Energy-Efficient Cooperative Routing in Multi-hop Wireless Ad Hoc Networks Fulu Li The Media Laboratory MIT, Cambridge, MA USA Email:
[email protected]
Kui Wu Dept. of Computer Sci., University of Victoria, Canada
[email protected]
Andrew Lippman The Media Laboratory MIT, Cambridge, MA USA
[email protected]
Abstract We study the routing problem for multi-hop wireless ad hoc networks based on cooperative transmission. We prove that the Minimum Energy Cooperative Path (MECP) routing problem, i.e., using cooperative radio transmission to find the best route with the minimum energy cost from a source node to a destination node, is NP-complete. We thus propose a Cooperative Shortest Path (CSP) algorithm that uses the Dijkstra's algorithm as the basic building block and reflects the cooperative transmission properties in the relaxation procedure. Simulation results show that with more nodes added in the network, our approach achieves more energy saving compared to traditional non-cooperative shortest path algorithms. Another interesting observation is that the proposed algorithm achieves better fairness among different nodes with denser networks. Implementation issues are also discussed.
transmissions from multiple transmitters to one receiver simultaneously. As a result, signals with the same channel from several different nodes to the same receiver simultaneously are not considered collision but instead could be combined at the receiver to obtain stronger signal strength. This fundamental difference from the traditional radio transmission model requires new routing algorithms to fully realize the power of new antenna technology. Routing problem under the cooperative radio transmission model is called cooperative path routing [10], with which it is allowed that multiple nodes along a path coordinate together to transmit a message to the next hop as long as the combined signal at the receiver satisfies a given SNR (Signal-to-Noise Ratio) threshold value. This new type of routing strategy, despite its great commercial potentials, has not gotten extensive attention in both industrial and academic research.
Keywords: cooperative routing, energy efficiency, wireless Cooperative path routing has two major benefits. First, networks, complexity theory, distributed algorithm cooperative path routing can achieve higher energy saving than non-cooperative shortest path routing. Our empirical 1. Introduction results indicate that with more nodes added in the network, Currently, great demands for self-organizing, fast deployable more energy saving can be achieved by cooperative routing multi-hop wireless ad hoc networks come along with the since a dense network offers more opportunities for advances in wireless portable technologies. Such networks are cooperative transmissions. Second, cooperative transmission formed by a group of wireless devices without requiring greatly alleviates the scalability problem in wireless expensive base stations or wired infrastructure. They are cheap networks. Previous theoretical analysis illustrates that the and ideal for commercial applications such as convention capacity of wireless networks does not scale [19]. Intuitively, centers, electronic classrooms, and community mesh networks. transmission with excessive power on one link often leads to Pushed by several well-known projects such as the Microsoft's severe interference to other nodes when the network is dense. mesh networks project [5] and the MIT's Roofnet project [1], With new antenna technology and new coding schemes, multi-hop wireless ad hoc networks are becoming however, simultaneous radio transmissions from different commercially feasible. cooperative nodes can be used to obtain strong signal strength at the receiver. With the cooperative radio With multi-hop wireless ad hoc networks, messages may be transmission model, previous analytical conclusion regarding transmitted via multiple radio hops, and thus a routing protocol the network capacity may not hold anymore: cooperative is essential for the success of such networks. After substantial transmission may allow a scalable routing solution for large research efforts in the last several years, routing for multi-hop and dense wireless networks. wireless ad hoc networks becomes a well-understood and broadly investigated problem [16]. It, for quite a while, does This paper is motivated to take advantage of these benefits to not stimulate further research interests when most problems achieve energy efficiency for wireless networks and has seem solved. Nevertheless, with the emergence of new antenna made the following contributions. First, we proved that the technology, existing routing solutions in the traditional radio Minimum Energy Cooperative Path (MECP) problem is NPtransmission model are not efficient anymore. For instance, complete. Second, we developed a Cooperative Shortest Path with RAKE receivers [9], it is feasible to coordinate the (CSP) algorithm for cooperative routing in stationary
