486 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 7, JULY 2009

Double-Sided Two-Way Ranging Algorithm to Reduce Ranging TimeHakyong Kim, Member, IEEE

Abstract—In this Letter we propose a novel ranging algorithmfor the asynchronous location positioning system. The main ideaof the proposed algorithm is to reply with multiple acknowledge-ment packets to a single ranging request. The ranging algorithmreduces the number of packets used in ranging process andimproves the ranging accuracy at the same time.

Index Terms—Ranging, ranging time, SDS-TWR, RTLS.

I. INTRODUCTION

THE ranging technique is the most fundamental and in-dispensable technology in the real-time locating systems

(RTLS). Ranging is a process to determine the distancebetween two nodes. A ranging scheme can be classified intoeither synchronous or asynchronous whether it uses globalsynchronization or not. Recently, the asynchronous rangingscheme catches on commercially since it does not requireglobal synchronization and an expensive and precise oscillator.

In an asynchronous ranging scheme, each node uses itsown clock or timing information to measure the flight timeof beacon signals, instead of using global synchronization.For this reason, each mobile node has to measure a round-triptime to obtain the propagation time between two nodes. Thisfeature makes it feasible to build an asynchronous rangingsystem with a relatively cheap oscillator. In order to estimatea location, however, a mobile node has to measure distancesto couples of fixed nodes in a sequential manner, which resultsin a considerable amount of ranging time.

Long ranging time caused by a series of rangings bringsabout several problems. First of all, it increases the collisionprobability of radio signals significantly, which again increasesthe ranging time more due to retransmission. Secondly, itmakes mobile nodes consume battery power more, whichentails short battery lifetime. Since mobile nodes have a finitebattery capacity, power saving is one of the most criticalissues. Furthermore, long transaction time limits the numberof mobile nodes handled by a fixed node in a specific timeduration.

Therefore, it is crucial to shorten the ranging time inan asynchronous ranging scheme. Nevertheless, studies arefocusing mostly on the improvement of ranging accuracy [1],[2]. In this paper, therefore, we suggest a ranging protocolwhich reduces ranging time fairly, while keeping rangingaccuracy high. The main idea of the proposed scheme isto reply with multiple acknowledgement packets to a singleranging request. This idea will be explained in the next sectionand the mathematical analysis will be followed.

Manuscript received January 15, 2009. The associate editor coordinatingthe review of this letter and approving it for publication was A. Banchs.

H. Kim is with the New Business Development Team, Samsung NetworksInc., ASEM Tower 8F, Samsung 1 Dong, Gangnam Gu, Seoul, 135-798, S.Korea (e-mail: hykim@ieee.org, honest72@korea.com).

Digital Object Identifier 10.1109/LCOMM.2009.090093

node A (mobile) node B (fixed)

REQ

ACK+REQ

ACK

DATA

DATA

to server

roundA

roundBreplyA

replyBt t

tt

pt

ACK

ranging phasereportin

g phase

pt̂

Fig. 1. Ranging procedure of SDS-TWR (Symmetric Double-Sided Two-Way Ranging).

II. PROPOSED RANGING ALGORITHM

In the previous section, we emphasized the importance ofreducing the ranging time in an asynchronous ranging scheme.In this section, we will propose a novel ranging scheme afterreviewing the existing asynchronous ranging scheme.

A. SDS-TWR

In general, the ranging procedure of an asynchronous rang-ing scheme is composed of three phases: scanning, ranging,and reporting phases. During the scanning phase, a mobilenode scans and selects fixed nodes, that will take part inthe ranging phase, by simply exchanging a pair of scanningand acknowledgement packets. In general, nodes are draftedaccording to the received signal strength, the arrival order ofacknowledgement packets, and so on. In the ranging phase,the mobile node performs ranging with the nodes selectedin the scanning phase. The ranging is either symmetric orasymmetric. After completing the ranging process, distancesto each fixed node are calculated and reported to a locationserver in the reporting phase.

Depending on the ranging scheme, scanning or reportingphase could be removed or performed by fixed nodes. Here, weconsider the ranging phase only unless mentioned separately.

1089-7798/09$25.00 c© 2009 IEEE

KIM: DOUBLE-SIDED TWO-WAY RANGING ALGORITHM TO REDUCE RANGING TIME 487

Fig. 1 shows the ranging procedure of SDS-TWR (SymmetricDouble-Sided Two-Way Raning) [3]. As shown in the figure,it exchanges 4 packets for ranging and 2 packets for reporting.

Let tscan, trange, and treport stand for the time duration ofscanning phase, ranging phase, and reporting phase, respec-tively. Then, the ranging time tR can be expressed as below:

tR = tscan + trange + treport.

