each path in the path set, the path with maximum achievable rate is selected to construct the optimal path set. In doing so, we can find the shortest path with the maximum achievable rate. Finally, a collaborative multi-hop routing with the maximum achievable rate is successfully built by clustering and collaboration. The rest of this paper is organized as follows. Section 2 is the system model and problem statement. Section 3 is to derive our collaborative method. Section 4 is simulation analysis. Finally, our work is concluded in Section 5.

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S YSTEM

cv T uv

cu Fig. 1. Transmission model of nodes. shown in Fig. 1 where cu and cv denote, respectively. The transmission and receiving nodes with omnidirectional antennas, duv is the distance from cu to cv , and θuv denotes the effective receiving angle of cv to receive the cu ’s signal. According to the wireless communication theory, in the wireless network in Fig. 1, there exist many statistically independent reflection and scattering paths for channel filter taps. The kth tap hk [m] follows the cyclic symmetry Gaussian distribution with the zero mean value and variance ζk . Generally, due to the dense barriers such as building in a city, there is not the line of sight between the sending node and receiving node. Thereby, the kth tap’s module y = |hk [m]| is well described with Rayleigh distribution and its density function can be denoted as: pk (y) =

In this section, we discuss the network model of this paper, including transmission model of nodes and multi-hop transmission model.

pk (x) =

y≥0

(1)

1 x exp(− 2 ) 2 ζk 2ζk

x≥0

(2)

Accordingly, according to the wireless communication theory, the transmission channel can be modeled into the Rayleigh Fading channel. For the Rayleigh Fading channel, the channel gain from node cu to node cv can be expressed as: guv =

1 (duv )

α

(3)

where α is the path loss exponent and generally holds the value from 2 to 4. The received power of node cv can then be represented by: Pvr = Pus × guv = Pus × (duv )−α

2.1 Transmission model of nodes In multi-hop wireless networks, to attain link or path rate as large as possible, the achievable rates of nodes or paths need to be maximized. To reach this aim, we employ the transmission model of nodes

y y2 exp(− 2 ) 2 ζk 2ζk

And the x = hk [m]2 meets the exponential distribution, namely:

MODEL AND PROBLEM STATE -

MENT

d uv

Pus

(4)

where denotes the transmitting power of node cu . Only when the Signal-to-Interference and Noise Ratio (SINR) of the receiver exceeds a certain threshold, the receiving node can correctly receive the signal, namely

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ci = |Ci | represents the number of collaborative nodes for transmission node pi , and i = 1, 2, ..., n − 1. The transmission model of node pi to node pi+1 in the path P can then be expressed as:

C3 C1 R4

s

R2 R1 C2

⎧ r r PC,pi+1 + PR,p  I i+1 ⎪ ⎪ ≥ PR,p + ⎪ i+1 ⎪ δpi+1 ⎨  I PC,pi+1 + ηpi+1 ⎪ ci ⎪  ⎪ r r ⎪ = Pj,p ⎩ PC,p i+1 i+1

d R3

C4

(7)

j=1

r Pj,p i+1

Fig. 2. Multi-hop transmission model.

δv ≤

Pvr ηv + ϕv

(5)

where ηv is the noise power, and ϕv indicates the interference power. Therefore, to achieve the communication between nodes cu and cv , the transmission power of cu should be Pus

δv × (ηv + ϕv ) ≥ guv = δv × (ηv + ϕv ) × (duv )α

(6)

2.2 Multi-hop transmission model To build an effective multi-hop routing, clustering and collaboration are used in the multi-hop transmission model, as shown in Fig. 2 where the network nodes are randomly distributed in the wireless network, the solid and dot lines denote the relaying and collaborative paths, respectively, R1 , R2 , R3 , and R4 are relaying nodes, C1 , C2 , C3 , and C4 are collaborative nodes, s and d, respectively, denotes source and destination nodes. The multi-hop transmission is exploited to build the feasible path from source node to destination node . Each node in Fig. 2 sends and receives signals using the omni-directional antenna. Without loss of generality, for the multi-hop transmission model indicated in Fig. 2, we assume that there are k nodes S = {1, 2, 3, ..., k} in the multi-hop wireless network, with interference between nodes being taken into account. If the transmission power of nodes meets the constraints in Equation (4), they can build a reliable communication. Here we only consider one pair of source and destination nodes to communicate each other in a certain period. We define P = {p1 , p2 , ..., pn } as the path from source node p1 to destination node pn , where R = {p2 , p3 , ..., pn1 } denotes the relaying node set. Additionally, we also define Ci = {ci1 , ci2 , ...., cici } as the collaborative node set of transmission node pi in the path P , where

