research article a rendezvous protocol with the...

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2013 Article ID 715816 18 pageshttpdxdoiorg1011552013715816

Research ArticleA Rendezvous Protocol with the Heterogeneous SpectrumAvailability Analysis for Cognitive Radio Ad Hoc Networks

Sylwia Romaszko

Institute for Networked Systems RWTH Aachen University Kackertstraszlige 9 52072 Aachen Germany

Correspondence should be addressed to Sylwia Romaszko sarinetsrwth-aachende

Received 4 May 2012 Revised 11 August 2012 Accepted 20 August 2012

Academic Editor Fangwen Fu

Copyright copy 2013 Sylwia Romaszko This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In cognitive radio ad hoc networks a frequently changing environment varying channel occupancy statistics and heterogeneousspectrum availability result in a need to meet on a common channel and to initiate a communication This process of two or moreCRs meeting each other in the same channel is called a rendezvous (RDV) RDV is essential for establishment of a communicationlink Hence methods guaranteeing that all nodesmeet periodically in reasonable periods of time should be developed In this studywe evaluate a torus Quorum System (QS) and Difference Set (DS) based rendezvous protocol in an asymmetric channel view case(heterogeneous channel availability) Regardless of the diversity of channels of CRs the protocol guarantees RDV on either allchannels or almost all channels Furthermore the nodes meet multiple times on different channels in a period which increases thechance of successful establishment of a communication link

1 Introduction

Cognitive Radio Networks (CRNs) can operate in licensedand unlicensed bands A spectrum hole is a frequency bandthat has been assigned to a primary user (PU) but is notutilized by this PU at a particular time and specific geographiclocation [1] Secondary Users (SUs) also called CognitiveRadio (CR) users have only an opportunistic spectrumaccess to these bands that is the licensed spectrum thatis temporarily vacant may be used by a CR user [2] Theappearance of a PUmeans that CRs must vacate immediatelythe occupied frequency band Hence link recovery informa-tion (and a new determined channel) cannot be circulatedover the previously used spectrum band The disseminationof control traffic signals (on a common control channelCCC) must be fast since the SU might have a limitedduration of time in which a spectrum hole is likely to beavailable Furthermore such dissemination should be robustand minimize the use of energy and computing resources[1] Hence the classical CCC of multichannel networks isnot an attractive solution for CRNs Moreover unlike in thecase of classical ad hoc networks a CR has the heterogeneousspectrum availability which is varying over time and spacedue to the licensed holdersrsquo activities In other words the

available radio resources (channel set) can be different fordifferent CRs (also known as asymmetric channel occupancyknowledge) in the same network due to different locationor PUs activities From all these unique CRN characteristicsarises a big research challenge namely how to achieve arendezvous between nodes Haykinrsquos question how can weestablish the dissemination of control traffic signals betweenneighboring SUs in cognitive radio ad hoc networks which israpid robust and efficient [1] is still not fully answered andis a challenging problem

In this study we investigate a distributed rendezvousprotocol for cognitive radio ad hoc networks employingfrequency hopping (FH) techniques in the case of hetero-geneous channel availability FH is known for decreasingthe probability of interference to PUs thanks to the fre-quent switching of the occupied channels However someundesirable assumptions of typical FH (eg the need ofsynchronization and exchange of hopping patterns the samelength of hopping sequence patterns)must be overcome (egincumbents presence and as consequence the need to vacatethe channel immediately by a SU heterogeneous channelavailability etc) Before going into details of the protocolwe formulate the rendezvous (RDV) problem with regardto channel switching and an asymmetric channel occupancy

2 Journal of Electrical and Computer Engineering

ChannelRendezvous (RDV)

Ch4

Ch3

Ch2

RDV

Ch1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time (slots)

CR1

CR2CR3

PU1PU2

PU3

1 2 3 4

1 2 3 41 2 3 4

Figure 1 Rendezvous in CRNs if there is no hatched rectangle of a PU on a particular channel it means that this PU is not active on thischannel for example there is no PUrsquos activity on Channel 3 (Ch3) CR1 not being in the range of any of PUs can use all four channels CR3can sporadically use Channel 1 due to the PU1 activity there CR2 has two available channels (1 3) while the availability in Channels 2 and 4is limited to spectrum holes of PU2 and PU3 Hence CRs have an asymmetric channel occupancy knowledge In a 16 slots of long time periodCR1 user can meet CR2 user on Channel 1 in slot 0 and on Channel 3 in slot 5 However they cannot communicate on Channel 4 in slot 9nor on Channel 2 in slot 12 due to the PU2 and PU3 activities there (CR2 cannot transmit)

knowledge A RDV problem in multichannel networks refersto the ability of two or more CRs to meet each other in thesame channel

Figure 1 illustrates an example of the channel occupancyby three primary users (hatched rectangles) and three sec-ondary users (solid filled squares or rectangles) hoppingthrough four channels (Ch1 Ch4) in a 16 slots of longcycle (for the sake of simplicity we illustrate the case wheresecondary users have a common time-slot system This isdone without losing generality and in fact we have alsopresented asynchronous operations in [3]) Here by a slotwe understand some period of time within which SUs cancommunicate with each other (ie exchanging informa-tion receiving and transmitting) The situation depicted inFigure 1 is very optimistic nodes are able to meet once twiceor even three times (CR1 and CR3) However while hoppingor switching channels randomly it might happen that nodesnever meet In order to deal with the aforementioned RDV

problem we proposed in [4] the protocol which is based onthe torus quorum system (tQS) concept

Thanks to the use of the quorum system (QS) and alsothe difference set (DS) concept we are able to guaranteemeeting on all 119903 channels in the case of nodes with asymmetric channel view (SCHv) and almost on all channelsin an asymmetric channel view (ACHv) case We emphasizethat CR nodes do not need to have mutual knowledge oftheir hopping sequences information because the use ofQS properties is sufficient Thanks to the QS intersectionproperty guarantee cognitive radios will meet (intersect)when selecting quorum-based hopping sequences from thesameQS Quorums satisfying the RotationClosure Propertyguarantee the intersection even if the cycles of the CRs arenot aligned and therefore can be used in asynchronousprotocolsThe torus QS [5] exploited in this work representsan intuitive and simple method to employ where a quorumset is chosen by selecting a column of an 119903 times 119904 rectangular

Journal of Electrical and Computer Engineering 3

array (119903 is the number of rows and 119904 is the number ofcolumns) and lfloor1199042rfloor elements from other columns Other QSmethods are much more complex for example cyclic QS(a cyclic QS is based on the cyclic block design and cyclicDSs in combinatorial theory [6]) proposed in [7] The QSconcept itself has already been used [8] in the context ofoperating systems In the last decade the use of QSs has beenextended to other applications for example power-savingprotocols (eg [9 10]) Quorum systems are also adoptedin order to overcome a rendezvous problem in multichannelnetworks (eg [11ndash14]) For additional review in the contextof cognitive radios we refer the reader to [4]

The content of this work is as follows For sake of under-standing the analyzed algorithm we give a short introductionto quorum systems focusing on a torus QS and DifferenceSets We describe the standard method of constructing atorus quorum [5] (forward manner) and the mirror method[15] Afterwards we shortly describe the construction rulesof the MtQS-DSrdv protocol designed in our previous work[4] followed by a throughout performance evaluation In arecent survey paper [4] we also discussed a possibility touse MtQS-DSrdv for RDV in the case of cognitive radionetworks However that discussion was more of illustrationof a possibility and contained only preliminary results Inthis paper we will provide more in-depth analysis andconsider also asymmetric channels We provide additionalanalysis in terms of time-to-rendezvous (TTR) and the meanoccurrence of rendezvous on a channel within a hoppingsequenceperiod In contrast to [4] we also consider theasymmetric channel view in terms of (maximal) (M)TTRRDV on 119909 channels and RDV occurrence on a channelwithin a hopping sequenceperiod Furthermore as opposedto [4] we show the advantage of the MtQS-DSrdv protocolagainst the related work both in SCHv andor ACHv in termsof (M)TTR metric and the probability of RDVs on differentchannels in one hopping sequence period

Section 2 presents the related work in this area InSection 3 we describe the QS and DS concepts with allrelevant definitions and properties The system model ispresented in Section 4We prompt theMtQS-DSrdv protocolin Section 5 The extensive evaluation of the protocol in thesymmetric and asymmetric channel view is described inSection 6 with the comparisonwith the selected related workin the last subsection Section 7 concludes this study

2 Related Work

A strict coordination or some degree of synchronizationbetween nodes is often assumed in dynamic spectrum accessliterature Either a TDMA or FH-like access schemes areused with the assumption that nodes can synchronize orcoordinate easily see for example [16ndash19] In [20] taxonomychallenges classification and comparison of rendezvousapproaches in CRNs can be found

Here we summarize the most recent related work bycategorizing methods into three branches The first categorycomprises nonquorum-based solutions representing blindor pseudorandom RDV techniques [21ndash26] The secondbranch contains either QS-based protocols proposed for a

multichannel Medium Access Control (MAC) [11 27 28] ornon-QS but sequence-based algorithms for CRNs [29ndash31]Finally in the third branch we have a number of quorumsystem-based protocols proposed for CRNs [12ndash14 32ndash34]

A-MOCH [30] the non-QS-based protocol for CRNs isbased on Latin Square (LS) (transmitter) and Identical-RowSquare (IRS) maps (receiver)This approach guarantees RDVon all channels in a period but only once on each channelMoreover while being in the reception mode receiversneed to switch channels constantly which is definitely notdesirable for wireless resource-constrained systems It mightalso happen (cf [30]) that a transmitter will select such LSwhich also implies switching channels constantly In otherwords in this approach the cost of channel switching timefor a receiver should be taken into account

In the asynchronous ASYNC-ETCH algorithm pre-sented in [31] there is no need of global clock synchro-nization no matter how the hopping processes of nodes aremisaligned A hopping sequence 119878

119894is composed of119873 frames

(119873 denotes the number of available channels) where eachframe is composed of a pilot slot and two subsequencessub 119878119894The pilot slots of 119878

119894 collected together are the channels

appearing in sub 119878119894in the same order The hopping sequence

is equal to (2119873 + 1) times 119873 for example with 5 channels itis composed of 55 slots If the pair of CRs selects the samehopping sequence RDV is guaranteed in one slot per hoppingperiod However while using different sequences there isRDV guaranteed in119873 slots

