A Practical Low Interference Topology Control for Mobile Ad hoc Networks

Transcription

1 A Practical Low Interference Topology Control for Mobile Ad hoc Networks Xiang Yu, Xinming Zhang, Can Que, Qiong Liu Department of Computer Science and Technology University of Science and Technology of China Anhui Province-MOST Co-Key Laboratory of High Performance Computing and Its Application Hefei, , PRChina Abstract The interference imposes a potential negative impact on the performance of a wireless network A device is interfered if it receives a transmission not intended for it In this paper, we introduce an explicit computation model of node interference based on its actual inducement on the physical layer We prove that there exists an optimal algorithm to solve the corresponding topology control problem, constructing a network topology with minimum node interference We also investigate the bad performance of existing methods of solving it and propose a revised algorithm, namely Low Interference-amount Neighborhood Tree (LINT), based on a new link cost metric The simulation results illustrate that our model is able to reduce node interference effectively and maintain the network performance Keywords-Interference; MANETs; Topology control I INTRODUCTION A mobile ad hoc network (MANET) [1] is a collection of wireless mobile devices that self-configure to form a network without aid of any pre-established infrastructure In a MANET, the packets transmitted by a wireless device are often received unconsciously by others in its vicinity, which possibly cause signal interferences at these valid neighbors, share their limited bandwidth, and even bring collisions and data retransmissions at the MAC layer Consequently, the network throughput degrades and the end-end delay increases In MANETs, each device can selectively decide which device to communicate either by adjusting its transmission power or its antenna direction Obviously, keeping relatively limited direct neighbors is helpful to speed up the routing protocols in addition to possibly alleviating the interference among simultaneous transmissions, and also possibly save the energy consumption How to construct such a topology depicted above is the central task of topology control In previous work, it has been well studied in conserving energy consumption and claimed implicitly to solve the interference issue [2] [3] [4] [5] Unfortunately, none of them take into account the explicit definition of interference and effectively confine interference at a low level, proven by Burkhart [6] This paper is partially supported by the National Natural Science Foundation of China under rant No and ; the National rand Fundamental Research 973 Program of China under rant No2006CB303006; the Open Foundation of Anhui Province Key Laboratory Proceedings of Software of the in Sixth Computing International and Communication Conference on Networking (ICN'07) [6] started a totally fresh realm named interferenceefficient topology control, which establishes an interference computation model and then employs the topology control methods well studied previously But his definition of interference is based on the number of nodes affected by communication over a given link, therefore it is argued that such sender-centric perspective hardly reflects real-world interference and performs badly in certain cases In this paper, different from previous studies, we firstly account for the credible and theoretical cause of interfering and being interfered through signal to noise ratio or SINR, and define interference amount of a node as the number of hidden neighbors located in a certain distinct contributing interference to it According to our new model, a topology control problem with interference amount consideration is raised, which is to find a structure such that the most interference suffered by nodes is minimized while the network connectivity constraint is satisfied Whether its optimal solution exists is also under discussion For the worse performance of existing algorithm in certain cases, we propose a heuristic algorithm, Low Interferenceamount Neighborhood Tree (LINT), based on the new interference measurement metric Its performances are verified via simulations Simulation results indicate that compared with the well known link-interference based algorithm, LINT works better in general cases The remainder of the paper is organized as follows We introduce the related works in Section II In Section III, the new interference computation model is presented after analysis of interference inducement, which supports rationality of optimality and algorithm LINT in Section IV Finally, the simulation results and conclusions are presented in the in Section V, VI, respectively IIRELATED WORKS In this section, we discuss related works in the field of topology control with special focus on the issue of interference Reducing interference effects is one of the main goals of topology control besides direct energy conservation by restriction of transmission power Burkhart et al [6] presents a traffic-independent model and defines the interference of a link e=(u, v) as the cardinality of the set of nodes covered by two disks centers at u and v with radius, denoted as coverage set of link e,cov(e) This model, named as link-interference via coverage is chosen