where denotes the received power of node r is the repi+1 from collaborative node cij , PR,p i+1 ceived power from node Pi ,  δpi+1 represents the I SINR threshold at node pi+1 , PR,p stands for i+1 the interference from the nodes in the path P except  I denotes the interference from other node pi , PC,p i+1 collaborative nodes except the nodes in Ci , and ηpi+1 is the noise at node pi+1 . Similarly, for collaborative node cij , the transmission model from node pi to node cij can be represented by: Pcrij δcij





I PR,,c + ij



I PC,c + ηcij ij

(8)

where Pcrij denotes the received power of collaborative node cij from node pi , δcij represents  I the SINR threshold at collaborative node cij , PR,cij is the interference from the nodes in the path P except node  I Pcij denotes the interference from other collabpi , orative nodes, and ηcij is the noise at collaborative node cij . 2.3

Multi-hop routing problem

In multi-hop wireless networks, the channel changes over time due to the impact of channel fading. Therefore, network node should transmit the most data in the shortest time. How to build effective multi-hop routing with maximum achievable rate is a challenge. As shown in Fig. 2, we exploit the collaboration to improve the forwarding performance from source node to destination node. For the possible path P = {p1 , p2 , ..., pn } from source node p1 to destination node pn , to achieve maximum achievable rate from p1 to pn , we exploit other nodes as many as possible to help the path P to complete the packet forwarding. This can be denoted as the following optimal problem with constraints: ⎧ max τ ⎪ ⎪ ⎨ s.t. δ¯cij ≥ δcij , ∀cij ∈ Ci , i = 1, 2, ..., n − 1 ⎪ ⎪ ⎩ δ¯pi+1 ≥ δpi+1 , ∀pi+1 ∈ P, i = 1, 2, ..., n − 1

(9)

where τ denotes the transmission rate from p1 to pn along with the path P , δ¯cij represents the SINR at collaborative node cij , δ¯pi+1 stands for the SINR at

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node Pi+1 , δ¯pi+1 and δ¯cij , respectively, are determined by Equations (7) and (8). By solving the above optimization, we can build the collaborative multi-hop routing with maximum achievable rate from source node p1 to destination node pn .

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O UR

COLLABORATIVE METHOD

To build an effective collaborative multi-hop routing, different from traditional collaborative transmission methods, the as many as possible nodes are to be exploited to complete the packet forwarding from source node to destination node. Moreover, the path performance can be improved by clustering network nodes. In the following, we discuss the maximum achievable rate of nodes and paths, clustering collaboration path, and shortest optimal path, respectively. 3.1 Maximum achievable rate To measure the maximum achievable rate of nodes and paths, we use information theory to characterize it as in [17]. Without loss of generality, for node pi+1 in the path P = {p1 , p2 , ..., pn } from source node p1 to destination node pn , its achievable rate [17] can be defined as: 1 βpi+1 (δ¯pi+1 ) = log(1 + δ¯pi+1 ) (10) 2 where i = 1, 2, ..., n − 1, δ¯pi+1 denotes the SINR at node pi+1 . According to (7), the objective function in Equation (9) can be converted into: βpi+1 (δ¯pi+1 ) =

1 2

log(1+ r r + PR,p PC,p i+1  I i+1  I ) PR,pi+1 + PC,pi+1 + ηpi+1

(11)

{βp2 (δ¯p2 ), βp3 (δ¯p3 ), .., βpn (δ¯pn )}

(12)