In order to have a RDV channel without the help ofCCC or synchronization and to guarantee rendezvous in atleast one channel for each searching sequence the BalancedIncomplete Block Design (BIBD) [35] has been used in[29] Authors introduce single-sequence and multisequenceMAC protocols where the latter builds hopping sequencesfor the multichannel case The protocol is compared to thepermutation sequence proposed in [36] and blind rendezvousin [37]

In DSMMAC [13] all nodes create the same channelhopping sequence and the only possible variation of thissequence is dependent on an offset (if cycles are not aligned)Moreover the process of the forming of channel hoppingsequences is not easy namely it is based on the DifferenceSets which must be chosen in a very careful manner in orderto ensure a high RDV probability

Since a torus QS is a special case of a grid QS wealso consider two grid quorum-based rendezvous algorithms[14 34] The schemes do not guarantee RDV although thepercentage of missed RDV is very low

In [4] we gave a comprehensive guidance on the useof quorum systems We also addressed RDV issues indecentralized CRNs surveying exhaustively channel hoppingapproaches Additionally channel hopping requirements forcognitive radio ad hoc networks have been proposed andthe most suitable related work to the RDV problem has beenappraised according to those requirementsTheMtQS-DSrdvprotocol rules were proposed in [4] along with its assessmentaccording to the proposed requirements

In [33] a sequence-based protocol has been implementedon Universal Software Radio Peripheral (USRP) boards and


0 2 36 7 8

12 13 14 15

51117

41016

19

0 1 36 7 8 912 13 14 15

51117

41016

2 0 1 36 7 8 912 13 14 15

51117

41016

2

170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16

A

A

B

B

C

C

Figure 2 Standard torus QS example node 119860 is built by pickingthe third column as its head and 3 randomly chosen slots fromsucceeding columns 119861 is formed by selecting the sixth column andits tail from succeeding columns in a wrap-aroundmanner119862rsquos headis the second column 119860 and 119861 intersect at slots 11 and 14 119861 and 119862 atslot 7 and 119860 and 119862 at slots 2 and 9

evaluated in terms of the time of the first encounter betweentwo SUs and the time for encounter on all channels Theprotocol itself is partly based onQS [38 39]The experimentsshow a big advantage of the sequence-based scheme over therandom sequence scheme with and without PUrsquos presence

In contrary to gQ-RDV method [34] or BIBD-basedapproach [29] the MtQS-DSrdv protocol guarantees ren-dezvous on all 119903 available channels in a symmetric channelview In comparison to A-MOCH [30] our scheme doesnot use two different sequences for receiver and transmitternodes switch channels less frequently and nodes can meetmore than once on the same channel during one period

3 Torus Quorum System andDifference Set Properties

In this section we present the (torus) QS and DS conceptsSince QSs are not commonly used in wireless communi-cations we present first some relevant definitions in thissection

A torus-based QS (tQS) [5] adopts a rectangular arraystructure called torus that is wrap-around mesh where thelast row (column) is followed by the first row (column) in awrap-aroundmanner (later in this work we call the standardtQS as the forward tQS since its tail is selected going forward(to the next columns)) The height 119903 (number of rows ieentire column) and width 119904 (number of columns ie entirerow) are defined where 119899 = 119903 times 119904 and 119904 ge 119903 ge 1

Definition 1 (Torus Quorum Systems) A torus quorum ina 119903 times 119904 torus is composed of 119903 + lfloor1199042rfloor elements formed byselecting any column 119862

119895(119895 = 1 sdot sdot sdot 119904) of 119903 elements plus one

element out of each of the lfloor1199042rfloor succeeding columns usingend wrap-around An entire column 119862

119895portion is called the

quorumrsquos head and the rest of the elements (lfloor1199042rfloor) its tail

Figure 2 gives an example for three nodes choosing threedifferent torus quorums under119880 = 0 1 17 where 119903 = 3and 119904 = 6 thus 119899 = 18

It is also possible to construct a tQ in a backward manneras shown in [40] However in order to select a torus tail ina more flexible manner themirror torus extension should beused [4 15] which allows to alternate selecting tailrsquos slot in aforward or backward manner

Definition 2 (Mirror Torus Extension) A tail of a torusquorum lfloor1199042rfloor elements can be selected from any positionof column 119862

119895+119896119894lowast119894(one element from a column) where 119896

119894isin

1 minus1 and 119894 = 1 sdot sdot sdot lfloor1199042rfloor in a wrap-around manner Torusesof the same torus QS need to select elements in the sameforwardbackward order

In other words if an element was selected from column119862

119895+1 the next element cannot be selected from 119862

119895minus1 but

needs to originate from the next succeeding (forward) col-umn (119862

119895+2) or the preceding (backward) column (119862

119895minus2) The

parameter 119896119894needs to be the same for all quorums of the same

torus QS that is the direction of the selection needs to be thesame Figure 3 shows the selection in a mirror way

The intersection property of quorum systems is notsufficient when the cycle of nodes is not aligned or nodes areasynchronous In order to have RDV guarantee in such casea quorummust satisfy the Rotation Closure Property (RCP)

Definition 3 (Rotation Closure Property) For a quorum 119877 ina quorum system 119876 under an universal set 119880 = 0 119899 minus 1and 119894 isin 1 2 119899 minus 1 one defines rotate(119877 119894) = (119909 +

119894) mod 119899|119909 isin 119877 A quorum system 119876 has the RotationClosure Property if and only if

forall119877

1015840 119877 isin 119876 119877

1015840cap rotate (119877 119894) = 0 forall119894 isin 1 2 119899 minus 1

(1)

A quorum system which satisfies the Rotation Closure Prop-erty ensures that two asynchronous mobile nodes selectingany two quorums have at least one intersection in their quo-rums The (forward backward and mirror) torus quorumsatisfies the Rotation Closure Property

TheDifference Sets [6] concept is very close to QSs beingactually the basis of the cyclic QS

Definition 4 (Cyclic Difference Set (DS)) A subset 119861 such as119861 = 119886

1 119886

2 119886

119896modulo 119899 for 119886

119894isin 1 2 119899 minus 1 is called

a cyclic (119899 119896 120582) difference set under 119885119899(119896 and 120582 are positive

integers such that 2 le 119896 lt 119899 and |119861| = 119896) if for every 119887 equiv

0(mod 119899) there are exactly 120582 ordered pairs (119886119894 119886

119895) where 119886

119894

119886

119895isin 119861 in such a way that 119886

119894minus 119886

119895equiv 119887(mod 119899)

If at least one ordered pair (119886119894 119886

119895) exists in (119899 119896) difference

set such set is called a relaxed DS

Since tQs also formDSswe show an example based on theset from Figure 2 Node 119860 has a set 2 4 8 9 11 14 where119899 = 18 The set is a relaxed DS because there is at least oneordered pair (119886

119894 119886

119895)

1 equiv 9 minus 8 2 equiv 4 minus 2 3 equiv 11 minus 8 4 equiv 8 minus 4


9 equiv 11 minus 2 10 equiv 14 minus 4 11 equiv 2 minus 9



(mod 18)

The reader should note that each cyclic DS satisfies the RCP


0 12 3 4 5 6 70 1

1

8 9 10 11 12 13 14 15 8 916 17 18 19 20 21 22 23 16 17

2 3 4 5 6 70 1

8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23

7

15

23

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

A B

A

B

1198621 1198622 1198621 11986221198623 1198624 1198625 1198626 1198627 1198628 1198621 1198622 1198623 1198624 1198625 1198626 1198627 11986281198628

Figure 3 Example of mirror torus QS119860 and 119861 initiate their tail selection in a backwardmanner that is the first element of node A is selectedfrom column 119862

5(a mirror of 119862

7) and the one of node 119861 is selected from column 119862


5) Then both nodes select the next tail

element in a forward manner thus from 119862

119895+2column which is 119862

8in case of node 119860 and 119862

6in case of node B The third tail element is

selected in a backward manner which is 1198623in case of node 119860 and 119862

1in case of node 119861 The last element of nodes 119860 and 119861 falls in the same

(mirror) column Nodes meet at slot 5 (they would meet in one element of column 1198626anyway) and additionally in slot 18 Hence nodes can

always alternate the manner either forward or backward while picking up elements however they need to have the same 119896119894 in this example

119896

119894= minus1 1 minus1 1 | minus1 where 119894 = 1 sdot sdot sdot lfloor82rfloor

4 System Model

We focus on Secondary Users in the presence of PrimaryUsers in the network where no central units for managementof spectrum allocation are present The rendezvous on thesame channel (hereafter terms channel and frequency willbe used interchangeably) between two SUs is crucial for theestablishment of the communication Each SU is equippedwith a single tunable half-duplex radio transceiver whichcan switch between 119903 different channels In cognitive radionetworks SUs must somehow identify spectrum holes whichvary in time and space and after that select available fre-quencies Based on a spectrum detection method (sensingdatabase) each CR recognizes a list of spectrum holes thatcan be used while respecting PU priority It is assumed thatchannels are slowly time-varying and that the system isslowly dynamic

SUs should find each other periodically and as soonas possible (ie Time-to-Rendezvous should be small andbounded (TTR) is an amount of time measured in slotswithin which two or more CRs meet each other once theybegan hopping or after the last RDV on a channel) Here weemphasize that the need of rendezvous on multiple availablechannels in a hopping sequence period is paramount asthanks to the guarantee of this property the channel accessdelay will be minimized If an RDV protocol cannot satisfya periodic overlap between channel hopping sequences ofcognitive radios on different channels this raises an RDVproblem because a single rendezvous channel might becomeunavailable due to the (sudden) appearance of primary usersignals If an RDV protocol can guarantee a rendezvous onevery available channel it provides the maximum robustnessTherefore we aim to guarantee rendezvous on every availablechannel in the case of the homogeneous spectrum availability(ie all SUs have the same channel set) and on multipledifferent available common channels in the case of theheterogeneous spectrum availability The latter objective ischallenging not only due to the different channels sets ofCRs but also because of different lengths of channel hoppingsequences

In our previous work [4] we developed MtQS-DSrdvalgorithm and showed that in the case of a symmetric channelview (homogeneous spectrum availability) CR nodes meetperiodically on every available channel As explained beforea periodic overlap is guaranteed thanks to the use of QSproperties and therefore there is no need of exchange of anyinformation in order to meet in a hopping sequence periodIn this work we extend the analysis of SCHv in terms of TTRand we evaluate the protocol for an asymmetric channel view(heterogeneous spectrum availability)