B. Proposed Ranging Algorithm: SDS-TWR-MA

In order to reduce the ranging time, we devised an asym-metric ranging algorithm which uses several acknowledgementpackets to a single ranging request [4]. However, the schemeis subject to clock drift or clock offset, which can be tackledby a symmetrical architecture [1]. Therefore, we ameliorateour original idea proposed in [4], as illustrated in Fig. 2.

As shown in the figure, node A (mobile node) initiatesthe ranging phase by transmitting a ranging request packet.Then, node B (fixed or reference node) replies with severalACK+REQ packets. node B transmits the packets one by one,considering packet length, data rate of the RF channel, pro-cessing delay in the opposite node, and so on. On transmittingeach ACK+REQ packet, node B calculates the reply time(treplyBi ) at node B.

node A waits these packets for a specific time after trans-mitting a request packet. The waiting time is determinedin advance, considering the number of ACK+REQ packets,packet length, data rate, and so on. As soon as the waitingtime is over, node A replies with a DATA packet. The DATApacket includes round-trip times (troundAi) and reply times(treplyAi) at node A.

On receiving the DATA packet, node B sends an ACKpacket back to node A to confirm the successful transmissionand measures round-trip times (troundBi) at node B. Finally,node B calculates the measured propagation time t̂p andtransmits it to the location server or location engine.

III. PERFORMANCE EVALUATION

A. Ranging Accuracy

In Fig. 2, the round-trip times have the relations as belows:

troundAi = 2tp + treplyBi , for 1 ≤ i ≤ n (1)

andtroundBi = 2tp + treplyAi , for 1 ≤ i ≤ n. (2)

Here, tp represents an real propagation time between thetwo nodes and n implies the number of REQ+ACK packetstransmitted by node B. Let’s assume that there are no packettransmission errors. Summing the above 2n equations andrearranging it in terms of tp, then we have

tp =14n

n∑

i=1

{(troundAi − treplyAi) + (troundBi − treplyBi)

}.

tp could be influenced by clock offset, clock drift, reflection,and others. Therefore, the measured propagation time t̂p couldbe different from tp. Let’s assume that eA and eB stand for the

node A (mobile) node B (fixed)

REQ

ACK+REQ

ACK+REQ

DATA

ACK+REQ

roundA1 replyB1

replyB2roundA2

roundAn replyBn

t

t

t

t

t

t

AnreplyAt ~1

pt

pt̂to server

ACK

BnroundBt ~1

Fig. 2. Ranging procedure of SDS-TWR-MA (SDS-TWR with MultipleAcknowledgement).

influence of these factors at node A and node B, respectively.Then, t̂p can be written as

t̂p =14n

n∑

i=1

{(troundAi − treplyAi) · (1 + eA)

+(troundBi − treplyBi) · (1 + eB)}.

Then, the ranging error can be expressed as the differencebetween t̂p and tp:

t̂p − tp =14n

n∑

i=1

{(troundAi − treplyAi) · eA

+(troundBi − treplyBi) · eB

}.

Substituting troundAi and troundBi of the above equation witheq. 1 and eq. 2 respectively, then we have

t̂p − tp =14n

n∑

i=1

{2(eA + eB) · tp

+(eA − eB) · (treplyBi − treplyAi)}. (3)

Here, since the propagation time between the two nodes isvery small compared with the packet processing time at nodes,we can neglect the first term of eq. 3. Then, it becomes

t̂p − tp =14n

(eA − eB)n∑

i=1

(treplyBi − treplyAi). (4)

As we increase the number of ACK+REQ packets, namelyincrease n in eq. 4, the ranging error decreases significantly.

When n = 1, eq. 4 becomes

t̂p − tp =14(eA − eB)(treplyB1 − treplyA1).

488 IEEE COMMUNICATIONS LETTERS, VOL. 13, NO. 7, JULY 2009

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16 18 20

SS-TWR-MASDS-TWR

time for transmission frequency [sec]

batte

ry li

fetim

e (d

ays)

Fig. 3. Comparison of the battery lifetime.

TABLE ITHE NUMBER OF PACKETS REQUIRED IN SDS-TWR AND

SDS-TWR-MA FOR DIFFERENT ITERATION TIMES (m) ORACK+REQ PACKETS (n).

m or n 1 2 3 4 5 6SDS-TWR 6 12 18 24 30 36

SDS-TWR-MA 4 5 6 7 8 9

It corresponds to the ranging error estimated for SDS-TWR(symmetric double-sided two-way ranging) [3]. According to[2], the ranging error of SDS-TWR or SDS-TWR with singleacknowledgement is reduced to half of that in asynchronousdouble-sided two-way ranging (ADS-TWR) approach.