2 from the assumption that, whenever a link (u, v) is used for a send-receive transaction all nodes whose distance to node u or node v is less than will be affected in a way [7] extends this work and proposes node-interference via coverage model The interference of a node u is defined as the imum coverage set of links, incident on u However, coverage model is based on the question how many other nodes can be disturbed by a given communication node or link, thus considered to be an issue at the sender instead of at the receiver, where message collisions actually prevent proper reception Secondly, its weakness is that only introduction of one addition node might lead the interference valued pushed up from a small constant to the imum possible value This behavior contrasts to the intuition that a single additional node represents one addition packet source potentially causing collisions Moreover, neglect of the case that a particular node might be influenced by multiple communication links with small coverage set, might lead discontented results of the proposed algorithms [6] as indicated in Section IV in detail An attempt to correct for this deficiency is made in [8], where an alternative, receiver-centric, interference model is introduced In this model, node u will be interfered by v whose distance to v is less than R v, its distance to reach the farthest neighbor, or { v R v } formally It is denoted as node-interference via transmission model Under the assumption that only symmetric edges are considered, it can be proved that that nodes set mentioned above equivalent to{ v R u } Unfortunately, one fatal drawback is that previous works consider the interference range equals to the transmission range According to the theoretical analysis of actual cause of interference in reference [9], interference range differs from transmission range generally and hidden terminals located within the 178d distance (d denotes the communication distance) of the receiver are also disturbing sources, which is neglected in previous works at all times Researches mistake nodes within the transmission range for the only hidden interfering nodes III NEWORK AND INTERFERENCE MODEL Summarily, interference-efficient topology control is to find a sub-graph H from the original graph to minimize interference while preserving fixed properties Thus such definitions should be explicit and reasonable, that is (i) construction of structure, (ii) interference measurement mechanism, and (iii) properties maintained A Network Model In this paper, a wireless ad hoc network is modeled as a well-known Unit Disk raph (UD) [10] with vertices in V representing network nodes, and the edges E representing communication links In the original communication graph = (V, E ), an edge (u, v) exists iff the Euclidean distance between such a pair is at most the imum transmission range R In order to prevent existing basic communication between neighboring nodes from becoming unacceptably cumbersome [11], only symmetric edges are considered First, we point out the inconsistency in pervious topology control works among reducing interference, conserving energy and also preserving symmetric edges using the omnidirectional antennas Previous studies claims that power consumption and interference reduction can be jointly achieved through topology control under the assumption of symmetric edges Nevertheless, any symmetric method must contain Nearest Neighbor Forest structure, which may have Ω( n) larger interference than the optimal topology proven in [8] Thus who claim interference efficiency may be dubious Using directional antennas, where the transmission is omnidirectional, but the reception is directional, is capable to prevent the inconsistency depicted above Adaptively adjusting both its transmission power and antennas direction according to different receivers would be complex, so the transmission power of any device is taken fixed, and nodes only adjust the direction of antennas to reflect its neighbors in our formulation And in the resulting topology H, reducing interference but not conserving energy consumption is our main issue in this paper Although it may contradict the primary aim of topology control energy conservation, it reflects another perspective of modeling and its development under the power adjustment is our future work B Measurement of Interference Intuitionally, a node in the network is interfered by others, if messages are received but not intended for it [12] This interpretation is our foundation of new metric of interference measurement From the perspective of the physical layer, a signal arriving at a receiver is assumed to be valid if the SINR is above a certain threshold T SINR We assume a transmission to a receiver with transmitter-receiver d meters and at the same time, an interfering node r meters away from the receiver starts another transmission According to analysis in [9], under the assumption of homogeneous radios and TWO-RAY ROUND pathloss model, a crucial conclusion is made that interference range is 4 TSNR d, with an approximation value 178 d when T SNR is set to 10 for instance Previous researchers mistake nodes within the transmission range for the only hidden interfering ones Distinctly, for a node, all active neighbors within its interference range are potential interfering sources Consequently, interference amount, defined as the imum cardinality of active interference neighbors set, is our new interference measurement metric Compared to the existed model, implicit but threatening neighbors are considered at the first time by us Definition 1 iven a structure H=(V,E), the interference neighbors set of a node u communicating with v in, denoted as INei ( u ), is defined as follows:

3 INei 4 ( u) = { w V w D( w, TSNR )}, where D(u,r) denotes the set of nodes located in the circular area centered at node u with radius r, and the communication distance If node u communicates with neighbors over multiple links, how much interference u may experience from other irrelevant nodes in the worst case is what we would like to know Definition 2 iven a topology H=(V,E), the interference amount of node u, denoted as IA(u), equals to the imum value of INei ( u ) incident on link (u, v), ie, IA( u)= INei ( u) Interference amount of the topology, E denoted as IA(H), is defined as u VIA( u) Notice that IA(H) is our metric to measure the interference of a network in the following sections Obviously, INei ( u ) includes all the threatening neighbors who may inflict interference potentially, while link (u, v) is active, thus IA( u) = INei ( u) gives an upper bound of E interference suffered by this node Moreover, this receivercentric model is based on the strict definition of interference, directly measuring the level of being interfered It is our main contribution in this paper C Properties Maintained Finally, we mainly discuss the connectivity property in this paper Connectivity is crucial since any working networks rely on it Our task is to fulfill the connectivity while reducing the interference amount possibly, denoted by MIN_IFAMOUNT Whether an optimal solution exists is also under discussion in Section IV IV LOW INTERFERENCE-AMOUNT TOPLOLOIES A Optimality In this section, firstly, we give an optimal solution to MIN_IFAMOUNT and prove it Note that the node interference now depends on the final topology H, which introduces a level difficulty compared with link interference studied previously To construct a topology with interference amount as low as possible, surprisingly, we observe that an analogy exists between our solution and MST after assigning weights to links Definition 3 iven a structure H, weight of link e= (u, v), denoted as W(e), equals to imal value of INei ( u ) and INei vu ( u ), ie, W( e)=( INei ( u), INei vu ( v ) ) It is not so obvious to obtain the conclusion that, the minimum spanning tree (MST) still produces the optimal network topology (OPT) with the minimal interference The edge weight in MST process is defined above Lemma iven a structure H, for any edge f, the inequation W( f ) IA( H) is correct Proof Consider the interference amount of structure H, denoted as IA(H) Obviously, for any node u V, H IA( u) IA( H) Now that the structure is connected, it is obvious that one link f adjacent to u and v ensures such that W( f)=( INei ( u), INei vu( v) ) ( INei ( u), INei ( v) ) uw E uw vw E INei uw ( u) = IA( u) Clearly, uw E IA( H) Putting these INei vw ( v) = IA( v) vw E properties together, we have W( f ) IA( H) Note that if node u maintains IA( u) = IA( H), (, ) E st W( ) = IA( H) H We can now prove that MST correctly finds the optimal solution to MIN-IFAMOUNT problem, thus construct a topology with least interference Theorem MST produces an optimal topology for MIN- IFAMOUNT problem Proof Assume the MST is not optimal and OPT is an optimal topology That is to say, IA(OPT) < IA(MST) Consider the edge with the highest weight in MST, e = (u, v) By the Lemma above, since e has the highest weight in MST, then W( e )=IA(MST) The link e does not belong to OPT, otherwise it contradict with optimality And the weights of all links in OPT is less than the weight of link e This means a connected graph can be constructed with using links whose weight is less than W(e), and this violates the process of MST Since an optimal solution is given with a polynomial time complexity, any comparison merely concentrating on interference amount is meaningless by reason of the unfair measuring criteria In what follows, for the worse performance in some cases, a polynomial time but approximate algorithm is proposed based on the metric interference cost B Interference Cost Metric It can be shown that the work presented in reference [6] performs badly when a particular node is interfered by multiple links with smaller link interference For example, consider seven nodes with equal imum transmission power distributed in a square area as shown in Fig1(a) Fig1(b) gives a topology in which the links that interfere with the least number of nodes are selected, as proposed in [6] The number associated with each node indicates the interference level of the node in the topology (ie, the number of communication links contributing interference to the node, differs from ours) We find that node o is the one interfered mostly in this graph Now consider another possible one in Fig1(c), in which link is selected instead of cd In this topology, node o is still the node interfered mostly, but this time it is interfered by four links, instead of five as in Fig1(b) Thus the proposed algorithm in [6] may not find a sub-graph with nodes suffering vw

