Guard Beacon: An Energy Efficient Beacon Strategy ...

JOURNAL OF LATEX CLASS FILES, VOL. 11, NO. 4, DECEMBER 2012

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Guard Beacon: An Energy Efficient Beacon Strategy for Time Synchronization in Wireless Sensor Networks Yongrui Chen1 , Fei Qin2 , Weidong Yi3 13 University

of Chinese Academy of Sciences, Beijing, 100049 China Laboratory of Wireless Sensor Network & Communication, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050 China 2 Key

In this paper, we present Guard Beacon, a beacon strategy to reduce the energy consumption of time synchronization in wireless sensor networks (WSNs). In a low duty-cycled sensor network, a node may miss incoming synchronization beacons because of wrong active/sleep mode due to clock drift. Therefore it is critical to guarantee beacons arrive at the receiver in the right time. The proposed method, Guard Beacon, can reduce the overall power consumption of synchronization while guarantee a very high probability that synchronization packet is received, by sending multiple beacons within a synchronization round. By investigations on the energy trade-off between sending and receiving beacons, we find an optimal iterative solution as well as a sub-optimal analytical solution, of how many beacons should be sent, and when to send. The strategy is implemented in a real-world testbed for experiment validation. The results show that the proposed Guard Beacon may save more than 40% synchronization power consumption compared to the existed Single Beacon strategy, and is also more energy efficient than RTSP in multi-hop networks. Index Terms—Wireless sensor networks, time synchronization, energy efficiency, low duty-cycled network, beacon strategy

I. I NTRODUCTION Accurately synchronized clocks are crucial for many applications and protocols in Wireless Sensor Networks (WSNs)[1]. Without accurate time information, sensed data may lose valuable context. Media Access Control (MAC) using Time Division Multiple Access (TDMA) requires accurate time information to avoid transmissions interference. And, sensor network protocols widely employ duty-cycling scheme [2] to save energy. An accurate clock can increase the energy efficiency by shortening the necessary wake-up guard times. However, due to the unpredictable clock drift, which is easily affected by the temperature, voltage and even more serious when multi-hop is considered [3], it is necessary for sensor node to periodically send and receive beacons to calibrate clocks, keep synchronization errors within an acceptable range. This consumes a large proportion of energy, especially for low duty-cycled wireless sensor networks, i.e., each sensor alternates between active and sleep mode to conserve energy with an average duty cycle typically less than 1%. In such networks, a node may be in sleep due to clock drift and miss incoming beacons, whether it sleeps too early or wakes-up too late. Therefore it is critical to guarantee synchronization packets arrive at the receiver when it is not in sleep mode. To deal with this problem, several approaches are adopted in many synchronized MAC protocols, such as increasing the beacon rate (e.g. Dozer [2]), setting a larger guard time for the receiver (e.g. Koloa [4]), and using continuous This work has been sponsored under the National Nature Foundation of China (Grant No. 61303240), the funding scheme of Key Laboratory of Wireless Sensor Network & Communication, Chinese Academy of Sciences (Grant No. 2013004), the Science and Technology Supporting Project of China (Grant No.2012BAJ24B01), and also supported in part by the President Fund of University of Chinese Academy of Sciences (Grant No. Y35102JN00). Corresponding author: Yongrui Chen (email: chen yong [email protected]).

