Clock-Sampling Mutual Network Synchronization for Mobile Multi-hop ...

Clock-Sampling Mutual Network Synchronization for Mobile Multi-hop Wireless Ad Hoc Networks Carlos H. Rentel† and Thomas Kunz Department of Systems and Computer Engineering, Carleton University Ottawa, Canada {[email protected], [email protected]} † Carlos H. Rentel is with Eaton Corp. Innovation Center. Milwaukee, Wisconsin, U.S.A

Abstract—This paper presents new performance results of a mutual network synchronization approach referred to as Clock-Sampling Mutual Network Synchronization (CSMNS). Different to other mutual synchronization approaches, CS-MNS timing information is exchanged explicitly using periodic packets referred to as beacons, which are used to carry timestamps, and hence compatibility to the widely adopted IEEE 802.11 standard is ensured, even for mobile multi-hop wireless ad hoc networks. Performance results are presented for two mobility models and large networks. Numerical comparisons demonstrate at least one to two orders of magnitude improvement in scalability and accuracy respectively relative to the IEEE 802.11 synchronization mechanism. CS-MNS also shows approximately five times better accuracy than the reported accuracies of the MANET-TSF (MATSF) and ASP under similar mobility and radio transmission range conditions. Keywords: Network time-synchronization, mobile multi-hop wireless ad hoc networks.

INTRODUCTION A mobile wireless ad hoc network is a distributed and autonomous computer network comprised of mobile nodes performing the network creation, management and regular data-communication operations over a wireless transmission medium. All, or part of the nodes, have the capability to be routers and forward traffic on behalf of other nodes. Advantages of ad hoc networks include the possibility of self-reconfiguration, self-healing, and deployment flexibility. These advantages make them attractive for battlefield communications, disaster relief scenarios, scientific exploration, mesh networks, and opportunistic networks [1] amongst others. I.

In this paper we are concerned with the fundamental problem of achieving network time-synchronization (NTS) amongst the nodes of a mobile multi-hop wireless ad hoc network. NTS is required in many wireless network applications to support time-slotted Medium Access Control (MAC) strategies, and many security, and network management protocols. It is, for instance, a key function in the IEEE 802.11 standard for power management and support of the channel hopping mechanism in the Frequency Hoping Spread Spectrum (FHSS) version of the physical (PHY) layer [2]. It is also a key component of recent wireless sensor network solutions and low rate 1-4244-1513-06/07/$25.00 ©2007 IEEE

personal area network standards, such as IEEE 802.15.4based networks. Network synchronization methods that perform fewer tasks to achieve a required accuracy, while being compatible to widely adopted standards, such as IEEE 802.11, are highly desirable. Additionally, these methods should incur as minimal bandwidth and energy utilization as possible. Clock-Sampling Mutual Network Synchronization (CSMNS) was first introduced in [3], and [4]. This paper shows CS-MNS’ performance in large mobile multi-hop wireless ad hoc networks. Synchronization is achieved with beacons that have the same content as those used in the IEEE 802.11 standard. This makes CS-MNS an IEEE 802.11, and potentially an IEEE 802.15.4, compatible multi-hop wireless network synchronization method. We present performance results of CS-MNS under two synthetic mobility models: The random waypoint (RWP) model [5], and the boundless area (BA) mobility model [6]. Mobility makes synchronization more challenging for several reasons. First, mobility can cause network partitions, which in turn cause two or more portions of the network to time-evolve differently. Second, methods that synchronize to a master or reference clock usually utilize ranked topology strategies, or bridge and gateway nodes to serve as proxies that synchronize different portions of a multi-hop network (e.g., [7], [8], and [9]). These methods usually require for each node to keep a record of its neighbors in order to decide which one will be used as a link to the reference clock. However, this is more challenging when the nodes move. Finally, mobility can cause more time and frequency (i.e., Fading and Doppler) wireless channel variations that affect the physical layer performance and therefore the efficient exchange of timing information in a synchronization method. A mutual network synchronization approach is particularly attractive because it is more resilient than a master-slave approach to the second impairment mentioned above. That is, since no hierarchies (i.e., ranking of nodes), reference or master clocks are needed, a node participating in a mutual network synchronization approach does not need to keep track of its position, or keep a record of any network topology information. However, mutual network synchronization approaches have not enjoyed much acceptance beyond the military domain due to the complexity of existing methods, which affects their cost and hence wider adoption. The combination of several factors make CS-MNS unique: 1) It is a simple mutual network synchronization