wireless networks. Finally, via extensive simulation, we by the maximum required power to reach the farthest node, investigated the impact of the CSP algorithm on energy saving and other nodes essentially get the transmission for “free”. and fairness, and compared its performance to that of existing This is referred to as WMA (wireless multi-cast advantage) routing approaches. by Wieselthier et al in [18]. Let d r1 ,t , d r2 ,t ,..., d rm ,t stand for
the distances from the transmitting node t to the destination nodes r1 , r2 ,..., rm , respectively. The required power is 2.1 The Network Model determined by Pbroadcast = max( d rλ1 ,t , d rλ2 ,t ,..., d rλm ,t ) (2) We consider an all-wireless network consisting of N devices, also called nodes. We assume the use of omni-directional Assume that nodes t , t ,...,t cooperatively transmit 1 2 m antennas and all nodes within communication range of a information to a given destination node, say node r , where transmitting node can receive its transmission. the received signal from each transmitting node is coherently Following [10], we also assume that the power level of a combined in the sense that signals from those transmitting transmission can be chosen at each node within a given range nodes arrive in phase at the receiving node with coordination, of values, say [0, Pmax ]. We assume that the channel e.g., pre-compensation [15]. We say the cooperative transmission is successful if and only if the SNR of the parameters are estimated by the receiver and fed back to the coherently combined signal at the receiving node r is above transmitter. Each node can thus dynamically adjust its λ λ transmitted signal phase to possibly synchronize with other a given threshold value. Let d t1 ,r ,..., d t m ,r denote the required nodes, which can be realized by pre-compensation before power for point-to-point transmission to the given destination transmitting based on the estimate of the phase and delay at node r from transmitting nodes t1 , t 2 ,...,t m respectively. The each path as discussed by Tu and Pottie in [15]. This discovery by Khandani et al in [10] reveals that the total assumption is reasonable for slowly varying channels in that the required power for this cooperative transmission is given by: channel coherence time is much longer than the block 1 transmission duration. Pcoop = m (3) 1
2. The System Model
∑ dλ
2.2 The Power Consumption Model It is well known that the signal power attenuation in wireless communication is non-linear. We consider a commonly used wireless propagation model [2,10,11,13,14,18] whereby the received signal power attenuates d − λ , where d stands for the distance between the transmitting node antenna and the receiving node antenna and λ takes a value between 2 and 4, depending on the characteristics of the communication medium. We assume that the communication medium is uniform, thus λ is a constant throughout the region. Following [14], we assume that the required power to support a wireless link at a given data rate between node i and node j is given by Pi , j = d iλ, j (1)
i =1
ti , r
And the required power for each of the transmitting node in this cooperative transmission is given by: d t−,λr 1 Pti = m i × m , (1 ≤ i ≤ m) (4) 1 −λ d t j ,r λ j =1 j =1 d t j , r
∑
∑
One observation for Eq. (3) is that if d tλ1 ,r = ... = d tλm ,r , the
total required power for this cooperative transmission is 1 × d tλi ,r in the sense that cooperative transmission can use m 1 as little as only of the individual point-to-point m transmission power if m nodes cooperatively transmit to a where d i , j denotes the distance between node i and node j . given destination node. We say node i can reach node j if and only if the transmitting
power at node
i is greater than or equal to d iλ, j . Notably, each 3. The Problem Formulation
node can add or remove links by adjusting its transmitting Consider an energy cost graph G = (V , E ) with weights d iλ, j , power levels, hence the network topology totally depends on the transmitting range of each node. where V is the set of nodes, E is the set of links, d iλ, j is the Regarding the transmission energy, we have the following weight on the edge < i, j >, < i, j >∈ E and i, j ∈ V . For a notations: source-destination pair S , D ∈ V , assume that V = N and
the last L predecessor nodes along the path are allowed for The power required for a transmitting node, say t , to directly cooperative transmission to the next hop. We want to find a reach a set of destination nodes, say r1 , r2 ,..., rm , is determined S − D path, say Path = S − > t1 , t 2 ,..., t k − > D and a
corresponding transmission sequence arrangement, i.e., a link Minimum Energy Cooperative Path (MECP) problem in schedule, such that the total required energy along this path is wireless networks: Px is minimal over all possible the least. That is, Instance: Consider an energy cost graph G = (V , E ) with x∈{S ,t ,t ,...,t , D}
∑
1 2
k
S-D paths and Px stands for the required power for node x . An example of cooperative transmission along the path from node S to node D is given in Figure 1, in which we allow the last two predecessor nodes along the path for cooperative transmission to the next hop, i.e., L = 2 .