In the MtQS-DSrdv algorithm we consider that each SUhops from one channel to another (Figure 1) according toits frequency hopping sequence in order to discover anotherSU Each CR determines its channel map for each of thechannels making use of a torus array (119903 times 119904) using torus QSand DS concepts and then combines them into a hoppingsequence This process requires no mutual knowledge ofhopping sequence information and available channels fromother CRs The resulting hopping sequence is cyclic and itcounts as many slots as there are elements in the torus arrayEvery element represents a time slot where a single channel isdesignated to be used Here we stress that a slot is an amountof time within which cognitive radio users can communicatethat is discover each other by exchanging messages

5 MtQS-DSrdv Epitome

In this section we describe MtQS-DSrdv algorithm Whileforming the channel map (hopping sequence) two conceptsare employed namely torus Quorum System and DifferenceSetsThe former is straightforward sincewe just select a torusquorum algorithmwhile the head (column) should follow theconstruction rules of the algorithm and tail can be chosenrandomly The reader should note that with 119903 gt 4 the firstfour channels have torus Quorum System-based maps andthe rest have Difference Set-based maps

Figure 4 depicts how each node constructs its hoppingsequence with a cycle of 119899 slots The column selection ofChannel 1 (step 2a1) specifies the start point of a map


Determine the number of available channels 119903 based on a spectrum detection mechanism (sensing database)

Build a torus array of n slots (elements)

giving each channel 119904

119903

slots 119904 = (119903 minus 1) times 2 + 1

119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)

0 1 2 middot middot middot middot middot middot

middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot


middot middot middot

0 1 2

middot middot middotmiddot middot middotmiddot middot middotmiddot middot middotmiddot middot middot


Select tQS heads (columns of 119903 slots)for the first four channels (2a)

(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)

For 119904minus 4 remaining channels (119903 gt 4) select119904 slots according to the DS rule

Select tails ([ 1199042 ]) of the first four channels

according to forward backward mirror tQS

TX

Channel mapcycle viewcycle of 119899 slots

Nodersquos channelsMap torus QS view

Creating map (hopping sequence with a cycle of 119899 slots)find 119904 slots fo each channel according to tQS-DSrdv algorithm

Each CR node determines its channel map (hopping sequence) independently

based on 119903times 119904 torus 119903times 119904 torus

119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623

Channel 1 head Select 119894 randomly

Channel 2 head column 119894 + [ 1199042 ]+1

Channel 3 head column 119904

Channel 4 head column 119894 + [ 1199042 ] + 2

1198621 1198623 11986231198622

Figure 4 MtQS-DSrdv steps of each node

construction A node can select its head in 119904 different waysbecause of 119904 existing columns In Figure 5 the head ofChannel1 is selected randomly to be 119862

1(the first column) The

remaining 119904minus4 channels (step 2b) search theirmap accordingto the DS rule (selecting a channel map by following the DSrulemeans that a relaxed DS set must be found of 119904 slots ie119904 remaining available elements are chosen so that at least oneordered pair (119886

119894 119886

119895) exists in (119899 119904) difference set where 119896 = 119904

from Definition 4) such that there are enough elements fortails of the first four channels

For a node with eight available channels Figure 5 depictstwo exemplary maps (Map8Chs(1) and Map8Chs(2)) in orderto showhow to form another tQS-basedmap by just replacingthe tail elements of the first four channels

In addition the reader should note that the selectionof the channels is not strict that is we can replace tQS-based channels with DS based Figure 6 illustrates a columnselection of Channel 1 with different 119894 (step 2a1 fromFigure 4)

Thanks to the flexible use of tQS and DS concepts theMtQS-DSrdv protocol allows automatically cognitive radionodes to meet on each channel at least once in the symmetricchannel view

6 Verification

In the symmetric channel view we assess MtQS-DSrdv asregards the TTR performance In the asymmetric channel


9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs

Map2ChsPeriod 6 slots



C1

Map5Chs period 45 slots

Map8Chs(1) period 120 slots Map8Chs(2) period 120 slots

Map6Chs period 66 slots Map7Chs period 91 slots

C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets

Figure 5 MtQS-DSrdv construction exemplary maps (Map119903Chs) for 119903 = 2 sdot sdot sdot 8 channels (Chs) Chri for 119894 = 1 sdot sdot sdot 119903 stands for a particularmap of channel 119894 With three available channels Channel 1 is selected according to the tQ forward manner and the next two channels areformed from DSs (Map3Chs) that is DSCh2 4 6 7 9 13 and DSCh3 3 8 11 12 14 These DSs are exemplary since others could also befound While having four available channels Channel 4 is selected according to the DS rule Starting with four available channels (Map4Chs)the mirror tQ is utilized changing twice the direction (119896

119894) With five available channels (Map5Chs) Channel 2 is built using a backward tQ

except of one mirror element

viewwe evaluate the protocol in respect to theRDVguaranteeand occurrence on each channel and TTR performance Thereader should note that we also compare the performanceof the pair of nodes using maps with the same number ofchannels against the pair of nodes usingmaps with a differentnumber of available channels Hence we analyze whether itis better to use a smaller map with only available channelsor a larger map also with unavailable channels The lattercase refers to the case where unavailable channels are alsovisited but only for spectrum sensing (this is a frequentlyused approach while dealing with ACHv in the related work[13 26 30])

We define the Rotation Closure Property for a completechannel map (map-RCP) as follows

Definition 5 (Map-Rotation Closure Property) For map 1198771and 1198772 of period (cycle) Θ = 0 119899 minus 1 and for all 119894 isin Θone defines for all slot offsetexist119894 1198771

119894cap1198772

(119894+slotOffset) mod 119873 = 0where slot offset isin Θ

The frequency map of a node must be checked with eachpossible cycle shift (slot offset = 0) With a slot offset 0 (cyclealignment case) nodeswill alwaysmeet on all channels at leastonce

Proof A hopping pattern for each channel is constructedaccording to Definitions 1 2 and 4 that is each channelset is a torus quorum or cyclic difference set as shown inFigure 5 A torus quorum and cyclic DS satisfy the RotationClosure Property from Definition 3 Therefore the set of allchannels map1198771 and1198772with the same periodΘ composedof elements from a 119903 times 119904 torus so that 119903119904 = 119899 satisfies themap-RCP from Definition 5 We do not need to check all119903 channels because the map-RCP definition is automaticallysatisfied due to the fact that each single channel map satisfiesthe RCP or DS

In all considered cases we show statistical results for thecomplete set (equal or different channels) of results obtainedby two maps We analyze the ACHv case with maximum


1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

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1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6

Column offset 0 Column offset 1

Column offset 3 RDVs column offset 0 1

RDVs column offset 0 3 RDVs column offset 1 3

Map6Chs

Figure 6 MtQS-DSrdv different column offsets CRs meet at least in 119903 slots

8 available channels using channel maps from Figure 5Moreover while talking about the MtQS-DSrdv protocolwe refer to Figure 5 and Map8Chs(1) for a map with eightchannels unless mentioned otherwise

61 MTTR in Symmetric Channel View In this subsectionwe evaluate MtQS-DSrdv in SCHv in terms of maximumTTR Table 1 shows TTR results in terms of the minimumof all TTR maxima (Υ) the maximum TTR (MTTR) themean (120583) of MTTRs the mean (120583) of TTRs and the meanof occurrences on a channel (120583119873ch) in a period

In Table 1 we show the results for a map with 8 channelsusing both Map(1) (8119872(1)) and Map(2) (8119872(2)) from Figure 5The reader should note that these are just two examples onhow the tQS-based nodes can easily select their tail elementsin a flexible manner

In the case of SCHv it is clear that MTTR lt 119899 (119899 = |Θ|where Θ is a period) for 119903 = 2 minus 4 and ≲ 1198992 for 119903 = 5 minus8 One should note that we refer to MTTR per shift that iswe take the maximum TTR in each shift where 120583MTTR is an

Table 1 MtQS-DSrdv in SCHv so is slot offsets (119903 119899) = (2 6)(3 15) (4 28) (5 45) (6 66) (7 91) (8 120)

119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18

average of all MTTRs from all shifts while rotating the cycleThe average MTTR is considerably lower than MTTR Notethat the averageTTR (120583TTR) is significantly lower thanMTTRand the average MTTR (120583MTTR)

In the worst case scenario while only one commonchannel is available and CRs can meet only once on thecommon channel MTTR = 119899 (other less extreme cases


Table 2 MtQS-DSrdv in ACHv RDV in a larger period of119861minRDV stands for the minimum number of RDVs (with thepercentage)

119860ndash119861 minRDV On all common CHs2-3 1 (13) 872ndash4sdot sdot sdot8 2 1003-4sdot sdot sdot5 3 1003ndash6 2 (5) 953ndash7 3 1003ndash8 2 (7) 934-5 3 (16) 844ndash6 3 (5) 954ndash7sdot sdot sdot8 4 1005-6 3 (5) 795ndash7 3 (2) 885ndash8 2 (1) 3 (5) 776-7 4 (3) 736ndash8 4 (1) 787-8 5 (10) 6 (33) 58

are discussed in Section 63) However as soon as a CRbecomes aware of the fact that some channels are not availableanymore it can adjust its hopping pattern

62 Minimum RDVOccurrence in Asymmetric Channel ViewIn this section we evaluate the MtQS-RDV protocol in theheterogeneous spectrum availability case where some of theavailable channels of one CR are unavailable to anotherWhile analyzing the ACHv case one should consider whetherit is better to use a map with a larger period or to use a mapwith available channels only For instance in the former casea CR with 3 currently available channels can select a mapwith 4 channels instead of 3 and while visiting an unavailablechannel only spectrum sensing is performed MtQS-DSrdvwith a symmetric channel set using a map for 4 channelswhile having 3 available channels still guarantees RDVs onall 3 available common channels

While usingMtQS-DSrdv maps for a different number ofchannels than available and the number of available channelsis not large there is also RDV guarantee on all availablecommon channels most of the time (in a larger period) Forinstance we compareMap3Chs (mapwith 3 available channelsfromFigure 5) of one nodewithMap4Chs of another node butin a larger period of 28 slots as it happens when both nodesuse Map4Chs In this case nodes also meet on all 3 availablechannels