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approach suitable for mobile multi-hop wireless networks that is compatible to existing standard beacon packets used in IEEE 802.11 and IEEE 802.15.4 systems, 2) The time is recursively corrected by simultaneous adjustment of clock skew and offset, and hence better accuracy and smaller overhead than existing approaches is possible, 3) A node in CS-MNS does not need to keep track of its neighbors, or know their relative position in the network; every node is independent of others except for the need to exchange timestamp information, and 4) CS-MNS is equally useful for non-mobile multi-hop networks, such as wireless mesh and wireless sensor networks, with no need to add extra functionality or implement any changes [3]. The remainder of this paper is as follows: In Section II we present related work. In Section III the existing method of synchronization used in the IEEE 802.11 standard (TSF) is discussed. In Section IV we describe the CS-MNS approach in detail. The numerical performance evaluation of CS-MNS and that of the TSF in a mobile multi-hop scenario is presented in Section V along with a qualitative comparison to other more recent methods, including the MANET-TSF method proposed in [7] and the multi-hop synchronization method in [8]. Concluding remarks are presented in Section VI. RELATED WORK Gersho and Karafin [10] were one of the first to analyze a system that mutually synchronized the phases of a group of geographically separated oscillators connected by communication links. The classical mutual network synchronization approach in [10] was originally designed for wired networks, and it requires dedicated circuitry to generate either narrow pulses or continuous waveforms that can potentially occupy a considerable portion of the allocated frequency spectrum. If used over wireless channels, the mechanism in [10] can impose tight restrictions on the turn-around times of the radios if a halfduplex strategy is used since nodes are expected to transmit and receive the timing signals simultaneously. Otherwise, full-duplex radios are needed, which are more complex, expensive, and require more energy to operate. Using methods that require continuous transmission of waveforms over a standard, such as IEEE 802.11 or IEEE 802.15.4 is not only prohibitive due to potentially large energy and bandwidth requirements, but also very difficult to implement in practice. That is, access to the physical clocks is required in order to adjust their frequency, or possibly different PHY layer components are necessary in order to transmit and receive the required waveforms. For the description of other similar synchronization methods see [3]. CS-MNS’ non-linear discrete control law differs from the ones used in [10] and other mutual synchronization approaches proposed in the past [10], [11], [12], [13], [14], which are either controlling the frequency of the clocks directly, or are designed and II.

analyzed in a continuous-time domain. CS-MNS’ nonlinear control law (5) is a consequence of adjusting time process skews rather than time offsets in the time domain. The control law has the interesting property of using a limited amount of information. The latter has the advantage of reducing the complexity of the algorithm and ensuring its compatibility to existing PHY/MAC standards as will become clearer in Section IV. The Reference Broadcasting Synchronization (RBS) scheme is proposed in [9] with multi-hop support. RBS achieves multi-hop synchronization through intermediate nodes that translate the times amongst different neighborhoods. RBS achieves clock skew adjustment through linear regression, and it utilizes the idea of receiver-synchronization to eliminate the timing inaccuracies caused by medium access uncertainty. The IEEE 802.11 TSF utilizes clock-sampling to explicitly distribute time throughout the network. Clock sampling refers to the use of messages carrying explicit timestamps rather than signals with embedded timing information, such as a train of pulses. The time is simply read from the clock and transmitted in amessage called beacon. The TSF is used to support power management and the channel hopping procedure used by the frequency hopping spread spectrum (FHSS) version of IEEE 802.11. The TSF utilizes the same principle of clock correctness introduced in [15]. Part of that principle states that a clock’s time shall not move backward. Therefore, nodes implementing the TSF in the ad hoc mode of operation adjust their time only to faster clocks in the network. The lack of scalability of the IEEE 802.11 TSF was first analyzed in [16] for single-hop networks. The authors in [16] also proposed a method to improve scalability by giving higher priority to the beacon transmissions of the node with the fastest clock in the network [16], [17]. However, the latter approaches are not suitable for multihop wireless ad hoc networks. A synchronization method for multi-hop wireless ad hoc networks based on an Automatic Self-time-correcting Procedure (ASP) is presented in [8]. ASP alleviates the scalability problem of the TSF and also works for multihop wireless ad hoc networks. However, ASP needs to modify the beacon of the standard IEEE 802.11 TSF in order to work properly. Additionally, clock adjustment is achieved through a modified additive time offset rule, which cannot achieve better accuracy than methods that correct the frequency or skews of clocks. The Selfadjusting TSF (SATSF) is proposed in [18] to improve accuracy of the ASP without changing the IEEE 802.11 beacon format, but for a single-hop network. Later in [7] another method is proposed (MANET-TSF) for multi-hop IEEE 802.11-based ad hoc networks. The MANET-TSF, similar to ASP, also modifies the standard beacon frame used in the IEEE 802.11 standard. However, MANET-TSF

