New Media Access Protocols for Wireless Ad Hoc. Networks Based on Cross-Layer Principles

Transcription

1 New Media Access Protocols for Wireless Ad Hoc Networks Based on Cross-Layer Principles S. Toumpis Telecommunications Research Center Vienna (ftw.) Donau-City-Straße, 1/3 Stock, A-1220, Austria A. J. Goldsmith Department of Electrical Engineering Stanford, CA, Abstract We introduce two new Medium Access Control (MAC) protocols for wireless ad hoc networks, the Progressive Backoff Algorithm (PBOA) and the Progressive Ramp Up Algorithm (PRUA). Both protocols divide time in frames in which a contention slot is followed by a data slot. PBOA is integrated with a well known power control algorithm. PRUA performs no power control, and so is not as energy efficient, but can achieve a tight packing of transmissions by allowing nodes to make educated decisions during the contention period. Under both protocols, contenting nodes try to select their potential destinations so that spatial reuse is as high as possible, even if that means transmitting a packet that is not on the head of their routing buffer. We compare both protocols with Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), and also with the Power Control MAC (PCM) protocol. We also compare them with a hypothetical MAC protocol that would be able to make optimal decisions and so achieve the network capacity. We show that both protocols perform better than CSMA/CA and PCM in terms of throughput and robustness with respect to the choice of the routing protocol. Also, PRUA is more energy efficient than CSMA/CA, and PBOA is more energy efficient than both CSMA/CA and PCM. However, due to their distributed nature, our protocols still can not achieve the network capacity, even in simple network topologies. Index Terms Cross-layer design, CSMA/CA, MAC, media access, network capacity, PCM, PBOA, PRUA, power control, wireless ad hoc networks. Work supported by the Office of Naval Research (ONR) under grants N and N , the Stanford Networking Research Center, and Kplus funding for the ftw. project I0. A preliminary version of this work appeared in ICC 2003.

2 1 I. INTRODUCTION Wireless ad hoc networks are collections of nodes communicating exclusively over a wireless channel. Since wireless signal power decays with distance and in the presence of obstructions, each node can communicate directly with only some of the other nodes, that typically lie in its vicinity. On the other hand, the traffic requirements of the nodes are taken to be arbitrary, therefore it is necessary that nodes relay other nodes packets to their final destinations. To avoid the waste of resources and reduction of throughput, it is necessary that nodes coordinate their transmissions, so that no intended receiver is overwhelmed by too much interference. On the other hand, it is also important that transmissions are placed as close as possible, so that the amount of spatial reuse of the available bandwidth is maximized, and the network operates close to capacity. It is the task of the Medium Access Control (MAC) layer to strike a balance between these conflicting goals, by coming up with the set of transmitter-receiver pairs that should be active at any given time [1], [2], [3], [4], [5], [6], [7], [8]. Since each transmitter-receiver pair represents a link, medium access is often called link activation. Link activation may be thought of as consisting of two tasks: Firstly, the set of transmitters must be decided upon (transmitter activation). Secondly, each transmitter must decide on its receiver (receiver selection). If each node maintains different queues for each of its potential receivers, the receiver selection problem corresponds to deciding which queue to draw from for a particular transmission. If, on the other hand, each node maintains a single queue where all the packets awaiting transmission are placed, the receiver selection problem is equivalent to finding a proper queuing discipline: deciding to whom to transmit is equivalent to deciding the order with which packets in the queue are serviced. Irrespective of how packets are actually stored (i.e. in one large queue per node or in many queues, one for each potential destination), we can always assume, with no loss of generality, that all packets exist in a large (perhaps virtual) queue, so that the receiver selection problem becomes a problem in queuing. This is the approach we adopt. In this work, we propose two media access protocols, the Progressive Back Off Algorithm (PBOA), and the Progressive Ramp Up Algorithm (PRUA). Time is divided in frames, and each frame consists of a contention slot and a data slot. Nodes try to gain access to the channel during the data slot by contending during the preceding contention slot. PBOA performs jointly medium access and power control. PRUA does not allow for power control (and therefore sacrifices energy efficiency) but can achieve a tight packing

3 2 of concurrent transmissions, by allowing the nodes to make educated decisions during the contention. Both protocols make use of queuing disciplines that are more relaxed than the First In First Out (FIFO) discipline. Because time is slotted, our protocols can easily be modified to reduce the control overhead, by assigning more than one data slot to each contention slot. Our strategy for evaluating the performance of our proposed protocols is two-pronged: On the one hand, we compare them with two other MAC protocols: the first is the most ubiquitous protocol, CSMA/CA (which includes an RTS/CTS handshake). The second is an idealization of the Power Control MAC (PCM) protocol, which was proposed in [9] and has since attracted significant research interest. This idealization, which we call Ideal-PCM, is supported by a genie, and can outperform all possible variants of PCM, both in terms of throughput and energy efficiency. On the other hand, we also compare the achieved throughput of our protocols with the network capacity. In other words, we compare their performance with that of a hypothetical media access protocol, that can make optimal, centralized decisions on how to allocate bandwidth, completely eliminating not only collisions, but also the suboptimal use of the medium. The comparison with the capacity also emphasizes the importance of decisions on other layers, notably the routing and power control layers, and highlights the interplay between protocols spanning different layers, thus motivating a cross-layer aware design. We find that PBOA and PRUA are superior to CSMA/CA and Ideal-PCM in terms of achieved throughput and robustness with respect to the routing protocol. Also, PBOA is more energy efficient than CSMA/CA and PCM, and PRUA is more energy efficient than CSMA/CA. However, both protocols fall short of achieving the network capacity, due to their distributed nature, even in simple network topologies. The rest of the paper is organized as follows: In Section II we specify the network model. In Section III we review the operation of CSMA/CA and discuss its limitations, and in particular those aspects that motivate the design of our protocols. The PBOA and PRUA protocols are introduced in Sections IV and V respectively. We introduce Ideal-PCM, and compare the performance of CSMA/CA, PBOA, PRUA, and Ideal-PCM in Section VI. We conclude in Section VII. II. NETWORK MODEL Consider a collection of n nodes communicating over a common wireless medium, by exchanging data packets. Each node is equipped with a transmitter, a receiver, and a buffer used for storing data. We assume