A D
S B
weights d iλ, j , where V is the set of nodes and E is the set of links, d iλ, j is the weight on the edge < i, j > and < i, j >∈ E , i, j ∈ V . For a source-destination pair S , D ∈ V , assume that
V = N and the last L predecessor nodes along the path are allowed for cooperative transmission to the next hop, where L ∈ {1,..., N − 1} . Let Px stand for the required power for node x . Question: Given some constant B ∈ ℜ + , is there a S − D path, Path = S − > t1 , t 2 ,..., t k − > D and a corresponding transmission sequence arrangement, i.e., a link schedule, such that Px ≤ B ?
∑
x∈{S ,t1 ,t 2 ,...,t k , D}
In the following, we prove that the MECP problem is NPFigure 1: An illustration of cooperative transmission ( L = 2 ). complete. We prove NP-completeness of MECP problem by The corresponding path can be stated as S − > A − > B − > D . showing that a special case of it is NP-complete. In order to (S ) ( A) obtain a special case of MECP, we specify the following The transmission procedure operates as follows: node S first restrictions to be placed on the instances of MECP. First, we transmits to node A , then node S and node A cooperatively only allow cooperative transmission to the destination node transmit to node B , then node A and node B cooperatively D and up to N − 1 nodes are allowed for this last-hop transmit to node D . The total energy cost for this path is give cooperative transmission. Further, we assume that the weight by difference between link < i , D > and link < j , D >, 1 1 λ PS − D = d S , A + + (5) where i , j ∈ V − {S , D} , is negligible, i.e., d iλ, D ≈ d λj , D . This 1 1 1 1 + + assumption is to simplify the calculation of the last-hop d Sλ, B d Aλ, B d Aλ, D d Bλ, D cooperative transmission cost and it is just for the We need to emphasize that the minimum energy cooperative convenience of analysis. path could be a combination of multicast (one to many), cooperative transmissions (many to one), and point-to-point transmissions (one to one). Note that the case of many-to-many transmission is not a valid option as synchronizing transmissions for coherent receptions at multiple receivers is not feasible [10].
4. Complexity Issues
We call this special case of MECP as S-MECP. We prove NP-completeness of the S-MECP problem by reduction from the minimum energy broadcast (MEB) problem in wireless networks, which is known to be NP-complete [2,11]. Minimum Energy Broadcast problem in wireless networks: Instance: Consider an energy cost graph G = (V , E ) with weights d iλ, j , whereV is the set of N nodes, E is the set of
The problem of finding the minimum energy cooperative path links, d λ is the weight on the edge < i, j >, < i, j >∈ E and i, j (MECP) in wireless networks appears to be hard to solve [10]. . Assume that S ( ∈ V ) is a source node. i , j ∈ V This is due to the fact that an optimal path could be a combination of cooperative transmissions, multicast, and point- Let Px stand for the required power for node x . Question: to-point transmissions. In the following we show that the Given some constant B ∈ ℜ , is there a subgraph of + minimum energy cooperative path problem in wireless ' ' ' G , say G = (V , E ) , where | V ' |=| V |= N and G ' is a tree networks is NP-complete.
∑
rooted at node S , such that Px ≤ B ? Note that the theory of complexity is designed to be applied x∈V ' only to decision problems, i.e., the problems with either yes or no as an answer [2,7]. However, each optimization problem For the transformation from MEB to MECP, we first give the can be easily stated as a corresponding decision problem. A following description of minimum energy i -node multicast decision problem related to the MECP problem can be problem. described as follows:
Given a source node S and N -1 potential destination nodes, a minimum energy i -node multicast tree with source node S is defined as a tree that is rooted at node S and reaches i -1 ( i ≤ N ) destination nodes with the least required power among N − 1 all possible i -node multicast trees. Note that there are i −1 i -node multicast trees in total. From the theorem in [2,11] that minimum energy broadcast problem in wireless networks is NP-complete, we have the following lemma.