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shows better accuracy than ASP due to the fact that it adjusts the frequency of the clocks. The methods in [7], [8], [16]-[18] depend on the identification of fastest clocks for beacon transmission prioritization, which may be a difficult task in a mobile ad hoc network. CS-MNS nodes do not need to synchronize to fastest clocks to avoid backward time movements as will be explained in Section IV. IEEE 802.11 TIMING SYNCHRONIZATION FUNCTION We are interested in the TSF in the Independent Basic Service Set (IBSS) mode of IEEE 802.11. The reader is referred to [2] for a detailed description of this method. III.

The probability of sending one beacon successfully regardless of the node that sent it ( Pany ), and the probability of sending a beacon successfully by a given node ( Pgiven ) were found in [16] under the assumption that all beacon contention windows start at the same real time. The analysis proves the inefficiency of the TSF to scale. The scalability problem is blamed on the beacon collisions, which cause a smaller Pgiven as the number of nodes in the network increase (see [3]). It is important to note that the results in [16], though severe, are optimistic, since beacon contention windows for all nodes are assumed to start at the same real time and no data traffic is assumed. CLOCK-SAMPLING MUTUAL NETWORK SYNCHRONIZATION State of the art clocks are relatively accurate. A typical range for the accuracy of clocks based on quartz crystals is ±40ppm. For instance, the IEEE 802.11 clock that drives the Pseudo-Noise sequence generator must be within ±25ppm [2], and the one used in the IEEE 802.15.4 standard must be within ±40ppm [19]. Equation 1 models the time process of an accurate clock [20], [21] IV.

T (t ) = β ⋅ t + ξ (t ) + T (0)

(1)

Where T (t ) is the time process of the clock, t is realtime, β is the skew of the clock with respect to real-time, ξ is a random process that models time jittering and ambient effects, and T(0) is the initial time of the clock. For accurate clocks, skew can be approximated by a timeinvariant constant, whereas ξ is usually modeled as a random process with power-law spectra. However, for practical purposes it is considered zero in what follows. Timing uncertainties due to environmental conditions are not considered in the model since they have long time constants that exceed the time update of network synchronization approaches. On the other hand, a major

source of uncertainties are the random delays caused by transmission, reception, and link lengths, which are not typically considered in the clock model, but rather in a separate network model. Consider a network of N nodes in which each node has a clock with a different skew and initial time. That is, Ti ( t ) = β i t + Ti ( 0 ), i = { 1,2 ,..., N }

(2)

The main goal of any time synchronization algorithm is to minimize the relative deviations of the time processes in (2). This is achieved in CS-MNS by multiplying every time process by a correction factor s i (t ) , which transforms (2) into the following Ti (t ) = s i (t )Ti (t ) = s i (t ) β i t + s i (t )Ti (0), i = {1, 2, ..., N }

(3)

CS-MNS corrects the time errors by adjusting the slope of the time process using a time-multiplicative factor. In what follows Ti (t ) and Ti (t ) in (3) are referred to as the real and controlled timestamps respectively. The real timestamp is the time read from the actual node’s clock, whereas the controlled timestamp is the one read after multiplying the real timestamp by a factor s that is updated in every node independently. The TSF and other synchronization approaches (e.g., [8]) correct the time errors based on an additive factor that changes the time offset between the clocks, but not their skew, or in other words, the slope of the time process. Time offset adjustment creates time error dynamics that make zero error convergence impossible. That is, the time difference between two clocks will continuously oscillate around a mean value different than zero. Other works adjust the frequency of the clocks (e.g., [7], [10]). However, adjusting the frequency of the clock requires either access to the physical clock’s oscillator, or extra functionality that adds or removes ticks to the ones generated by the original clock. By simply multiplying the time read from the clock, CS-MNS achieves transparent clock frequency and offset adjustment. CS-MNS adjusts frequency and offset in the time domain.