repeated wake-up frames instead of beacons (e.g. SyncWUF [5]). However, all these ways will significantly increase the overhead in synchronization. Another approach is improving the synchronization accuracy to guarantee distributed nodes waking up at almost the same time ([6]-[8]). Most works are energy inefficient by requiring exchanging messages several times each round to estimate the clock skew and offset. Several recent studies investigate the energy efficiency issue for synchronization. [9] significantly reduces the overall number of synchronization messages by overhearing time message exchanges of neighboring nodes, [10] further explores the Maximum Likelihood Estimator (MLE) for clock offsets of the listening nodes. The latest study RTSP [11], further reduces the energy consumption for global synchronization in multi-hop networks, using adaptive re-synchronization interval, aggregation of the synchronization requests, and skew estimation via least square linear regression on two data points (2LR) instead of 8LR. However, all these schemes didn’t consider the typical duty-cycling mechanism in WSNs, where node is in sleep most of the time, therefore will not always overhear the time messages from other nodes. In this paper, we present a new method called Guard Beacon for energy efficient time synchronization in low duty-cycled networks. With Guard Beacon, a node will send optimally scheduled beacons to minimize the idle listening time for the receiver caused by synchronization errors. Different from the previous works, it is target to reduce the overall power consumption of sender and receiver in the synchronization process, instead of just reduce the number of synchronization messages (as [9]-[11]). For the situation where heterogeneous duty-cycle configurations are applied over the set of nodes in the network, Guard Beacon can also reduce the energy consumption of beacon exchanging, and is more energy efficient than using long wake-up preambles by the sender or large


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guard times by the receiver. II. S YSTEM M ODEL Consider two nodes as A and B. A sent a beacon to B at A’s local time t1 , and B received it at B’s local time t2 . B get the value of t1 from the timestamp inserted in the beacon. Then t1 and t2 can be expressed as: t2 = f t 1 + τ + θ

(1)

where f and θ are the relative frequency and offset deviation of the two clocks. τ is the the delay of beacon delivery. Generally, we may use any of the existing time synchronization schemes (e.g. FTSP [8]) to evaluate the value of f , τ and θ as fˆ, τˆ and ˆ Therefore, node B will calibrate local clock as follows to θ. keep synchronized with node A when the beacon is received: tˆ2 = fˆt1 + τˆ + θˆ

(2)

The deviation of the clock time of node B is: ∆t2 = t2 − tˆ2 = ∆f t1 + ∆τ + ∆θ

(3)

where ∆f , ∆θ and ∆τ are the estimation error of the skew, the offset and the message delay respectively. Ideally, the calibration will not introduce additional clock errors, which means B gets the exact same clock time as A after the calibration. As a result, clock errors will not accumulated over time. When the next beacon is arrived, the deviation of clock B and A is: e = ∆f Ts + ∆τ + ∆θ

Typically, if the distribution of clock deviation is bilateral symmetrical, the most efficient way is setting tg = 2ta . We denote ta = Kσe , where in the time-line, (−ta , ta ) is the confidence interval of synchronization, corresponding to a synchronization confidence level β positively correlated to K. Then, we consider a multi-hop network. We assume a tree-based topology is adopted and the sink is the root as well as the reference node of synchronization. A node can automatically join and leave the network by searching a parent and be synchronized with it. The routing cost and other topology information can be piggybacked in the synchronization beacons(as in [2], or reverse), without posing more additional control overhead than several bits. Therefore, the power consumption per node will not scale with the network size, since the frequency of sending beacons (broadcast to children) and receiving beacons (only from parent) is typically a constant. III. G UARD B EACON S TRATEGY In each synchronization round, node A sequentially sends several beacons (fig.1). When node B wakes up, it will keep listening until any of the beacons is successfully received. On receiving the beacon, it will calibrate local clock. The problem is, given a successful synchronization probability β0 , how many beacons , and what exact time these beacons should be sent, to minimize the total power consumption for synchronization?

(4)