The following definition considers the case where node119860which has a smaller period Θ still meets with node 119861 whichhas a larger period Φ

Definition 6 (nM-Maps-Rotation Closure Property) Formap 1198771 with period Θ = 0 119899 minus 1 and for all 119894 isin Θ andmap 1198772 with periodΦ = 0 119898 minus 1 and for all 119895 isin Φ andwhere 119899 lt 119898 there is defined for all Φ exist119894 exist119895 1198771

119894cap 1198772

119895= 0

Table 2 shows the analysis of the combination of maps(with minimum 119903 = 2 and maximum 119903 = 8) while checkingthe number of RDVs in a larger period Φ The results show

that in many cases there is still RDV on all common channelsof a node with fewer available channels The probabilityto have an RDV on all shared channels is very high forexample node with three available channels meets node withsix available (3ndash6 case) at least on two channels in a period(minRDV = 2) and this can happen with only 5 probabilityotherwise nodes meet on three common channels

Let us next analyze an example where a node has fouravailable channels in a set and another node has threeavailable channels In Figure 7 the first one (node 1198601) usesthe map Map4Chs from Figure 5 and the second (node 1198602)uses Map3Chs While both nodes are aligned at slot 0 theymeet on each channel in a smaller period on Channels 2 and3 twice We also show RDVs in a larger period that is apartfromR1 rendezvous (inΦwe have1198771+1198772RDVs) nodesmeetin R2 slots (15 18-19 and 22) on each channel While shiftingthe alignment of a smaller period (Θ) map we show RDVsonly in a smaller periodTheminimal number of channels onwhich a RDV occurs in a smaller period is one Nodes usuallymeet on all three channels in a smaller period Note that whileanalyzing RDVs in a larger period Φ of 28 slots nodes haveRDVs on all available channels of A2 in all shifts

For the sake of clarity we show in Figures 8 and 9 theRDVoccurrence of Map4Chs in SCHv and a combination of mapswith 3 and 4 channels In both cases CR nodes meet on allthree available channels We can additionally notice that thecombination of 3-4 channels maps is better than that usingmaps with 4 channels Single RDV on a particular channel ina period is decreased significantly since nodes have multipleRDVs in a period on all three channels If we take a mean ofRDV occurrence in a period for each channel we obtain 18with Map4Chs (SCHv) and 23 with the combination of maps(ACHv) In other words it is better to use an asymmetricchannel set in spectrum availability heterogeneity in thisparticular case

In Figures 11 and 13 we show an example where nodes donot meet on each channel namely the combination of mapswith 4 and 6 channels and the combination of maps with 5and 7 channels In the former case nodes do not have RDVon four channels (minRDV = 3) in 3 shifts (once on the firstchannel and twice on fourth channel) However as one cansee in Figure 11 they meet very often at least three timeson each channel in a period (a mean of RDV occurrenceis circa 28) Contrary while using a symmetric channel setmap (Map6Chs in Figure 10) nodes meet on all channelsbut most often once or twice in a period (a mean of RDVoccurrence is circa 17) We also show an example while thepair of nodes uses Map7Chs (symmetric channel set) againstthe combination of maps with 5 and 7 channels (Figures12 and 13) While using different maps (combination case)nodes have RDV guarantee on three channels (minRDV = 3)where RDV on three channels only happens in 2 shifts RDVon four and five channels is the most frequent

Although nodes do not meet on all channels there is stilla question whether this map should not be used since nodesmeet more often (mean of RDV occurrence is circa 26) thanin the case of a symmetric channel set with 7 channels map(mean of RDV occurrence is circa 17)


Table 3 MtQS-DSrdv in ACHv RDV in a larger period of B

119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch

2-3 2 11 (3 so) 67 26 252ndash4 4 10 (5 so) 81 17 352ndash5 4 17 (7 so) 11 5 452ndash6 11 16 13 2 552ndash7 10 18 158 26 65Map (1) 2ndash8 7 29 215 103 75Map (2) 2ndash8 7 29 21 10 753-4 4 14 (4 so) 94 37 233ndash5 6 22 (3 so) 13 45 33ndash6 7 22 (4 so) 15 3 373ndash7 8 33 (6 so) 207 7 43Map (1) 3ndash8 6 70 (8 so) 215 17 5Map (2) 3ndash8 6 65 (8 so) 23 18 53lowastndash8lowast 14 54 (8 so) 25 10 54-5 6 31 (2 so) 14 6 234ndash6 9 29 (2 so) 18 57 284ndash7 13 42 (4 so) 246 7 334ndash7lowast 9 31 (3 so) 19 5 33Map (1) 4ndash8 12 51 (4 so) 288 9 38Map (2) 4ndash8 12 45 (4 so) 276 8 384ndash8lowast 12 57 (4 so) 25 9 385-6 9 39 (1 so) 18 68 225-6lowast 6 32 (3 so) 17 6 225ndash7 8 45 (2 so) 227 7 265ndash7lowast 9 47 (2 so) 21 9 26Map (1) 5ndash8 12 65 (3 so) 267 94 3Map (2) 5ndash8 10 70 (3 so) 27 11 35ndash8lowast 10 56 (3 so) 24 10 36-7 10 66 (1 so) 229 88 176lowast-7lowast 10 43 (2 so) 19 7 22Map (1) 6ndash8 11 51 (2 so) 26 76 25Map (2) 6ndash8 10 49 (2 so) 258 8 256lowastndash8lowast 8 46 (2 so) 25 8 25Map (1) 7-8 13 55 (2 so) 277 95 22Map (2) 7-8 9 64 (1 so) 25 9 227lowast-8lowast 12 58 (1 so) 26 10 22

63 MTTR in Asymmetric Channel View In Table 3 MTTRstatistics are presented for the asymmetric channel view Oneshould note that we refer to MTTR per shift (slot offset ldquosordquoin table) that is we take the maximum TTR in each shiftwhere 120583MTTR is an average of all MTTRs from all shifts whilerotating the cycle

In ACHv 119860 minus 119861 denotes combinations of maps of node119860 with node 119861 where the number of channels of node 119860 issmaller than the number of channels of node 119861 as definedbefore In this table we also show the results for a mapwith 8 channels using both Map8Chs(1) and Map8Chs(2) fromFigure 5 In addition in some of the combinations we haveshown two cases with or without (lowast) The case without (lowast)stands for the maps as proposed in Figure 5 that is the first

channels are assigned to tQS maps and the next to DS mapsIn the case with (lowast) in the map where there are more DSsthan one (with 119903 = 3 and 119903 = 6 8) the first channels areassigned toDSs (following the order fromFigure 5 thus mapof Ch1 becomes Ch5 then Ch2 larr Ch6 Ch3 larr Ch7 andCh8 larr Ch4) where the remaining channels are assigned totQS-based maps also following the order from Figure 5 (egmap Ch5 larr Ch1) Note that the described results below arewithout (lowast) unless mentioned otherwise in the text

For ACHv the situation is naturally different than thatfor SCHv (Table 1) due to different period sizes of thecompared channel sets The results below are shown fromthe perspective of larger period (Φ) in order to compare itwith the SCHv case Depending on the combination of the


MtQS-DSrdvA1 1234

A2 123A1(0)-A2(0)1 RDV on 1 channel-on 3 channels1 RDV on 1 channel-on 3 channels2 RDV on 2 channels-on 3 channels-on 3 channels1 RDV on 2 channels2 RDV on 2 channels-on 3 channels-on 3 channels-on 3 channels-on 3 channels-on 3 channels-on 3 channels-on 3 channels1 RDV on 2 channels-on 3 channels1 RDV on 1 channel-on 3 channels-on 3 channels3 RDV on 2 channels2 RDV on 2 channels3 RDV on 2 channels-on 3 channels1 RDV on 1 channel-on 3 channels-on 3 channels

R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

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R1

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R1

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R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

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R1

R1R1

R1

R1R1R1 R1

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R1R1R1 R1

R1R1

R1R1R1

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R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4

Figure 7 Asymmetric channel view combination of maps with 3 and 4 channels while rotating the cycle RDV consideration in Θ blacksquare stands for channel 1 gray square for channel 2 and white square for channel 3 R stands for Rendezvous

0

5

10

15

20

0 1 2 3 4 5Cumulative RDV amount in one period

Channel distribution

Channel 1Channel 2

Channel 3Channel 4

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Figure 8 Symmetric channel set Map4Chs (28 slots)

channels of nodes119860 and 119861 the maximumTTR varies usuallybetween1198982 and (1198983) (119898 = |Φ|) where the average MTTRis lower than 30 slots in all cases varying usually between1198983 and1198984 We also show some of the combinations whereDS channel maps are reordered with tQS channel maps thecase with (lowast) One can see that assigning first DS maps andthen tQS maps to channels usually decreases MTTR andorMTTR mean We observe that the selection of different

0

2

4

6

8

10

12

14

0 1 2 3 4 5

Cumulative RDV amount in one period


Channel 1Channel 2Channel 3

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Figure 9 Asymmetric channel set combination of maps with 3 and4 channels

tail elements (as exemplary shown with maps Map8Chs) canimprove MTTR or 120583MTTR

Cognitive radio nodes that use a different map increasesignificantly RDV occurrences (120583119873ch) on a channel in aperiod The reader should note that in comparison with theperformance in SCHv RDV occurrence only once in a period


5045

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25201510

50

0 1 2 3 4 5 6



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Figure 10 Common channel set Map6Chs (66 slots)

0

5

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0 1 2 3 4 5 6Cumulative RDV amount in one period


Channel 1Channel 2

Channel 3Channel 4

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Figure 11 Asymmetric channel set combination ofmaps with 4 and6 channels

is insignificant since multiple RDVs are the dominant caseHowever in order to answer the question which map oneshould use the one imposing a symmetric channel view orthe one using an asymmetric channel set the comparison ofTables 1 and 3 will not provide conclusive answer Thereforein Table 4 we show theMTTR statistics in respect to a smallernumber of available common channels 120581 although usingmaps with a larger number of channels

Note that in this implicit way the related work papershandle an asymmetric view case [13 26 30] In this case itis also easy to verify an upper bound of MTTR of the MtQS-DSrdv design (due to the RCP guarantee CRs always meet onevery channel in a sequence period) which will be MTTR le(119898 minus 120581) in the worst case scenario (the worst possible chosenmaps) For example with 119903 = 8 and 120581 = 2(8 rArr 2) such