4 3 that a given node cannot transmit and receive at the same time (i.e., communication is half-duplex). Nodes are not interested in multicasting packets, so that each created packet has a single destination. When node i transmits with power P i, node j receives the signal with power G ij P i. We define the channel gain matrix to be the n n matrix G = {G ij }. Its diagonal elements are not important since a node does not transmit to itself. Thus, we set G ii = 0 for i = 1,..., n. We model thermal noise and background interference (e.g. interference from other networks) jointly as a single source of noise with power η i for node i. Let T be the set of transmitting nodes at a given time and assume that node j T is receiving information from node i T. Then the Signal to Interference and Noise Ratio (SINR) at node j will be γ ij = G ij P i η j + k T,k i G kjp k. We assume that nodes use for all transmissions a common transmission rate R, and that the receiving node j will be able to decode the signal from i, with a negligible probability of error, provided the signal to interference and noise ratio γ ij is constantly above a given threshold γ T : γ ij γ T. Otherwise, the signal is lost. This is a somewhat pessimistic assumption, as in many practical receivers designed to function above a given SINR threshold, there is a non-negligible probability that a packet that is below but close to the SINR threshold will be correctly decoded. However, we will use this assumption for clarity of exposition, as the design of our protocols will not be affected and the numerical results will not change significantly if a more accurate model is used. III. CARRIER SENSE MULTIPLE ACCESS WITH COLLISION AVOIDANCE (CSMA/CA) The MAC protocol that has attracted the greatest attention of the research community for use in wireless ad hoc networks is Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA), coupled with a RTS/CTS handshake. For example, it is used in IEEE [1] 1. Under this protocol, a node that wants to send a data packet will first wait for the channel to become idle and then transmit a short RTS (Request To Send) packet. The potential receiver, assuming it also perceives an idle channel, will immediately respond with a CTS (Clear To Send) packet that authorizes the initiating node to transmit, 1 We note that in IEEE the use of the RTS/CTS handshake is optional, but leads to very poor performance wherever hidden terminals are present [10]. IEEE also includes a polling protocol, suitable for communication with a central Access Point, and therefore beyond the scope of this work.

5 4 and also informs neighboring hidden nodes (defined as nodes that are outside the communication range of the transmitter but within the communication range of the receiver) that they will have to remain silent for the duration of the transmission. In most incarnations of the protocol, for example the one used in IEEE , the successful reception of the data packet is followed by the transmission of an acknowledgment (ACK) packet by the recipient of the data. Nodes that overhear the RTS packet will refrain from transmitting until the CTS packet can be received, and those overhearing the CTS packet will refrain from transmitting until the whole data packet is sent. A node perceives an idle channel only if it does not detect an ongoing transmission by carrier sensing and has not been silenced by a control packet. The RTS/CTS handshake is coupled with a collision avoidance mechanism that ensures nodes do not transmit immediately after the channel becomes idle, but rather wait for a random period, to minimize the probability of a collision. In the following, we will refer to this protocol simply as CSMA/CA [9]. CSMA/CA has many shortcomings, that have been well documented in the literature over the last several years, in the context of performance analysis for IEEE [10], [11]. We now discuss some of them, very briefly, and in particular those that motivated the design of PBOA and PRUA. First of all, CSMA/CA does not completely eliminate collisions due to the presence of hidden nodes, since, for example, it is still possible that two or more CTS packets will collide with each other, and hidden nodes will never be informed that they must keep quiet. Secondly, hidden nodes (which we have defined as nodes within the communication range of the receiver but not within the communication range of the transmitter) are not the only nodes that can interfere with, and potentially destroy, an ongoing transmission. To gain some intuition on the nature of this problem, let us consider the simple case when a receiver R is receiving a packet from a transmitter T, in the presence of interference from a single interferer I. Let both transmitter and interferer transmit with the same power P, and assume that the receiver is subject to thermal noise η. Also, let d IR and d T R be the distances ( ) a ( ) a d between I and R and between T and R respectively. Finally, let G IR = K 0 d IR and d GT R = K 0 d T R be the power gains between I and R, and T and R, respectively, where K, α and d 0 are appropriately chosen constants. If the interferer were not transmitting, the maximum possible range of communication would be d max T R = d 0 ( KP ) 1 α ηγ T. Simple algebra shows that, in order for the SINR not to drop below γ T, I