It can be observed from (11)-(12) that to attain maximum achievable rate of nodes and paths, the SINR should be maximized at node pi+1 where i = 1, 2, ..., n − 1. The optimization problem in Equation (9) can be formulized as: ⎧ max βpi+1 (δ¯pi+1 ) ⎪ ⎪ ⎨ s.t. δ¯cij ≥ δcij , ∀cij ∈ Ci , i = 1, 2, ..., n − 1 ⎪ ⎪ ⎩ δ¯pi+1 ≥ δpi+1 , ∀pi+1 ∈ P, i = 1, 2, ..., n − 1

(13)

While considering (12), the optimal problem can be further modeled as

(14)

By solving (13)-(14), we can achieve the maximum achievable rate of nodes and paths. To resolve (13)(14), we should maximize the received signal power of node and minimize its received noise and interference power. Hence, the nodes as many as possible should take part in the collaboration with source and relaying nodes to complete packet forwarding from source node to destination node. Different from the general multi-hop communication (5)-(6), we exploit the collaboration to turn the interference signal from other nodes outside the path P into a useful signal for the path P , so as to enhance the receive SINR . To attain maximum achievable rate, we use a relation matrix to describe the collaborative and neighbor relations between nodes. The relation matrix can be expressed as: ⎛

··· ··· .. .

a1,2 a2,2 .. .

a1,1 a2,1 .. .

⎜ ⎜ ⎜ Π=⎜ ⎜ ⎝ ak−1,1 ak,1

··· ···

ak−1,2 ak,2

a1,k−1 a2,k−1 .. .

a1,k a2,k .. .

ak−1,k−1 ak,k−1

ak−1,k ak,k

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (15)

with

ai,j =

For the path P = {p1 , p2 , ..., pn } from source node p1 to destination node pn , its achievable rate [17] can be defined as: βP = min

⎧ max βP ⎪ ⎪ ⎨ s.t. δ¯cij ≥ δcij , ∀cij ∈ Ci , i = 1, 2, ..., n − 1 ⎪ ⎪ ⎩ δ¯pi+1 ≥ δpi+1 , ∀pi+1 ∈ P, i = 1, 2, ..., n − 1

1, 0,

δ¯ij ≥ δij δ¯ij < δij

i, j ∈ {1, 2..., k}

(16)

where aij describes the relationship between nodes i and j; aij = 1 indicates that node j can help node i as a collaborative node deliver data packets, or it can not; δ¯ij and δij , denote, respectively, the SINR and SINR threshold of node j to receive the signal from node i. The row i of Π denotes which nodes can be covered by node i, while the column j denotes that node j can receive the signal from that nodes. If ai,j = 1, node j is in the coverage of node i. In this case, node j can act as a collaborative and neighbor node of node i. Otherwise, it can not serve as collaborative and neighbor node of node i. For the possible path P = {p1 , p2 , ..., pn } , the maximum received power of its node pi+1 is Ppri+1 ,max

=

k 

r (ah,pi+1 × Ph,p ) i+1

(17)

h=1 r where r represents the receiving signal, Ph,p dei+1 notes the power received by node pi+1 in the path P from node h, h = 1, 2, ..., k.

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nodes. If the next hop node is in the path from source node to current node, the path holds a loop, and the path is removed from the link, as shown in Fig. 4. In Fig. 4, the node n8 is source node and node n7 is neighbor node of node n4 . According to Strategy 3.21, a new path from source node n8 to neighbor node n7 is built, namely Pn7 = {n8 , n9 , n7 , n6 , n4 , n7 } . The path {n7 , n6 , n4 , n7 } constructs a loop in the path Pn7 , which is indicated with the red arrow line in Fig. 4. Hence, we should delete the path Pn7 from possible path set with node n8 as source node according to Strategy 3.2-2. Strategy 3.2-1 can let as many nodes as possible take part in the collaboration process, while Strategy 3.2-2 can effectively avoid the path loop. Different from the existing methods, by covering as large area as possible, Strategies 3.2-1 and 3.2-2 seek more nodes to construct the energy-efficient collaboration transmission. At the same time, they can guarantee the effective communication from source node to all destination nodes. By performing the above process step by step, we can obtain the set of the paths from source node to destination node. This process can be summarized in Algorithm 3.1. Therefore, we can build all the achievable paths from source node cs to destination node cd , namely creating the path set P . 3.3

Fig. 4. Removing the path with loop.