last-hop cooperative transmission. Let C (i, D) stand for the required power for the last-hop cooperative transmission from i already-covered nodes, including the source node S , to the final destination node D . Recall that among the restrictions on the instance of MECP we assume that the link weight difference between link < k , D > and link < j , D >, where k , j ∈ V − {S , D} , is negligible, i.e., d kλ, D ≈ d λj , D . Lemma 3: The series of C (1, D) , C (2, D ) , …, C (i, D) ,
C (i + 1, D ) , …, C ( N − 1, D) is strictly decreasing, i.e., Lemma 1: Minimum energy i -node ( 1 ≤ i ≤ N ) multicast C (i, D) > C (i + 1, D ) , where 1 ≤ i ≤ N − 2 . (MEiM) problem with one source node and N − 1 potential Proof: according to the definition and the restriction destination nodes is NP-complete. assumptions, we have C (1, D ) = d Sλ,D , Proof: It is easy to see that minimum energy i -node multicast 1 1 problem belongs to the NP class since a nondeterministic C (2, D) = ,…, C (i, D) = , 1 1 1 i −1 algorithm needs only to guess a set of nodes, i.e., i nodes, and + + checks in polynomial time whether there is a path from the d Sλ, D d xλ, D d Sλ, D d xλ, D source node to any of the remaining i -1 destination nodes in a 1 final solution, and whether the cost of the final solution is not C (i + 1, D ) = ,…, 1 i larger than a given constant B . Since the minimum energy + d Sλ, D d xλ, D broadcast problem is a special case of the minimum energy i node multicast (MEiM) problem when i is equal to N , and 1 . minimum energy i -node multicast problem belongs to the NP C ( N − 1, D ) = 1 N −2 + λ class, the MEiM problem is NP-complete too. d Sλ, D d x, D Let T ( S , i ) denote the required power of a minimum energy i - As x ≠ D , we have d λ > 0 . Notably, all the link weights x, D node multicast tree with source node S . Regarding the series are non-negative. Without loss of generality, let us consider of T (S ,1) , T (S ,2) , …, T ( S , i ) , T ( S , i + 1) , …, T ( S , N ) , we two consecutive elements C (i, D) and C (i + 1, D ) . Based on have the following lemma. the above analysis, we have Lemma 2: The series of T ( S , i ) is monotonically increasing, d S2,λD × d xλ, D C (i, D ) − C (i + 1, D ) = λ >0. i.e., T ( S , i ) ≤ T ( S , i + 1) , where 1 ≤ i ≤ N . (d x, D + (i − 1)d Sλ, D )(d xλ, D + i × d Sλ, D ) Proof : We prove this lemma by contradiction. Assume that there is a minimum energy (i + 1) -node multicast tree and a So, the series of C (i, D ) s is strictly decreasing. minimum energy i -node multicast tree for the same given settings and T ( S , i + 1) < T ( S , i ) holds. For the minimum energy (i + 1) -node multicast tree, there must be at least one leaf node among the i destination nodes. The removal of this leaf node will not cause the connectivity changes of other nodes, and the total cost of the remaining i -node multicast tree,
Lemma 1 and Lemma 2, coupled with Lemma 3, make up the basis for the proof of Theorem 1. Theorem 1: The minimum energy cooperative path problem (MECP) in wireless networks is NP-complete.
Proof: we first show that S-MECP is NP-complete. As Ssay T ( S , i ) , is equal or less than the original minimum energy MECP is a special case of MECP, the theorem follows. To see that S-MECP is NP-complete, we first show that S(i + 1) -node multicast tree, i.e., T ( S , i + 1) . Hence, MECP belongs to the NP class, and then prove that MEiM T * ( S , i ) ≤ T ( S , i + 1) . From the assumption, we also polynomially reduces to S-MECP. *
have T ( S , i + 1) < T ( S , i ) . So, we have T * ( S , i ) < T ( S , i ) . This It is easy to see that S-MECP problem belongs to the NP contradicts the assertion that the original i -node multicast tree class since a non-deterministic algorithm needs only to guess is the minimum energy i -node multicast tree. a set of nodes and checks in polynomial time whether a given link schedule for the corresponding cooperative path from the As discussed before, for the special case of MECP, i.e., S- source node S to the destination node D is feasible in a final MECP, we only allow cooperative transmission to the solution, and whether the cost of the final solution is not destination node D and up to N − 1 nodes are allowed for this larger than a given constant B .