6 5 must keep at a minimum distance from R equal to Note that d min IR d min IR = [( d 0 d 0 d T R ) α 1 γ T is an increasing function of d T R. When d T R is very small, d min IR ] 1. (1) η α KP d T R γ 1 α T. However, as d T R approaches d max T R, dmin IR approaches infinity, and can clearly be arbitrarily larger than the maximum range of successful communication, d max T R. It can also be so large, so that an interferer I placed at a slightly smaller distance will not be able to use carrier sensing to sense the ongoing activity of the transmitter. To conclude, in certain environments, if the transmitter and receiver are not sufficiently close there can be potential interferers lying well beyond the communication range of the receiver, that will never be notified by a CTS to remain silent, and will also be so far away from the transmitter so as not to be able to sense the ongoing transmission. CSMA/CA has no mechanism of silencing those potential interferers. Another problem of CSMA/CA is that, since the potential transmitter must receive a CTS packet (and possibly also an ACK packet), it is necessary not only that the receiver is not overwhelmed by interference, but also the transmitter. This need for bidirectionality in the communication between the data transmitter and the data receiver places an additional restriction on how close transmissions of data can be packed in the network. We will refer to this issue as the bidirectionality problem. A final point is that CSMA/CA is formally only a transmitter activation algorithm, and not a link activation algorithm. In other words, CSMA/CA specifies who will transmit, and when, but not to whom. As discussed in Section I, such decisions are also the responsibility of the MAC protocol. However, research in CSMA/CA typically neglects this point. Apparently, the reason is historical: CSMA/CA evolved out of random access algorithms such as CSMA, that were originally applied in topologies with no hidden terminals. There, regardless of the chosen receiver, the interference experienced by the rest of the nodes is always the same, and from a network throughput perspective the receiver selection algorithm is unimportant. The design of a receiver selection algorithm to complement CSMA/CA falls beyond the scope of this paper, so in the following we will assume that it is coupled with FIFO queuing: nodes always attempt to transmit the packet at the head of their queues. Note that the problems mentioned plague not only CSMA/CA, but many other protocols that based to some extend on CSMA/CA. For example, the hidden terminal is not completely solved and the bidirectionality problem remains in the protocols that appear in [9], [12], and [13].

7 6 A. Performance of CSMA/CA in Simple Topologies As a first example, let us consider the chain network of Fig. 1. The network consists of 60 nodes 1, 2,..., 60, arranged along the closed chain The gain coefficient between any pair of immediate neighbors is G, and 0 for all other pairs of nodes. All nodes are subject to a common level of thermal noise η, and can transmit with any power between 0 and a maximum P max, using a transmission rate R = 1 Mbps. We assume that GPmax η γ T, so that each node can receive a signal from one of its two neighbors, if the other neighbor is not transmitting. We also assume that γ T > 1, so that if two nodes transmit with power P max at the same receiver, the receiver will not be able to decode any of the two signals. All nodes create packets with the same rate, and each node picks as the destination for each packet one of its two immediate neighbors, at random and with equal probabilities. Packet arrivals are Poisson, and all packets have a size of 10 Kbits. Since the topology is highly symmetric, and the traffic pattern is very simple, it is straightforward to calculate upper bounds on the maximum aggregate throughput that any MAC protocol can achieve. On the one hand, there can be no more than 30 nodes transmitting, as each transmitter must be associated with a distinct receiver, and there are 60 nodes in all. On the other hand, we can use a time division that divides time in 4 equal parts, each devoted to one of the four following groups of transmissions: {..., 60 59, 1 2, 4 3,...}, {..., 1 60, 2 3, 5 4,...}, {..., 59 60, 2 1, 3 4,...}, and {..., 60 1, 3 2, 4 5,...}. Assuming that the nodes have sufficiently large buffer sizes to cushion bursts of packet arrivals, it is clear that packet arrival rates arbitrarily close to 0.5 packets node can be supported. Therefore, using a centralized scheme, aggregate throughputs arbitrarily close to 30 Mbps are achievable. Let us now assume that the nodes operate using CSMA/CA, and that at a given point in time there is an ongoing transmission, for example from node 2 to node 3. Clearly, node 1 cannot be receiving a packet at the same time. In addition, it cannot be transmitting (necessarily to node 60) because that would imply that nodes 1 and 2 transmitted their RTS packets, and received their CTS packets, in sync. This kind of behavior is very unlikely in CSMA/CA for any reasonable value for the propagation delay (impossible if we ignore propagation delays). So node 1 does not participate in any transmission. By a similar argument, node 4 does not participate in any transmission also. To summarize, because of the bidirectionality problem, each node participating in a data packet transmission, either as a transmitter or as

