Combined Sector and Channel Hopping Schemes for Efficient

Research ArticleCombined Sector and Channel Hopping Schemes for EfficientRendezvous in Directional Antenna Cognitive Radio Networks

AbdulMajid M Al-Mqdashi1 A Sali1 Nor K Noordin1

Shaiful J Hashim1 and Rosdiadee Nordin2

1Wireless and Photonic Networks Research Centre of Excellence (WiPNEt) Department of Computer andCommunication Systems Engineering Faculty of Engineering Universiti Putra Malaysia 43400 Serdang Selangor Malaysia2Department of Electrical Electronic and Systems Engineering Universiti Kebangsaan Malaysia 43600 Bangi Selangor Malaysia

Correspondence should be addressed to AbdulMajid M Al-Mqdashi abdulmajidalmqdashigmailcom

Received 27 August 2017 Accepted 24 October 2017 Published 12 December 2017

Academic Editor Ahmed M Al-Samman

Copyright copy 2017 AbdulMajid M Al-Mqdashi et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Rendezvous is a prerequisite and important process for secondary users (SUs) to establish data communications in cognitive radionetworks (CRNs) Recently there has been a proliferation of different channel hopping- (CH-) based schemes that can providerendezvous without relying on any predetermined common control channel However the existing CH schemes were designedwith omnidirectional antennas which can degrade their rendezvous performance when applied in CRNs that are highly crowdedwith primary users (PUs) In such networks the large number of PUs may lead to the inexistence of any common available channelbetweenneighboring SUswhich result in a failure of their rendezvous process In this paper we consider the utilization of directionalantennas in CRNs for tackling the issue Firstly we propose two coprimality-based sector hopping (SH) schemes that can provideefficient pairwise sector rendezvous in directional antennaCRNs (DIR-CRNs)Then we propose an efficient CH scheme that can becombined within the SH schemes for providing a simultaneous sector and channel rendezvous The guaranteed rendezvous of ourschemes are proven by deriving the theoretical upper bounds of their rendezvous delay metrics Furthermore extensive simulationcomparisons with other related rendezvous schemes are conducted to illustrate the significant outperformance of our schemes

1 Introduction

The inefficiency of radio spectrum utilization due to thefixed assignment of spectrum bands coupled with the hugeincrease in the number of wireless devices recently leadsto the emerging of cognitive radios (CRs) CRs have beenintroduced as an efficient solution for the spectrum scarcityissue They allow unlicensed users also known as secondaryusers (SUs) to opportunistically use licensed bands as longas this use does not create any interference to the bandslicensed users that is primary users (PUs) In distributedCRNs SUs need to meet each other on a common channeland exchange control messages in order to set up theirdata transmissions [1] This operation is called rendezvouswhich is a fundamental and a vital process for initiating theconnection of the SUs data communications

The use of a dedicated common control channel (CCC)is one widely adopted rendezvous approach in the literature[2ndash6] Although this approach can simplify the rendezvousprocess it hasmanydrawbacks such as theCCC susceptibilityto long-time blocking by PUs early saturation by SUs or jam-ming by attackers [7 8] Moreover the spectrum heterogene-ity among SUs caused by the spatial and temporal variationsof the spectrum opportunities (influenced by neighboringPU activities) makes this approach not practical Thereforechannel hopping (CH) has been proposed as an alternativeapproach for rendezvous without the need for any predefinedCCC The existing CH-based rendezvous schemes weredesignedwith omnidirectional antenna according to differentmathematical structures (eg [9ndash18]) in order to provide asuccessful channel rendezvous between a pair of single-hopSUs In the CH approach each SU generates its CH sequence

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 5748067 19 pageshttpsdoiorg10115520175748067

2 Wireless Communications and Mobile Computing

based on the available channels that are sensed to be idle fromany PU activities within its omnidirectional range Thenthe SU keeps hopping over the channels according to thegenerated CH sequence for achieving channel rendezvousThe rendezvous occurs between a pair of communicating SUswhen they hop during the same time slot over a channelthat is commonly available for both of themThe existence ofcommon available channels (at least one) between the pair ofcommunicating SUs is a common and essential assumptionmade by all the existing CH schemes Their designs relymainly on this assumption to take place for ensuring thesuccess of the rendezvous operation However none of theexisting CH rendezvous designs were tailored for high-density PU networks where the number of active PUs in thenetwork is larger than the number of the channels In suchnetworks the channel availabilities may vary dramaticallyamong the SUswithin the single-hop rendezvous region itselfThis can lead to the inexistence of any common availablechannel between a pair of SUs and hence the failure of therendezvous process

One approach to overcome this serious rendezvous prob-lem is using directional antennas instead of the convention-ally used omnidirectional ones [19] Directional antennashave been utilized in emerging wireless networks such asthe millimeter-wave (MMW) networks for providing highlyreliable transmission and multi-Gigabit data rates This ismainly due to their capabilities in enlarging the transmissionrange and limiting the interference [20 21] However InCRNs equipping SUs with directional antennas for channelrendezvous can bring about many advantages First of all itallows SUs to transmit their rendezvous messages towardsspecific directions which can reduce the amount of inter-ference to the PUs in the network as compared with theomnidirectional antennasThis is because the transmission ofthe SU that is equipped with directional antenna is directedto a particular region which can only cause interferenceto those PUs that are within this region On the contrarywhen using the omnidirectional antennas the transmissionof the SU is scattered towards all the directions Thus it cancause interference to all the surrounding PUs within the SUtransmission range Second as related to the interferencerestriction imposed by the CR concept SUs can use only thechannels that are idle from any PU activities within theirtransmission range According to that and due to its directedtransmission range using directional antenna will increasethe number of available channels that can be utilized by theSU in each of its transmission sectors As a consequencethe probability for any pair of neighbouring SUs to haveat least a common available channel within their crossedsectors is high regardless of the number of PUs in the CRNNote that in omnidirectional antennas this probability couldbe less than 01 for some scenarios when the number ofPUs is larger than the network channels [19] Increasing theprobability of existing common available channel betweenthe SUswill significantly enhance the probability of successfulchannel rendezvous Therefore in this paper we study therendezvous problem in directional antenna CRNs where SUsare equipped with directional antennas

While the use of directional antennas for channel ren-dezvous in CRNs can bring about the above-mentionedadvantages it also imposes some unique challenges Amongthese challenges is the sector rendezvous which must beachieved in advance between the pair of communicating SUsbefore they can achieve channel rendezvous Specifically theSUs need to steer their antennas towards each other in orderto communicate over their commonly available channelsThis necessitates the design of a deterministic sector hopping(SH) scheme that can guarantee that any pair of neighbouringSUs will steer their antennas to the proper directions (ietowards each other) at a certain time instance So when theSH scheme is combined with a suitable and deterministicCH scheme SUs can achieve successful sector and channelrendezvous simultaneously within a bounded time Howeversince the SUs do not know the relative locations of each otheras well as the available channels before they rendezvous thecombined sector and channel hopping (SCH) scheme shouldbe designed in fully distributed manner without any priorinformation or synchronization Designing such combinedSCH schemes for achieving rendezvous in DIR-CRNs isintuitivelymore challenging as compared with the traditionalomnidirectional antenna paradigm

In spite of the existing research in the literature there havebeen some papers that addressed the utilization of directionalantennas in CRNs However most of the proposed worksinvestigated issues other than the rendezvous issue such assensing [22 23] routing [24 25] and connectivity [26 27]To the best of our knowledge the works in [19 28] are theonly proposals that tackle the sector and channel rendezvousissue in DIR-CRNS In [19] an efficient framework forbeamforming was proposed to provide a pairwise sector andchannel rendezvous in DIR-CRNs However the SH schemein [19] is not a blind design where it assumes that the receivermust have prior knowledge of the sender number of sectorsin order to achieve a successful sector rendezvous This isnot practical since SUs do not know any information abouteach other before they rendezvous On the other hand Li andXie in [28] proposed a blind prime-based SH scheme wherethe number of sectors is adjusted to primes for achievinga guaranteed sector rendezvous However since the schemerelies on the coprimality between prime numbers only theauthors added an initiating rotated SH sequence on thesender sideThis is in order to ensure a successful rendezvouswith the receiver when the sender and the receiver constructtheir sequences with the same prime Accordingly the extrasequence overhead incurs extensively long sector rendezvouslatency and hence a long time-to-rendezvous (TTR) willresult when the SH is combined with a CH sequenceFurthermore the SH schemes in [19 28] are designed only forasymmetric-role environment where SUs have preassignedrole (ie SU is either a sender or receiver) However thisdesign limits the applications of the schemes for exampleSUs cannot work as a forwarder (ie receive packets fromone SU and then forward them to another SU) due to thepermanent role assignment [29] Another drawback of theseworks is their limitations to provide a complete solutionfor combining the SH scheme with a suitable and efficientCH scheme which consider the unique traits of DIR-CRNs

Wireless Communications and Mobile Computing 3

They claimed that their SH schemes can work on top ofany existing deterministic CH schemes which were designedfor the omnidirectional antennas paradigm However thecombined CH scheme must be designed appropriately bytaking into account the unique traits of DIR-CRNs such asthe channelsrsquo qualities in the different sectors

In this paper we propose efficient schemes for achievingrendezvous in DIR-CRNs The main contributions of thispaper are summarized as follows

(i) We propose two asymmetric- and symmetric-rolecoprimality-based SH schemes called PES-SH andIPES-SH for pairwise sector rendezvous in DIR-CRNs

(ii) We combined our SH schemes with an efficient grid-quorum-based CH scheme where the CH sequencesare generated based on the best-quality channels inthe sectors The combined SCH schemes will provideguaranteed sector and channel rendezvous betweenthe pair of SUs

(iii) We derive the upper bound of the rendezvous delaymetrics for all of our schemes Also we conductextensive simulations to study their performanceunder various network settings and compare themwith the related existing works in [19 28 30]

The rest of this paper is organized as follows The systemmodel and problem formulation are presented in Section 2The design and theoretical analysis of the proposed SHschemes are presented in Sections 3 and 4 In Section 5 wepresent the combined sector and channel hopping schemesUsing simulations in Section 6 we evaluate the performanceof our proposed schemes and compare their performancewith other comparable schemes Finally we conclude thepaper in Section 7

2 Models and Problem Definition

In this section we present the system model and rendezvousproblem definition in DIR-CRNs

21 System Model We consider a CRN consisting of 119870 SUsthat coexist with several PUs in an119908times119908 areaThere are totally119871 primary channels which can be accessed opportunisticallyby the SUs in order to communicate with each other Each SU119894 isin 119870 is equipped with a directional antenna with beamwidth120579119894 (0 lt 120579119894 lt 2120587) Accordingly the 2120587 communication rangeof the SU 119894 is divided into 119873119894 = (2120587120579119894) nonoverlappingsectors that are indexed from 1 to119873119894 However the number ofsectors and the orientation of the sector indexing (ie eitherclockwise or anticlockwise) by each SUmay be different fromthe others (see Figure 1)This is a very practical issue becauseeach SU will configure its sectors based only on its own viewto the surrounding environment Each SU can transmit overany of its transmission sectors as long as it does not make anyinterference to any active PU transmission Accordingly weassume that the transmission sectors are also used as sensingsectors by which every SU can sense the appearance of theactive PUs within themThus the SU can obtain the channel

availability information per each sector We consider a time-slotted communication where time is divided into discreteslots that have fixed and equal durations During each timeslot we assume that a SU can only transmit in one sector overa single channel

22 Definitions of Sector and Channel Rendezvous In thispaper we mainly focus on the pairwise sector and channelrendezvous between any pair of SUs in a DIR-CRN Firstlywe define the sector rendezvous problem as follows

221The Sector Rendezvous Problem For any two neighbourSUs (say SU119894 and SU119895) that are equipped with directionalantennas and want to communicate with each other assumethat SU119894 is located in the sector ℎ119895 isin [1119873119895] of SU119895 andSU119895 is situated in the sector ℎ119894 isin [1119873119894] of SU119894 The pair ofthe sectors (ℎ119894 ℎ119895) is called the sector rendezvous pair SUsare said to achieve a successful sector rendezvous if and onlyif they steer their antennas towards each other where theirtransmission sectors can cover each other Formally let 119878119894 =1198780119894 119878