3.2 Clustering path Although (17) gives the possible maximum received power at node pi+1 , it is very difficult to attain. Let as many nodes as possible help node pi+1 to receive the useful signal. In this case, node pi+1 can receive the signal power as much as possible and thus maximum achievable rate from node pi to node pi+1 can be obtained. We propose the following clustering-based path strategies: Strategy 3.2-1: Each node uses its maximum transmission power to establish its coverage. All other nodes in this coverage act as the neighbor nodes of this node, as shown in Fig. 3. In Fig. 3, the nodes n4 and n9 use their possible maximum transmission power to cover the neighbor nodes as many as possible. The neighbor nodes of node n4 include nodes n1 , n2 , n3 , n5 , n6 , n7 , and n15 , while the neighbor nodes of node n9 are nodes n7 , n15 , n20 , n14 , n8 , n10 , and n11 . The corresponding columns of relation matrix Π can be ascertained. Strategy 3.2-2: Begin with the source node, build the next hop links to all neighbor nodes according to neighbor matrix step by step, and then construct all the paths from source node to all current neighbor

Optimal collaboration path

For the path set P constructed in the above section, some paths do not achieve the maximum achievable rate of paths. So, we further use collaboration to raise the received power of each node using the following collaboration strategies: Strategy 3.3-1: Choose the node located in the semicircle in Fig. 5 as collaborative nodes. In such a case, the transmission power of collaborative nodes is generally lower than that of transmission node. This is helpful to reduce the interference between nodes. Strategy 3.3-2: Based on Strategy 3.3-1, collaborative node can perform multi-hop collaboration shown in Fig. 6. The node n9 can not only help node n15 to forward data packets, but also collaborate node n 14 to complete packet delivery. Strategy 3.3-1 can effectively send data packets via the lower transmission power and decrease the interference among nodes; Strategy 3.3-2 can implement multi-hop collaboration and further reduce the transmission power of nodes, and then this is helpful to attain the larger energy efficiency of networks. Using Strategies 3.3-1 and 3.3-2, we can use (11) to calculate the achievable rate of each node. At the same time, we use (12) to attain the achievable rate of each path from source node to destination node. Then we choose from the path set P the paths with the achievable path rate to construct the optimal path set Pa with maximum achievable path rate. To construct the optimal and

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Algorithm 3.1 Input: S = {c1 , c2 , ..., ck }; % all the nodes % where cs ∈ S and cd ∈ S are, respectively, source % node and destination node. Output: P (pathset) Run procedure: % Construct relation matrix Π = (πc1 , πc2 , ..., πck ) ; % Attain neighbor node matrix B = (Bc1 , Bc2 , ..., Bck ) ; % where Bci = {ci,1+k , ci,2+k , ..., ci,ni +k } denotes % neighbor node matrix of node i and % ci,z (z = 1 + k, 2 + k, ..., kj + k) is node cz % corresponding to ai,z = 1. Step 3: Let j = 1 and k = 0; Step 4: Select source node c s ; % Find the cs ’s neighbor node matrix Bcs = {ci,1+k , ci,2+k , ..., ci,kj +k }; % Build new link set Lj = {L1+k , L2+k , ..., Lkj +k }; % where L1+k = {cs , ci,1+k } , % L2+k = {cs , ci,2+k }, ..., and Lkj +k = {cs , ci,kj +k } Let k = kj + k , j = j + 1; If j ≤ ni−1 do Choose cs = ci−1,j ; goto Step 4; End If % Build the link set L = {L1 , L2 , ..., Lni−1 }; ni = k; Combine path set P and link set L; % Construct new path set For z = 1 to ni do Pz = {cs , c11 , ..., ciz }; End For P = {P1 , P2 , ..., Pni }; % Find the connections from source node % to other nodes from P . G = φ; Place the connections from source node to other nodes into G; If G == φ do i = i + 1; goto Step 3; End If For z = 1 to ni do Find destination node zd of path Pz ; If Pz ∈ P & cd ∈ Pz & cd = zd do Remain the links from cs to cd ; Remove other link in path Pz ; End IF End For Update the path set P ; For z = 1 to ni do Find destination node zd of path Pz ; If cd = zd do