8 7 a receiver, must have an idle neighbor. Therefore, the maximum number of simultaneously communicating node pairs is 20, and the bidirectionality problem means that the aggregate throughput can not possibly be greater than 20 Mbps. In Fig. 1 a set of 20 pairs of nodes than can be simultaneously active appears shaded. However, because CSMA/CA is a distributed protocol, it is impossible for nodes to coordinate so that the transmissions are so tightly packed. Indeed, the actual maximum aggregate throughput of CSMA/CA, as determined by simulating IEEE , is 10.9 Mbps, or only around 36% of the maximum possible aggregate throughout. This is assuming, as in all simulations in this paper, that buffers can hold 100 packets, and a maximum acceptable packet dropping probability P b = As a second example, let us consider the regular grid network of Fig. 2, in which 64 nodes are placed on a torus, so that each node has exactly 4 neighbors. Each created packet picks one of the 4 neighbors of the node at random, and uniformly, as destination. The rest of the parameters are chosen as with the chain network. Because of the symmetry of the grid network and the traffic pattern, it is straightforward to calculate the maximum possible aggregate throughput. Working as in the chain network, we find that a maximum possible aggregate throughput arbitrarily close to 32 Mbps is possible. However, because of the bidirectionality problem, CSMA/CA can not achieve more that 16 Mbps. In Fig. 2, a maximal set of 16 pairs of transmissions that can simultaneously exist appear shaded. Furthermore, because of its distributed nature, control overhead, and imperfect protection against hidden nodes, the maximum aggregate throughput that CSMA/CA can support, as determined by simulating IEEE , is equal to 4.56 Mbps, or only around 14% of the maximum possible aggregate throughput. The parameters used in the simulation were the same as in the case of the chain network. As a last example, let us now move to the random network of Fig. 3. The n = 12 nodes are placed in the box {0 x 400 m, 0 y 100 m} randomly. All nodes can transmit with any power up to a maximum P max i = 0.3 W, η i = W = 90 dbm, the threshold SINR is γ T = 10 db and the common communication rate is R = 1 Mbps. The link gain between nodes i and j is set to G ij = K( d 0 d ij ) α, with K = 10 8, d 0 = 1 m, and α = 4, so that the power of the transmitted signal decays polynomially

9 8 with distance 2. In the figure, nodes that can communicate with each other, in the absence of interference and with the transmitters using the maximum available power, are connected by straight lines. Nodes that can communicate directly but are not very close are more sensitive to the interference of competing transmissions. The packet arrivals are Poisson, and all packets have a size of 10 Kbits. Let us define the following three routing protocols for the random network of Fig. 3: Two nodes will use a single, minimum-hop route to communicate, with the requirement that they only use links whose SNR (in the absence of competing transmissions) is above a given threshold. For the three routing protocols, the thresholds are set to 10 (so that all links may be used for routing), 30, and 120 (so that only the strongest links are used), respectively. We call these protocols RP-10, RP-30 and RP-120, respectively. 3 The topology of the random network does not permit us to use any symmetry arguments, as in the previous cases, to evaluate any theoretical bounds on its traffic carrying capabilities. However, due to its modest size, the methods of [14] can be readily applied. For example, let us assume a uniform traffic load, under which all nodes create traffic for all other nodes, and traffic is created with the same rate for all = 132 distinct source-destination pairs. Using the techniques in [14], the maximum possible aggregate throughput, termed the uniform capacity in [14], can be found to be C u = 0.93 Mbps. This is achieved only if the nodes coordinate optimally, using optimal power control, medium access, and routing, and the node buffers are sufficiently large to cushion the effects of traffic bursts. If, however, no power control is allowed, so that nodes can only transmit with their maximum power, the uniform capacity is reduced by 7.5% to C NPC u = 0.86 Mbps. If the nodes are restricted to route their traffic using the routing protocols RP-10, RP-30, and RP-120, the uniform capacity will be further decreased. In Fig. 4 we plot the uniform capacities of the network for all three routing protocols, with (curve (c)) and without (curve (d)) power control. Let us study the performance of CSMA/CA in this network, as it is implemented in IEEE All simulation parameters are chosen as in the previous cases. Curve (e) of Fig. 4 shows the maximum achievable throughput under a uniform traffic load, for the three routing protocols, and assuming buffers 2 Note that the gain coefficients do not contain any fading term. This is done for simplicity, and the operation of the protocols we will introduce is not affected at all by the presence of fading, as long as the changes in the gain coefficients are not excessively frequent. We elaborate on this point later on. 3 Our choice of threshold levels (10, 30, and 120) for the three routing protocols was motivated by our assumptions on the underlying channel model and the capabilities of the receivers. Under a different set of assumptions, other thresholds will be more appropriate. The important thing about our protocols is that they represent different levels of how aggressive the nodes want to be in using weak links.