As we mentioned earlier, the ranging time is a crucialfactor in designing a ranging algorithm. The ranging timecan be measured sketchily by counting the number of packetsexchanged. In SDS-TWR-MA, only 4 packets are neededwhen n = 1 while SDS-TWR requires 6 packets includingthe packets exchanged in the reporting phase. (In Fig. 1,SDS-TWR can be completed without reporting phase byletting fixed nodes calculate and forward ranging results. Thisapproach, however, causes a problem in correlating multipleranging results in the location server, especially when it isiterated couples of times. To unload the processing burden oflocation server, handling multiple ranging results is given tomobile nodes in practice.)

In this time, let us consider the cases when we iterateranging algorithms several times for a stable ranging result.This can be translated such that SDS-TWR-MA uses asmany ACK+REQ packets as the iteration times, instead ofrepeating the whole ranging procedure. Table 1 compares thenumber of packets exchanged in SDS-TWR and SDS-TWR-MA for the different number of iteration times or ACK+REQpackets. As shown in the table, the number of packets requiredin SDS-TWR is linearly proportional to the iteration times.By contrast, SDS-TWR-MA requires only one more packetadditionally as the iteration times increase.

B. Battery Lifetime of Mobile Nodes

Mobile nodes alternate its operation mode between activeand sleep modes to save its power consumption. Let tactive

and tsleep denote the time duration of active and sleep modes,respectively. pactive and psleep are the amount of the power

consumption during active and sleep mode, respectively. As-suming that C designate the battery capacity used in a mobilenode, then the battery lifetime can be calculated as follows:

LT =C

24× tactive + tsleep

tactive · pactive + tsleep · psleep(5)

In eq. 5, let’s substitute variables with practical numbers.The numbers are from an RTLS solution using the IEEE802.15.4 and IEEE 802.15.4a technologies [3]. In the systemdeveloped by Samsung Networks Inc., pactive = 60 mA andpsleep = 20 µA. We use the Lithium-Polymer rechargeablebattery whose capacity is 720 mAh [5].

tactive is equal to the total ranging time of a single locationpositioning and is calculated by multiplying the number ofpackets used for the whole ranging process with the averagepacket processing time tproc. In our test, tproc was about1.8msec. Assuming the transmission frequency of locationinformation is 1 second, then tsleep = 1000 − tactive msec.

Fig. 3 shows the battery lifetime for different frequencyintervals. Here we assume that SDS-TWR is performed twiceand 2 ACK+REQ packets are used for SS-TWR-MA. Thenumber of fixed nodes is 4, which adds 5 packet exchangesfor scanning. That is, 17 and 10 packets are used for rangingwith SDS-TWR and SDS-TWR-MA respectively. Accordingto the figure, we can use battery 66% and 33% longerwith SDS-TWR-MA, when the frequency is 1 second and20 seconds respectively. It means that the proposed rangingscheme is more appropriate for real-time applications than fornon-real-time asset management applications. The effect ofmultiple acknowledgements becomes obvious as the numberof acknowledgement packets or iteration times increases.

IV. CONCLUSION

In this Letter, we proposed a symmetric double-sided two-way ranging algorithm which replies to a single rangingrequest with multiple ACK+REQ packets. The algorithm canreduce the number of ranging packets by 33% or more, com-pared to the well-known SDS-TWR algorithm. Consequently,it prolongs the battery lifetime of mobile nodes while keepingthe ranging accuracy high.

REFERENCES

[1] L. J. Xing, L. Zhiwei, and F. C. P. Shin, “Symmetric double side twoway ranging with unequal reply time,” in Proc. 66th IEEE VehicularTechnology Conference (VTC) 2007 Fall, pp. 1980–1983, Sept. 2007.

[2] Y. Jiang and V. C. M. Leung, “An asymmetric double sided two-wayranging for crystal offset,” in Proc. Int’l. Symp. On Signals, Systems andElectronics (ISSSE) 2007, Montreal, pp. 525–528, July 2007.

[3] IEEE Computer Society, IEEE Std 802.15.4a - 2007, Aug. 2007.[4] H. Kim, “A ranging scheme for asynchronous location positioning sys-

tems,” The 6th Workshop on Positioning, Navigation and Communication2009 (WPNC’09), Hannover, Germany, Mar. 19, 2009

[5] Sansung Networks’ RTLS system (in Korean),http://www.samsungnetworks.co.kr/03business/rtls/rtls.jsp