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Fig. 6. Multi-hop collaboration. Delete path Pz from path set P ; End IF End For Update the path set P ; Output path set P ; % attain the final path set P End effective path from source node and destination node, we remove the nodes of the paths in Pa to build the path as short as possible. Hence, the shortest and optimal path set Po is satisfied with the following conditions: Condition #1: P i ∈ Pa , for ∀Pi ∈ Po , i = 1, 2, ..., |Po |; Condition #2: |P i | = min{|P1 |, |P2 |, ..., |P|P | |}, for ∀Pi ∈ Po , i = 1, 2, ..., |Po |; Condition #3: VPi = max{VP1 , VP2 , ..., VP|P | } , for ∀Pi ∈ Po , i = 1, 2, ..., |Po |. For the paths in the shortest optimal path set Po , they may be not shortest and do not achieve the maximum achievable rate. Because the last node of the receiving node is removed, this node can probably take as the collaborative node of the receiving node in terms of clustering and collaboration. Thus this can raise the achievable rate of the receiving node

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and further shorten the hops from source node and destination node. Finally, the shortest and optimal path needed can be attained. The detailed process can be described in Algorithm 3.2. In this way, we can get the shortest and optimal path from the path set with the maximum achievable rate of paths. This provides the necessary information to further construct collaborative multi-hop cognitive path with maximum achievable rate. Algorithm 3.2 Input: P ; % Path set attained in Algorithm 3.1 Output: Ps (shortestpath) Run procedure: % Calculate the achievable path rate set V % of each path in P V = {VP1 , VP2 , ..., VP|P | }; Calculate the maximum achievable rate Vmax from the achievable path rate set V ; Select all the paths with the achievable rate Vmax to construct the optimal path set Pa ; Choose the paths with the shortest hops from source node to destination node from Pa to create the shortest and optimal path set Po ; Let i = 0 and No = |Po |; Step 5: Select the path P i ∈ Po , and let Ni = |Pi |; If Ni = 2 do goto Step 10; Else let j = 2 and Pˆi = Pi ; End If Step 7: Delete from Pˆi the jth node in path Pi , and attain new path P˜i ; If path P˜i is connected, then do Calculate the achievable rate VP˜i of P˜i ; End IF If VP˜i ≥ Vmax , then do Update path Pˆi = P˜i ; End If Let j = j + 1; If j ≤ Ni , then do goto Step 7; End If Step 10: Update path P i = Pˆi . Let i = i + 1; If i ≤ No , then do goto Step 5; End If Choose the shortest path Ps from Po ; Save Ps to file and exit. End 3.4 Algorithm Here we give the complete steps for our algorithm which is called as Clustering-based Collaborative

TABLE 1 Simulation and evaluation parameters. Simulation parameter

scenario number of nodes max transmission radiuses Evaluation metrics

50 × 50 15, 20, 25 10, 15, 25 node collaborations achievable rate

Multi-hop Routing (CCMR) with maximum achievable rate. According to the above discussion, the CCMR’s steps are summarized as follows: Step 1: Give the information of all primary users and secondary users, including position, usable channel, the number of primary and secondary users, and so on. And give the source and destination nodes. Step 2: Use Algorithm 3.1 and get all possible paths from source node to destination node according to clustering and collaboration. Step 3: The shortest path with maximum achievable rate of the path from source node to destination node is attained with Algorithm 3.2. Step 4: Save the optimal path to the file and exit.

4

S IMULATION

RESULTS AND ANALYSIS

In this section, we conduct a series of tests to validate our method. We use matlab simulation software to perform simulation analysis. Our simulation scenario is a square field by 50 × 50, including 15, 20, 25 network nodes that communicate each other with maximum possible transmission radiuses 10, 15 , and 25, respectively. The Shortest Collaborative Multi-hop Routing (SCMR) and Not Collaborating Multi-hop Routing (NCMR) algorithms are used to compare and discuss the performance of CCMR. In our simulation process, for each method, simulation inputs are same and include randomly distributed nodes in the forementioned scenario, our simulation environment uses the computer with the 4-core Intel 3.0GHz CPU and 15G memory. Our simulation procedure includes the following four steps. Firstly, we let network nodes be randomly distributed in a square field by 50 × 50. Secondly, all the methods are run under the same conditions. Thirdly, for each method, we perform 1000-run simulations to overcome the occasionality of simulation process. Finally, we calculate the mean value of 1000-times simulations to attain the resulting simulation results. Our simulation parameters and evaluation metrics are shown in Table 1. 4.1

Collaborative multi-hop path

We cluster the given network nodes according to the possible coverage of transmission nodes. They can collaborate with the transmission node as possible to forward the data packets. Figs. 7, 8, and 9 plot the clustering collaborative path in a network with

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Fig. 7. Clustering collaboration path in a network with 15 network nodes.