4 from low interference, thus failing in finding the minimum interference level structure edges is 6, so (o,c) instead of (c,d) is added and the worse results are avoided b a c o d f e b( 2) o( 5) f(2) e( 2) b( 2) o( 4) f(3) (a) (b) (c) Figure 1 Two topologies with nine nodes (a)a network with seven nodes (b) A topology with five links interfering with node o (c) A topology with four links interfering with node o Moreover, since adding one edge e to a topology may cause different levels of interference to each node v cov( e) For nodes with higher interference level, including edge e will result in higher incremental of contention to them even though e may interfere fewer number of nodes in the network In other words, it is the main deficiency that nodes influence never participate into the process of edge chosen Contrarily, our proposed solution inspires concerns with establishing a feedback mechanism to avoid such phenomena mentioned above in a way To measure the interference increment caused by such an edge included into the topology, we map node s influence into link, named as interference cost on link as follows Definition 4 iven a structure and an active link e=(u, v), link interference cost, denoted as IC(e), is defined as cardinality of the union set of interference neighbors of nodes within the link s coverage set, ie, IC( e= ) IC( ) = INei wx ( w) w cov( ) wx E,where cov( ) is the coverage set of link (u, v), representing the nodes located in the region D(u, d(u, v)) or D(v, d(v, u)) produced by the communication link (u, v) b( 3) 7 f(3) f(3) 6 6 e( 3) 6 o( 6) 6 b( 3) o( 6) b( 3) e( 3) f(3) o( 6) e( 3) C LINT Algorithm Accordingly, a heuristic algorithm is proposed, namely, Low Interference amount Neighborhood Tree (LINT) LINT is then compared to LIFE in [6], which also aim at the problem above but may perform badly sometimes illustrated above Note that the framework of two algorithms is similar, except that link interference cost substitute for link interference via coverage in [6] The main idea of LINT is to add an edge with the least interference cost for each pair of nodes that is not connected Starting from the edge with minimum value, in each iteration of the algorithm an edge (u, v) is proceeded If node u and v are already connected, (u, v) is just ignored or otherwise it will be added to the resulting topology After adding, update the interference amount of node w cov() and also interference cost of remaining edges in As a result, the topology constructed by LINT maintains the connectivity of the original network with the least possible interference amount The overall time complexity is polynomial through simple analysis Tab 2 Algorithm LINT INPUT: a set of nodes V, the imum transmission radius R OUTPUT: graph H Function LINT: create the original graph with R E H =Φ while E Φ e=(u,v) E with the minimum interference cost if u and v are not connected in H then E H = E H {e} update the interference amount of node w cov(e) update the interference cost of related links end if E = E \{e} end while H =(V, E H ) END 6 6 c(3) 7 d( 3) (a) (b) (c) Figure 2 An illustrated example Based on the observations above, if more than one edge can be selected to connected two connected components, the edge which interferes to the node with the largest interference cost should be avoided As a example, in Fig 2(a), the edges (a,b), (b,c), (d,e), (e,f), (o,f) are included into the resulting topology Till now, the smallest cost of remaining candidate V SIMULATION STUDIES A Simulation Environment and Parameters In this section, we conducted extensive simulations to study and compare the performance of the proposed topology control algorithm LINT with Burkhart s LIFE in [6] The networks are constructed by randomly distributing nodes in a square area Without loss of generality, the mean result is derived from 20 networks, randomly generated with

5 different number of nodes N and the imum transmission range R In order to measure the interference reduction quantitatively, interference amount reduction ratio R IA is defined as 1 2 R IA= 100% I( H2) I( H ) I( H ), where I( H1) denotes the interference amount of the topology generated by LIFE, and I( H 2) represents the interference amount of the resulting structure constructed by LINT with the metric defined in Definition 4 The total interference amount of a structure H, is formulated as TI( H) = IA( u) u V H Approximate estimation of the throughput is another parameter concerned Since the static instinct of topology control, we calculate the independent set (ISet) of a structure instead Then in a way, Thr( H ) ( ISet ) i i and the curves is flat, for the reason of fewer edges in and no guarantee of connectivity For instance, the value is about 30 in our simulations when R is 10 Figure 4 Total Interference amount for LINT and LIFE (R =10) B Topology Comparison First of all, to evaluate the average performance between the proposed LINT and LIFE, we put different number of nodes N from 20 to 80 with the increment 5 and the imum transmission range R is set from 5 to 15 with the increment 25 Ratio RIA% R=5 R=10 R= Number of Nodes Figure 3 