where Ts is the beacon interval. According to the law of large numbers, if we consider a pair of clocks among many nodes in the network, it’s reasonable to determine that the random variables are normally distributed. This assumption is justified in [1] and also supported by the tests in [6]. That is: ∆f ∼ N (0, σf2 ), ∆τ ∼ N (0, στ2 ) and ∆θ ∼ N (0, σθ2 ). Therefore, e ∼ N (0, σe2 ), where √ (5) σe = Ts2 σf2 + στ2 + σθ2 Generally, to make sure node B will not miss beacon from A with high probability, B has to turn on its radio in advance with a short time, named as advanced time ta , and keep listening for a longer time, named as guard time tg , to receive the coming beacon from A, before switching off. If a beacon is received in this period, B will calibrate its clock; If not, B will enter a synchronization recovery phase, double the guard time and wait for the next beacon. Therefore, high probability of successful synchronization should be kept, since synchronization recovery not only affects normal data transmission, but also consumes additional energy. The Guard Beacon can work effectively against the unsuccessful delivery of beacons not only contributed by the time difference between Transmitter and Receiver, but also the unstable wireless channel. However, we only discuss the former reason for simplicity of analysis, while the analysis of overall effects will be discussed in our future work. To guarantee a high probability of successful synchronization (denoted as β), tg and ta has to be carefully chosen.

Fig. 1. Sending & Receiving Beacons with Guard Beacon

Assume that node A sends N beacons in a synchronization round. Node B is expected to wake up at time 0. Denote the sending time of these N beacons as x1 , x2 , ..., xN respectively, where xN = ta . And we set x0 = −ta . Therefore, the average waiting time of node B for the coming beacon is: ∫ xi N N ∫ xi ∑ ∑ ¯ f (t)(xi − t)dt = xi f (t)dt (6) tw = i=1

xi−1

i=1

xi−1

where f (t) is the Probability Density Function (PDF) of synchronization error, which is a Gaussian function as discussed in section 2. Then, the total synchronization power consumption can be expressed as: Tb N Tb t¯w Pl + Pr + Ps (7) Psync = Ts Ts Ts


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√ where ta = K Ts2 σf2 + στ2 + σθ2 . Nopt is the round-up to ′ the closest integer of Nopt . When Nopt = 1, Guard Beacon is backward compatible with the traditional Single Beacon scheme. Therefore, as (13) depicts, when ta Pl > 2 ∗ Tb Ps , Guard Beacon will have better performance than the Single Beacon strategy. This condition can be easily satisfied in common WSN applications such as environment monitoring, where Ts may be several minutes or more, and σf is usually 30-100ppm, leading to Ts ≫ ta > Tb .

f(t) Receiver Wake-up Beacon #1

Beacon #2

Beacon #3

x2

x3

tw x1

ta tg

IV. P ERFORMANCE E VALUATION

t

Fig. 2. The Beacon Waiting Time of Guard Beacon

where Ps ,Pr and Pl is the power consumption in transmission, receiving and idle listening mode respectively. And Tb is the duration of sending/receiving a beacon. Then, the optimization problem of Guard Beacon is: min Psync , sub β ≥ β0 , N ∈ N +, i = 1, ..., N

(8)

xi ,N

It is easy to prove that if N is a deterministic parameter, xi has one and only one optimal solution, when equation ∂ t¯w /∂xi = 0 is satisfied. i.e. for i = 1, ..., N : ∫ xi f (t)dt = (xi+1 − xi )f (xi ) (9) xi−1 −

t2

1 where x0 = −ta , and xN = ta , and f (t) = √2πσ e 2σe2 . e It is a N dimension nonlinear equation set. It is hard to be analytically solved but can be simply calculated through iteration method. Similarly, it is also hard to find Nopt analytically. However, as Nopt has to be an integer, it can be decided by calculation and comparison. The numeric results of Nopt and xi under different conditions will be shown in the next section. Since the computation capacity of WSN node is limited, the iterative optimal solution may not be applicable in a real-world application. Therefore, we have to find out a sub-optimal but easy calculable analytical solution. Assume each beacon has the same opportunity to be caught by the receiver. Denote x′1 , x′2 ,...,x′N as the beacon sending times, there is: ∫ x′2 ∫ ta ∫ x′1 1 f (t)dt ≈ f (t)dt = ... = f (t)dt = (10) ′ ′ N xN −1 x1 −ta

It’s easy to derive that: √ 2i x′i = 2σe erf −1 ( − 1) N And the average waiting time is: ∫ x′i N N ∑ 1 ∑ ′ ta ′ ¯ tw = xi f (t)dt = xi = N i=1 N x′i−1 i=1

To evaluate the performance of proposed Guard Beacon, we implement this strategy into a real-world test-bed. The target hardware platform is T-mote sky node, and the software platform is contiki, an embedded operating system widely used in WSN. The synchronization power is measured by calculating the transceiver’s operating time in different modes when sending, receiving and idle listening on beacons. The default parameters of evaluation is shown in Table.1. Nodes are placed closely to exclude the effects of unreliable link.