Fig. 8. Clustering collaboration path in a network with 20 network nodes.

15, 20, and 25 network nodes, where the red solid arrow line denotes the direct path from source node to destination node, the red and purple dot arrow line represents the collaborative path from transmission node to receiving node, the blue star notation is network node whose order number is near it, the blue dot circle denotes the coverage field of transmission node, and the blue dot arrow line represents the coverage radius of transmission node. It can be seen from Fig. 7 that, for the network with 15 network nodes, CCMR successfully constructs the path {1, 13, 12, 10, 14, 5} from source node 1 to destination node 5. The nodes 9, 7, 4, 15, 11, 2, 6, and 8 are collaborative ones that cooperate with transmission nodes 13, 12, 10, and 14. Since no nodes in the coverage of node 1 other than receiving node 13, no nodes collaborate with node 1. More importantly, Fig. 5 tells us that different from previous collaborative methods, CCMR can let the collaborative nodes cooperate with the transmission nodes as more as possible. In Fig. 7, collaborative node 7 cooperates with transmission nodes 13 and 12, collaborative nodes 11, 2, 6 collaborate with transmission nodes 10 and 14. This shows that CCMR can well use the clustering and collaboration to construct the effective path. Fig. 8 indicates that after clustering the nodes in the network with 20 network nodes, CCMR successfully builds the path {2, 7, 12, 3, 20, 6, 17} from source node 2 to destination node 17. Nodes 19, 18, 8, 9, 4, 13, 16, 11 and 14 are collaborative ones that cooperate with transmission nodes 2, 7, 12, 3, 20, and 6. From Fig. 8, we can also find that collaborative nodes 8 and 9 cooperate with transmission nodes 12 and 3, collaborative node 4 collaborates with transmission nodes 12, 3, and 6, and collaborative node 16 cooperates with transmission nodes 3, 20, and 6. This

Fig. 9. Clustering collaboration path in a network with 25 network nodes.

shows that CCMR can let more nodes take part in the collaboration from source node to destination node. Similarly, Fig. 9 shows that CCMR exploits clustering and collaboration to create effectively the path {1, 24, 5, 10, 18, 23, 11} from source node 1 to destination node 11 the nodes in the network with 25 network nodes. Nodes 16, 13, 19, 3, 25, 6, 4, 14, 15, 20, 12, and 9 are collaborative ones that cooperate with transmission nodes 1, 24, 5, 10, 18, and 23. Fig. 9 illustrates that collaborative node 25 cooperates with transmission nodes 5 and 10, collaborative nodes 14 and 15 collaborates with transmission nodes 10 and 18. This further indicates that CCMR can effectively build the collaborative delivery path from source node to destination node in the multi-hop wireless network.

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Fig. 10. Achievable rate with different network sizes.

Fig. 11. sizes.

Collaborative nodes with different network

4.2 Achievable rate Now we further discuss CCMR’s achievable rate. Fig. 10 demonstrates CCMR’s achievable rate for the different network sizes with 15, 20, and 25 network nodes, respectively. We discuss the impact of different maximum transmission radiuses to CCMR’s achievable rate. Fig. 10 illustrates that when maximum transmission radius changes from 10 to 25, for network size with 15 network nodes, CCMR can attain the achievable rate near about 0.62 on average. Likewise, for the network size with 20 and 25network nodes, CCMR can arrive at average achievable rate by about 0.92 and 1.25, respectively. This indicates that maximum achievable rate has no obvious impact to CCMR’s achievable rate. Additionally, Fig. 10 also shows that when network size varies from 15 to 25, for different maximum transmission radiuses, CCMR exhibits the increasing achievable rate. This is because the more network nodes are, the more the number of network nodes taking part in collaboration is. And thus receiving node can receive the more signal power. In a result, this adds the achievable rate of receiving nodes and paths in turn. Fig. 11 shows the number of collaborative nodes with the different network sizes when maximum transmission radius changes from 10 to 25. From Fig. 11, we can see that when maximum transmission radius increases, there are more network nodes participating in collaboration to help other nodes to forward data packets. Moreover, we can also find that with network sizes becoming larger, more network nodes can perform the collaboration with other nodes. This indicates that CCMR can more effectively let more network nodes take part in the collaboration when maximum transmission radius and network size increase. Thus CCMR can build the more effective path that attains the achievable rate as large as possible.