10 9 that can hold 100 packets, and a maximum acceptable blocking probability P b = In Fig. 5 we plot the average energy consumed for the transportation of a packet to its final destination with CSMA/CA, and under the three routing protocols RP-10, RP-30, RP-120 (curves (a), (d), (g) respectively), again under a uniform traffic load. As Fig. 4 shows, because of the various shortcomings of CSMA/CA that we mentioned, the throughput achieved is only 50% of the theoretical maximum, in the case of RP-30 and RP-120, i.e., those protocols that avoid weak links. More dramatically, CSMA/CA performs very poorly when coupled with the protocol that is using all links, RP-10, achieving less than 20% of the theoretical maximum. As the simulations reveal, transmissions over weak links, i.e. links between nodes that are barely within communication range, have a very small success rate. Indeed, as suggested by (1), for the transmissions over the weaker links there are many nodes that can potentially destroy an ongoing transmission if they start to transmit, all lying so far away that they can not receive, or even sense any transmission between the communicating pair. A by-product of this problem is that the average energy required for the successful relaying of a packet becomes very large when the network operates under heavy traffic (see curve (a) of Fig. 5). The above result is not an artifact of the particular topology used (see also Section VI), but rather highlights a general problem: CSMA/CA should not be used for communication over relatively weak links. Rather, it should be coupled with a routing protocol that actively avoids such links. Even if this is the case, using CSMA/CA is still problematic. For example, a strong link may simply not exist. Secondly, even if it does, the routing protocol may fail to find it because of collisions. We can summarize this discussion in the following statement: CSMA/CA violates the basic cross-layer principle that a MAC protocol must be robust with respect to the network topology and the choice of routing protocol. To the best of our knowledge, this fact has not been reported in the literature, probably because typically no comparison with the capacity is made, to reveal the large discrepancy, and because simpler channel models are typically assumed, that suppress the fact that the minimum acceptable distance between an interferer and the receiver can be arbitrarily large. IV. PROGRESSIVE BACK OFF ALGORITHM (PBOA) A careful look at the RTS/CTS handshake reveals that its effectiveness can be improved significantly if time is slotted, and nodes start the contention at prearranged times. In the context of Fig. 1, let us assume that at some point in time nodes 2 and 3 have one packet each awaiting transmission, for nodes 1 and 4

11 10 respectively. If the two nodes transmit their RTS packets simultaneously, they will hear the CTS packets also simultaneously, and then will start transmitting at the same time (the geometry is such that all SINR requirements are satisfied). The situation is similar if node 1 has a packet for 2 and node 4 has a packet for 3. Therefore, slotting time seems to solve the bidirectionality problem of plain CSMA/CA, and permit a tighter packing of transmissions. In addition, by imposing structure on the contention period, we can place control packets closer, and reduce the duration of the contention. These observations were taken into account in the design of the Progressive Back Off Algorithm (PBOA), which we now present. A. Frame Format We start by defining the frame format used by PBOA. As shown in Fig. 6, time is partitioned in consecutive frames of fixed duration and each frame consists of a contention slot, followed by a data slot. In turn, the contention slot is divided into m pairs of minislots. The first minislot of each pair is reserved for the transmission of RTS packets, and the second slot for the transmission of CTS packets. The nodes contend for channel access during the minislot period and, depending on the outcome of the contention, some will transmit a data packet during the data slot. The time that must be devoted to a minislot will depend on the system parameters. As a typical case, let us assume that nodes transmit with a rate of 1 Mbps, the size of data packets is 10 Kbits (similar to those used in IEEE ), and the maximum channel propagation delay is 2 µs. Also, assume that the amount of time required by a transceiver to switch from receive mode to transmit mode is 10 µs, a guard time of 3 µs is chosen, and the time required for receiver synchronization is another 5 µs (These parameters are typical for of-the-shelf transceivers, for example those used in IEEE ). As will be shown, each RTS packet will contain the MAC addresses of the source and the destination. Each CTS packet will also contain the source and destination MAC addresses, and in addition a scaling factor used for power control. Assuming that each of the addresses and the scaling factor are 8 bits long, the combined payload of an RTS-CTS pair is 40 bits. This brings the duration of a minislot pair to 80 µs, or 0.8% of the duration of the data packet. This calculation is only indicative and the actual overhead may be different if other system requirements are set. For example, if the communication rate is on the order of a few tens of Kbps, as in most deployed (or proposed) wireless WANs, the overhead will be less. If, on the other hand, the protocol is used in

12 11 a high speed wireless LAN with a communication rate of 55 Mbps, the duration of each minislot as a percentage of the data packet transmission time will be larger. We have also assumed that MAC addresses are only 8 bits long, as they only have to be locally unique, and not globally unique. If, however, using addresses that are unique only locally is not an option, the node addresses may be significantly longer. Finally, we have assumed that data slots are large enough to accommodate data packets with a size of 10 Kbits. If the nodes are running an application that creates much smaller packets, and placing multiple packets on the same data slot is not an option, the data slot will have to be reduced in size, and the control overhead will become more severe. To conclude, the precise level of control overhead will depend on the particular setting. Although our back of the envelope calculations show that the level of control overhead will be manageable in many settings, it is clear that in some more challenging settings the control overhead will be unacceptably high. From the above discussion, it is also clear that nodes must be equipped with clocks, and the clocks of neighboring nodes must be synchronized with an accuracy of a few microseconds. A simple way to achieve this is to equip nodes with GPS receivers. If, however, this is not an option, a synchronization algorithm is needed, that will require neighboring nodes to exchange their clock times. This can be done either implicitly, by monitoring when a neighbor starts to transmit its RTS and CTS packet, or explicitly, by piggy-backing clock information on DATA packets. In the rest of this work, we will assume that neighboring nodes either use GPS, or achieve synchronization implicitly, so that no time is wasted on synchronization other than the guard times. The important issue of time synchronization has received significant attention from the research community, and for a detailed discussion we refer the reader to [2], [15], [16], [17] and the references therein. Finally, we assume that the mobility of nodes does not cause the channel gains to fluctuate significantly over the duration of a contention slot and the accompanying data slot. Using the parameters above, this duration is on the order of 10 milliseconds, so our assumption is justified even for vehicular levels of mobility provided fast fading is suppressed by the use of techniques such as polarization, frequency, and antenna diversity. If fast fading is not suppressed, our assumption is only valid for pedestrian speeds [18].