60

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00 1 2 3 4 5 6 7

Channel 1Channel 2Channel 3Channel 4


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Channel 4Channel 5

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Figure 13 Asymmetric channel set combination ofmapswith 5 and7 channels

upper bound ismet in two cycle shifts (2 so in the table) sinceMTTR = 118 which is exactly (119898 minus 120581) the same situation isin cases 119903 = 3 and 120581 = 2 119903 = 6 and 120581 = 2 and 119903 = 7 and120581 = 2 In other cases MTTR is lower or significantly lower

Combining the results from Tables 3 and 4 it is clear thatin terms of (M)TTR it ismore advantageous to use amapwitha number of locally available channels instead of using a largermap MTTR of asymmetric channel set maps is always lowerexcept for a few cases and even in those exceptional cases120583

MTTR of asymmetric channel set maps is better than that ofsymmetric channel set maps Nevertheless an investigationshould be done combining the selection of a map includingthe duration of nonavailability of channels It might be better


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0 1 2 3 4 5 6 7 8 9Cumulative RDV amount in one period



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Figure 14 MtQS-DSrdv 8 channels (120 slots)

to use a larger map keeping in mind a probability of thechannel release (predicting channel availability based on pastobservations) of the channel occupied by a PU recentlyHence an RDV protocol should closely cooperate with aspectrum decision mechanism which will be the topic ofinterest in our future work

64 Comparison with the Related Work In the subsectionwe compare the MtQS-DSrdv protocol with the related workwhere the designed approaches guarantee RDV either on allchannels or in a very small TTR time Hence we consider theDSMMAC (Difference-Set-based asynchronous Multichan-nel MAC) [13] A-MOCH (Asynchronous Maximum Over-lapping CH protocol) [30] ASYNC-ETCH (AsynchronousEfficient Channel Hopping) [31] and Balanced IncompleteBlock Design- (BIBD-) based [29] algorithms in the syn-chronous channel view and consider also asynchronouschannel view if applicable In all considered cases we showresults including the rotation of a whole cycle that is allpossible cases without cycle alignment are checked

641 Comparison with DSMMAC In Figure 14 we depictresults of MtQS-DSrdv with 8 channels according to themap presented in Figure 5 Figure 15 illustrates DSMMACresults with 8 channels We remind the reader that the mapfrom [13] is constructed entirely fromDifference Sets MTTRof MtQS-DSrdv equals 86 slots (using Map(1) but 57 slotswith Map(2)) which happens in two shifts only The averageMTTR (120583MTTR) is 288 with a standard deviation of 12However one should note that nodes meet often multipletimes (120583119873ch = 18) in a period as it can be seen in the figureIn this particular example the MTTR of DSMMAC is betterthan that ofMtQS-DSrdv since it equals 44 slots with ameanof 23 slots and a standard deviation of 81 However as canbe clearly seen in Figure 15 on DSMMAC channels 2 sdot sdot sdot 8

0

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0 05 1 15 2Cumulative RDV amount in one period




Channel 7Channel 8

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Figure 15 DSMMAC [13] 8 channels (73 slots)

nodes always meet only once in a period and no more InDSMMAC Channel 1 gets an extra slot since all DSs havebeen chosen from a period of 73 slots having 9 elements in aset The remaining slot (slot 0) has been assigned to Channel1 and therefore on Channel 1 nodes also have RDV twice in aperiod (Figure 15)

The fact that nodes meet only once in a period on2 sdot sdot sdot 8 channels diminishes the chance of the protocol to beadaptable in ACHv which was dismissed in this work In [13]it is assumed that every node should use the same hoppingsequenceTherefore we also check theMTTR statistics whileboth CRs apply 8 channel maps but they can meet only on2 common channels because only these two are available forone of the CRs The MTTR of DSMMAC will increase until71 slots (which happens twice) whereas 120583MTTR is increasedto 504 with 120590MTTR

= 104 Those MTTR results are clearlymuch worse than using the 2ndash8 combination of maps ofMtQS-DSrdv (Table 3)

We also analyze the possibility of the combination ofmaps with 2 and 8 channels for this approach Figures 16 and17 show the results for both protocols

With both protocols nodes meet on each channel TheMTTR of DSMMAC is slightly lower (25 slots) than that ofMtQS-DSrdv (29 slots see Table 3) 120583MTTR is similar (205of DSMMAC) but 120583119873ch of DSMMAC is lower than that ofMtQS-DSrdv (for both channels 75) since the average RDVoccurrence on Channel 1 equals to 44 and on Channel 2 is51 which can also be observed from the figures

The DSMMAC map with eight available channels hasseven neighboring pairs of slots one of each channel (2 sdot sdot sdot 8)except of Channel 1 having once three neighboring slotsWhereas the MtQS-DSrdv map has more neighboring slotsand can have even more thanks to the flexible design ofthe protocol This characteristic is paramount with asyn-chronous nodes (without slot alignment) since nonover-lapping slots influence badly the chance for actual RDV


40

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00 2 4 6 8 10 12

Channel 1Channel 2



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Figure 16 MtQS-DSrdv in ACHv the combination of maps with 2and 8 channels (120 slots)

on a channel Hence the MtQS-DSrdv map predominatesDSMMAC in this context However further comparison ofboth approaches is difficult due to the unavailability of mapswith other number of channels

642 Comparison with A-MOCH In Table 5 we show theresults of the A-MOCH protocol [30] for 119903 = 2 sdot sdot sdot 8

channels We remind that in the A-MOCH algorithm asender generates its hopping sequence based on the LSarray and the receiver map is based on the IRS array Sinceaccording to the algorithm nodes may randomly select apermutation of 0 1 119873minus1 where119873 denotes the numberof channels we created all the maps in the same way thatis rotating each row in a forward wrap-around manner toreceive easily an LS square For instance with 5 channelsthe sender channel hopping sequence in the example belowis 0 1 2 3 4 4 0 1 2 3 3 4 0 1 2 2 3 4 0 1 1 2 3 4 0The receiver with 5 channels adopts the following sequence0 1 2 3 4 01 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4Thismap construction gave us the worst possible map cases sincethemeanMTTR is always equal to theMTTR and is constantas shown in the table that is there are no differences betweenMTTR Υ (minimum of MTTR maxima) and 120583MTTR Thusthe meeting points will always have the same occurrence(MTTR = 1198732 minus119873+1 as reported in [30]) In addition nodeswill always meet once on each channel in each period (120583Nch

)In comparison with MtQS-DSrdv the MTTR of A-MOCH isslightly better we say slightly since MTTR of MtQS-DSrdvhappens to be maximum in 4 cases (usually 2 cases) whereasfor A-MOCH for every shift Of course as a consequencethe mean (120583MTTR) of A-MOCH is significantly worse than ofMtQS-DSrdv

As mentioned above the table shows the worst cases ofMTTR If we select other sequences we can improve theMTTR for example with 5 available channels and the senderadopting the following sequence 0 1 2 3 4 1 2 0 4 3

0

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0 1 2 3 4 5 6 7 8Cumulative RDV amount in one period


Channel 1Channel 2

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Figure 17 DSMMAC [13] the combination of maps with 2 and 8channels (73 slots)

2 3 4 0 1 3 4 1 2 0 4 0 3 1 2 and the receiver withthe sequence4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 34 0 1 2 3 we can improve 120583MTTR to 15 with 120590MTTR

= 54

and Υ = 8 The MTTR stays 21 but it occurs 10 timesThe reader should note that 120583Nch can never be changed

(independently of chosen sequence) and remains always oneRDVon each channel in a period which diminishes the RDVchances of asynchronous nodes (partial overlap of a singleslot might not be sufficient to have a successful RDV)

Moreover the protocol does not work explicitly withthe heterogeneous spectrum availability since if we takethe sender map with for example 5 channels and thereceiver with for example 8 channels then there is no RDVguarantee even in a larger period where there are eight shiftswith no matchesTherefore the only possible option is to usethe map with 8 channels that is also hopping on unavailablechannels For instance if the 120581 = 5 but 119903 = 8 then theMTTR of A-MOCH equals 60 (occurring 32 times) with120583

MTTR= 585 which is automatically worse than MtQS-

DSrdv with the combination of maps with 5 and 8 channels(5ndash8 in Table 3)

If we take 120581 = 2 and 119903 = 8 for A-MOCH then we obtainMTTR = 63 (56 times)with120583MTTR

= 623 which is definitelyworse than the results of MtQS-DSrdv with the combinationof maps with 2 and 8 channels (2ndash8 in Table 3)

Taking a better (aforementioned) map with 5 channelsand checking the least extreme case namely with 120581 = 4then we get MTTR = 22 with a mean of 154 The MTTRis somewhat better than that of MtQS-DSrdv but the mean issimilar However with 120581 = 3 MTTR is 23 (5 times) andmean19 which is already worse than the asymmetric channel setwith 3 and 5 channelsrsquo combination of maps of MtQS-DSrdv(3ndash5 in Table 3)

In [30] the metric Maximum Conditional TTR(MCTTR) has been defined which refers to the maximumTTR between two hopping nodes when PU traffic is presentand at least one channel is available for the two nodes


Table 4 MtQS-DSrdv maximum time-to-RDV performance of 120581

119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch

3rArr 2 4 13 (2 so) 73 32 144rArr 2 3 26 (2 so) 156 66 164rArr 3 3 22 (2 so) 124 53 165rArr 2 4 41 (2 so) 252 95 165rArr 3 4 33 (2 so) 19 66 165rArr 4 4 27 (4 so) 164 63 166rArr 2 5 64 (2 so) 41 159 176rArr 3 5 55 (8 so) 34 138 176rArr 4 5 51 (2 so) 30 118 176rArr 5 5 42 (4 so) 242 93 177rArr 2 6 89 (2 so) 577 205 177rArr 3 6 82 (2 so) 444 163 177rArr 4 6 63 (2 so) 383 139 177rArr 5 6 57 (2 so) 31 117 177rArr 6 6 53 (2 so) 268 99 178rArr 2 7 118 (2 so) 73 256 188rArr 3 7 101 (2 so) 57 214 188rArr 4 7 101 (2 so) 478 198 188rArr 5 7 93 (2 so) 397 164 188rArr 6 7 93 (2 so) 356 153 188rArr 7 7 86 (2 so) 33 149 18