1119894 119878

119879119894119894 and 119878119895 = 1198780119895 119878

1119895 119878

119879119895119895 denote the sector

hopping sequences for SU119894 and SU119895 with periods 119879119894 and 119879119895respectively Also let 120575 denote the clock drift between SU119894

and SU119895 in the asynchronous scenarioThe sector rendezvousproblem can be formulated as follows

If forall120575 forall119873119894 119873119895 exist119905 isin [0 119879119894119879119895 minus 1] st (119878119905119894 = ℎ119894 and119878119905+120575119895 = ℎ119895) then the sector rendezvous is achievedover the sector rendezvous pair (ℎ119894 ℎ119895)

222 The Sector and Channel Rendezvous Problem Whena SU steers its directional antenna to each sector of itstransmission sectors it performs CH over the availablechannels within the sector according to a CH sequenceThis is in order to attempt channel rendezvous with anotherSU over a commonly available channel between them Thecombined CH scheme should be designed in such a way thatguarantees a successful channel rendezvous within boundedtime whenever the communicating SUs already achieved asuccessful sector rendezvous During the current sector if theSU does not achieve channel rendezvous with its intendedcommunicating SU within the bounded time slots it thensteers its antenna to the next sector of its SH sequence andexecutes the CH scheme based on the available channelswithin this sector

One approach to view the problem is to look at it ina hierarchical way in which time is divided into frameswhere the SU tunes its antenna to one sector during eachframe In other words the SH is implemented on the framescale Then each frame is divided into number of time slotswhere the combined CH sequence is executed (ie the CHis implemented on the time slot scale) The main goal of thispaper is to design deterministic combined SCH scheme so asto tackle the sector and channel rendezvous problem

223 Metrics The proposed SH schemes as well as thecombined SCH schemes will be evaluated according to thefollowing metrics


21

54

3X

21

3X

2 143

Y

(a) Pair of119883 and 119884 SUs

1

2

3 z 1

2

3 z

4 3

1 2v

(b) Pair of 119881 and 119885 SUs

Figure 1 Examples of directional antenna configurations in two pairs of communicating SUs (a) SU119883 and SU119884 divide their transmissionrange into119873119883 = 5 and119873119884 = 4 sectors the rendezvous sector pair is (2 3) (b) SU119881 and SU119885 divide range into119873V = 4 and119873119911 = 3 sectors therendezvous sector pair is (4 1)

(i) Sector rendezvous latency (SRL) it is defined as therequired latency (in number of sector frames) for apair of SUs to achieve sector rendezvousWe considerthe maximum and average latency (MSRLASRL)MSRL is defined as the upper bound of the SRLbetween the SUs for all the possible clock driftsbetween them

(ii) Time-to-rendezvous (TTR) it is defined as therequired time (in number of time slots) for a pair ofSUs to achieve sector and channel rendezvous simul-taneously Maximum and average time-to-rendez-vous (MTTRATTR) are considered MTTR meansthe required time for a guaranteed rendezvous evenin the worst case

3 Prime- and Even-Based Sequences SectorHopping (PES-SH) Scheme

In this section we propose an asymmetric-role SH schemecalled prime- and even-based sequences sector hopping(PES-SH) scheme and then we analyze its theoretical perfor-mance

31 Scheme Design For ensuring a successful sector ren-dezvous between a pair of communicating SUs the key for thedeterministic design of our PES-SH scheme is to constructtwo SH sequences based on two coprime numbers Howeverthe coprimality is maintained between a pair of primeand even numbers that are relatively prime (ie coprime)In our PES-SH scheme we assume that 119873max is a globalvariable known by all SUs which indicates the maximumnumber of sectors by which any SU is allowed to divide itsomnidirectional 2120587 transmission range The value of119873max isobtained based on the number of channels in the network forexample for 119871 number of channels the value of 119873max couldbe 2 times 119871 Accordingly we consider two avoided sets

(1) The Avoided Prime Set (APS) which contains theprimes 2 3

(2) The Avoided Even Set (AES) which contains any evennumber in the range [2 119875max] such that this evennumber is dividable by any prime number in therange [5 119875max]119875max is the smallest primenot less than119873max For example if119873max = 20 then 119875max = 23 andhence AES = 10 14 20 22

TheAPS and AES sets are avoided by the sender and receiverrespectively when they construct their SH sequences With-out loss of generality assume that sender and receiver have119873119904 and 119873119903 antenna sectors respectively where 119873119904 119873119903 isin[1119873max] The main idea for the rendezvous of our PES-SHscheme is to let one SU (sender) adjust the number of itssectors to be the smallest prime number greater than119873119904 Onthe other hand the other SU (receiver) adjusts the numberof its sectors to the smallest even number which is notsmaller than119873119903 and not in theAES Accordingly the adjustedprime number of sectors for the sender and the adjustedeven number of sectors for the receiver are guaranteed to berelatively prime

Algorithms 1 and 2 are used by the sender and receiverrespectively to construct each round of their SH sequencesThe generating steps of the PES-SH sequences are as follows

311 Sender Sequence in PES-SH When a SU has data totransmit it serves as a sender and hence generates a prime-based (PS-SH) sequence as follows First given the sectorset 119878 = 1 119873119904 randomly select a starting sector index119894 isin [1119873119904] and rotate 119878 circularly starting from 119894 as 119878 =rotate(119878 119894 minus 1) Second adjust 119873119904 to be the smallest primenumber 119875119904 which is not smaller than119873119904 and is not in the APSset (ie 119875119904 should be 5 when 119873119904 lt 5) Third construct eachround of the PS sequence which has a length equal to 119875119878 asfollows the 119896th sector index of the PS round is 119878(119896) if 119896 le 119873119904otherwise the 119896th sector is selected randomly form 119878 when119896 gt 119873119904 The sender will keep steering its antenna accordingto the PS sequence until it achieves sector rendezvous with itsintended receiver

Consider the cases for the sender SUs119883 and119881 in Figure 1SU 119883 in Figure 1(a) has a prime number of sectors 119873119909 = 5


Input119873119904 119878119904Output a round 120596 of the PS sequence for the sender 119904(1) Find the smallest prime (119875119904 gt 3) that is not smaller

than119873119904(2) for 119905 = 0 119875119904 minus 1 do(3) if ((119905mod119875119904) lt 119873119904) then(4) 120596119904(119905) = 119878119904(119905 + 1)(5) else(6) 119903 is a random number isin [1119873119904](7) 120596119904(119905) = 119878119904(119903)(8) end if(9) end for(10) return 120596119904

Algorithm 1 The sender SH generation algorithm (PS-SH)

Input119873119903 119878119903 AESOutput a round 120574 of the ES-SH sequence for the receiver 119903(1) Find (119864119903 119864119903 notin AES) as the smallest even number that

is not smaller than119873119903(2) for 119905 = 0 119864119903 minus 1 do(3) if ((119905mod119864119903) lt 119873119903) then(4) 120574119903(119905) = 119878119903(119905 + 1)(5) else(6) 119903 is a random number isin [1119873119903](7) 120574119903(119905) = 119878119903(119903)(8) end if(9) end for(10) return 120574119903

Algorithm 2 The receiver SH generation algorithm (ES-SH)

where 119878119909 = 1 2 5 is not rotated Then the first roundof the PS119883 SH sequence with a length 5 is [1 2 3 4 5] Thisround is repeated many times where SU119883 continues steeringits directional antenna into its sectors as shown in Figure 2(a)to achieve sector rendezvous with its receiver SU119884 On theother hand the sender SU119881 in Figure 1(b) has119873119881 = 4 numberof sectors so it selects 119875119881 = 5 as the smallest prime whichis larger than 119873119881 119878119881 is rotated to start from 3 and hence119878V = 3 4 2 1 Then the first round of the PS119881 SH sequencewhich has adjusted length equal to 119875V = 5 is [3 4 2 1 119903]where 119903 indicates a randomly selected sector from 119878119881 ThePS119881 SH sequence is constructed as many rounds as shownin Figure 2(b) where SU119881 keeps hopping on its sectors toachieve sector rendezvous with the receiver SU119885

312 Receiver Sequence in PES-SH If a SU has nothing totransmit it serves as a receiver and generates an even-based(ES-SH) sequence as follows First randomly select a startingsector index 119895 isin [1119873119903] and circularly rotate the sector set119878 = 1 119873119903 starting from 119895 as 119878 = rotate(119878 119895 minus 1) Secondadjust 119873119903 to be the smallest even number 119864119903 which is notsmaller than 119873119903 and is not in the Avoided Even Set (AES)Finally construct each round of the ES sequence which has a

length equal to 119864119903 as follows the 119896th sector index of the ES-SH round is 119878(119896) if 119896 le 119873119903 otherwise the 119896th sector is selectedrandomly form 119878

Consider the receiver SU119884 in Figure 1(a) which has aneven number of sectors119873119884 = 4 which is not in AES and doesnot rotate its 119878119884 set The round of the ES119884 SH sequence witha length 4 is [1 2 3 4] This round is repeated many times bySU119884 in order to be paired by a sender as shown in Figure 2(a)On the other hand the receiver SU119885 in Figure 1(b) has119873119885 = 3sectors hence it finds 119864119885 = 4 as the smallest even numberlarger than119873119885 and not inAES SU119885 rotates its 119878119885 to start fromsector 2 and hence 119878119881 = 2 3 1 Accordingly a round of theES119885 SH sequencewith a length adjusted to119864119911 = 4 is [2 3 1 119903]where 119903 is a randomly selected sector from 119878119911 The ES119885 SHsequence is constructed in rounds as shown in Figure 2(b)

32 Scheme Analysis In this subsection we study the theo-retical performance of the PES-SH where theMSRL betweenany two arbitrary SUs performing the PES-SH is derived

eorem 1 The MSRL under the PES-SH scheme is (119875119904119864119903)where 119875119904 and 119864119903 denote the adjusted prime and even numbersof the sectors for the sender and receiver SUs respectively

Proof Suppose that the sector rendezvous pair is (ℎ119904 ℎ119903) isin1 2 119873119904 times 1 2 119873119903 where times here indicates theCartesian product of the two SUs sectors sets Without loss ofgenerality we assume that 119875119904 lt 119864119903 Also we assume that thereceiver SU119903 starts its SH sequence with 120575 sector slots earlierthan the start of the sender SU119904 Accordingly in each PS-SHperiod of SU119904 the ES-SH sequence of SU119903 is rotate(ES119903 120575)In the first round of the SH when the sender SU119904 is on itsℎ119904 sector the receiver SU119903 is on the (1199061 = 1199060 mod 119864119903 + 1)sector where 1 le 1199060 le 119873119903 During the subsequent 119864119903 minus 1rounds while the sender SU is on its ℎ119904 sector the receiverSU119903 must be sequentially on 1199062 = ((1199060 +119875119904)mod119864119903 +1) 1199063 =((1199060+2119875119904)mod119864119903+1) 119906119864119903 = ((1199060+(119864119903minus1)119875119904)mod119864119903+1)As 119875119904 and 119864119903 are relatively prime it can be easily provenwith the help of the Chinese Reminder Theorem [31] thatthese 1199061 1199062 119906119864119903 sectors where the receiver resides in the119864119903 rounds are all different Hence there must exist a sectoramong themwhich is equal to ℎ119903 According to that and sinceevery round of the PS-SH contains 119875119904 sector hops the SRLrequired to guarantee a sector rendezvous is upper bound by119875119904119864119903

4 Interleaved Prime- andEven-Based Sequences SectorHopping (IPES-SH) Scheme

In the previous section the PES-SH scheme was designedusing the asymmetric approach which requires that each SUhave a preassigned role as either a sender or a receiver Inthis section we introduce our interleaved prime- and even-based sequences (IPES-SH) scheme which is symmetric (ieno preassigned role assumption)