Similar to TSF, and in order to be compatible to IEEE 802.11 and other standards, we propose to exchange explicit timing information using beacon message transmission. A node contends to send its time in periodic beacon transmissions with period T. Therefore, the time processes in (3) can be written as a set of discrete equations Ti (nT ) = s i (nT ) β i nT + s i ( nT )Ti (0), i = {1, 2, ..., N }, n ∈ Z +

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(4)

By multiplying the time process of a clock by a factor s, we are changing the slope of the time process. We look for a control strategy that modifies the multiplicative factor in such a way that the slope and time offsets of all the time processes in the network converge toward zero. Note that having only the same slope is not enough since two clocks can have the same slope, but never be equal (i.e., parallel time processes). In order to force time offsets to converge towards zero, the adjustment of the multiplicative factors is first made proportional to the difference between the timestamp received from the other node Trx _ time (the one the given clock is trying to synchronize to) and the given clock’s timestamp Ti . In this way, even when clocks have the same slope but different times, the multiplicative factor will still be adjusted to drive the error towards zero. The correction, however, needs to be different depending on the time at which the time-difference is measured. In other words, nodes that have spent more time in the network and that have a time difference ∆Te will have closer slopes than those that have the same ∆Te time difference, but that have spent less time in the network. Therefore, the adjustment of the multiplicative factor is also made inversely proportional to the time the given node has spent in the network. Based on the previous reasoning we propose to update s i (nT ) via the following recursion s i ((n + 1)T ) = s i ( nT ) + k p

(Trx _ time (nT ) − Ti ( nT )) Ti ( nT ) − Ti (0)

(5)

Where T is the sampling period, k p is a design constant referred to as the proportional gain, Trx _ time is the timestamp of the node that successfully transmitted the beacon message and that was received by the ith node. Looking at (5), it is important to realize that all a node needs are timestamps from any other node in its neighborhood. Once a node receives a valid timestamp, it is able to immediately make use of it to adjust its time recursively. The importance of the latter can not be underestimated. That is, the procedure in (5) contrasts with the MATSF [7] and the ASP [8] adjustment methods. In those approaches, a node can only adjust its clock after two timestamps have been received from the same node. The latter requirement is an extra task that may be difficult to guarantee in a mobile environment, and in fact, requires modifications to the beacon payload to work properly, which make them incompatible to the standard IEEE 802.11 beacons. It is also interesting to note that, to the best of our knowledge, a system of equations such as (5) does not have a closed solution. In [22], however, some convergence and stability properties for these equations are analyzed based on the discrete Lyapunov direct

method. Substituting (4) into (5) and normalizing the sample time by T yields

si (n +1) = si (n) + kp

(sj (n)βj ⋅ n + sj (n)Tj (0) − si (n)βi ⋅ n − si (n)Ti (0)) (6) si (n)βi ⋅ n + si (n)Ti (0) − si (0)Ti (0)

The j and i sub-indexes ( j ≠ i ) identify the node that transmitted and received the beacon respectively. Figure 1 depicts the idea of the time adjustment in CSMNS. Two node’s time processes are depicted in this diagram for simplicity. Node i’s time process is denoted as Ti ( n ) = β i n + Ti ( 0 ) , while node m’s time process is Tm ( n ) = β m n + Tm ( 0 ) . Assume that node m wins the contention at time n = 1 . After receiving node m’s timestamp, node i computes a correction of its slope that is applied (via multiplication) to its real time process. The correction is computed based on equations (4) and (5). After the correction is applied, the slope of node’s i time process becomes larger (i.e., θ i (2) > θ i (1) ) and tends towards Tm (n) . Note that in principle node i could wait for another timestamp from node m in order to compute the exact correction of its slope. The latter is easy to achieve in a network of two nodes, however, not so in a network of (say) 500 nodes moving and contending for access to the wireless medium. Also note, from the discontinuity at n = 1+ , that it is not necessary to have an additive factor to drive the error close to zero from the time the update is applied. More importantly, it is also not necessary to synchronize to a faster clock. If an updated value of the parameter s is smaller than the previous one (i.e., si (nT + ) < si (nT ) ), the new timestamp will be smaller (i.e., Ti (nT + ) < Ti (nT ) ) and time will go backward for an instant of time. This will happen in Figure 1, for instance, if the node with the slower clock transmits its beacon rather than the node with the faster clock. In some applications this backward time movement is not desirable. A solution to this problem is to momentarily freeze the controlled timestamp Ti (nT ) of the fastest clock until its real timestamp Ti (t ) increases up to a point where s newTi (t ) ≥ Ti (nT ) . Let us call that freezing time ∆Tint . After ∆Tint time units, the controlled timestamp is updated again, in this way when a slower clock updates a faster one, the faster clock just slows down, but no backward time jumps are observed. It is desirable to know the value of ∆Tint . Let us assume that the value of s is updated from sold to a smaller value s new just after receiving a new beacon. ∆Tint is given by

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Tim e Process

Transmission side: 1. A node contends to send its controlled timestamp in the next periodic contention window (the node randomly selects a new time-slot for every contention window). 2. If no beacon has been received so far in the present contention window, the node transmits its controlled timestamp. Otherwise, it waits for the next contention window and goes back to 1. Reception side: 1. A node updates to a new multiplicative s factor using (5) iff it receives a controlled timestamp ( Trx _ time ).