Table 5 A-MOCH [30] in SCHv (119903 119899) = (2 4) (3 9) (4 16)(5 25) (6 36) (7 49) (8 64)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch

2 3 3 (4 times) 3 0 13 7 7 (9 times) 7 0 14 13 13 (16 times) 13 0 15 21 21 (25 times) 21 0 16 31 31 (36 times) 31 0 17 43 43 (43 times) 42 0 18 57 57 (57 times) 57 0 1

MCTTR of A-MOCH is at least 1198732 (119873 denotes the numberof channels) thus with 5 channels MCTTR = 25 and with8 channels MCTTR = 64 Coming back to our protocolif we know that only one channel is incumbent-free for along period of time (such information can be obtained forinstance from Radio Environmental Maps) and we cannotvisit other channels then the MCTTR will equal 119904 forexample for 5 channels 119904 = 9 for 8 channels 119904 = 15

643 Comparison with ASYNC-ETCH In Figures 18 and 19we show the cumulative channel distribution of A-ETCH [31]in a hopping period for all shifts with 5 available channelsWeremind that in A-ETCH a hopping sequence 119878

119894is composed

of 119873 frames (119873 denotes the number of available channels)where each frame is composed of a pilot slot and twosubsequences sub 119878

119894 The pilot slots of 119878

119894 collected together

are the channels appearing in sub 119878119894in the same order thus

|119878

119894| = (2119873 + 1) lowast 119873 for example with 5 channels a period

is composed of 55 slots in total since |119878119894| = (2 lowast 5 + 1) lowast

5 = 55 Figure 18 depicts the case when nodes select thesame sequence where we show the following sequence (119878

0)

0 0 1 2 3 4 0 1 2 3 4 1 0 1 2 3 4 0 1 2 3 4 2 0 12 3 4 0 1 2 3 4 3 0 1 2 3 4 0 1 2 3 4 4 0 1 2 3 4 01 2 3 4 Figure 19 depicts the case when one CR selects (119878

0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3

The average TTR (120583TTR) is reported to be (21198732+119873)(119873minus1) asymp 2119873 Hence with 119873 = 5 we have 120583TTR asymp 11 which isindeed the case but with two different maps (see Figure 19)If the pair of CRs selects the same hopping sequence RDVis guaranteed in one slot in a hopping period Using differentsequences RDV is guaranteed in119873 slots

The reader should note that this guarantee does nothappen on all channels which is clearly noticeable in thefigures With different maps there are shifts where RDVhappens on one or two channels As a consequence it mighthappen that there is indeed RDV guarantee on even 11 or 12slots of 55 slots but only on 1 2 or 3 channels which is highlyundesirable especially in the case when these channels are ofbad quality Moreover RDV on particular channels is morerandom since it depends on the shift and sequence To bemore precise there are 40 shifts where nodes meet on threechannels but they will never meet on four or five channelsin one hopping period What Figure 19 also shows is that theRDV frequency on a channel is alternating from very low(once or twice) to moderate (5 or 6 times) or to very high(10 times) with this scheme

In the case that the nodes select the same hoppingsequence (Figure 18)MTTR is 54 slots with themean value of


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d

Figure 18 A-ETCH with the same sequences (5 channels)

0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d

Figure 19 A-ETCH with the different sequences (5 channels)

32 slots An interesting observation is that in this case thereare 14 shifts in which nodes meet on all five channels in onehopping period but on the remaining shifts (40) they meetonly on 1 or 2 channels

We also compare A-ETCH in ACHv using the order ofmaps as in 119878

0and 1198781(ie 119894 = 0 1 in Algorithm 2 from [31]) in

Table 6 The rows without (lowast) stand for the case when nodesselect the same maps 119878

0(but of course for a different number

of channels119873) The rows with (lowast) show results with the same119878

1map and finally information with (lowastlowast) is about selection of

different sequences (1198781and 1198780)

One observes that having maps with a different numberof channels allow nodes to meet always on all channelsin a period However the choice of the maps is extremelyinfluential on MTTR statistics since it can be much worse

Table 6 A-ETCH in ACHv with 1198780sequence combinations for119873 =

3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch

3ndash5 8 36 (9 times) 21 9 36(lowast) 3ndash5 8 18 (20 times) 14 4 36(lowastlowast) 3ndash5 6 12 (19 times) 10 2 363ndash7 15 51 (25 times) 38 10 5(lowast) 3ndash7 15 26 (60 times) 24 3 5(lowastlowast) 3ndash7 9 24 (25 times) 175 4 55ndash7 19 79 (14 times) 44 204 3(lowast) 5ndash7 19 40 (8 times) 265 8 3(lowastlowast) 5ndash7 10 17 (48 times) 14 3 3

than that of MtQS-DSrdv (the case without star ie 1198780maps

combinations) similar to that of MtQS-DSrdv (the case with(

lowast) ie 119878

1maps combinations) and better than that ofMtQS-

DSrdv (combination of 1198781and 1198780maps)Hence the algorithm

from [31] has room for improvement especially in the casewhile nodes have the same channel view (SCHv) sinceTTR asymp2119873 is definitely not sufficient if nodes meet on one or twochannels while having much more in a set In ACHv thereis a need for a kind of avoidance of the selection of thesame sequence in order to improve TTR statistics Finally thealgorithm assumes that 119873 must be prime but it can be alsogeneralized for a nonprime119873

644 Comparison with Balanced Incomplete Block Design-Based RDV Approach In order to guarantee RDV the Bal-anced Incomplete Block Design (BIBD) (a BIBD [35] isan arrangement of 119907 distinct objects into 119887 blocks so thateach block contains exactly 119896 distinct objects each objectoccurs in exactly 119903 different blocks and every pair of distinctobject 119886

119894 119886

119895occurs together in 120582 blocks A BIBD has five

parameters 119907 119887 119903 119896 120582 so that 119887119896 = 119907119903 and 119903(119896 minus 1) =120582(119907 minus 1) While 119907 = 119887 and then 119896 = 119903 then such BIBDis called symmetric using three parameters 119907 119896 120582) featurehas been used in [29] With two available channels a BIBD of7 3 1 is used in [29] In order to have an RDV guaranteefor multiple channels all channels 119862 are divided into twogroups 1198661 = 1 2 1198622 and 1198662 = 1198622 + 1 (1198622) +

1 119862 Each group is assigned to a different BIBD statefor example BIBD of 7 3 1 has 1 1 0 1 0 0 0 Hencewe obtain 1198661 1198661 1198662 1198661 1198662 1198662 1198662 Each group is dividedinto two subgroups for example 1198661 = 11986611 11986612 and1198661 = 11986621 11986622 Afterwards each subgroup is assignedagain to a different BIBD state for example using the sameBIBD sequence 1198661 is assigned into 11986611 11986611 11986612 1198661111986612 11986612 11986612 and 1198662 into 11986621 11986621 11986622 11986621 1198662211986622 11986622 The steps (iterations) are repeated until eachchannel has a subgroupThis algorithm is indeed very simpleand it is very easy to form an RDV sequence using forexample the same BIBD sequence However one must notethan there are also shortcomings of this scheme first it is nota problem to assign 2119904 channels where 119904 = 1 2 4 5 sincethis number of channels is easy to divide multiple times ingroups according the aforementioned algorithm However if


119899 = 3 5 6 7 some of the channels must be assigned toboth leaf groups (the final last subgroups) in order to form asymmetric BIBD satisfying intersections of all channels in allblocks (RCP using QS context) Moreover the 119888119910119888119897119890 of suchsequences increases very fast In [29] it is stated thatMTTR =119907

119894 where 119907 is the number of building blocks (slot offsets orshifts) where 119894 is the number of building iterations of thissequence and 119894 = log

2119862 (119862 number of channels) Therefore

with two channels we have MTTR = 7 for aforementionedexample of BIBD (7 3 1) with four channelsMTTR = 72 =49 with eight channels MTTR = 73 = 343 and with sixteenchannelsMTTR = 74 = 2401 MTTR is also equivalent to thesize of the whole sequence that is the size of a 119888119910119888119897119890 that iswith sixteen channels the sequence has 2401 slots

Both protocols MtQS-DSrdv and BIBD based guaranteeRDVon all channels in the period defined by the correspond-ing approach If we compare in terms of MTTR for examplethe case with available 4 channels the cycle of MtQS-DSrdvis much lower (28 instead 49 slots) and MTTR is also muchlower 18 slots with a mean of 10 slots instead of 49 slotsthe case with 8 available channels the cycle of MtQS-DSrdvis significantly lower (120 instead of 343 slots) and MTTRsignificantly lower 86 slots with a mean of 29 slots insteadof 343 slots

Analyzing BIBD approach in the case with heterogeneousspectrum availability for example with one node with 4available channels and the other with 8 available channelswe observe than nodes still meet on four channels of the firstnode with MTTR equal to 172 slots whereas with MtQS-DSrdv we have MTTR of 51 slots with a mean of 29 slotswhich is significantly better than the BIBD approach

7 Conclusion and Future Work

In this work we evaluated a torus-QS- and DS-based ren-dezvous protocol while having symmetric and asymmetricchannel views We showed that the heterogeneous spectrumavailability does not decrease the performance of our RDVprotocol since nodes either can still meet on all availablecommon channels in each period or they meet multipletimes on the visited common channels MTTR is boundedand usually being smaller than half of a larger period Wehave also shown that our algorithm is more efficient andmore stable in comparison with the related approaches Wepointed out that a small MTTR value is not sufficient if CRnodes do notmeet onmultiple channels in a sequence periodsince we cannot provide the reliable performance in CR adhoc networks due to an easier link breakage caused by theappearance of PU signals In the future work we will addressunderlying MAC protocol and will implement the proposedprotocol on a CR platform

Acknowledgments

The authors thank Professor Petri Mahonen for fruitfuldiscussions The authors thank the financial support fromDeutsche Forschungsgemeinschaft and RWTH Aachen Uni-versity through UMIC Research Centre This work hasbenefited significantly from discussions with participants of

EuropeanUnion fundedACROPOLISNetwork of Excellence(Grant ICT-257626)

References

[1] S Haykin Fundamental Issues in Cognitive Radio Edited by SHaykin SpringerLink 2007