41 Scheme Design In our symmetric IPES-SH schemeevery SU generates its SH sequence with the help of a binary


1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)

(a) Sector rendezvous between the sender 119883 and the receiver 119884 on the rendezvous sector pair (2 3)for the cases when 119884 starts its SH with 119894 slots later than119883 where 119894 isin [0 (119875119883 minus 1)]

3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)

(b) Sector rendezvous between the sender 119881 and the receiver 119885 on the rendezvous sector pair(4 1) for the cases when 119885 starts SH with 119894 slots earlier where 119894 isin [0 (119864119885 minus 1)]

Figure 2 Successful synchronous and asynchronous sector rendezvous for the two pairs of communicating SUs in Figure 1

bit sequence such as its globally unique ID The SH sequenceis constructed as an interleaved sequence of several PS and ESSH sequences through a two-step approach Firstly each SUtransforms its unique ID according to a certain design intoanother ID sequence so that it is cyclically unique that is theresulting ID sequences of any two SUs are cyclic rotationallydistinct to each other Secondly the SU replaces any bit of1 (or 0) in its new ID sequence with a PS-based (or ES-based) SH sequence Accordingly for any pair of SUs thecyclic uniqueness property will guarantee the existence ofsome time instances where the two SUs are playing differentroles Hence the sector rendezvous is achieved when one SUis hopping according to its PS sequence while the other SU ishopping based on its ES sequence and vice versa

Several methods have been proposed in the literatureto transform the unique ID into another cyclically uniquebinary sequence In [32] a method was proposed to expandthe119898-bit ID into another 3119898-bit extended ID that is cyclicallyunique The unique 119898-bit ID in that method is expandedby appending 119898-bit consecutive 0rsquos into the beginning ofthe ID and other 119898-bit consecutive 1rsquos at the end of theID Another method for generating cyclically unique IDsthat are used for the construction of symmetric role SHsequences has been proposed in [30] The method appendsthe original 119898-bit ID with other (119898 + 1)-bits of consecutive0rsquos and 1rsquos which results in (2119898 + 1)-bits expanded IDsequence However the extended ID sequences generatedby these methods are relatively long especially for theformer method This results in long rendezvous delay whenthey are used for constructing symmetric role sequencesTherefore we propose an alternativemethod for constructing

cyclic rotationally distinct sequences which provides shorterextended ID lengths than the methods in [30 32] So itprovides shorter sector rendezvous delay when it is usedfor constructing symmetric role sequences in our IPES-SHscheme

411 Constructing the Cyclic Unique ID Sequences In ourmethod each119898-bit ID is extended by appending only119898-bitsof 1rsquos and 0rsquos in the beginning and in the end of the ID

Lemma 2 Given any two119898-bit ID sequences120572 = 1205721 120572119898and 120573 = 1205731 120573119898 let a and b be two 2119898-bit expanded IDsequences generated from 120572 and 120573 as follows

a def= 1(lceil1198982rceil)1205720(lfloor1198982rfloor) and b def

= 1(lceil1198982rceil)1205730(lfloor1198982rfloor) where 1(sdot) is a bit sequence composedof only 1rsquos and 0(sdot) is a bit sequence composed of only 0rsquosThen a and b are cyclic rotationally distinct from eachother which means that

If a = b 997904rArr a = 119903119900119905119886119905119890 (b 119896) forall119896 isin (0 2119898 minus 1] (1)

Proof To prove the above lemma we consider all the possiblecases that may happen when sequence 119887 is rotated with (119896 isin(0 2119898minus1]) We show in each case that bits in sequence a andother bits in sequence 1198871015840 = rotate(b 119896) have different valueseven though these bits are in the same positions Consideringthe five cases in Figure 3 it is sufficient to prove that a andb1015840 =rotate(b 119896) are cyclic rotationally distinct to each other

Case 1 (119896 isin (0 lceil1198982rceil]) As indicated by the red arrow inFigure 3 it holds that 1198862119898 = 0 and 11988710158402119898 = 1


middot middot middot m


middot middot middot m middot middot middot m




K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a

middot middot middot

middot middot middot middot middot middot





















b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)






Figure 3 Illustration of the five cases in the proof of Lemma 2

Case 2 (119896 isin (lceil1198982rceil119898)) As indicated by the red arrow inFigure 3 it holds that 119886(lceil1198982rceil+119898+1) = 0 and 119887

1015840(lceil1198982rceil+119898+1) = 1

Case 3 (119896 = 119898) As indicated by the 119898 red arrows inFigure 3 the 119898 bits of sequence a starting from 119886(lceil1198982rceil+1) are1205721 120572119898minus1 while the 119898 bits of 1198871015840 in the same positionsare 0(lfloor1198982rfloor) 1(lceil1198982rceil) On the other hand as indicatedby the 119898 purple arrows in Figure 3 the first lceil1198982rceil bits ofsequence a are 1rsquos and the last lfloor1198982rfloor are 0rsquos whereas the firstlceil1198982rceil bits of 1198871015840 are 120573(lceil1198982rceil) 120573119898 and the last lfloor1198982rfloor bitsare 1205731 120573(lfloor1198982rfloor) And because 120572 = 120573 it holds that theremust be at least a single bit that is different in 119886 and 1198871015840

Case 4 (119896 isin (119898119898 + lfloor1198982rfloor]) As indicated by the red arrowin Figure 3 it holds that 119886(lceil1198982rceil) = 1 and 119887

1015840(lceil1198982rceil) = 0

Case 5 (119896 isin (119898 + lfloor1198982rfloor 2119898 minus 1]) As indicated by the redarrow in Figure 3 it holds that 1198861 = 1 and 119887

10158401 = 0

According to these possible cases we conclude that a =rotate(b 119896) forall119896 isin (0 2119898minus1] In Figure 4 we give an examplefor two ID sequences of original lengths 119898 = 4 which areexpanded to 119898 = 8 bits The figure illustrates the cyclicuniqueness property between the IDs for all the rotation cases(ie forall119896 isin [0 7])

412 Generating the Interleaved Sector Hopping SequenceWe now explain how to generate the symmetric IPES-SHsequence for any SU say SU119894 Let the number of sectors for

Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)

Figure 4 An illustrative example for the correctness of our cyclicrotationally distinct sequences construction method when119898 = 4

SU119894 be 119873119894 and hence the sector set 119878119894 = 1 119873119894 Supposethat SU119894 has 119898-bits globally unique ID sequence 120572 whichis extended by our above method to 2119898-bits sequence a =1(lceil1198982rceil)1205720(lfloor1198982rfloor)

(i) Select randomly a starting index 119896 isin [1119873119894] andgenerate a rotated set 119878119875119894 by rotating 119878119894 circularlystarting from 119896 as 119878119875119894 = rotate(119878119894 119896minus1) Also generateanother sector indices set as a reverse of 119878119875i which is119878119864119894 = Reverse(119878119875119894 )

(ii) Find (119875119894 119875119894 gt 3) as the smallest prime number that isnot smaller than 119873119894 Also find (119864119894 119864119894 notin AES) as thesmallest even number that is not smaller than119873119894

(iii) Define an empty matrix119872119894 that has 2119898 columns and119875119894 times 119864119894 rows

(iv) Fill the matrix by mapping each bit in a to a certaincolumn as described in Algorithm 3

(v) Generate the SH sequence by concatenating thematrix rows (row by row) SU119894 keeps hopping accord-ing to this generated SH sequence and repeats it inorder to rendezvous with its pair partner SU

Figure 5 illustrates the IPES-SH sequence constructionmatri-ces for SU119881 and SU119885 in our previous example in Section 31(Figure 1(b)) In Figure 5 the ID sequence of SU119881 that has119873V = 4 sectors is 120572 = 1 0 which is expanded to a =1 1 0 0 On the other side the ID sequence of SU119881 thathas 119873119911 = 3 sectors is 120573 = 0 1 which is expanded alsoto b = 1 0 1 0 The constructed matrix for SU119881 has 119875V times119864V = 5 times 4 = 20 rows and 2119898 = 4 columns SimilarlySU119885 constructs its matrix with 119875119911 times 119864119911 = 5 times 4 = 20rows and 2119898 = 4 columns Each SU will assign its matrixcolumnswith either PS sequence or ES sequence based on thecorresponding bits of its extended ID sequence For examplesince the first bit of SU119881 extended ID is one SU119881 firstly


(1) for 119888 = 1 2119898 do(2) if (119886119888 == 1) then(3) Invoke Algorithm 1 with 119878119875119894 and119873119894 to construct

a round 120596 of an PS sequence(4) generate 1205961015840 by repeating 120596 for 119864119894 times(5) Map the 119888th column of the matrix with 1205961015840(6) 119878119875119894 = Rotate(119878119875119894 1)(7) else(8) Invoke Algorithm 2 with 119878119864119894 and119873119894 to construct

a round 120574 of an ES sequence(9) generate 1205741015840 by repeating 120574 for 119875119894 times(10) Map the 119888th column of the matrix with 1205741015840(11) 119878119864119894 = Rotate(119878119864119894 1)(12) end if(13) end for

Algorithm 3

generates its first sector sets as 119878119875V = 3 4 1 2 and theninvokes Algorithm 1 with 119878119875V and119873V = 4 to construct a roundof a PS sequence 120596 = [3 4 1 2 119903] This round 120596 is repeatedfor 119864V = 4 times and assigned to the first column of SU119881

matrix Similarly since the second bit of SU119881 extended IDis one the second column of SU119881 matrix is assigned with arepeated sequence of the PS sequence [4 1 2 3 119903] which isconstructed after rotating the sector set 119878119875V by one On theother hand SU119881 assigns the third and fourth columns of itsmatrix with ES sequences because the corresponding 3rd and4th bits of its extended ID sequence are zeros Specifically SU119881

invokes Algorithm 2 with 119878119864V = Reverse(119878119875V ) and 119873V = 4to construct a round of an ES sequence 120574 = [2 1 4 3] Thisround 120574 of the ES sequence is then repeated for 119875V = 5 timesand assigned to the third columnof SU119881matrix Similarly thefourth column of SU119881 matrix is filled with the ES sequence[1 4 3 2] after repeating it for 119875V = 5 times Note that SU119885

will follow the same procedures as SU119881 to construct itsmatrixwith taking into account the different expanded ID sequence119887119911 = 1 0 1 0 and119873119911 as well as the initial sector sets 119878

119875119911 and

119878119864119911 Figure 6 shows partial sector slots of the IPES-SH

sequences for the two SUs (SU119881 and SU119885) As depicted fromthe figure the IPES-SH sequence of each SU is generatedby concatenating the rows of the SU constructed matrix inFigure 5 row by row The sequences are generated as inter-leaved slots of PS (light blue) and ES (gray) slots according tothe respective columns types in the matrices The figure alsoillustrates the rendezvous sector occurrence between the SUs(indicated by the green circle) on the sector rendezvous pair(4 1)

42 Scheme Analysis In this subsection the theoreticalperformance of IPES-SH scheme is studied where the MSRLis derived

eorem 3 Under the IPES-SH scheme the MSRL between apair of SUs (119878119880119894 and 119878119880119895) is 2119898 times (max(119875119894119864119895) (119864119894119875119895))

1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0

2 1 3 33 3 1 21 2 2 1r r r rr 1 r 32 3 3 23 2 1 11 r 2 rr 1 r 3r 3 r 22 2 3 13 r 1 r1 1 2 3r 3 r 2r 2 r 12 r 3 r3 1 1 31 3 2 2r 2 r 1r r r r

(a) IPES matrix MV for ３５V (b) IPES matrix MZ for ３５Z

Figure 5 The construction of the IPES matrices 119872119881 and 119872119885 forSU119881 and SU119885 respectively 119873119881 = 4 and 119873119885 = 3 120572119881 = 1 0 and120573119885 = 0 1 So the expanded ID sequences are a119881 = 1 1 0 0 andb119885 = 1 0 1 0