Interference amount improvement ratio for LINT Fig 3 depicts the interference amount reduction ratio R IA of LINT in comparison to LIFE The results show that R IA is positive, with approximate peak value 1182% in our simulation We find that R IA improves as R and N increase, because the choices of paths between any two nodes of the network also increase Hence, our revised mechanism may work more efficiently A critical observation is that when R t equals to a value 15 and the density of nodes is large, in our simulation, it has little influence on R IA because such a value R has great probability to include all the possible neighbors in the resulting topology In the same way, when N is less than a fixed value, determined by R, R IA equals to 0 nearly Figure 5 Throughput for LINT and LIFE (R =10) Fig 4 and Fig 5 illustrate the performance comparisons of LINT and LIFE simultaneously in terms of total interference amount TI( H) and throughput Thr( H ) with the transmission range 10 Note that when N is less than 30, meaninglessness occurs due to disconnectivity These results above demonstrate that LINT can significantly reduce the interference amount for a given network while the total interference amount and the throughput are still maintained, far from degradation The difference between topologies of resulting graph is depicted distinctly in Fig6 Another group is illustrated in Fig7 We plot the circles on vertices to demonstrate whose adjacent links are varied in the process of choosing links For example, node A suffers the most interference amount 15 in the resulting topology computed by LIFE Due to edges chosen in a marginal distinct, node B with only interference 13 is the greatest Simultaneously, the total interference amount is 303 and 299, respectively while two throughputs are all 27 An observation is that LINT choose edges in a marginal district to avoid more nodes interfered by the communicating neighbors, which is illustrated in Section IV, thus we can get the conclusion that LINT can reduce interference amount correspondingly

6 VI CONCLUSIONS Topology control draws considerable attentions recently in wireless ad hoc networks for interference reduction In this paper, we propose a new interference computation model that aims to reflect the interference inducement on the physical layer The advantages of this model are twofold: On the one hand this definition corresponds to the intuition due to its receiver-centricity On the other hand, it accords with the real cause of interfering quantitatively Then we investigate the corresponding topology control problem of minimizing the interference of the constructed structure, namely, MIN_IFAMOUNT, and optimally solve it in Section IV Additionally, in order to correct the drawback of algorithms proposed in [6], link interference cost as the metric is applied The results via simulation show that, compared with existing version LIFE, the revised algorithm LINT outperforms on the fact that interference amount can be reduced up, while the total interference and the throughput of the network are still not degraded As a future work, we would like to analyze the approximation of the optimal solution to LINT, and apply the interference measurement mechanism into routing protocols Additionally, our crucial interference computation model, may require to be reconsidered under transmitting power adaptation and reestimated in a more practical and reasonable way B A Figure 6 Topology generated by LIFE and LINT Figure 7 Topology generated by LIFE and LINT REFERENCES [1] I Chalmtac, M Conti, J J N Liu, Mobile ad hoc networking: imperatives and challenges, Journal of Ad hoc Networks, 1(1): 13-64, Jan 2003 [2] L Hu, Topology control for multihop packet radio networks, IEEE Trans on Communications, Vol 41, pp , 1993 [3] RRamanathan, R Rosales-Hain, Topology control of multihop wireless networks using transmit power adjustment, Proc of IEEE Infocom, pp90-100, 2000 [4] V Rodoplu, TH Meng, Minimum energy mobile wireless networks, IEEE JSelect Areas Communications, Vol17, no8, pp , 1999 [5] X Li, Y Wang, W Song, Applications of k-local mst for topology control and broadcasting in wireless ad hoc networks, IEEE Transactions on Parallel and Distributed Systems, 2004 [6] M Burkhart, Pvon Richenbach, R Wattenhofer, A Zollinger, Does topology control reduce interference?, Proc of ACM MobiHoc, 2004 [7] K Moaveni, X Li, Low-Interference Topology Control for Wireless Ad Hoc Networks, Ad Hoc & Sensor Wireless Networks, Vol 1, pp 41-64, 2005 [8] Pvon Richenband, S Schmid, R Wattenhofer, A Zollinger, A robust interference model for wireless ad-hoc networks, Proc of IPDPS, 2005 [9] K Xu, M erla, S Bae, Effectiveness of RTS/CTS handshake in IEEE based ad hoc networks, Journal of Ad Hoc Networks, 2003,1(1): [10] BN Clark, CJ Colbourn, DS Johnson, Unit Disk raphs, Discrete Mathematics, 86: , 1990 [11] R Prakash, Unidirectional Links Prove Costly in Wireless Ad-Hoc Networks, Proc of the 3rd Int Workshop on Discreet Algorithms and Methods for Mobile Computing and Communications (DIALM), 1999 [12] XM Zhang, Q Liu, D Shi, YZ Liu, X Yu, An Average Link Interference-aware Routing Protocol for Mobile Ad hoc Networks, Proc of 3rd International Conference on Wireless and Mobile Communications, March 2007