Tm ( 1 ) = β m + Tm ( 0 )

Tm ( n ) θi ( 2 ) > θ i ( 1 )

Ti ( n )

θi ( 1 ) Ti ( 1+ ) = si ( 2 ) β i 1+ + si ( 2 )Ti ( 0 )

Ti ( 1 ) = si ( 1 )β i + si ( 1 )Ti ( 0 )

si ( 2 ) = 1 + k p

Tm ( 1 ) − Ti ( 1 ) Ti ( 1 )

si ( 1 ) = 1

Discrete norm alized real-time

n=1

2. If the received timestamp is smaller than its controlled

timestamp (i.e., Trx _ time < Ti ), then wait ∆Tint (7)

Figure 1: CS-MNS adjustment of time processes

∆Tint ≥

Ti (nT ) Ti (nT ) − s new s old

(7)

Where Ti (nT ) is the value of the timestamp in the controlled clock used to compute s new . Using Equation (5) with Ti (0) = 0 we obtain

(

k p Trx _ time − Ti (nT )

s new = s old +

)

Ti (nT )

(8)

Substituting (8) into (7), and after some algebra ∆Tint ≥

(

− k p Trx _ time − Ti (nT )

)

s new s old

(9)

Note that s new < s old ⇒ Ti (nT ) > Trx _ time , which implies that ∆Tint is positive. In Section V we show that the time difference Trx _ time − Ti (nT ) can be in the order of few microseconds at steady state. Therefore, Trx _ time ≈ Ti (nT ) , which implies s new ≈ s old based on (8). Furthermore, given s(0) = 1 and reasonably accurate clocks ( β ≈ 1 ), we can assume s new ≈ s old ≈ 1 . Therefore (9) can be simplified to

(

∆Tint ≥ − k p Trx _ time − T (nT ) i

before multiplying the real timestamp by the new s (waiting ∆Tint is only necessary if backward time jumps are not allowed).

)

(10)

Equation (10) states that it is only necessary to wait as much as the maximum time difference between any two clocks in the network. After ∆Tint elapses, the controlled timestamp is reestablished as the regular product of s new and the real timestamp. The following summarizes the CSMNS procedure.

NUMERICAL PERFORMANCE RESULTS Performance results are presented for different network sizes, two mobility models, and two different radio transmission/detection ranges. The performance is measured in terms of the maximum time difference between any two clocks at every beacon transmission time. This is denoted as Tmax ( given in microseconds - µs). We also compare the accuracy of CS-MNS to the ones reported in [7] and [8] for MATSF and ASP respectively. V.

The RWP mobility model is simulated with a maximum speed of 5 m/s, and maximum pause time of 50s. The BA model does not make use of pauses, it has a maximum speed of 5 m/s, a max. acceleration of 0.5 m/s2, and a maximum change in direction of 0.5 rad/s. In both models the area is [1000m x 1000m]. The BA model area is effectively a toroid, therefore nodes leaving one side will reappear on the other side, whereas nodes in the RWP model will move inside the area if they hit the edges. Studies have shown problems with the convergence of the RWP model [23]. In order to avoid this, the minimum speed is set different from zero in the simulations. Accuracy of the clocks in the network vary randomly in the range [-25ppm, +25ppm], and all the clocks start asynchronous to one another in the range (0, 200µs]. The rest of the simulation parameters are the same as in [3].