[2] I F Akyildiz W Y Lee M C Vuran and S Mohanty ldquoNeXtgenerationdynamic spectrum accesscognitive radio wirelessnetworks a surveyrdquo Computer Networks vol 50 no 13 pp2127ndash2159 2006

[3] S Romaszko D Denkovski V Pavlovska and L GavrilovskaldquoAsynchronous rendezvous protocol for cognitive radio ad hocnetworksrdquo in Proceedings of the International Conference on AdHoc Networks (ADHOCNETS rsquo12) October 2012

[4] S Romaszko and P Mahonen ldquoQuorum systems towards anasynchronous communication in cognitive radio networksrdquoHindawi Journal of Electrical and Computer Engineering vol2012 Article ID 753541 22 pages 2012

[5] S Lang and L Mao ldquoA torus quorum protocol for distributedmutual exclusionrdquo in proceedings of the International Conferenceon Parallel and Distributed Systems (ICPADS rsquo98) December1998

[6] J M Hall Combinatorial Theory John Wiley amp Sons 1986[7] W S Luk and T T Wong ldquoTwo new quorum based algorithms

for distributed mutual exclusionrdquo in Proceedings of the 17thInternational Conference on Distributed Computing Systems(ICDCS rsquo97) pp 100ndash106 May 1997

[8] M Singhal and N G Shivaratri Advanced Concepts in Operat-ing Systems McGraw-Hill New York NY USA 1994

[9] J R Jiang Y C Tseng C S Hsu and T H Lai ldquoQuorum-basedasynchronous power-saving protocols for IEEE 802 11 ad hocnetworksrdquo in Proceedings of the IEEE International Conferenceon Parallel Processing (ICPP rsquo03) October 2003

[10] Z T Chou Y H Lin and R H Jan ldquoOptimal fully adaptivepower management protocols for asynchronous multi-hop adhoc wireless networksrdquo in Proceedings of the 11th IEEE SingaporeInternational Conference onCommunication Systems (ICCS rsquo08)pp 569ndash573 November 2008

[11] E K Lee S YOh andMGerla ldquoRandomized channel hoppingscheme for anti-jamming communicationrdquo in Proceedings of theIFIP Wireless Days (WD rsquo10) October 2010

[12] K Bian J M Park and R Chen ldquoA quorum-based frameworkfor establishing control channels in dynamic spectrum accessnetworksrdquo in Proceedings of the 15th Annual ACM InternationalConference on Mobile Computing and Networking (MobiComrsquo09) pp 25ndash36 September 2009

[13] F Hou L X Cai X Shen and J Huang ldquoAsynchronousmultichannel MAC design with difference-set-based hoppingsequencesrdquo IEEE Transactions on Vehicular Technology vol 60no 4 pp 1728ndash1739 2011

[14] S Romaszko and P Mahonen ldquoGrid-based channel mappingin cognitive radio ad hoc networksrdquo in Proceedings of the 22ndAnnual IEEE International Symposium on Personal Indoor andMobile Radio Communications (PIMRC rsquo11) September 2011

[15] S Romaszko and P Mahonen ldquoTorus quorum system anddifference setbased rendezvous in cognitive radio ad hoc net-worksrdquo in Proceedings of the International Conference on Cog-nitive Radio Oriented Wireless Networks and Communications(CrownCom rsquo12) June 2012


[16] WHu DWillkommM Abusubaih et al ldquoDynamic frequencyhopping communities for efficient IEEE 80222 operationrdquo IEEECommunications Magazine vol 45 no 5 pp 80ndash87 2007

[17] H Su andX Zhang ldquoChannel-hopping based single transceiverMAC for cognitive radio networksrdquo in Proceedings of the 42ndAnnual Conference on Information Sciences and Systems (CISSrsquo08) pp 197ndash202 March 2008

[18] L Jiao and F Y Li ldquoA single radio based channel datarate-aware parallel rendezvous MAC protocol for cognitive radionetworksrdquo in Proceedings of the IEEE 34th Conference on LocalComputer Networks (LCN rsquo09) pp 392ndash399 October 2009

[19] S Geirhofer J Z Sun L Tong and B M Sadler ldquoCognitivefrequency hopping based on interference prediction theoryand experimental resultsrdquoACMSIGMOBILEMobile Computingand Communications vol 13 pp 49ndash61 2009

[20] H Liu Z Lin X Chu and Y W Leung ldquoTaxonomy and chal-lenges of rendezvous algorithms in cognitive radio networksrdquoin Proceedings of the International Conference on ComputingNetworking and Communications (ICNC rsquo12) January2012

[21] M D Silvius F Ge A Young A B MacKenzie and C WBostian ldquoSmart radio spectrum access for first respondersrdquo inWireless Sensing nand Processing III vol 6980 of Proceedings ofthe SPIE 2008

[22] C Cormio and K R Chowdhury ldquoCommon control channeldesign for cognitive radio wireless ad hoc networks usingadaptive frequency hoppingrdquo Elsevier Ad Hoc Networks vol 8no 4 pp 430ndash438 2010

[23] C Cormio and K R Chowdhury ldquoAn adaptive multiplerendezvous control channel for cognitive radio wireless ad hocnetworksrdquo in Proceedings of the 8th IEEE International Confer-ence on Pervasive Computing and Communications Workshops(PERCOMWS rsquo10) pp 346ndash351 April 2010

[24] N C Theis R W Thomas and L A DaSilva ldquoRendezvous forcognitive radiosrdquo IEEE Transactions on Mobile Computing vol10 pp 216ndash227 2010

[25] H Liu Z Lin X Chu and Y W Leung ldquoRing-walk basedchannelhopping algorithms with guaranteed rendezvous forcognitive radio networksrdquo in Proceedings of the InternationalWorkshop on Wireless Sensor Actuator and Robot Networks(WiSARN-FALL rsquo10) in conjunction with IEEEACM CPSComChina December 2010

[26] Z Lin H Liu X Chu and Y W Leung ldquoJump-stay basedchannel-hopping algorithm with guaranteed rendezvous forcognitive radio networksrdquo in Proceedings of the IEEE Interna-tional Conference on Computer Communications (INFOCOMrsquo11) pp 2444ndash2452 April 2011

[27] CMChaoHC Tsai andK JHuang ldquoAnew channel hoppingMAC protocol for mobile ad hoc networksrdquo in Proceedings ofthe International Conference on Wireless Communications andSignal Processing (WCSP rsquo09) November 2009

[28] C M Chao and Y Z Wang ldquoA multiple rendezvous multi-channelMACprotocol for underwater sensor networksrdquo inPro-ceedings of the IEEE Wireless Communications and NetworkingConference (WCNC rsquo10) April 2010

[29] M Altamimi K Naik and X Shen ldquoParallel link rendezvousin ad hoc cognitive radio networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[30] K Bian J M Park and R Chen ldquoControl channel establish-ment in cognitive radio networks using channel hoppingrdquo IEEEJournal on Selected Areas in Communications vol 29 no 4 pp689ndash703 2011

[31] Y Zhang Q Li G Yu and B Wang ldquoETCH efficient ChannelHopping for communication rendezvous in dynamic spectrumaccess networksrdquo in Proceedings of the IEEE InternationalConference on Computer Communications (INFOCOM rsquo11) pp2471ndash2479 chn April 2011

[32] K Bian and J M Park ldquoAsynchronous channel hoppingfor establishing rendezvous in cognitive radio networksrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo11) pp 236ndash240 April 2011

[33] Y S Hsieh CW Lien andC T Chou ldquoAmulti-channel testbedfor dynamic spectrumaccess (DSA) networksrdquo inProceedings ofthe 7th ACM workshop on Wireless multimedia networking andcomputing (WMUNEP rsquo11) Miami Fla USA October 2011

[34] S Romaszko and P Mahonen ldquoQuorum-based channel allo-cation with asymmetric channel view in cognitive radio net-worksrdquo in Proceedings of the 6th ACM Performance MonitoringMeasurement and Evaluation of Heterogeneous Wireless andWired Networks Workshop (PM2HW2N rsquo11) October 2011

[35] D R Sinson Combinatorial Designs Constructions and Analy-sis Springer 2004

[36] L A DaSilva and I Guerreiro ldquoSequence-based rendezvousfor dynamic spectrum accessrdquo in Proceedings of the 3rd IEEESymposium on New Frontiers in Dynamic Spectrum AccessNetworks (DySPAN rsquo08) pp 440ndash446 October 2008

[37] Y R Kondareddy P Agrawal and K Sivalingam ldquoCognitiveradio network setup without a common control channelrdquo inProceedings of the IEEE Military Communications Conference(MILCOM rsquo08) November 2008

[38] R Zheng J C Hou and L Sha ldquoAsynchronous wakeup forad hoc networksrdquo in Proceedings of the 4th ACM InternationalSymposium on Mobile Ad Hoc Networking and Computing(MOBIHOC rsquo03) pp 35ndash45 June 2003

[39] J R Jiang Y C Tseng C S Hsu and T H Lai ldquoQuorum-basedasynchronous power-saving protocols for IEEE 80211 ad hocnetworksrdquo Mobile Networks and Applications vol 10 no 1 pp169ndash181 2005

[40] S Romaszko ldquoMaking a blind date the guaranteed rendezvousin cognitive radio ad hoc networksrdquo in Proceedings of the 18thEuropean Wireless Conference (EW rsquo12) April 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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



ChannelRendezvous (RDV)

Ch4

Ch3

Ch2

RDV

Ch1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Time (slots)

CR1

CR2CR3

PU1PU2

PU3

1 2 3 4

1 2 3 41 2 3 4

Figure 1 Rendezvous in CRNs if there is no hatched rectangle of a PU on a particular channel it means that this PU is not active on thischannel for example there is no PUrsquos activity on Channel 3 (Ch3) CR1 not being in the range of any of PUs can use all four channels CR3can sporadically use Channel 1 due to the PU1 activity there CR2 has two available channels (1 3) while the availability in Channels 2 and 4is limited to spectrum holes of PU2 and PU3 Hence CRs have an asymmetric channel occupancy knowledge In a 16 slots of long time periodCR1 user can meet CR2 user on Channel 1 in slot 0 and on Channel 3 in slot 5 However they cannot communicate on Channel 4 in slot 9nor on Channel 2 in slot 12 due to the PU2 and PU3 activities there (CR2 cannot transmit)

knowledge A RDV problem in multichannel networks refersto the ability of two or more CRs to meet each other in thesame channel