3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ



Figure 6 IPES-SH sector rendezvous between SU119881 and SU119885 for thesynchronous case

Proof To prove that IPES-SH has MSRL = 2119898(max(119875119894119864119895)(119864119894119875119895)) it is sufficient to prove that any arbitrary pair of IPES-SH sequences for example IPES119894 and IPES119895 can achieve asuccessful sector rendezvous within 2119898 (max(119875119894119864119895) (119864119894119875119895))sector slots

Let IPES119894 and IPES119895 be the corresponding IPES-SHsequences of IPES matrices119872119894 and119872119895 (ie IPES119894 and IPES119895are generated by concatenating the rows of matrices119872119894 and119872119895 resp) For example Figures 5(a) and 5(b) show the IPESmatrices119872119881 and119872119885 respectivelyWithout loss of generalityassume that SU119895 starts its SH sequence 120575 sector slots earlierthan the start of SU119894 In each SH period of SU119894 the SHsequence of SU119895 is rotate(IPES119895 120575) Clearly the rendezvousbetween this pair of SUs is the same as the rendezvous of119872119894 and 119872(119895120575) Suppose that the sector rendezvous pair is(ℎ119894 ℎ119895) isin 1 2 119873i times 1 2 119873119895 The rendezvous of thematrices is a pair of entries in the matrices whose value in119872119894

is ℎ119894 and its values in119872(119895120575) is ℎ119895 Without loss of generalitysuppose that the sector slot shift 120575 = 2119898 times 120575119877 + 120575119862 where120575119877 isin [0 (119875119895times119864119895)minus1] is the shift of row and 120575119862 isin [0 (2119898)minus1]is the shift of column Below we consider the two differentcases for rendezvous of IPES119894 and IPES119895


1 0 1 0

2 2 3 13 r 1 r1 1 2 3r 3 r 2r 2 r 12 r 3 r3 1 1 31 3 2 2r 2 r 1r r r r2 1 3 33 3 1 21 2 2 1r r r rr 1 r 32 3 3 23 2 1 11 r 2 rr 1 r 3r 3 r 2

0 1 0 1

2 3 1 3r 1 r 11 2 3 r3 r 2 r2 r 1 2r 3 r 31 1 3 13 2 2 r2 r 1 rr r r 21 3 3 33 1 2 12 2 1 rr r r r1 r 3 23 3 2 32 1 1 1r 2 r r1 r 3 r3 r 2 2

(a) M(Z40) C = 0 and R = 10 (b) M(Z41) C = 1 and R = 10

Figure 7 The IPES matrix119872119885 for SU119885 when it is circularly rotatedwith (a) 120575 = 2119898times10+0 = 40 sector slots and (b) 120575 = 2119898times2+1 = 41slots

Case 1 (120575119862 = 0) In this case it is implied that there isno column shift Recall that the expanded ID sequencesof SU119894 and SU119895 are distinct Since the columns types ofthe matrices are assigned based on these distinct expandedIDs it is guaranteed that there must exist at least a singlecommon column 119891 in both matrices which is a PS-columnin one matrix and an ES-column in the other matrix andvice versa In other words the 119891th column of 119872119894 containsa PS-SH sequence (reps ES-SH) while the same position119891th column in 119872(119895120575) contains an ES-SH (resp PS-SH) ByTheorem 1 we know that when SU119894 and SU119895 repeat the PS-SH (resp ES-SH) and the ES-SH (resp PS-SH) sequencesrespectively they rendezvous within 119875119894 times 119864119895 (resp 119864119894 times 119875119895)Meanwhile since the elements of a specific column of eachmatrix appear in the corresponding IPES-SH sequence every2119898 slots for any value of the row shift 120575119877 119872119894 and 119872(119895120575)

are guaranteed to rendezvous on their 119891th columns no laterthan 2119898 times max(119875119894119864119895) (119864119894119875119895) Specifically the rendezvoushappens when an entry of the 119891th column in 119872119894 is ℎ119894 whilethe same position entry of the 119891th column in119872(119895120575) is ℎ119895 Forexample Figure 5 shows the rendezvous of 119872119881 and 119872119885 forthe synchronous case where the slots shift 120575 = 2119898times0+0 = 0The sector rendezvous occurs between the second columnsof119872119881 and119872119885 which is indicated by the green entry in119872119885However Figure 7(a) shows the IPES matrix of SU119885 whenit is shifted with row shift 120575119877 = 10 Hence this means that120575 = 2119898times10+0 = 40The rendezvous between119872119881 in Figure 5and119872(11988540) in Figure 7(a) is achieved at their third columns

Case 2 (120575119862 = 0) In this case it holds that there is a columnshift 120575119862 isin [1 (2119898 minus 1)] Let a and b be the expanded IDsequences of SU119894 and SU119895 respectively By Lemma 2 we know

that a and b1015840 = rotate(b 119896) where 119896 isin (2119898 minus 1) are cyclicrotationally distinct to each other Thus for a column shift120575119862 isin [1 (2119898 minus 1)] of matrix119872119895 there must exist a column 119891in matrix119872119894 which has different type than the same position119891th column in the shifted matrix 119872(119895120575119862)

Accordingly therendezvous is guaranteed to occur at the 119891th columns in thematrices despite any value of the row shift 120575119877 For exampleFigure 7(b) shows the shifted IPES matrix of SU119885 when thecolumn shift 120575119862 = 1 and the row shift 120575119877 = 10 which resultsin 120575 = 2119898 times 10 + 1 = 41 slots The first rendezvous between119872119881 in Figure 5 and 119872(11988541) in Figure 7(b) is achieved at theforth columns

Summarizing the discussion above we show that inIPES-SH any two SUs are guaranteed to rendezvous ontheir sector rendezvous pair within SH period 2119898 timesmax(119875119894119864119895) (119864119894119875119895)

5 Combined Sector and ChannelHopping Schemes

While we explained in the previous sections the proceduresof our SH schemes by which the SUs keep steering theirantennas in order to achieve sector rendezvous with theircommunicating partners the scheme for channel hopping(CH) exposed by the SUs in their sectors for achieving achannel rendezvous between them was not explained Inthis section the design of the exposed CH scheme and theprocedure for the combined sector and channel hopping(SCH) schemes are presented The key for the design ofthe exposed CH scheme is to construct two different typesof CH sequences which will be combined within the twodifferent types of PES-SH sequences These CH sequencesmust guarantee a successful channel rendezvous betweenthe pair of SUs as long as they achieve a successful sectorrendezvous (ie directing their antenna beams towards eachother) Furthermore the CH sequences should be designedin such a way that the pair of communicating SUs stay fora similar period (ie number of time slots) in each sector oftheir SH sequences By doing this the pair of communicatingSUs are guaranteed to achieve successful sector and channelrendezvous within a bounded and short time despite anyasynchronous time offsets between their local clocks

51 Asymmetric Grid Quorum-Based Channel Hopping Inthis subsection we explain the design of our AsymmetricGrid Quorum-based Channel Hopping (AGQ-CH) schemethat is executed by the SUs in each sector of their SHsequences The AGQ-CH scheme utilizes the grid quorumsystem (GQS) in asymmetric-role design where two types ofCH sequences are constructed These types of CH sequenceswill be combined within the two different types of our SHsequences Some preliminary definitions related to grid quo-rum systems are presented first to facilitate the understandingof the CH scheme

Definition 4 For a set Z119899 = 1 2 119899 a quorum system 119876underZ119899 is a group of nonempty subsets ofZ119899 each called aquorum such that forall119883 and 119884 isin 119876 119883cap119884 = 0 HereZ119899 is theset of integers less than or equal to n


Definition 5 AGQS arranges the elements ofZ119899 as aradic119899timesradic119899square grid array where 119899 must be a square of a positiveinteger Hence a quorum is formed as a union of the elementsof one column and one row of the grid There are 119899 gridquorums in a GQS that is constructed under Z119899 and eachquorum has a size of (2 times radic119899 minus 1)

For example a GQS 119876 under Z119899 = 1 2 3 4 is 119876 =1198761 1198764 = 1 2 3 1 2 4 1 3 4 2 3 4

Definition 6 For a given integer 119894 and a grid quorum G in aGQS119876 underZ119899 we define rotate(G 119894) = (119909 + 119894)mod 119899 119909 isinG to denote a cyclic rotation of quorumG by 119894

Definition 7 AGQS119876 underZ119899 satisfies the rotation closureproperty because forallG1198941G1198942 isin 119876 and forall1198951 1198952 isin Z119899rotate(G1198941 1198951) cap rotate(G1198942 1198952) = 0

GQSs have been utilized to construct CH sequences thatachieve asynchronous communications because they satisfythe intersection and the rotation closure properties [33 34]In the conventional GQS each grid quorum is formed asa union of the elements of one column and one row ofthe grid array However different from the conventionalGQS our asymmetric GQS (AGQS) uses semigrid quorumsOne semiquorum called the Grid Column-based Quorum(GCQ) is formed from the elements of a single columnof the grid Meanwhile the other semiquorum called GridRow-based Quorum (GRQ) is formed from the elementsof a single row in the grid The nonempty intersection androtation closure properties in the AGQS are inherited fromthe conventional GQS Specifically for any arbitrary pairof GCQ and GRQ there must exist one common elementbetween them despite any rotation of the grid

The GCQs and GRQs in the AGQS are used to constructtwo asymmetric CH sequences that can be combined withinthe different types of sectors in our SH schemes The con-structed CH sequences are guaranteed to achieve a successfulchannel rendezvous between a pair of communicating SUs aslong as there exists at least a single common channel betweenthe available channel sets of the SUs In ourAGQ-CH schemeto construct CH sequences for assigning 119899 channels 119899times119899 gridarray is built In the GCQ-based CH sequence the 119899 rows ofthe grid are used for assigning the 119899 channels into the CHsequence where the elements of each row are used to map asingle channel On the other side the 119899 columns of the gridare used for the assignment of the 119899 channels into the GRQ-based CH sequence For example Let 119899 = 4 be the numberof channels for a sender SU119909 and a receiver SU119910 Supposethat SU119909 has the channel set C119909 = Ch1Ch2Ch3Ch4while the channel set of SU119910 is C119910 = Ch3Ch5Ch6Ch8Accordingly a grid array of size 4 times 4 is formed by bothSUs as shown in Figure 8 Without loss of generality assumethat the sender uses the 4 GCQs to map its channels intothe time slots of its CH sequence as depicted in Figure 8(a)while the receiver SU119910maps its channels based on the 4GRQsas depicted in Figure 8(b) The CH sequences for both SUsare shown in Figure 8(c) where they map each channel oftheir channel sets into the time slots of their CH sequence

according to the selected (GCQ or GRQ) semiquorum Asshown in Figure 8(c) the channel rendezvous is achieved onthe common channel Ch3 between the SUs despite the timeoffsets between their local clocks

52 Channel Ranking As explained in the beginning of thesection the sector frame length which represents the numberof time slots by which every SU spends on each sector forexecuting CH should be the same in all SUs This is inorder to guarantee channel rendezvous between any pair ofneighbouring SUs side by side with the sector rendezvousdespite any time offsets between their local clocks To achievethis we let the SUs construct their combined CH sequencesbased on the best-quality (119899 sube 119871) channels The channelrsquosquality is generally represented by the quantity of the mea-sured PU noise on the channel within the correspondingsector However for cases where some of the channels havethe same measured PU noise channels indices are used todifferentiate between their ranking levels Specifically thebigger the channel index the higher the quality We highlighthere that the similarity of the measured PU noises for somechannels is a practical issue in DIR-CRNs which happenwhen the channels are idle from any PU activity within thesector area