Consider an energy cost graph G = (V , E ) with weights d iλ, j , where V is the set of nodes and E is the set of links, d iλ, j is the weight on the edge < i, j > and < i, j >∈ E , i, j ∈ V . Given a source-destination pair S , D ∈ V and some constant B ∈ ℜ + , let us consider the instances of MEiM in which the destination nodes belong to V ' = V − {S , D} . According to Lemma 2, the T ( S , i ) series, which stands for the power of the minimum energy i -node multicast tree with source node S and destination nodes belong to V ' , monotonically increases. According to Lemma 3, the C (i, D) series, which denotes the cooperative transmission cost from all the nodes in the minimum energy i -node multicast tree to the destination node D , monotonically decreases. The cost of the corresponding S − D path, which satisfies the assumptions of S-MECP, is P( S , i, D ) = T ( S , i ) + C (i, D ) . Note that the series of P( S , i, D) s does not monotonically increase or monotonically decrease. By evaluating the instances of P( S ,0, D ) , P( S ,1, D ) , …, P( S , N − 1, D ) , we can obtain the instance of S-MECP. Clearly, this instance of S-MECP can be constructed in a polynomial time of O(N ) from MEiM instances. This concludes the proof that S-MECP is NP-complete.
of the cooperative shortest path from the source node S to node u with respect to the cooperative transmission cost along the path and π (u ) to represent predecessors of node u along the cooperative shortest path. π (u ) only needs to keep as many as L -1 predecessors, i.e. , the last L -1 predecessors along the cooperative shortest path. Relax (u,v) 1 if d[v] >d[u] + Coop(u,v) then 2 d[v] = d[u] + Coop(u,v); 3 set node u as node v’s predecessor; 4 endif Coop(u,v) // calculate the cooperative transmission cost from node u // and its predecessors to node v Assume Pathu
2
if (k+2)
3
= {S , t1 ,..., t k , u}
*
1
≤L
1
cost =
k
1
+
d Sλ,v 4 5
∑ dλ i =1
5. Cooperative Shortest Path Algorithm
8 9 10 11
7
t i ,v
1 d uλ,v
1
cost =
k
1
i =1
6
+
else if (k+1)==L
∑ dλ
Since S-MECP is a special case of MECP problem, and MECP belongs to the NP class, which can be shown along the similar line as for the S-MECP problem, MECP problem is NPcomplete too.
1
t i ,v
else if (k+1) > cost =
+
1 d uλ,v
L 1 k
∑
1
λ i = k − L + 2 d t i ,v
endif endif endif return cost
+
1 d uλ,v
In this section, we present a cooperative shortest path (CSP) algorithm that uses the Dijkstra’s algorithm as the basic building block and reflects the cooperative transmission Figure 2: New relaxation procedure for CSP algorithm properties in the relaxation procedure. The CSP algorithm takes λ as input an energy cost graph G = (V , E ) with weights d i , j , We omit the description of the rest of the CSP algorithm as it has the same structure as that of the Dijkstra’s algorithm, source-destination pair S , D ∈ V . We assume that the last L which can be found in virtually every algorithm book, e.g., predecessor nodes along the path for cooperative transmission the one by Cormen, Leiserson, Rivest and Stein [4]. to the next hop. The CSP algorithm uses the basic structure of the Dijkstra’s algorithm and uses a modified relaxation The complexity of the presented cooperative shortest procedure to reflect the cooperative transmission cost along the algorithm for cooperative routing is in the order of O( N 2 ) , path. The presented approach (CSP algorithm) differs from the where N is the number of nodes in the network. The CAN heuristics in [10] in the sense that we directly change the (cooperative along non-cooperative shortest path) algorithm relaxation procedure of the Dijkstra’s algorithm to adopt the and the PC (progressive cooperative) algorithm [10] have the cooperative transmission cost instead of calculating the noncomplexities of O( N 2 ) and O( N 3 ) cooperative shortest path first. We refer interested readers to computational respectively, but with performance poorer than that of CSP. [10] for details. This is verified by the experimental results in the following The new relaxation procedure for CSP is described in Figure 2 section. and the rest of the CSP algorithm has the same structure as that of Dijkstra’s algorithm. Notably, the algorithm maintains two labels for each node: d [u ] to represent the estimated total cost
more cooperative transmission opportunities, which lead to more power savings.
In this section, we compare the performance of the basic CSP algorithm, regarding the average path energy consumption and fairness, to that of the CAN (cooperative along non-cooperative shortest path) algorithm presented in [10] and the USP (uncooperative shortest path) algorithm. The basic idea of CAN is to run a non-cooperative shortest path algorithm to obtain the cooperative path. All the three algorithms have the same computational complexity of O(N2).