(11)

(12)

Apply (12) into (7) and (8). Then if we relax N as a real N ′ , the optimal N ′ can be derived as: √ ta P l ′ (13) Nopt = Tb Ps

TABLE I D EFAULT PARAMETERS OF E VALUATION Network size Network topology Max. hops Synchronization interval (Ts ) Beacon duration (Tb ) Estimated deviation of clock drift rate (σf ) Estimated deviation of clock offset (σθ ) Estimated deviation of message delivery delay(στ ) Power consumption for data transmission (Ps ) Power consumption for data receiving (Pr ) Power consumption for idle listening (Pl ) Synchronization confidence level (β0 )

10 tree 4 100s 2ms 50ppm 20us 11us 52.2mW 59.1mW 59.1mW 99%

Table.2 displays the optimal number of beacons N under the condition of different synchronization interval Ts (the same configuration as Dozer [3]) and different clock drift rate σf . The optimal beacon sending times xi , and the average waiting time t¯w are shown in Table.3, when the beacon number N is given. TABLE II O PTIMAL NUMBER OF BEACONS (N ) WITH VARIABLE SYNCHRONIZATION INTERVAL (Ts ) AND CLOCK DRIFT RATE (σf )

PP PPTs σf P P 50ppm 100ppm 150ppm

50s

100s

150s

200s

2 3 3

3 4 4

3 4 5

4 5 6

In Fig.3, the average synchronization power consumption (almost linearly proportional to the average duty cycle) per node in a multi-hop tree based network for three schemes are compared. Please be aware that the accuracy of synchronization was not the optimization aim of Guard Beacon, since we were trying to design an algorithm to enable the system work even with poor synchronization. In other word, we traded the synchronization accuracy for power consumption,


AVERAGE WAITING TIME WHEN THE BEACON NUMBER (N ) IS GIVEN

N 1 2 3 4

optimal beacon sending time (xi (ms)) 12.88 2.71, 12.88 -0.66, 4.93, 12.88 -2.55, 1.73, 6.13, 12.88

(t¯w )

t¯w (ms) 12.88 5.62 3.66 2.72

overhead and complexity. Therefore, we provide the power consumption not the synchronization accuracy as results in Fig.3. The synchronization power of Guard-Beacon decreases more quickly than Single-beacon with the increasing synchronization interval Ts , indicating that less idle listening time is spent for Guard beacon. However, with a synchronization interval less than 20s, i.e. the optimal beacon number drops to 1, Guard-Beacon has the same performance with the SingleBeacon demonstrating the backward compatible. RTSP[9] is also implemented in the motes. RTSP can significantly reduce the number of time messages (14% of FTSP) mainly by using overhearing other beacons and adaptive resynchronization interval, which means a node sends a resynchronization request only when the local time is much deviated from global time. For fair comparison, we integrate the same periodically duty-cycling into RTSP as other schemes. In Fig.3, we can see when the beacon interval is small, RTSP has a much higher power consumption than Guard-beacon. The reason is that, although a node running RTSP only sends time messages when necessary, it has to periodically wakeup and listening for a guard time to overhear beacons from neighboring nodes to capture the global time, and decide whether it needs re-synchronization. Moreover, the two-way message exchanging (REQ/REP) and 2LR skew estimation also consume considerable more energy then Guard Beacon. In other word, RTSP can only save the power consumption of sending beacons, but not the power consumption of receiving and idle listening for beacons. As the beacon interval becomes larger, the idle listening power consumption of RTSP is greatly reduced, and it’s performance is quickly closed to Guard beacon. Finally, the experiment results have shown that the performance of sub-optimal solution of Guard Beacon is very closed to optimal solution. Since the sub-optimal solution can be analytically solved with on-line calculation fashion, it enables the practical deployment. V. C ONCLUSION In this paper, we present a beacon strategy in the context of low duty-cycled sensor networks, aiming to reduce the overall power consumption of time synchronization, instead of the number of time messages. By sending the optimal number of beacons at the optimal times, Guard Beacon can reduce the idle listening time for coming beacon, therefore minimize the total synchronization power consumption of sending and receiving beacons. Experiment results in multi-hop network show that Guard Beacon is more energy efficient than Single Beacon when beacon interval is large, while more energy