13 12 B. Protocol Operation Before going into the details of how PBOA operates, we present the main idea: At the beginning of the contention period, all nodes that have a packet awaiting transmission will start contending for the channel. As the contention period progresses, nodes that are unsuccessful progressively back off, so that others can be successful in accessing the channel. At the same time, nodes that have succeeded in capturing the channel take advantage of the remaining time in the contention period to discover the minimum amount of power that is needed to transmit their data packet. The benefits are two-fold: (i) energy is conserved and (ii) other nodes may find that interference is reduced and so may also succeed in capturing the channel. We now specify in detail the operation of the protocol during the contention period. At any time, a node will belong to one of three groups: the contending nodes, the locked nodes and the silent nodes. At the beginning of the contention period each node that has a packet awaiting transmission will be placed in the contending group. It will initially try to transmit the packet at the head of its queue (to the node that represents the final destination of the packet or the next hop in its route). The rest of the nodes form the silent group. During the i-th RTS minislot: 1) Silent nodes listen to the channel. 2) Contending nodes transmit an RTS packet to their intended receiver with maximum power. 3) Locked nodes transmit an RTS packet to their intended receivers. The power they use for transmitting was specified by the intended receiver at a previous CTS minislot. During the i-th CTS minislot: 1) Silent nodes that received an RTS packet from a contending node successfully ( i.e., the SINR γ i was greater than or equal to the threshold SINR γ T ) will send, with maximum power, a CTS packet to notify that node of its success. Each of them will specify a factor equal to g = min((1 + ɛ) γ T γ i, 1) by which the potential transmitter must lower its power, where ɛ is a small design parameter that compensates for imperfect SINR estimation. Therefore, provided the potential transmitter decodes the CTS packet successfully, it will transmit in the next RTS slot with power P i+1 = gp i P i where P i is the power used in the RTS minislot that just passed. The success in the next RTS minislot is guaranteed, as no other node will be powering up, transmissions with a SINR above the threshold are always successful, and the parameter ɛ adequately compensates for changing channel

14 13 conditions. 2) Silent nodes that received an RTS packet (intended for them) from a locked node with an SINR γ i > (1 + )γ T (2) will transmit a CTS packet notifying the transmitter that it can power down to P i+1 = min((1 + ɛ) γ T γ i, 1) P i. We require that > ɛ. 3) All other nodes remain silent. At the end of the i-th CTS minislot: 1) Contending nodes that received a CTS packet (intended for them) become locked. 2) Contending nodes that did not receive a CTS packet will remain in the contending group with probability p, or will move in the silent group with probability 1 p. Any node that remains in the contending group tries to pick a new potential receiver. Specifically, it moves down its queue of buffered packets awaiting transmission (possibly returning to the head once the tail is reached) and searches for a packet with a different destination from the current. If such a packet does not exist, the node will contend for the same packet in the next minislot pair. At the start of the data slot period, all locked nodes transmit their data packet, with the power level that was last specified to them by their intended receivers. The protocol guarantees that the data packets will be received successfully. A flowchart with the operation of PBOA appears in Fig. 7. Note that the nodes do not use the FIFO queuing discipline. Rather, nodes that are not being successful try to pick a new potential receiver, for which the conditions may be more favorable (for example, maybe the first potential receiver is also contending, but the second is not). Also, a locked node will keep sending RTS packets during all the remaining RTS minislots. Otherwise, another node might be successful in becoming locked, and when both locked nodes try to send their data packet during the data slot, there will be a collision. Note that there is no power control during the CTS minislots. To reduce the contention during the CTS minislot period, a CTS packet is transmitted to a locked node, only if (2) is satisifed, i.e., the CTS packet would result in a significant reduction of the transmission power of the locked node. Otherwise, no CTS packet is transmitted, and other, more critical, CTS packet will get through much more easily. Note that locked nodes have guaranteed access to the channel, and so do not need to receive CTS packets.