The channel ranking is done by each SU before executingthe rendezvous process based only on its own view ofthe available channels in its sectors Each SU119894 ranks the 119871network channels in each sector 119878119896 of its sectors set 119878119894 =1198781 1198782 119878119873119894 based on their qualities within the sector 119896Thus a ranking table of size 119871times119873119894 is maintained by each SU119894

which contains the ranked channels in all the sectors Thistable is called Sectors Ranked Channels Table (SRCT) whereeach column 119896 of it indicates a sector of the119873119894 sectors Thesecolumns contain the 119871 network channels ranked decreasinglyfrom the best to the worst according to their qualities withinthe corresponding sectors We note here that since each SUin the DIR-CRN performs the same ranking mechanismthis will increase the probability of having a similar rankedchannel list among any pair of neighbouring SUs on theirrendezvous sectors

53 Combined SCH Sequence Generation We now explainthe generation procedures for the combined PES-SCH andIPES-SCH sequences

531 Combined PES-SCH Scheme Since our PES-SH schemeis designed based on two different types of coprimality-basedsequences (ie either PS or ES) we combine each sector ofthe SH sequences according to its type with a correspondingtype from the two AGQ-CH sequences Specifically eachsector of the sender PS-SH sequence is combined with aGCQ-CH sequence while each sector of the receiver ES-SHsequence is combined with a GRQ-CH sequence Algorithms4 and 5 describe the SCH generation procedures for thesender and receiver SUs respectively As illustrated by thealgorithms each SU will keep hopping on its best 119899 qualitychannels in each sector of its SH sequence according tothe corresponding CH sequence This will guarantee thatwhen a successful sector rendezvous occurs between a sector


1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ1 Cℎ2 Cℎ3 Cℎ4

(a) GCQs for mappingC119909

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8

(b) GRQs for mappingC119910

1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1

(c) Channel rendezvous between SUs on the common channel Ch3 when SU119910 start itsCH with 0 1 and 5 slots later than SU119909

Figure 8 An example of AGQ-CH sequences constructions and rendezvous for a pair of communicating SUs

Input119873119904 119878119904 SRCT119904 119899(1) Invoke Algorithm 1 with119873119904 and 119878119904 to construct a round

120596119904 of an PS-SH sequence(2) 119905Frame = 0(3) while (not rendezvous) do(4) Current-sector= 120596119904((119905Frame mod 119875119878) + 1)(5) Steer the antenna to (Current-sector)(6) Select the best channel list (BCL) in (Current-sector)

as BCL = SRCT119904 [1 n][Current-sector](7) Construct a GCQ-CH sequence based on BCL(8) for (119905 = 1 1198992) do(9) Attempt rendezvous on channel GCQ119904(119905)(10) end for(11) 119905Frame = 119905Frame + 1(12) end while

Algorithm 4 The sender SCH generation algorithm (PS-SCH)

Input119873119903 119878119903 SRCT119903 119899(1) Invoke Algorithm 2 with119873119903 and 119878119903 to construct

a round 120574119903 of an ES-SH sequence(2) 119905Frame = 0(3) while (not rendezvous) do(4) Current-sector= 120574119903((119905Frame mod 119864119903) + 1)(5) Steer the antenna to (Current-sector)(6) BCL = SRCT119904 [1 n][Current-sector](7) Construct a GRQ-CH sequence based on BCL(8) for (119905 = 1 1198992) do(9) Attempt rendezvous on channel GRQ119903(119905)(10) end for(11) 119905Frame = 119905Frame + 1(12) end while

Algorithm 5 The receiver SCH generation algorithm (ES-SCH)

frame of the sender SU119904 and a sector frame of its receiverSU119903 a successful channel rendezvous is achieved betweenGCQ-CH119904 and the GRQ-CH119903 The channel rendezvous isguaranteed as long as there is a common channel betweentheir 119899 best channels where they can set up a link throughthe exchange of RTSCTS messages

For example consider the pair of sender SU119883 andreceiver SU119884 in our previous example in Figure 1(a) TheSCH sequences constructions for the pair of SUs and therendezvous among themwhen they construct their combinedCH sequences based on 119899 = 2 best-quality channels areillustrated in Figure 9 As a sender SU119883 in Figure 9(a)combines each sector of its PS-SH sequence with a gridcolumn (GCQ-CH) sequence based on the two best-rankedchannels of the respected column for the sector in SRCT119883For instance the sector 1198781 is combined with a GCQ-CHsequence generated based on the two best channels 2 4of the 1st column of SRCT119883 the GCQ-CH is [2 4 2 4] Onthe other hand each ES sector of the ES-SH sequence forthe receiver SU119884 in Figure 9(b) is combined with a gridrow (GRQ-CH) sequence based on the best two channelsof the SRCT119884 column which corresponds to the sectornumber For instance SU119884 combine the GRQ-CH sequence[6 6 8 8] within its sector 1198781 which is constructed based onthe best channels 6 8 The sector and channel rendezvousbetween the SUs when they start their PES-SCH sequencessynchronously is shown in Figure 9(c) The rendezvous isachieved during the 25th and 28th time slots on the sectorrendezvous pair (1198782 of SU119883 1198783 of SU119884) as well as on therendezvous channels 1 6 However when SU119883 starts itsSCH 4 time slots later than SU119884 the channel and sectorrendezvous is achieved after 5 time slots only from the SCHstart time of SU119883

532 Combined IPES-SCH Scheme For this symmetric rolescheme any SU can generate its SCH sequence according


2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C

(a) The combined PES-SCH sequence construction for the sender SU119883

6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C

(b) The combined PES-SCH sequence construction for the receiver SU119884

121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY

(c) Synchronous sector and channel rendezvous between SU119883 and SU119884

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46

(d) Asynchronous sector and channel rendezvous between the SUs when SU119884 starts its hopping earlier than SU119883 by 4 slots

Figure 9 Rendezvous between SUs 119883 and 119884 according to the combined PES-SCH scheme 119873119883 = 5 and 119873119884 = 4 Number of best-qualitychannels per each sector 119899 = 2

to Algorithm 6 During each sector frame of its inter-leaved SH sequence that is constructed using the methodin Section 412 the SU executes one type of the AGQ-CHsequences according to the type of the frame Specifically ifthe sector frame is a prime-based (P-frame) the SU generatesa GCQ-CHbased on the 119899 best-quality channels in the sectorOn the other hand when the sector is an even-based (E-frame) the SU generates a GRQ-CH This will ensure thatwhenever the sector rendezvous occurs between a P-frameof IPES119894 and an E-frame of IPES119895 channel rendezvous isachieved between the GCQ119894 CH sequence and the GRQ119895 CHsequence and vice versa

54 Performance Analysis of the Combined SCH SchemesIn this subsection we analyze the theoretical performancefor the combined SCH schemes Specifically we prove theguaranteed rendezvous between any two SUs performing thecombined SCH scheme by deriving the maximum time-to-rendezvous (MTTR)

eorem 8 For any scheme S of our SH schemes whichis combined with the AGQ-CH scheme for 119899 best-qualitychannels the MTTR of the combined SCH is (MSRL (S) times

1198992) MSRL (S) here denotes the maximum sector rendezvouslatency for the S SH scheme

Input119873119894 119878119894 Extended-ID a SRCT119894 119899(1) Construct an IPES-SH sequence 119880119894 as explained in

Section 412(2) period = (119875119894 times 119864119894times length(a))(3) 119905Frame = 0

(4) while (not rendezvous) do(5) Current-sector = 119880119894((119905Frame mod period) + 1)(6) Steer the antenna to (Current-sector)(7) BCL = SRCT119894 [1 n][Current-sector](8) if (Current-sector is a P-sector) then(9) Construct a GCQ-CH sequence based on BCL(10) for (119905 = 1 1198992) do(11) Attempt rendezvous on channel GCQ119894(119905)(12) end for(13) else(14) Construct a GRQ-CH sequence based on BCL(15) for (119905 = 1 1198992) do(16) Attempt rendezvous on channel GRQ119894(119905)(17) end for(18) end if(19) 119905Frame = 119905Frame + 1(20) end while

Algorithm 6 IPES-SCH generation algorithm


Proof To prove that the combined PES-SCH has MTTR =(119875119894119864119895) times119899

2 it suffices to prove that the pair of combined PES-SCH sequences for example SCH119894 and SCH119895 can achievesuccessful sector and channel rendezvous within (119875119894119864119895) times 119899

2

time slotsWithout loss of generality assume that SU119895 starts its SCH

sequence120575 time slots earlier than the start of SU119894 In each SCHperiod of SU119894 the SCH sequence of SU119895 is rotate(SCH119895 120575)As we stated before the SCH sequence can be viewed as aseries of sector frames which are composed of 1198992 channeltime slots Let the clock drift 120575 = 1198992 times 120575119865 + 120575119878 where 120575119865 isin[0 119864119895 minus 1] denotes the shift amount of the sector frames and120575119878 isin [0 (1198992) minus 1] denotes the shift of the channel time slotsNext we prove the theorem in the following two cases

Case 1 (120575119878 = 0) This case implies that the sector framesare perfectly aligned In this case since the SUs stay forsimilar number of time slots in each sector which is (1198992) forexecuting their corresponding AGQ-CH sequences for anyvalue of 120575119865 there must exist an entire overlap between a PS-frame of SCH119894 and an ES-frame of SCH119895 where the sectorrendezvous happened ByTheorem 1 we know that the sectorrendezvous is guaranteed to occur between a PS sector frameℎ119894 and an ES sector frame ℎ119895 within (119875119894119864119895) sector framesAs a consequence the channel rendezvous is guaranteed tohappen between the GCQ119894 CH sequence of ℎ119894 and the GRQ119895

CH sequence of ℎ119895 Thus the MTTR is (119875119894119864119895) multiplied bythe sector frame length 1198992 Figures 9(c) and 9(d) show thesector and channel rendezvous between SU119883 and SU119884 when120575119878 = 0 for two different values of 120575119865 and for 119899 = 2 InFigure 9(c) when 120575119865 = 0 and hence the clock drift 120575 =

(1198992 times 0 + 0) = 0 SU119883 can achieve the sector rendezvouswith SU119884 on the second round of its SH frames The SUsrendezvous on their commonly available channels (ie CH1

and Ch6) However when 120575119865 = 1 and 120575 = (1198992 times 1 + 0) = 4SU119883 can rendezvous with SU119884 earlier where it rendezvouswith SU119884 during the first round of its SH frames

Case 2 (120575119878 = 0) When there is a time slot shift 120575119878 isin [1 1198992]it implies that the sector frames are not aligned For anyvalue of 120575119865 it is easily verified that each PS sector frame ofSCH119894 is overlapped with partial channel time slots form twoconsecutive ES frames of SCH119895 Specifically the PS frame ofSCH119894 overlaps with 1198992 minus 120575119878 time slots from the former ESframe and 120575119878 time slots from the later ES frame of SCH119895Recall the proof ofTheorem 1when SU119894 repeats each roundofits sector frames for119864119903 times each occurrence of the ℎ119894 sectorframe must overlap with different sector frame from the 119864119903sector frames of SU119895The sector rendezvous is achieved whenℎ119894 overlapswith ℎ119895 However considering the time slot shift 120575119878of the SCH119895 sequence we can prove in the same way as case 1that within the same rendezvous delay bound ((119875119894119864119895) times 1198992

time slots) there must exist at least two occurrences of ℎ119894which overlaps with different partial time slots of ℎ119895 In oneof these occurrences the overlap happens between the first1198992 minus 120575119878 time slots of ℎ119894 and the last 1198992 minus 120575119878 time slots ofℎ119895 On the other occurrence the overlap happens between

the last 120575119878 time slots of ℎ119894 and the first 120575119878 time slots of ℎ119895Accordingly channel rendezvous can be achieved in any ofthese two partial sector rendezvous chances where partialslots of the GCQ119894 CH sequence in ℎ119894 overlap with otherpartial slots from the GRQ119895 CH sequence in ℎ119895 For exampleFigure 10 illustrates the asynchronous rendezvous betweenSU119883 and SU119884 when 120575119865 = 0 for three different values of 120575119878

Summarizing the discussion above we show that underthe combined PES-SCH any two SUs are guaranteed toachieve channel rendezvous within ((119875119894119864119895)times119899