Network Size: Figures 2 and 3 show Tmax (µs) using TSF and CS-MNS respectively under RWP mobility. The network sizes are 100, 300, and 500 nodes. In all cases the transmission and detection ranges are 250m and 500m respectively. TSF

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1400

1200 500 Nodes

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Tmax

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Time (seconds)

Time (seconds)

Figure 2: TSF Tmax for different network sizes

Figure 4: CS-MNS and TSF Tmax for 500 nodes and BA mobility

BA Mobility: 1000

Figure 4 shows Tmax for CS-MNS and TSF for 500 nodes using the BA mobility model. The transmission and detection ranges are 250m and 500m respectively. CSMNS coverges for both the RWP and BA mobility models, even for 500 nodes. The BA model shows a slightly larger overshoot in the transition period, which lasts approximately 200s. The final is approximately 9µs when using the BA mobility model, and 6µs when using the RWP mobility model. The average Tmax for TSF (Figure 4) is 721µs, this is slightly smaller than the result obtained with the RWP model (730µs). There is no substantial difference observed in the performance under both mobility models.

900 800 700

Tmax

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Time (seconds)

Figure 3: CS-MNS Tmax for different network sizes

(Fig. 2) shows average Tmax of 233µs, 644 µs, and 730µs, and max{Tmax } of 520µs, 925µs, and 1,026µs for 100, 300, and 500 nodes respectively. CS-MNS’ behaviour (Fig. 3) is different to that of TSF, there is a transition period that reaches peaks of 667µs, 805µs, and 917µs for 100, 300, and 500 nodes respectively. After approximately 40s, 120s, and 250s, CS-MNS converges to a value less than 10 µs. CS-MNS reduces the time difference amongst the clocks as time progresses, a property TSF cannot claim due to the fact that it adjusts time based on time-offsets only. Note that as the density of the network increases, it is more difficult to have successful beacon transmissions, and the average maximum deviation between the clocks tends to increase. CS-MNS however, is less affected by the density increase because nodes make use of any beacon transmitted, not only of those from faster clocks.

Figure 5 shows Tmax for TSF and CS-MNS with 500 nodes using the RWP mobility model, and transmission and detection ranges of 150m and 300m respectively. The average Tmax for TSF is 705µs, and the max{Tmax } is 1,505µs. The final Tmax after convergence for CS-MNS is 6µs. This shows that under the two most typical transmission ranges (i.e., 150m and 250m) CS-MNS achieves convergence. The number of hops a message has to traverse increases as the transmission and detection ranges decrease. Therefore performance can be expected to decrease after some point. On the other hand, as these ranges increase, the beacon contention increases, and successful beacons are less probable. The optimum transmission and detection ranges depend, amongst other factors, on the number of nodes and the area covered by these. The previous simulations show the ability of CS-MNS to converge under different network sizes, mobility patterns, and typical transmission ranges. The values reported in [7]

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1000

[5] TSF

900 800 700

[6]

Tmax

600 500 400

[7]

300 CS-MNS

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100 0

0

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[9]

Figure 5: CS-MNS and TSF Tmax for a shorter range

and [8] for similar parameters are summarized in Table I. Note that CS-MNS also achieves better accuracy while being compatible to the beacons of IEEE 802.11. Table I shows Tmax for CS-MNS, MATSF, and ASP. As shown, CS-MNS can be approximately five times more accurate than MATSF, and one hundred times more than ASP according to the reported accuracies of these two methods. TABLE I. Tmax for CS-MNS, MATSF, and ASP N CS-MNS (µs) MATSF (µs) ASP (µs) (µs) 100 2 24 214 300 3 24 ≈ 200 500 6 43 ≈ 200

[10]

[11]

[12]

[13]

[14]

CONCLUSION An accurate and simple mutual network synchronization algorithm suitable for mobile multi-hop wireless ad hoc networks, and compatible to the IEEE 802.11 standard, has been presented. The time adjustment is based on an automatic control of the time process’ slope of the clocks in the network. This paper has shown evidence that fewmicrosecond accuracies are possible even for networks of 500 nodes. The core method is simpler and more accurate than other recent methods proposed in the literature. VI.

[15]

[16] [17]

[18]

[19]

REFERENCES L. Pelusi, A. Passarella, and M. Conti, “Opportunistic networking: Data forwarding in disconnected mobile ad hoc networks,” IEEE Communications Magazine Decenber 2006. [2] IEEE Std. 802.11. “Wireless LAN medium access control (MAC) and physical layer specification,” 1999. [3] C. H. Rentel and T. Kunz, “A clock-sampling mutual network synchronization algorithm for wireless ad hoc networks,” Proceedings of the IEEE Wireless Communications and Networking Conference, New Orleans, USA, March 2005, p. 638 – 644. [4] C. H. Rentel and T. Kunz, “A distributed network synchronization algorithm for wireless ad hoc networks,” ACM Poster, MobiCom 2004, Philadelphia, USA, October 2004. [1]

[20]

[21]

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