30 Average Synchronization Power Consumption(uW)

TABLE III O PTIMAL BEACON SENDING TIME (xi ) AND

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Single−beacon RTSP Guard−beacon(sub−optimal) Guard−beacon(optimal)

25

20

15

10

5

0 20

40

60

80 100 120 140 Synchronization Interval(s)

160

180

200

Fig. 3. Power consumption of synchronization, depending on synchronization intervals

efficient than RTSP when beacon interval is small. A suboptimal but analytical solution is also proposed, which shows a close performance with the optimal solution, but can be practically deployed in common WSN devices. R EFERENCES [1] Wu, Yik-Chung, Qasim Chaudhari, and Erchin Serpedin. ”Clock synchronization of wireless sensor networks.” Signal Processing Magazine, IEEE 28.1 (2011): 124-138. [2] Burri, Nicolas, Pascal Von Rickenbach, and Roger Wattenhofer. ”Dozer: ultra-low power data gathering in sensor networks.” Proceedings of the 6th international conference on Information processing in sensor networks. IPSN. IEEE, 2007. [3] Marti, Mikls, et al. ”The flooding time synchronization protocol.” Proceedings of the 2nd international conference on Embedded networked sensor systems. ACM, 2004. [4] Liang, Chieh-Jan Mike, and Andreas Terzis. ”Koala: Ultra-low power data retrieval in wireless sensor networks.” Proceedings of the 7th international conference on Information processing in sensor networks. IEEE Computer Society, 2008. [5] Shi, Xiaolei, and Guido Stromberg. ”SyncWUF: An ultra low-power MAC protocol for wireless sensor networks.” Mobile Computing, IEEE Transactions on 6.1 (2007): 115-125. [6] Leng M, Wu Y C. On clock synchronization algorithms for wireless sensor networks under unknown delay[J]. Vehicular Technology, IEEE Transactions on, 2010, 59(1): 182-190. [7] Kim H, Ma X, Hamilton B R. Tracking low-precision clocks with time-varying drifts using kalman filtering[J]. Networking, IEEE/ACM Transactions on, 2012, 20(1): 257-270. [8] Ahmad A, Zennaro D, Serpedin E, et al. A factor graph approach to clock offset estimation in wireless sensor networks[J]. Information Theory, IEEE Transactions on, 2012, 58(7): 4244-4260. [9] Noh, Kyoung-Lae, Erchin Serpedin, and Khalid Qaraqe. ”A new approach for time synchronization in wireless sensor networks: Pairwise broadcast synchronization.” Wireless Communications, IEEE Transactions on 7.9 (2008): 3318-3322. [10] Chaudhari, Qasim M., Erchin Serpedin, and Jang-Sub Kim. ”Energyefficient estimation of clock offset for inactive nodes in wireless sensor networks.” Information Theory, IEEE Transactions on 56.1 (2010): 582596. [11] Akhlaq, Muhammad, and Tarek R. Sheltami. ”RTSP: An Accurate and Energy-Efficient Protocol for Clock Synchronization in WSNs.” Instrumentation And Measurement, IEEE Transactions on 62.3 (2013): 1-12.