2) SCH periodWe highlight here that the theoretical MTTR for the com-bined IPES-SCH is (2119898 timesmax(119875119894119864119895) (119864119894119875119895)) times 119899

2 It can beproven in a similar way to the proof of the PES-SCH MTTRby considering the two alignment cases of the sector frames

6 Results and Discussions

In this section we evaluate the performance of our developeddirectional antenna rendezvous schemes and compare themwith three related works in [19 28 30] The former twoselected schemes for comparisons are the only schemes in theliterature which tackle the rendezvous issue in DIR-CRNsHowever since both of them are asymmetric-role we selectthe third scheme [30]which is proposed for rendezvous in the60GHz networks for the comparison with our symmetric-role IPES scheme This scheme follows a similar ID-basedapproach to our IPES-SH scheme However the extended IDin this scheme is relatively longer and the adjusted parametersof the number of sectors which are used for constructing theinterleaved SH sequences are different

61 Performance Comparison of the SH Schemes We firstcompare the performance of our SH schemes with the twoblind SH schemes in [28 30] The SH scheme in [19] is notcompared here because it is not a blind scheme Extensivesimulation experiments are conducted to compute the sectorrendezvous latency (SRL) between two neighboring SUs(a sender SU119894 and a receiver SU119895) In the simulationswe consider different antenna configurations for the SUswhere we simulate several combinations for the numberof sectors (119873119894 and 119873119895) The relative locations of SU119894 andSU119895 represented by (ℎ119894 ℎ119895) as well as the clock drift arerandomly generated For the ID-based schemes two different7-bit IDs are randomly assigned to the SUs For each (119873119894

and 119873119895) combination the simulation results are obtainedby conducting 105 independent runs where we accordinglycompute the average and maximum SRL (ASRL and MSRL)

Figure 11 depicts the SRL results for the asymmetric-role SH schemes (our PES-SH and Li and Xiersquos SH [28])The results illustrate the significant reduction on the SRLprovided by our PES-SH in terms of ASRL and MSRL underall the different antenna configurations of the pair of SUs Forsome antenna configurations PES-SH can reduce the ASRLandMSRL significantly up to 80 and 84 respectivelyTheshorter ASRL and MSRL provided by the PES-SH schemeare due to its efficient design which relies on the coprimalitybetween the adjusted prime and even numbers of 119873119894 and119873119895 respectively And since 119873119894 is prime for all the sender


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46

Figure 10 Asynchronous rendezvous between SU119883 and SU119884 according to the combined PES-SCH scheme for 119899 = 2 best-ranked channelsSCH119884 is started earlier than SCH119883 with 120575119878 isin [1 3]

PES-SH MSRLPES-SH ASRLLi and Xiersquos SH MSRLLi and Xiersquos SH ASRL

4 6 8 12 182Number of receiver sectors (Nj)

0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17

Figure 11 Comparison of the sector rendezvous latency between our PES-SH scheme and Li and Xiersquos SH scheme [28] under fixed119873119894 andvarying119873119895

SU119894 antenna configurations while the values of 119873119895 are evennumbers that are valid for use (ie not in the AES set)this allows the sender SU119894 in our PES-SH to achieve sectorrendezvous with its receiver SU119895 within119873119894119873119895 SH period

On the other side the design of Li and Xiersquos SH schemerequires 119873119894 and 119873119895 to be adjusted to primes Furthermorethe sender should perform an initiating round-robin SHsequence with a length of1198732

119894 before it converts to the regularprime-based sequence Accordingly this will prolong the SHperiod needed for achieving the sector rendezvous to (1198732

119894 +119873119894119875119895) which actually represents the theoretical upper boundfor the MSRL of Li and Xiersquos SH scheme when (119873119894 = 119875119895)We can notice that this upper bound is tight for some (119873119894

and119873119895) combinations while it is not for others Specificallywhen (119873119894 119875119895 = 1) where 119875119895 is the adjusted prime for 119873119895the sender SU119894 cannot rendezvous with its receiver duringits initiating 1198732

119894 round-robin SH sequence However whenit starts following the regular prime-based SH sequence thesector rendezvous happens within the subsequent119873119894119875119895 slotswhich results in (1198732

119894 +119873119894119875119895) MSRL For example when119873119894 =11 and 119873119895 = 4 in Figure 11(b) the sector rendezvous occursin (121 + 11 times 5) = 165 sector slots The same thing can benoticed for the cases when119873119895 = 2 in Figures 11(a) 11(b) and11(c) where the MSRL is (1198732

119894 + 119873119894 times 2) This explains theirregular increased results in the figures for such (119873119894 and119873119895)combinations

In Figure 12 the SRL results for the symmetric-role SHschemes (our IPES-SH and the Chen et alrsquos SH scheme [30])are shown In the figure it is shown that our IPES-SH schemeoutperforms the other compared scheme especially in termsof MSRL This improvement is due to the shorter SH periodprovided by IPES for achieving the sector rendezvous Inboth schemes the SH period for sector rendezvous dependsmainly on the extended ID length as well as the adjustednumbers for (119873119894 and 119873119895) that are used for constructingthe interleaved sequences However the adjusted parametersused by our IPES scheme are smaller than those used by theother scheme Firstly in the IPES-SH scheme the extendedID length is 2119898 = 14which is relatively smaller than the 2119898+1 = 15 extended ID used by the other scheme Furthermorethe interleaved SH sequences in Chen et alrsquos SH scheme areconstructed by adjusting the number of sectors to a primenumber as well as to a number that is a power-multiple oftwo (ie 119902119896 = 2119887119896 where 119887119896 is the smallest integer satisfying2119887119896 ge 119873119896) However these adjusted numbersmust be coprimewith the extended ID length in order to achieve a successfulsector rendezvous Meanwhile in IPES-SH the interleavedPS and ES sequences are constructed based on the closestprime number and the closest even number which is not inthe AES set Hence under most of the simulated antennaconfigurations the adjusted 119864119894 and 119864119895 in IPES are smallerthan the adjusted 119902119894 and 119902119895 parameters in the other scheme


IPES-SH MSRLIPES-SH ASRLChen et alrsquos SH MSRLChen et alrsquos SH ASRL

0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17

Figure 12 Comparison of the sector rendezvous latency between our IPES-SH scheme and Chen et alrsquos SH scheme [30] under fixed119873119894 andvarying119873119895 ID length = 7 bits

For example in our IPES-SH scheme 119864119895 = 119873119895 for all the119873119895

values while the 119902119895 adjusted parameters for the119873119895 values inChen et alrsquos SH scheme are 2 4 8 8 16 32 Moreover when119873119894 or119873119895 is le5 the adjusted prime number used in IPES is 5while it is 7 on the other scheme because 7 is the closest primethat is coprimewith the 15-bit extended IDAccording to thatSUs in the IPES scheme can achieve the sector rendezvousfaster than Chen et alrsquos SH scheme

62 Performance Comparison of the Combined SCH SchemesIn this subsection we compare the channel rendezvousperformance of our SCH schemes with the other worksunder a practical DIR-CRN The simulation configurationparameters are shown in Table 1

We start our SCH simulation by comparing the per-formance of our combined PES-SCH with the combinedSCH schemes of Song and Xie [19] and Li and Xie [28]We evaluate our PES-SCH for 119899 = 4 best-quality channelswhich correspond to a AGQ-CH period of 16 time slots ineach sector (ie the frame length = 16) The other selectedschemes for comparison are simulated with their proposedCH schemes In [19] the SH scheme is combined with theasymmetric-role CH scheme in [35] where the sender SUstays for 1198712 slots on each sector frame of its SH sequenceperforming a sequential fast CH on the (119862119894 sube 119871) availablechannels within the sector Meanwhile the receiver SU staysfor (119873119894 + 1) times 1198712 slots on each sector of its 119873119894 sectorsperforming a slow CH on all of its (119862119895 sube 119871) availablechannels On the other side the SH scheme of Li and Xie[28] is combined with the EJS-CH scheme [10] Howeverdue to the long period of the EJS-CH scheme required toguarantee channel rendezvous Li and Xie simulated theirSCH scheme by letting SUs stay for smaller period on eachsector of their SH frames During this period SUs executethe corresponding subsequences of their generated EJS-CHsequence Therefore we simulate Li and Xiersquos SCH scheme

Table 1 Simulation parameters

Network area deployment 500m times 500mNumber of channels (119871) 10

Number of PUs 50

The radius of the SU sensingtransmission range 150mSlot duration for sending a packet on a channel 2msThe PU packet arrival rate 10 packetssThe length of a PU packet 120 slots

with a similar sector frame length to our PES-SCH scheme(ie 16 slots) All the schemes are simulated under differentasynchronous settingswhere the clock drifts amount betweenSUs is selected randomly in each experiment

Figure 13 depicts the TTR simulation results for the threeschemes when they are evaluated under different antennaconfigurations for the pair of SUs Even though the combinedSCH scheme of Song and Xie is not a blind scheme itproduces very long TTR resultsThis is due to the large sectorframe length where the sender and receiver stay for 1198712 and1198712 times (119873119894 + 1) time slots respectively on each sector forperforming their corresponding CH sequence As a conse-quence the SCH period needed for achieving rendezvousis 119873119895 times (1198712 times (119873119894 + 1)) which is very long as comparedto the period of our PES-SCH scheme On the other sideLi and Xiersquos SCH scheme can provide shorter ATTR thanSong and Xiersquos scheme because it is simulated with smallerframe length However the MTTR of this scheme cannot betraced because we observe that TTR in some cases cannot beachieved within the whole simulation duration which is setto 5 times 104 slots The reason for the indeterministic behaviourof Li and Xiersquos SCH scheme is because the stay period in eachsector (ie 16 slots) is insufficient to guarantee rendezvouswhile using the EJS-CH scheme According to the EJS-CH


Song and Xiersquos SCHLi and Xiersquos SCHPES-SCH

0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)


Song and Xiersquos SCHPES-SCH

0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)


Figure 13 Comparison of the time-to-rendezvous (TTR) between the asymmetric-role SCH schemes when119873119894 = 5

[10] the rendezvous cannot be guaranteed unless the EJS-CH sequences of the communicating SUs are overlappedfor at least 4119875119871(119875119871 + 1 minus 119866) = 44(12 minus 119866) time slots 119875119871is the smallest prime number greater than 119871 while 119866 isthe number of common available channels between the SUsavailable channels Hence to ensure rendezvous regardlessof any misalignment of their local clocks the SUs shouldstay for at least 41198752119871 on each sector of their SH sequences toperform their EJS-CH sequences This trade-off between theboundedMTTR of Song and Xiersquos SCH scheme and the smallATTR of Li and Xiersquos SCH scheme illustrates the efficiency ofour proposed AGQ-CH scheme which allows PES-SCH toguarantee rendezvous with the shortest TTR results

In the second setting of the SCH simulation we combinethe SH schemes of Li and Xie [28] and Chen et al [30]with our proposed AGQ-CH scheme This is in order toevaluate their channel rendezvous performance when theyare combined with an efficient and suitable CH schemeFigures 14 and 15 show the TTR results of these schemes andour schemes when they are simulated for different values ofthe best-quality channel 119899 (2 ⩽ 119899 ⩽ 5) In the simulationwe consider different values for the sender number of sectors(119873119894 = 4 6 12) while the receiver number of sectors119873119895 is set as 4 The figures show that our schemes alwaysoutperform the other schemes under all the different antennaconfigurations of the SUs This is mainly due to the shorterSRL of our SH schemes and as explained in Section 54TTR depends on the SRL of the SH scheme coupled with thelength of the sector frame (1198992)Moreover the figures illustratethe effect of 119899 (ie the number of best-quality channels)on the rendezvous performance where we can notice thatas 119899 increases the TTR results for all the schemes increase

This is because the larger 119899 the longer the frame length 1198992Accordingly when SUs spend longer period in each sectorthey may waste more time while attempting rendezvous onother sectors rather than the rendezvous sector This willresult in a longer TTR until they can achieve a successfulsector and channel rendezvous