From Fig. (3.b) and Fig. (3.c), we also observe that the gap between CSP and the uncooperative shortest path (USP) approach slightly shrinks with the increment of the value of power attenuation constant λ . This suggests that in a fast power-attenuating environment the advantage of cooperative routing approach over conventional uncooperative routing method slightly decreases. We determined that a deep power attenuation environment offers less cooperative transmission opportunities for power savings over uncooperative counterpart. Another observation is that the gap between CSP and CAN widens with a larger value of power attenuation factor, λ . We determined that the energy savings due to the use of the CSP algorithm, over the CAN algorithm is most notable in a deep power attenuation environment.
N
∑ STD =
( Ri
∑ −
i =1
N
N j =1
N
Ri
)2
CSP
1.45 1.4 1.35 1.3 1.25 1.2 1.15 1.1 1.05 1
CAN USP
20
60
80
100
(3.a) λ = 2, L = 2 CSP
1.7 1.6 1.5 1.4 1.3 1.2 1.1 1
CAN USP
20
,
40
number of nodes in the network
Mean normalized path power
Following [10,14], we simulate networks of a varying number of nodes, N , placed randomly within a 10 × 10 plane, in a variety of circumstances, i.e., with the power attenuation factor, λ =2,4, and L = 2,4 . We use Pmax =2 × 10 λ for each node and this allows every node being able to reach every other node in one hop so long as it transmits at a sufficiently high power level. As discussed before, each node is able to adjust its transmitting power in the range of [0, Pmax ] to add or remove links in the energy cost graph. For the calculation of mean normalized path power, the results are averaged over 100 randomly-chosen source-destination pairs in randomlygenerated networks in a variety of circumstances with different N , λ and L values. For the performance comparison between the algorithms, we consider normalized path power. Let the variable Ri stand for the ratio of the number of transmission sessions in which node i is either the source or the destination node to the total number of transmission sessions that node i participates. We call Ri as node i ’s utility function. Clearly, the bigger the value of Ri , the more benefits node i can get from the cooperation with other nodes. Let STD be the standard deviation of Ri s among all the nodes in the network, we have
Mean normalized path power
6. Performance Evaluation
(6)
40
60
80
100
number of nodes in the network
(3.b) λ = 2, L = 4 Mean normalized path power
where N is the total number of nodes in the network. 1.5
CSP We begin with the evaluation of the mean normalized path 1.4 CAN power by CSP, CAN and USP. As shown in Figure 3, we first USP 1.3 observe that CSP consistently outperforms CAN and USP in all circumstances. With more nodes added in the network, the gap 1.2 between CSP and uncooperative shortest path (USP) approach 1.1 slightly widens, ranging from 30~50% power savings. CSP 1 outperforms CAN by a margin around 10% for the same 20 40 60 80 100 settings. We also observe that as we allow more nodes along number of nodes in the network the path for cooperative transmission to the next hop, i.e., a larger value of L , both CAN and CSP achieve more power savings compared with the non-cooperative shortest path (3.c) λ = 4, L = 4 approach. This is due to the fact that a larger value of L offers Figure 3: Mean normalized path power over 100 random source-destination pairs by CSP, CAN and USP in a variety
of circumstances ( N ranges from 20 to 100, λ = 2,4 and L = 2,4 ). We next explore the performance of CSP, CAN and USP with respect to fairness defined in Eq. (6) over 100,000 randomlychosen S-D pairs in the network in a variety of circumstances, with varying N , λ and L . 0.36
CSP CAN
0.32 STD
USP 0.28 0.24
number of nodes in the network
CSP CAN
A distributed implementation of routing algorithm is desirable in multi-hop wireless ad hoc networks without a centralized control. Fortunately, the cooperative shortest path algorithm presented in this paper lends itself to easy distributed implementation, as there already exist efficient implementations of the traditional shortest path algorithms, for instance, the distributed Bellman-Ford algorithm. Cooperative transmission is not for free. The signaling cost on time synchronization and on the coordination among the transmitters and the receiver may be prohibitive if the network topology changes frequently. For this reason, we stress that cooperative routing, with current technology, may be feasible only for stationary wireless networks, where steady network topology facilitates the nodes' coordination and reduces the update cost once a cooperative scheme is generated. Cooperative routing in highly dynamic wireless networks is still a very challenging research topic.