Figure 1 illustrates an example of the channel occupancyby three primary users (hatched rectangles) and three sec-ondary users (solid filled squares or rectangles) hoppingthrough four channels (Ch1 Ch4) in a 16 slots of longcycle (for the sake of simplicity we illustrate the case wheresecondary users have a common time-slot system This isdone without losing generality and in fact we have alsopresented asynchronous operations in [3]) Here by a slotwe understand some period of time within which SUs cancommunicate with each other (ie exchanging informa-tion receiving and transmitting) The situation depicted inFigure 1 is very optimistic nodes are able to meet once twiceor even three times (CR1 and CR3) However while hoppingor switching channels randomly it might happen that nodesnever meet In order to deal with the aforementioned RDV

problem we proposed in [4] the protocol which is based onthe torus quorum system (tQS) concept

Thanks to the use of the quorum system (QS) and alsothe difference set (DS) concept we are able to guaranteemeeting on all 119903 channels in the case of nodes with asymmetric channel view (SCHv) and almost on all channelsin an asymmetric channel view (ACHv) case We emphasizethat CR nodes do not need to have mutual knowledge oftheir hopping sequences information because the use ofQS properties is sufficient Thanks to the QS intersectionproperty guarantee cognitive radios will meet (intersect)when selecting quorum-based hopping sequences from thesameQS Quorums satisfying the RotationClosure Propertyguarantee the intersection even if the cycles of the CRs arenot aligned and therefore can be used in asynchronousprotocolsThe torus QS [5] exploited in this work representsan intuitive and simple method to employ where a quorumset is chosen by selecting a column of an 119903 times 119904 rectangular





2 Related Work

















0 2 36 7 8

12 13 14 15

51117

41016

19

0 1 36 7 8 912 13 14 15

51117

41016

2 0 1 36 7 8 912 13 14 15

51117

41016

2

170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16

A

A

B

B

C

C
















119894isin




119895minus1 but



119895minus2) The






forall119877

1015840 119877 isin 119876 119877


(1)




1 119886

2 119886

119896modulo 119899 for 119886





119895) where 119886

119894

119886


119894minus 119886

119895equiv 119887(mod 119899)





119894 119886

119895)






(mod 18)



0 12 3 4 5 6 70 1

1

8 9 10 11 12 13 14 15 8 916 17 18 19 20 21 22 23 16 17

2 3 4 5 6 70 1

8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23

7

15

23

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

A B

A

B

1198621 1198622 1198621 11986221198623 1198624 1198625 1198626 1198627 1198628 1198621 1198622 1198623 1198624 1198625 1198626 1198627 11986281198628














119896


4 System Model












119903


119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)





0 1 2




(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)




TX






119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623





1198621 1198623 11986231198622





119894 119886






6 Verification



9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

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r of R

DV

on a

chan

nel i

n a p

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60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

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DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













2 Related Work

















0 2 36 7 8

12 13 14 15

51117

41016

19

0 1 36 7 8 912 13 14 15

51117

41016

2 0 1 36 7 8 912 13 14 15

51117

41016

2

170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16

A

A

B

B

C

C
















119894isin




119895minus1 but



119895minus2) The






forall119877

1015840 119877 isin 119876 119877


(1)




1 119886

2 119886

119896modulo 119899 for 119886





119895) where 119886

119894

119886


119894minus 119886

119895equiv 119887(mod 119899)





119894 119886

119895)






(mod 18)



0 12 3 4 5 6 70 1

1

8 9 10 11 12 13 14 15 8 916 17 18 19 20 21 22 23 16 17

2 3 4 5 6 70 1

8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23

7

15

23

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

A B

A

B

1198621 1198622 1198621 11986221198623 1198624 1198625 1198626 1198627 1198628 1198621 1198622 1198623 1198624 1198625 1198626 1198627 11986281198628














119896


4 System Model












119903


119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)





0 1 2




(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)




TX






119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623





1198621 1198623 11986231198622





119894 119886






6 Verification



9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

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DV

on a

chan

nel i

n a p

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0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

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r of R

DV

on a

chan

nel i

n a p

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60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

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r of R

DV

on a

chan

nel i

n a p

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d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 36 7 8

12 13 14 15

51117

41016

19

0 1 36 7 8 912 13 14 15

51117

41016

2 0 1 36 7 8 912 13 14 15

51117

41016

2

170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16170 1 3 4 5 7 8 10 11 13 14 15962 12 16

A

A

B

B

C

C
















119894isin




119895minus1 but



119895minus2) The






forall119877

1015840 119877 isin 119876 119877


(1)




1 119886

2 119886

119896modulo 119899 for 119886





119895) where 119886

119894

119886


119894minus 119886

119895equiv 119887(mod 119899)





119894 119886

119895)






(mod 18)



0 12 3 4 5 6 70 1

1

8 9 10 11 12 13 14 15 8 916 17 18 19 20 21 22 23 16 17

2 3 4 5 6 70 1

8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23

7

15

23

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

A B

A

B

1198621 1198622 1198621 11986221198623 1198624 1198625 1198626 1198627 1198628 1198621 1198622 1198623 1198624 1198625 1198626 1198627 11986281198628














119896


4 System Model












119903


119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)





0 1 2




(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)




TX






119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623





1198621 1198623 11986231198622





119894 119886






6 Verification



9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

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d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

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DV

on a

chan

nel i

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d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 12 3 4 5 6 70 1

1

8 9 10 11 12 13 14 15 8 916 17 18 19 20 21 22 23 16 17

2 3 4 5 6 70 1

8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 23

7

15

23

0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

A B

A

B

1198621 1198622 1198621 11986221198623 1198624 1198625 1198626 1198627 1198628 1198621 1198622 1198623 1198624 1198625 1198626 1198627 11986281198628














119896


4 System Model












119903


119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)





0 1 2




(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)




TX






119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623





1198621 1198623 11986231198622





119894 119886






6 Verification



9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119903


119904

(1)

Step

(3)Step

Step

Step

Step

Step

Step

Step

Step

Step

(2)





0 1 2




(2a1)

(2a2)

(2a3)

(2a4)

(2b)

(2c)




TX






119899 minus 1

119899 minus 1

119904minus 1

1198621 11986221198624 1198623





1198621 1198623 11986231198622





119894 119886






6 Verification



9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










9 10 11 12 13 14 15 16 1718 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 34 3536 37 38 39 40 41 42 43 44

10 2 3 4 5 6 7 8 1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 90

45

0 1 2 3 4 5 6 7 8 9

10

11 12 13 25242322212019181716151426

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 141312111098765432115 292827262524232221201918171630 444342414039383736353433323145 595857565554535251504948474660 747372717069686766656463626175 898887868584838281807978777690 104103102101100999897969594939291

105 119118117116115114113112111110109108107106

0 1 23 4 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 67 8 9 10 11 12 13

14 15 16 17 18 19 2021 22 23 24 25 26 27

Ch1

Ch2

Ch2

Ch3

Ch3

Ch4

Ch4

Ch5

Ch6

Ch7

ChR

Torus QSs




C1




C2 C3C1 C2 C3 C4 C5

C1 C2 C3 C4 C5 C6 C7

Difference sets







119894cap1198772






1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

1011 12 13 14 15 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 3233 34 35 36 37 38 39 40 41 42 4344 46 47 48 49 50 51 52 53 5455 56 57 58 59 60 61 62 63 64 65

0 1 2 3 4 5 6 7 8 9

45

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6




Map6Chs







119903 Υ MTTR 120583

MTTR120583

TTR120583

119873ch

2 1 4 (2 so) 3 15 123 4 9 (2 so) 57 25 144 3 18 (2 so) 103 35 165 4 21 (2 so) 126 45 166 5 35 (4 so) 206 55 177 6 47 (2 so) 236 65 178

119872(1) 7 86 (2 so) 29 75 188

119872(2) 7 57 (2 so) 30 75 18











119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















119894cap 1198772

119895= 0









119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119860ndash119861 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch







MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










MtQS-DSrdvA1 1234


R1R1

R1

R1

R1

R1R1

R1

R1 R1R1 R1

R1

R1R1

R1R1R1

R1

R1R1

R1R1

R1

R1

R1R1

R1R1

R1

R1R1

R1R1

R1R1R1R1

R1R1

R1

R1R1

R1

R1R1

R1

R1

R1

R1R1

R1

R1 R1

R1R1 R1

R1 R1R1

R1

R1R1

R1R1 R1

R1

R1 R1 R1R1

R1

R1

R1R1

R1

R1R1

R1

R1R1R1 R1

R1R1

R1R1R1 R1

R1R1

R1R1R1

R1R1R1

R1R1R1

R1

R1

R1 R1 R2 R2 R2 R2R1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6 7 8 9 10 11 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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

MtQS-DSrdv4 4 4 4 4 4 4 4 4 4 4 4


0

5

10

15

20



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



0

2

4

6

8

10

12

14

0 1 2 3 4 5




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d





5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5045

3530

40

25201510

50

0 1 2 3 4 5 6



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30



Channel 1Channel 2

Channel 3Channel 4

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




60

50

40

30

20

10

00 1 2 3 4 5 6 7



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d




0

5

10

15

20

25

30

35




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d






0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40

50

60

70

80




Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio






0

10

20

30

40

50

60

70

80





Channel 7Channel 8

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d









40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










40

35

30

25

20

15

10

5

00 2 4 6 8 10 12

Channel 1Channel 2



Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d







0

5

10

15

20

25

30

35



Channel 1Channel 2

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d



= 54












119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119903 rArr 120581 Υ MTTR 120583

MTTR120590

MTTR120583

119873ch



Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




119894is composed





|119878




0)


0)

and another (1198781) 0 0 2 4 1 3 0 2 4 1 3 2 0 2 4 1 3 0

2 4 1 3 4 0 2 4 1 3 0 2 4 1 3 1 0 2 4 1 3 0 2 4 1 33 0 2 4 1 3 0 2 4 1 3





0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d


0

5

10

15

20

25

30




Channel 4Channel 5

Cum

ulat

ive n

umbe

r of R

DV

on a

chan

nel i

n a p

erio

d












3 5 7 (119903 119899) = (3 21) (5 55) (7 105)

Υ MTTR 120583

MTTR120590

MTTR120583

119873ch




lowast) ie 119878





119894 119886













Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Acknowledgments



References












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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