Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

arXiv:1004.1058v1 [cs.NI] 7 Apr 2010 Optimal Tradeoffbetween Exposed and Hidden Nodes in Large Wireless Networks P.M. van de Ven1,2 A.J.E.M. Janssen2,3 J.S.H. van Leeuwaarden1,2 October 28, 2018 Abstract Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoffbetween collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies. 1 Introduction Carrier sense multiple-access (CSMA) type protocols form a popular class of medium access proto- cols for wireless networks. The first CSMA protocol was introduced by Kleinrock and Tobagi [10] in 1975, and has seen many incarnations since, including the widely used 802.11 standard. In this paper we provide an asymptotic analysis of large wireless networks operating under CSMA, in the presence of collisions. CSMA is a randomized protocol that allows nodes to access the medium in a distributed man- ner. The absence of a centralized scheduler creates more flexibility and allows for the deployment of larger networks. An early example of such a randomized procedure is the ALOHA protocol [1], which forces nodes to wait for some random backoffperiod before starting a transmission, in order to reduce the likelihood of nearby nodes transmitting simultaneously. The latter event would cause the signals to interfere with each other, and may result in a collision that renders the transmissions useless. CSMA improves upon ALOHA by letting nodes sense their surroundings to detect the presence of other transmitting nodes. If a node detects at least one active (i.e. transmitting) node within its sensing range, its backofftimer is frozen, deferring the countdown until the channel is sensed clear. Using this mechanism, collisions can be further reduced. A key performance measure in wireless networks is throughput, which we define as the average number of successful transmissions per unit of time. We investigate the relation between the sensing range and the throughput. The effect of the sensing range can be understood as follows. A small sensing range allows for more simultaneous transmissions, but is less effective in reducing collisions. On the other hand, a large sensing range admits fewer transmissions, but also mitigates interference. The main contribution of this paper is the examination of this tradeoffin relation to its effect on the throughput. The network is characterized by the sensing range and the interference range. A node can only initiate a new transmission when all nodes within its sensing range are inactive. This transmission 1Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 2Eurandom, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 3Eindhoven University of Technology, Department of Electrical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 1 is successful when all nodes within the interference range of the destination node are inactive, and fails otherwise. The network performance suffers from two complementary issues: hidden nodes and exposed nodes (see [15]). Hidden nodes are nodes located outside the sensing range of the transmitter and are therefore not detected by the carrier-sensing mechanism. Hidden nodes cause collisions as they are within the receiver’s interference range. Exposed nodes are nodes located outside the receiver’s interference range but inside the sender’s sensing range. So despite being harmless to the transmission, exposed nodes are nevertheless blocked. As the sensing range grows, the number of hidden nodes decreases, and the number of exposed nodes increases. In recent years the carrier-sensing tradeoffbetween hidden and exposed nodes has received much attention [11, 12, 18, 20]. Most of these analytic studies make the assumption that the activity of nodes and their backoffprocesses are independent, which greatly simplifies the analysis. The interaction between nodes, however, should be taken into account, as it is typical for the distributed control and has a large impact on the performance of the network. We do take into account this interaction, by keeping track of the activity of nodes over time. The classical model for such interaction in wireless networks is developed in Boorstyn and Kershenbaum [4]. This model has been used in recent years to study throughput-optimality [14] and fairness [7, 8, 17, 16] in a setting without collisions. The stability

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