Fig. 12. Analysis of achievable rate for CCMR and SCMR.

4.3

Comparison analysis

To validate further CCMR’s performance, we compare CCMR’s achievable rate and collaborative node number with SCMR’s and NCMR’s ones. Fig. 12 indicates the comparison analysis of achievable rate for CCMR and SCMR when maximum transmission radius and network size changes. In contrast to SCMR, when maximum transmission radius increases from 10 to 25, CCMR hold much larger achievable rate. Furthermore, when network size changes from 15 network nodes to 25 network nodes, CCMR exhibits higher achievable rate than SCMR. This tells us that CCMR hold the better performance than SCMR. Now we further discuss and analyze CCMR’s and SCMR’s performance by comparing the number of

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achievable rate for CCMR and NCMR in the case of different maximum transmission radiuses and different network sizes. In contrast to NCMR, CCMR exhibits much larger achievable rate when maximum achievable rate changes from 10 to 25. Moreover, when network size adds, CCMR also indicates much higher achievable rate than NCMR. This tells us that collaborations can more effectively increase the achievable rate than non-collaboration. Hence, comparing with NCMR, CCMR exploits collaborations to attain better performance. 4.4

Fig. 13. Analysis of collaborative nodes for CCMR and SCMR.

Fig. 14. Analysis of achievable rate for CCMR and NCMR. network nodes taking part in collaboration. Fig. 13 plots the number of network node performing collaboration for different network sizes and maximum transmission radiuses. When maximum transmission radius adds from 10 to 25, CCMR always has more network nodes to participate in collaboration than SCMR. More importantly, comparing with SCMR, when network size changes from 15 to 25, CCMR also holds much more network nodes to perform collaboration with other network nodes. In contrast to SCMR, due to more network nodes taking part in collaboration, CCMR can obtain larger achievable rate. Thus CCMR holds much better performance than SCMR. To analyze CCMR’s performance, we compare it with NCMR without collaboration. Fig. 14 shows

Performance improvement

Here we analyze the performance improvement of CCMR to SCMR and NCMR. Fig. 15 formulates the improvement ratio of CCMR’s achievable rate to SCMR’s in the case of different maximum transmission radiuses and different network sizes. When maximum transmission radius is 10, 15, and 25, for 15 network nodes, the average improvement ratio of CCMR’s achievable rate to SCMR’s one is about 55%, while for 20 and 25 network nodes, the average improvement ratios are, respectively, 58% and 53% or so. This further demonstrates that relative to SCMR, CCMR can obtain the higher achievable rate. Fig. 16 plot the improvement ratio of CCMR’s achievable rate to NCMR’s when maximum transmission radius and different network size change. When maximum transmission radius varies from 10 to 25, the average improvement ratio of CCMR’s achievable rate to NCMR’s one is about 65% in the network with 15 network nodes, while for 20 and 25 network nodes, the average improvement ratios are, respectively, about 84% and 79%. This also indicates that CCMR can obtain the higher achievable rate and hold the better performance than NCMR. Fig. 17 shows the improvement ratio of CCMR’s collaborative node number to SCMR’s for different maximum transmission radiuses and different network sizes. From Fig. 17, we can see that when maximum transmission radius increases from 10 to 25, for the network with 15 network nodes, CCMR’s collaborative nodes will add 80% than SCMR on average, while for the network with 20 network nodes, CCMR has more nodes taking part in collaboration by 70% than SCMR. Similarly, when network nodes are 25, CCMR holds collaborative nodes more by 68% than SCMR. Due to more nodes participating in collaboration, the lager achievable rate can be attained. Thus this also illustrates that CCMR exhibits better performance than SCMR.