Finally to illustrate the performance gain broughtby applying directional antennas for channel rendezvouswe compare the performance of our combined PES-SCHscheme with the AAsync-CH omnidirectional antenna ren-dezvous scheme [16] The AAsync-CH is selected amongthe other omnidirectional CH schemes since it is designedfor asymmetric-role environment (ie SUs have preassignedrole) similar to our PES-SCH The schemes are compared interms of their probabilities for achieving a successful channelrendezvous under different number of PUs in the networkarea In our PES-SCH the simulated sender and receiver SUshave 119873119894 = 5 and 119873119895 = 6 number of sectors and the numberof best-quality channels 119899 = 3

Figure 16 shows the significant outperformance of ourdirectional antenna scheme as compared with the omnidi-rectional antenna scheme It can be noticed from the figurethat when the number of PUs in the network increasesthe probability of the successful channel rendezvous for theomnidirectional scheme decreases dramatically Meanwhilein the PES-SCH this probability is almost 1 for most ofthe cases and only decreases slightly when the number ofPUs is close to 100 This is due to the smaller interferenceregion of the directional antenna which results in higherchannel availability for the SUs as compared to the omnidi-rectional antenna So when the total number of PUs in thenetwork area increases only few of them may reside within


25 3 35 4 45 52Number of best-quality channels (n)

0

100

200

300

400

500

600

700AT

TR (s

lots)

PES-SCH (Ni = 4)Ni = 4)Li and Xiersquos SCH ( Li and Xiersquos SCH (

Li and Xiersquos SCH (Ni = 6)Ni = 12)Li and Xiersquos SCH (

Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)

Li and Xiersquos SCH (Ni = 6)

PES-SCH (Ni = 6)Li and Xiersquos SCH (Ni = 12)PES-SCH (Ni = 12)



200

400

600

800

1000

1200

1400

ATTR

(slo

ts)

IPES-SCH (Ni = 4)Ni = 4)Chen et alrsquos SCH (

Chen et alrsquos SCH (Ni = 6)

IPES-SCH (Ni = 6)Chen et alrsquos SCH (Ni = 12)IPES-SCH (Ni = 12)




05

1

15

2

25

3

35

MTT

R (s

lots)

times104


Figure 15 Comparison of the TTR between the symmetric-role SCH schemes when119873119895 = 4 ID length = 7 bits

the SUs rendezvous sectors where they can only impose aslight change in the channel availability Accordingly theprobability of having common channels between the SUs ontheir sector rendezvous pair is always high which increasesthe probability of successful channel rendezvous

These results justify the motivation of our proposedschemes where equipping SUs with directional antennas cansignificantly enhance the channel rendezvous performance inhigh-density PU networks as compared with the omnidirec-tional antennas paradigm


Directional PES-SCHOmnidirectional AAsync-CH

40 60 80 10020Number of PUs in the network area

0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous

Figure 16 Comparison of the successful channel rendezvousprobability between our PES-SCH directional antenna scheme andthe AAsync-CH omnidirectional scheme

7 Conclusions

In this paper we studied the sector and channel rendezvousproblem for SUs in DIR-CRNs Two efficient coprimality-based sector hopping schemes have been proposed for pro-viding sector rendezvous in asymmetric- and symmetric-role environments The SH schemes are combined with anefficient grid-quorum-based CH scheme for providing aguaranteed sector and channel rendezvous simultaneouslybetween the SUs in DIR-CRNs Theoretical analysis andextensive simulations are conducted to demonstrate theefficiency of the proposed schemes The simulations resultsverify that our schemes significantly outperform the previ-ous directional antenna rendezvous schemes (in terms ofSRL and TTR) Furthermore they demonstrate that ourdirectional antenna rendezvous paradigm is more resistantto rendezvous failures under high-density PU CRNs ascompared with the omnidirectional antenna rendezvousparadigm

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to acknowledge Malaysian Min-istry of Higher Education for funding this study under theFundamental Research Grant Scheme (FRGS) entitled ldquoOnthe Cogitation of Primary User Reappearance in CognitiveRadio Networkrdquo (Project Code MOHE FRGS12015TK10UPM022 UPM03-01-15-1626FR Vote no 5524731)

References

[1] N C Theis R W Thomas and L A DaSilva ldquoRendezvous forcognitive radiosrdquo IEEE Transactions on Mobile Computing vol10 no 2 pp 216ndash227 2011

[2] B F Lo ldquoA survey of common control channel design incognitive radio networksrdquo Physical Communication vol 4 no1 pp 26ndash39 2011

[3] M-R Kim and S-J Yoo ldquoDistributed coordination protocol forad hoc cognitive radio networksrdquo Journal of Communicationsand Networks vol 14 no 1 pp 51ndash62 2012

[4] P Ren YWang andQDu ldquoCAD-MAC a channel-aggregationdiversity basedMACprotocol for spectrum and energy efficientcognitive Ad Hoc networksrdquo IEEE Journal on Selected Areas inCommunications vol 32 no 2 pp 237ndash250 2014

[5] G Prasad Joshi S Y Nam S W Kim and B-S Kim ldquoAdaptivewindow size-based medium access control protocol for cog-nitive radio wireless sensor networksrdquo Journal of Sensors vol2016 Article ID 2049859 9 pages 2016

[6] S Omar O E Ghandour and A M A El-Haleem ldquoMultipathactivity based routing protocol for mobile cognitive radio AdHoc networksrdquo Wireless Communications and Mobile Comput-ing vol 2017 Article ID 5380525 12 pages 2017

[7] A Mahmud Y Lee and I Koo ldquoA fully distributed resourceallocation mechanism for CRNS without using a commoncontrol channelrdquo Mathematical Problems in Engineering vol2015 Article ID 537078 9 pages 2015

[8] G P Joshi S Y Nam and S W Kim ldquoRendezvous issues inad hoc cognitive radio networksrdquo KSII Transactions on Internetand Information Systems vol 8 no 11 pp 3655ndash3673 2014

[9] S Romaszko ldquoA rendezvous protocol with the heterogeneousspectrum availability analysis for cognitive radio ad hoc net-worksrdquo Journal of Electrical and Computer Engineering vol2013 Article ID 715816 18 pages 2013

[10] Z Lin H Liu X Chu and Y-W Leung ldquoEnhanced jump-stay rendezvous algorithm for cognitive radio networksrdquo IEEECommunications Letters vol 17 no 9 pp 1742ndash1745 2013

[11] J Kim G Park and K Han ldquoA Rendezvous Scheme for Self-Organizing Cognitive Radio Sensor Networksrdquo InternationalJournal of Distributed Sensor Networks vol 10 no 1 article315874 2014

[12] E O Guerra V A Reguera R D Souza E G Fernandez andM E Pellenz ldquoSystematic construction of common channelhopping rendezvous strategies in cognitive radio networksrdquoEURASIP Journal onWireless Communications and Networkingvol 2015 no 1 2015

[13] G-Y Chang J-F Huang and Y-S Wang ldquoMatrix-basedchannel hopping algorithms for cognitive radio networksrdquo IEEETransactions on Wireless Communications vol 14 no 5 pp2755ndash2768 2015

[14] B YangW LiangM Zheng andY-C Liang ldquoFully distributedchannel-hopping algorithms for rendezvous setup in cognitivemulti-radio networksrdquo IEEE Transactions on Vehicular Technol-ogy vol PP no 99 2015

[15] J-P Sheu C-W Su and G-Y Chang ldquoAsynchronous quorum-based blind rendezvous schemes for cognitive radio networksrdquoIEEE Transactions on Communications vol 64 no 3 pp 918ndash930 2016

[16] P K Sahoo and D Sahoo ldquoSequence-based channel hoppingalgorithms for dynamic spectrum sharing in cognitive radionetworksrdquo IEEE Journal on Selected Areas in Communicationsvol 34 no 11 pp 2814ndash2828 2016


[17] W Chen G Yang M Chang and W C Kwong ldquoConstruc-tion and analysis of shift-invariant asynchronous-symmetricchannel-hopping sequences for cognitive radio networksrdquo IEEETransactions on Communications vol 65 no 4 pp 1494ndash15062017

[18] A Al-Mqdashi A Sali M J Abdel-Rahman N K NoordinS J Hashim and R Nordin ldquoEfficient rendezvous schemes forfast-varying cognitive radio ad hoc networksrdquo Transactions onEmerging Telecommunications Technologies article e3217 2017httpdxdoiorg101002ett3217

[19] Y Song and J Xie ldquoEnhancing channel rendezvous in cognitiveradio networks with directional antennasrdquo in Proceedings of theIEEE International Conference on Communications ICC 2015pp 3702ndash3707 June 2015

[20] H Jung and I-H Lee ldquoConnectivity Analysis of Millimeter-Wave Device-to-Device Networks with Blockagerdquo InternationalJournal of Antennas and Propagation vol 2016 Article ID7939671 9 pages 2016

[21] A M Al-Samman T A Rahman M H Azmi et al ldquoSta-tistical modelling and characterization of experimental mm-wave indoor channels for future 5G wireless communicationnetworksrdquo PLoS ONE vol 11 no 9 pp 1ndash29 2016

[22] Y Zhao Z Wei Y Liu Q Zhang and Z Feng ldquoAngle-Domain Spectrum Holes Analysis with Directional Antennain Cognitive Radio Networkrdquo in Proceedings of the 2017 IEEEWireless Communications and Networking Conference (WCNC)pp 1ndash6 San Francisco CA USA March 2017

[23] H Yazdani and A Vosoughi ldquoOn cognitive radio systemswith directional antennas and imperfect spectrum sensingrdquoin Proceedings of the 2017 IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP) pp 3589ndash3593 New Orleans LA USA March 2017

[24] Y Dai and J Wu ldquoBoundary helps Efficient routing protocolusing directional antennas in cognitive radio networksrdquo inProceedings of the 10th IEEE International Conference on MobileAd-Hoc and Sensor Systems MASS 2013 pp 502ndash510 October2013

[25] S Anamalamudi M Jin and J M Kim ldquoHybrid CCC basedAODV routing protocol for cognitive radio ad-hoc networkswith directional antennasrdquo in Proceedings of the 7th Interna-tional Conference on Ubiquitous and Future Networks ICUFN2015 pp 40ndash45 July 2015

[26] Y Wang Q Wang H-N Dai H Wang Z Zheng and JLi ldquoOn local connectivity of cognitive radio ad hoc networkswith directional antennasrdquo in Proceedings of the 2016 IEEEInternational Conference on Communication Systems ICCS2016 pp 1ndash6 December 2016

[27] L TDung TDHieu S-G Choi B-S Kim andBAn ldquoImpactof beamforming on the path connectivity in cognitive radio adhoc networksrdquo Sensors vol 17 no 4 2017

[28] J Li and J Xie ldquoDirectional antenna based distributed blindrendezvous in cognitive radio ad-hoc networksrdquo in Proceedingsof the 58th IEEE Global Communications Conference GLOBE-COM 2015 pp 1ndash6 December 2015

[29] C-M Chao H-Y Fu and L-R Zhang ldquoA fast rendezvous-guarantee channel hopping protocol for cognitive radio net-worksrdquo IEEE Transactions on Vehicular Technology vol 64 no12 pp 5804ndash5816 2015

[30] L Chen Y Li and A V Vasilakos ldquoOblivious neighbordiscovery for wireless devices with directional antennasrdquo inProceedings of the 35th Annual IEEE International Conference

on Computer Communications IEEE INFOCOM 2016 pp 1ndash9April 2016

[31] I Niven H S Zuckerman and H Montgomery An Introduc-tion to the Theory of Numbers John Wiley amp Sons New YorkNY USA 1991

[32] K Bian and J-M J Park ldquoMaximizing rendezvous diversityin rendezvous protocols for decentralized cognitive radio net-worksrdquo IEEE Transactions on Mobile Computing vol 12 no 7pp 1294ndash1307 2013