15 14 Finally, note that we have integrated the RTS/CTS mechanism with a power control algorithm similar to that of [19], [20]. We achieved this in a very straightforward manner, without having to resort to using a separate control channel [21], [6] or a centralized scheduling algorithm [8]. Also, we have totally dispensed with the carrier sense mechanism. As discussed in [11], this makes PBOA immune to the exposed terminal problem. In addition, slotting time allows transmissions to be placed close, solving to a large extent the bidirectionality problem. Finally, under PBOA packets are much better protected (and in fact cannot be destroyed if we assume a stationary channel). To conclude, PBOA addresses effectively the problems of CSMA/CA mentioned in Section III. C. Parameter Selection The number of minislot pairs m and the probability of retransmission p are design variables. Given m and a network topology, there is an optimal value p opt for p, but we have experimentally determined that the performance of the protocol is rather insensitive to p (values of p within 0.1 of p opt that are not too close to 0 or 1 typically achieve 90% of the maximum performance). As m increases, so does p opt, since when there are more minislots it is better for the nodes to be more persistent, so that they back off progressively over the whole minislot period. Also, the denser the network is, i.e., the more neighbors within its communication range a node has, the smaller p opt becomes, as nodes should be less persistent when there is a lot of contention and the expected probability of success of an individual node is small. In Fig. 8 we plot the maximum aggregate throughput of the random network of Fig. 3 under PBOA and our three routing protocols, versus the number of minislot pairs m, and assuming uniform traffic. The curves are determined by simulations. We assume buffers that can hold 100 packets, and a maximum packet dropping rate P b = For each value of m, the optimal value of p is chosen. As m increases, the performance of the protocol at first increases, since the nodes are given more time to resolve the congestion efficiently. However, after some value of m the incremental improvement in the resolution of conflicts is outweighed by the cost of reducing the time devoted to the transmission of data by an extra minislot. The optimal value of m depends on the control overhead incurred by each minislot. For the random network a near-optimal choice of parameters (as determined by extensive simulations), under any traffic pattern, and assuming the overhead of Section IV-A, is m = 15, p = 0.8. However, as Fig. 8 shows, even if we set m = 6, p = 0.7, the throughput is reduced very little.

16 15 D. Performance of PBOA in Simple Topologies Let us study the performance of PBOA in the chain network of Fig. 1. Because PBOA does not suffer from the bidirectionality problem, it is, in principle, possible to have 30 simultaneous transmissions in the network. On the other hand, because PBOA is distributed, the chances of having such a tight packing of transmissions are negligible. Indeed, by simulation, we find that PBOA actually achieves only 17.2 Mbps, still an improvement of 57% over CSMA/CA. In the simulation we assumed the parameters of Section IV-A, we set m = 15, p = 0.85, and we assumed buffers that can hold 100 packets and a maximum blocking probability P b = To quantify the benefits of using non-fifo routing, we also ran our simulations assuming that nodes are only allowed to transmit the packets at the head of their queues. The maximum aggregate throughput then was 13.3 Mbps. Finally, to quantify the benefits of using power control, we also ran the simulations assuming GPmax η = c γ T, with c = 20 and c = With non-fifo routing, the maximum aggregate throughputs were 19.6 Mbps and 20.2 Mbps respectively. We summarize our results in the first column of Table I. We also simulated the grid network of Fig. 2, and arrived at similar findings. The results are summarized in the second column of Table I. Moving to the random network of Fig. 3, in curve (f) of Fig. 4 we plot the maximum aggregate throughput of PBOA for each of the three routing protocols RP-10, RP-30, RP-120, under uniform traffic conditions. Curves (b), (e), and (i) of Fig. 5 show the average energy required for the end-to-end transport of a data packet, under PBOA and RP-10, RP-30, and RP-120 respectively. As in the chain and grid networks, the performance of PBOA in the random network, in terms of throughput, is clearly superior to that of CSMA/CA for all three routing protocols. Furthermore, PBOA performs much better than CSMA/CA especially in the case of the routing protocol that uses weak links, RP-10. PBOA is therefore robust with respect to the topology and the routing protocol. In addition, as Fig. 5 shows, PBOA is far superior to CSMA/CA in terms of energy efficiency. For example, under RP-10, PBOA uses 2.24 mj per packet under low traffic conditions and 2.53 mj under heavy traffic conditions. (Under low traffic conditions there are fewer transmissions going on and lower power levels can be used.) On the other hand CSMA/CA needs 6.35 mj per packet under low traffic and mj under heavy traffic. (Under heavy traffic data packet collisions are frequent, so data packets need to be retransmitted, and more energy is lost.)

17 16 Although PBOA is significantly better than CSMA/CA, in terms of achieved throughput, robustness with respect to the routing protocol, and energy efficiency, it is still far off from achieving the capacity. It is intuitively clear that one of the reasons is the following: During the contention period there are nodes that contend for the channel in vain. For example, a node may be sending an RTS to a node that has already sent an RTS and received a CTS in reply. The first node would have no possibility of success, but it would still be transmitting, thus hurting other nodes that still have a chance. If the nodes could make more informed decisions, the contention for the channel would be more efficient. This idea is the motivation for the Progressive Ramp Up Algorithm (PRUA). V. PROGRESSIVE RAMP UP ALGORITHM (PRUA) A. Protocol Operation PRUA uses the same frame format as PBOA (see Fig. 6). However, the rules of contention are very different. Before we specify its operation in detail, we briefly discuss the main idea: During the contention period, a node that has a packet awaiting transmission monitors the channel. Whenever it senses favorable conditions, it transmits an RTS with some small probability at the beginning of the next RTS minislot. If it is successful, it will persist sending RTS packets (so that it makes it known to competitors that it was successful). Otherwise, it backs off and may try again at a later RTS minislot. Nodes do not control their transmitter power. We now specify in detail the operation of the protocol. During the i-th RTS minislot, a node A will transmit an RTS packet to a destination B if, in the previous minislot pair, it sent an RTS packet and received a CTS packet from B in reply. Alternatively, node A will send an RTS packet if all of the following conditions are met: 1) Node A has not sent a CTS packet in the previous minislot (i.e., it is not awaiting a packet in the coming data slot). 2) During the previous CTS slot, the combined power of all signals received at node A did not exceed a predetermined threshold P T (Otherwise, node A may interfere with other transmissions). 3) Node A must perform a biased coin toss with probability of success p, and succeed. 4) If node A has not decoded an RTS packet in the previous RTS minislot, then node A will need to have a non-empty queue (otherwise it makes no sense to try to transmit). It will contend for the