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C ONCLUSION

This paper studies collaborative multi-hop communication technology in next generation wireless communications. A collaborative multi-hop routing algorithm with maximum achievable rate is proposed to raise

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Fig. 15. Improvement ratio of CCMR’s achievable rate to SCMR’s.

Fig. 17. Improvement ratio of CCMR’s collaborative nodes to SCMR’s. results show that the algorithm proposed in this paper exhibits better performance than conventional methods.

ACKNOWLEDGMENTS This work was supported in part by the National Natural Science Foundation of China (No. 61071124), the Program for New Century Excellent Talents in University (No. NCET-11-0075), the Fundamental Research Funds for the Central Universities (Nos. N120804004, N130504003), and the State Scholarship Fund (201208210013). The authors wish to thank the reviewers for their helpful comments.

R EFERENCES Fig. 16. Improvement ratio of CCMR’s achievable rate to NCMR’s. the performance of multi-hop wireless networks. A relation matrix is defined to describe the possible coverage of network nodes. We present a clusteringbased path strategy to create neighbor node matrix and effective next-hop link. The corresponding clustering path algorithm is proposed to create the multihop path set from source node to destination node. A collaborative strategy is proposed to create the collaborative matrix, where the maximum achievable rates of paths is taken as the optimal object. Then by calculating the maximum achievable rate of each path in the path set ., The shortest path with maximum achievable rate can be found by further optimizing the optimal path set. In this way, a collaborative multihop routing with maximum achievable rate is successfully built by clustering and collaboration,. Simulation

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Dingde Jiang received the Ph.D. degree in communication and information systems from School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, China, in 2009. He is currently an Associate Professor in College of Information Science and Engineering, Northeastern University, Shenyang, China. His research interests include network measurement, network security, Internet traffic engineering, and communication networks. Dr. Jiang is a member of IEEE and IEICE.

Zhengzheng Xu received the Ph.D. in management science and engineering in College of Information Science and Engineering, Northeastern University, Shenyang, China. She was ever a Research Member at Key Lab of Comprehensive Automation of Process Industry of Ministry of Education, College of Information Science and Engineering, Northeastern University, Shenyang, China. She was ever also a Research Member at Systems Engineering Research Institute at the same university. She is with the School of Economics and Management, Anqing Normal University, Anqing, China. Her research interests include supply chain and logistics management, decision analysis, modeling, and optimization.

Wenqin Wang received a B.S. degree in electrical engineering from Shandong University, Shandong, China, in 2002, and M.E. and Ph.D. degrees in information and communication engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2005 and 2010, respectively. From March 2005 to March 2007, he was with the National Key Laboratory of Microwave Imaging Technology, Chinese Academy of Sciences, Beijing, China. Since September 2007, he has been with the School of Communication and Information Engineering, UESTC, where he is currently an Associate Professor. From June 2011 to May 2012, he was a visiting scholar at the Stevens Institute of Technology, Hoboken, New Jersey. Currently he is a visiting scholar at the City University of Hong Kong. His research interests include communication and radar signal processing and novel radar imaging techniques. He has authored two books, Multi-Antenna Synthetic Aperture Radar (CRC Press, 2013) and Near-Space Remote Sensing: Potential and Challenges (Springer, 2011). Dr. Wang was the recipient of the Hong Kong Scholar in 2012, the New Century Excellent Talents in University in 2012, the Distinguished Young Scholars of Sichuan Province, the Young Scholar of Distinction of UESTC in 2012, the National 100 Excellent Doctoral Dissertation Award nomination in 2012, and the Excellent Paper Award of the 12th Chinese Annual Radar Technology Conference in 2012.

Yuanting Wang received BSc in College of Information Science and Engineering, Northeastern University, Shenyang, China, in 2012. He is currently a Master at the same university. His research interests include network measurement and cognitive networks.

Yang Han received BSc in College of Information Science and Engineering, Hainan University, Hainan, China, in 2012. He is currently a Master in Communication and Information System, Northeastern University, China. His research interests include cognitive radio network and cooperation communication.