16 0
14 0
12 0
10 0
80
60
USP
40
20
STD
(4.a) λ = 2, L = 2 0.39 0.37 0.35 0.33 0.31 0.29 0.27 0.25
From Fig. 4, another observation is that CAN performs slightly worse than USP with respect to fairness. This may be due to the fact that CAN uses the same path found by USP for cooperative transmission but it gives biased treatment for the source and destination nodes. Notably, both source and destination nodes have less cooperative transmission participation opportunity than that of those in the middle of the path. In particular for the destination node, it has no participation to the cooperative transmission at all.
7. Distribution and Implementation Issues
16 0
14 0
12 0
10 0
80
60
40
20
0.2
As shown in Figure 4, an interesting observation is that as more nodes added in the network, the CSP algorithm achieves more fairness among nodes in terms of the cooperative transmission participation. In particular, when the number of nodes in the network exceeds 60, CSP outperforms CAN and USP in all circumstances.
number of nodes in the network
(4.b) λ = 2, L = 4
We point out that the hardware requirement of cooperative routing is realistic. With the current commercial tuner receivers for phase coherence or RAKE receivers for CAN 0.36 wideband communications, it is practical to coordinate the USP 0.32 transmissions from multiple transmitters to one receiver simultaneously to obtain stronger signal strength. 0.28 Furthermore, our empirical study on radio signal combining 0.24 indicates that even the signals from two transmitters for cooperative transmissions to the same receiver arrive with 0.2 phase difference of π/2, the combined signal is still much 20 40 60 80 100 120 140 160 stronger than the signal from an individual transmitter. This number of nodes in the network suggests that the constraint of coherent combining of the signals for cooperative transmissions can be relaxed to some (4.c) λ = 4, L = 4 extent. As such, very accurate time synchronization is Figure 4: STD among each node’s utility function values for unnecessary, making real implementation much easier. 100,000 random S-D pairs by CSP, CAN and USP in a variety of circumstances. 8. The Related Work STD
0.4
CSP
The minimum energy cooperative path routing problem for wireless networks has also been recently addressed in [10]. Several heuristic algorithms were developed to approximate the minimum energy route based on non-cooperative shortest-path algorithm. In [10], the authors assume that conventional receivers are used and the channel parameters are estimated by the receiver and fed back to the transmitter. Nevertheless, the basic framework of the algorithm in [10] is equally applicable to other cooperative routing environment such as that with different fading/attenuation models and different types of receivers. Another closely related work by Catovic et al. [3] referred the concept of cooperative routing as “power combining. ” They present approaches to explore transmit diversity via user cooperation in the next generation wireless multi-hop networks. In [3], the authors assume that the m-finger RAKE receivers are used for wideband communications and each finger is in charge of the reception of the signal from a different transmitter. There is a lot of work on the physical layer that utilizes cooperative radio transmission [9,19]. The main focus of these papers is on designing channel coding schemes or new types of antennas to make cooperative transmission feasible. The work at the physical layer lays the practical foundation for the cooperative routing algorithm presented in this paper.
9. Conclusions and Future Directions In this paper, we study minimum energy cooperative path (MECP) routing in all-wireless networks. The cooperative routing scheme combines route selection, i.e., a network layer function, and the transmit diversity via cooperative transmission, i.e., a physical layer function. Such a cross-layer design approach is beneficial for wireless networks. The basic idea is that by coordinating the transmissions from several nodes to a given node that receives those transmissions and processes them in some appropriate way, information can be propagated from a source node to a destination node with potentially far greater energy efficiency than in conventional packet forwarding. To the best of our knowledge, we are the first to present indepth analysis on the complexity of MECP problem and prove that MECP problem in wireless networks is NP-complete. We then present a cooperative shortest path (CSP) algorithm to approximate the MECP. The empirical results show that the presented CSP algorithm consistently outperforms other existing approaches in both energy efficiency and fairness. We will further explore efficient ways for the distributed implementation of the CSP algorithm as well as collaborative MAC protocols, adaptive scheduling algorithms, node mobility issues as our future directions.
Acknowledgement The authors would like to thank the Digital Life consortium at MIT Media Lab and the Motorola fellowship for the support.
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