[33] M J Abdel-Rahman and M Krunz ldquoGame-theoretic quorum-based frequency hopping for anti-jamming rendezvous inDSA networksrdquo in Proceedings of the 2014 IEEE InternationalSymposium on Dynamic Spectrum Access Networks DYSPAN2014 pp 248ndash258 April 2014

[34] A Al-Mqdashi A Sali N K Noordin S J Hashim RNordin and M J Abdel-Rahman ldquoAn efficient quorum-basedrendezvous scheme for multi-radio cognitive radio networksrdquoin Proceedings of the 2016 IEEE 3rd International Symposium onTelecommunication Technologies (ISTT) pp 59ndash64 November2016

[35] Y Song and J Xie ldquoQB2IC A QoS-based broadcast protocolunder blind information for multihop cognitive radio ad hocnetworksrdquo IEEE Transactions on Vehicular Technology vol 63no 3 pp 1453ndash1466 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



based on the available channels that are sensed to be idle fromany PU activities within its omnidirectional range Thenthe SU keeps hopping over the channels according to thegenerated CH sequence for achieving channel rendezvousThe rendezvous occurs between a pair of communicating SUswhen they hop during the same time slot over a channelthat is commonly available for both of themThe existence ofcommon available channels (at least one) between the pair ofcommunicating SUs is a common and essential assumptionmade by all the existing CH schemes Their designs relymainly on this assumption to take place for ensuring thesuccess of the rendezvous operation However none of theexisting CH rendezvous designs were tailored for high-density PU networks where the number of active PUs in thenetwork is larger than the number of the channels In suchnetworks the channel availabilities may vary dramaticallyamong the SUswithin the single-hop rendezvous region itselfThis can lead to the inexistence of any common availablechannel between a pair of SUs and hence the failure of therendezvous process

One approach to overcome this serious rendezvous prob-lem is using directional antennas instead of the convention-ally used omnidirectional ones [19] Directional antennashave been utilized in emerging wireless networks such asthe millimeter-wave (MMW) networks for providing highlyreliable transmission and multi-Gigabit data rates This ismainly due to their capabilities in enlarging the transmissionrange and limiting the interference [20 21] However InCRNs equipping SUs with directional antennas for channelrendezvous can bring about many advantages First of all itallows SUs to transmit their rendezvous messages towardsspecific directions which can reduce the amount of inter-ference to the PUs in the network as compared with theomnidirectional antennasThis is because the transmission ofthe SU that is equipped with directional antenna is directedto a particular region which can only cause interferenceto those PUs that are within this region On the contrarywhen using the omnidirectional antennas the transmissionof the SU is scattered towards all the directions Thus it cancause interference to all the surrounding PUs within the SUtransmission range Second as related to the interferencerestriction imposed by the CR concept SUs can use only thechannels that are idle from any PU activities within theirtransmission range According to that and due to its directedtransmission range using directional antenna will increasethe number of available channels that can be utilized by theSU in each of its transmission sectors As a consequencethe probability for any pair of neighbouring SUs to haveat least a common available channel within their crossedsectors is high regardless of the number of PUs in the CRNNote that in omnidirectional antennas this probability couldbe less than 01 for some scenarios when the number ofPUs is larger than the network channels [19] Increasing theprobability of existing common available channel betweenthe SUswill significantly enhance the probability of successfulchannel rendezvous Therefore in this paper we study therendezvous problem in directional antenna CRNs where SUsare equipped with directional antennas

While the use of directional antennas for channel ren-dezvous in CRNs can bring about the above-mentionedadvantages it also imposes some unique challenges Amongthese challenges is the sector rendezvous which must beachieved in advance between the pair of communicating SUsbefore they can achieve channel rendezvous Specifically theSUs need to steer their antennas towards each other in orderto communicate over their commonly available channelsThis necessitates the design of a deterministic sector hopping(SH) scheme that can guarantee that any pair of neighbouringSUs will steer their antennas to the proper directions (ietowards each other) at a certain time instance So when theSH scheme is combined with a suitable and deterministicCH scheme SUs can achieve successful sector and channelrendezvous simultaneously within a bounded time Howeversince the SUs do not know the relative locations of each otheras well as the available channels before they rendezvous thecombined sector and channel hopping (SCH) scheme shouldbe designed in fully distributed manner without any priorinformation or synchronization Designing such combinedSCH schemes for achieving rendezvous in DIR-CRNs isintuitivelymore challenging as compared with the traditionalomnidirectional antenna paradigm

In spite of the existing research in the literature there havebeen some papers that addressed the utilization of directionalantennas in CRNs However most of the proposed worksinvestigated issues other than the rendezvous issue such assensing [22 23] routing [24 25] and connectivity [26 27]To the best of our knowledge the works in [19 28] are theonly proposals that tackle the sector and channel rendezvousissue in DIR-CRNS In [19] an efficient framework forbeamforming was proposed to provide a pairwise sector andchannel rendezvous in DIR-CRNs However the SH schemein [19] is not a blind design where it assumes that the receivermust have prior knowledge of the sender number of sectorsin order to achieve a successful sector rendezvous This isnot practical since SUs do not know any information abouteach other before they rendezvous On the other hand Li andXie in [28] proposed a blind prime-based SH scheme wherethe number of sectors is adjusted to primes for achievinga guaranteed sector rendezvous However since the schemerelies on the coprimality between prime numbers only theauthors added an initiating rotated SH sequence on thesender sideThis is in order to ensure a successful rendezvouswith the receiver when the sender and the receiver constructtheir sequences with the same prime Accordingly the extrasequence overhead incurs extensively long sector rendezvouslatency and hence a long time-to-rendezvous (TTR) willresult when the SH is combined with a CH sequenceFurthermore the SH schemes in [19 28] are designed only forasymmetric-role environment where SUs have preassignedrole (ie SU is either a sender or receiver) However thisdesign limits the applications of the schemes for exampleSUs cannot work as a forwarder (ie receive packets fromone SU and then forward them to another SU) due to thepermanent role assignment [29] Another drawback of theseworks is their limitations to provide a complete solutionfor combining the SH scheme with a suitable and efficientCH scheme which consider the unique traits of DIR-CRNs














1119894 119878

119879119894119894 and 119878119895 = 1198780119895 119878

1119895 119878









21

54

3X

21

3X

2 143

Y


1

2

3 z 1

2

3 z

4 3

1 2v

(b) Pair of 119881 and 119885 SUs































1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)


3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)




















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















1119894 119878

119879119894119894 and 119878119895 = 1198780119895 119878

1119895 119878









21

54

3X

21

3X

2 143

Y


1

2

3 z 1

2

3 z

4 3

1 2v

(b) Pair of 119881 and 119885 SUs































1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)


3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)




















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










21

54

3X

21

3X

2 143

Y


1

2

3 z 1

2

3 z

4 3

1 2v

(b) Pair of 119881 and 119885 SUs































1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)


3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)




















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)


3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)




















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4

3 4

2 3 4

1 2 3

ESY1

ESY2

ESY3

ESY4

PSX SH (Tx)

ESY SH (Rx)


3 4 1 2 r 3 4 1 2 r 3 4 1 2 r 3 4 1 2 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r 2 3 1 r

ESZminus1

ESZminus2

ESZminus3

ESZ SH (Rx)

PSV SH (Tx)




















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















K

K

K

K

K

Case 1

Case 2

Case 3

Case 4

Case 5

a

a

a

a

a























b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)

b = rotate(b k)








1015840(lceil1198982rceil+119898+1) = 1



1015840(lceil1198982rceil) = 0


10158401 = 0



Case 1

Case 2

Case 3

Case 4

Case 5

a

b

b = rot(b 1)

b = rot(b 2)

b = rot(b 3)

b = rot(b 4)

b = rot(b 5)

b = rot(b 6)

b = rot(b 7)













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Algorithm 3





119875119911 and





1 1 0 0

3 4 2 14 1 1 41 2 4 32 3 3 2r r 2 13 4 1 44 1 4 31 2 3 22 3 2 1r r 1 43 4 4 34 1 3 21 2 2 12 3 1 4r r 4 33 4 3 24 1 2 11 2 1 42 3 4 3r r 3 2

1 0 1 0




3 4 2 1 4 1 1 4 1 2 4 3 2 3 3 2 r r 2 1 3 4 1 4

2 1 3 3 3 3 1 2 1 2 2 1 r r r r r 1 r 3 2 3 3 2

Row 1

IPESV

IPESZ








1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 0 1 0


0 1 0 1




























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16



1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Cℎ3

Cℎ5

Cℎ6

Cℎ8


1 2 3 41 2 3 4 1 2 3 4 1 2 3 4

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8

3 3 3 3 5 5 5 5 6 6 6 6 8 8 8 8Y5

１X CH

２QY CH

２Q

２Q

Y1














2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 4 2 4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 6 1 6 4 3 4 35 6 5 6CH

12 14 12 14 21 26 21 26 35 36 35 36 43 47 43 47

SH

SCH 54 53 54 53 12 14 12 14 21 26 21 26 35 36 35 36

SRCT

3 7 3 7


S S S S S

C C C C C

C C C C

C

C

C C C C


6 6 8 8

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

4 4 9 9 1 1 6 6 5 5 6 6CH

16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16 16 18 18 24 24 29 29 31 31 36 36 45 45 46 46

SH

SCH

SRCT


S S S S

C C

C

CC

C C

CC C

C C


121616 18 18 24 24 29 29 31 31 36 36 45 45 46 46 16161818 24 24 29 29 31 3136 36 45 45 46 46 16 16 1818 24 24 2929

14 1214 1214 21 26 21 26 35 3635 36 43 47 43 4754 53 54 5312 2126 2126 35 36 35 43 47 43 54 53 54 53473614

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Time slot

SCHX

SCHY


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35Time slot

SCHX

SCHY4

12 14 12 2126 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 5314 12 14 12 2126 21 26 35 3635 361416161818 24 24 29 29 313136 36 45 45 46 4616161818 24 24 29 29 16161818 24 24 29 29313136 36 45 45 46 46














2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












2



















0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36Time slot

SCHX

SCHY1SCHY2SCHY3

1214 1214 21 26 21 26 35 36 35 36 43 47 43 47 43 47 43 4754 53 54 54531214 1214 2126 212635 36 35 3616 16 16 1618 18 18 1824 24 24 24 16 1618 18

16 1618 1824 24

24 242424

292929

29 2916 1618 18 24 24 29 29

16 16 18 18 24 24 29 29

29 2916 161818

1616 18 1824 2429 29

3131 313136 36 36 363131

24 24 29 29 31 3136 36

45 45 45 4546 463131 36 36

3131 36 3645 45 46 46

45 45 46 46

46 4645 45

36 36 45 4546 46

16 16 18 1846 46




0

20

40

60

80

100

120

Sect

or re

ndez

vous

late

ncy

(SRL

)

(a) 119873119894 = 5


0

50

100

150

200

250

300

350

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

100

200

300

400

500

600

700

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17













0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0200400600800

1000120014001600

Sect

or re

ndez

vous

late

ncy

(SRL

)


(a) 119873119894 = 5


0

500

1000

1500

2000

2500

3000

3500

Sect

or re

ndez

vous

late

ncy

(SRL

)


(b) 119873119894 = 11


0

1000

2000

3000

4000

5000

Sect

or re

ndez

vous

late

ncy

(SRL

)


(c) 119873119894 = 17








Number of PUs 50






0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

500

1000

1500

2000

2500

3000

3500AT

TR (s

lots)



0

1000

2000

3000

4000

5000

6000

7000

8000

MTT

R (s

lots)










0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

100

200

300

400

500

600

700AT

TR (s

lots)



Ni = 6)PES-SCH (

PES-SCH (Ni = 12)

0

500

1000

1500

2000

MTT

R (s

lots)


PES-SCH (Ni = 4)

Ni = 4)





200

400

600

800

1000

1200

1400

ATTR

(slo

ts)







05

1

15

2

25

3

35

MTT

R (s

lots)

times104








0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

02

04

06

08

1

Prob

abili

ty o

f suc

cess

ful c

hann

el re

ndez

vous


7 Conclusions




Acknowledgments


References






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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