18 17 packet at the head of the queue. If node A has correctly decoded an RTS packet in the previous RTS minislot from some node C, then node A will need to have a packet in the queue (otherwise it makes no sense to try to transmit), and in addition this packet must be intended for some node B, such that B is able to decode the packet from node A in the presence of interference from node C, and no other source of interference. A will choose to contend for the packet that is closest to the queue head and satisfies this condition 4. During the i-th CTS minislot, all nodes that successfully decoded in the i-th RTS minislot an RTS packet intended for them reply with a CTS packet. In order to transmit a data packet, a node must receive a CTS packet in the last CTS minislot. A flowchart with the operation of PRUA appears in Fig. 9. According to these rules, nodes do not necessarily try to transmit the packet at the head of their queue, but rather the packet closest to the head of the queue for which the conditions appear more favorable. As in CSMA/CA, nodes employ carrier sense. However, nodes now sense the power transmitted from other receivers, as in [4], [21], and not the power of ongoing transmissions, as in CSMA/CA, so the decisions they make are based on much more relevant information. B. Parameter Selection The number of minislots m, the probability p and the carrier sense threshold P T are design variables. If p is set too high, then collisions of RTS packets will be frequent. If, on the other hand, p is set to a very small value, too many minislot pairs will be wasted. Given m and a network topology, there is an optimal choice of p, p opt, but we have determined experimentally that the performance is rather insensitive to the actual choice of p. (values of p within 0.1 of p opt, that are not too close to 0 or 1, typically achieve 95% of the maximum performance). As m increases, p opt decreases, since now the nodes can afford to be less persistent, thus reducing the probability of RTS packet collisions, and still have ample opportunity to capture the channel. Also, the higher the node density, the smaller p opt is, since it does not make sense 4 Note that there can still be a collision; node A is merely trying to minimize the probability of a collision occurring. Also note that, in order for node A to know if it can transmit to node B while node C is transmitting, it will need to have some estimation about the quality of the channel between nodes A and B, and the channel between nodes B and C. As this information is local, and nodes need to perform routing decisions based on such information, it is reasonable to assume that the nodes have it. Even if the nodes do not have such information, at the very least node A will refrain from transmitting to node C.

19 18 for the nodes to be very aggressive when there is a lot of competition in their neighborhood. In Fig. 8 we plot the maximum aggregate throughput (under a uniform traffic load) of the random network of Fig. 3 under PRUA and the routing protocols RP-10 (curve (d)), RP-30 (curve (e)), RP-120 (curve (f)), versus the number of minislot pairs m. For each value of m, the optimal value of p is chosen. As in PBOA, as m increases the performance of the protocol at first increases, since the nodes are given more time to resolve congestion efficiently. However, after some value of m the incremental improvement in the resolution of conflicts is outweighed by the cost of the time that must be set aside for an extra minislot. For the random network of Fig. 3, using the transmitter parameters of Section IV-A, and under any traffic condition, a near-optimal choice of parameters is m = 8, p = 0.3. Because of its design, PRUA typically needs fewer minislot pairs than PBOA to resolve contentions. Therefore, PRUA has an advantage over PBOA when the system parameters are such that the minislot overhead is significant. The optimal value for P T, P opt T, depends on the SINR threshold γ T and the power of the background thermal noise η i, but the performance of the network is insensitive to its exact value. In the example network of Fig. 3, P opt T W = 80 dbm. C. Performance of PRUA in Simple Topologies Let us consider the chain network of Section. III-A. Like PBOA, PRUA does not suffer from the bidirectionality problem, and in principle 30 concurrent transmissions are possible. However it is intuitively clear that, due to its distributed nature, the average number of concurrent transmissions will be smaller. Indeed, the maximum aggregate throughput, as determined by simulation, and setting m = 8, p = 0.35, P T = GP max, is 20.5 Mbps, an 88% improvement over CSMA/CA. To quantify the benefits of using non-fifo routing, we ran the simulation again with a modified protocol that only allows nodes to transmit packets at the head of their queue. The new throughput was found to be 18.6 Mbps. We summarize these results in the first column of Table I. We also simulated PRUA in the grid network, and arrived at similar findings. The results appear in the second column of Table I. Moving to the random network of Fig. 3, in curve (g) of Fig. 4 we plot the maximum aggregate throughputs of the network for the three routing protocols RP-10, RP-30, RP-120. Finally, in Fig. 5 we show the average energy consumed per packet under PRUA and for RP-10, RP-30, RP-120 (curves (c), (f), (i)). Since transmitters always transmit with their maximum power, and transmissions are always