PAPER Optimization of Learning Time for Learning-Assisted Rendezvous Channel in Cognitive Radio System

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1 360 IEICE TRANS. COMMUN., VOL.E98 B, NO.2 FEBRUARY 2015 PAPER Optmzaton of Learnng Tme for Learnng-Asssted Rendezvous Channel n Cogntve Rado System Osamu TAKYU a), Member, Takayuk YAMAKITA, Student Member, Takeo FUJII, Ma OHTA, Members, Fumhto SASAMORI, Senor Member, and Shro HANDA, Member SUMMARY Ths paper derves the optmal learnng tme for the learnng-asssted rendezvous channel. One problem wth the dynamc spectrum access system of cogntve rado s access channel msmatch between two wreless termnals. In the learnng-asssted rendezvous channel, before exchangng packets for lnk connecton, the rate of channel occupancy by the other system s estmated wthn the learnng tme; t s referred to as the channel occupancy rate (COR). Hgh speed packet exchange s made possble by selectng a low COR channel. However, the optmal learnng tme and the mpact of COR estmaton errors have not been clarfed yet. Ths paper analyzes the tme to rendezvous channel (TTR), where TTR s the tme needed to complete the rendezvous wth a certan probablty. The results ndcate that the learnng tme and TTR have a concave relatonshp whch means that the optmal learnng tme can be determned. key words: cogntve rado, rendezvous channel, Channel Occupancy Rate (COR) 1. Introducton The problem of frequency spectrum exhauston has become a much more serous problem but cogntve rado (CR) s a powerful soluton. CR s aware of the wreless communcaton envronment and then adjusts the wreless communcaton parameters for explotng the frequency spectrum [1]. The CR can be categorzed nto two: heterogeneous type and spectrum sharng one [2]. In heterogeneous type, the user selects the exstng wreless communcaton systems n accordance wth the acheved user throughput and the requred communcaton qualty. In spectrum sharng type, the CR bundles or selects the vacant partal frequency bands and tme slots. Ths paper pays attenton to the spectrum sharng type of CR. In the spectrum sharng type of CR, there are two systems, prmary system (PS) and secondary system (SS). PS has the prorty to access the frequency spectrum and SS can access t whle the PS does not use t, where the temporal vacant of frequency spectrum wthout PS access s whte space [3]. Snce the whte spaces appear over varous channels and Manuscrpt receved August 31, The authors are wth the Department of Electrcal & Electronc Engneerng, Shnshu Unversty, Nagano-sh, Japan. The author s wth Advanced Wreless Communcaton Research Center (AWCC), The Unversty of Electro- Communcatons, Chofu-sh, Japan. The author s wth the Department of Electroncs Engneerng and Computer Scence, Fukuoka Unversty, Fukuoka-sh, Japan. a) E-mal: takyu@shnshu-u.ac.jp DOI: /transcom.E98.B.360 tme slots, the SS explots the whte space by changng the accessng channel n each tme slot. Therefore, the spectrum sharng type of CR s a dynamc spectrum access (DSA) system [4]. In DSA systems, when the wreless termnal (master) attempts to establsh a new communcaton lnk, the other termnal (slave) may not catch the sgnal from the master due to access channel msmatch [5]. The rendezvous channel scheme can be used to elmnate ths msmatch. The rendezvous channel scheme s the ntal connecton protocol for fndng one another n multple frequency channels [5]. Varous knds of rendezvous channel schemes have been consdered so far. There are manly two types: Centralzed type and Dstrbuted one. In centralzed type, the central controller, such as base staton, nforms all the termnals about the channel number for rendezvous channel [6]. In dstrbuted type, the master and the slave exchange the control sgnal for rendezvous channel [5]. The dstrbuted type does not need the other accessng channel to the central controller and has the easy mplementaton owng to the low dependency to the other system. The dstrbuted type s categorzed nto sngle rendezvous and parallel one [7]. In sngle rendezvous, the steady tme perod [5], [8], the steady frequency channel [5], [8], and the steady hoppng pattern [9], [10] are used for the rendezvous channel. If the steady resources for rendezvous channel are used by PS, the constructon of rendezvous channel s dffcult. Snce the steady resources are exclusve use for rendezvous channel, the sngle rendezvous channel suffers from the low effcency of frequency spectrum [5]. In the parallel rendezvous, the plural resources for the rendezvous channel are adaptvely selected. In [11], the termnal constructs the hoppng sequence, ndependently and nforms each other termnal about ts own hoppng sequence. However, the sgnalng overhead requred for nformng s huge. Reference [12] [14] constructs the flexble hoppng sequence by removng the channel numbers where the PS s access s sensed. However, Refs. [12] [14] does not obvously show the rule for excludng the channel number. The CR explots the frequency channel durng the temporal vacant perod of PS. Even f the carrer sensng detects the PS s access, the SS could wat the next vacant perod. As a result, t s possble for SS to have the opportunty to use the channel. However, Refs. [12] [14] does not consder ths possblty. In Ref. [15], before exchangng the control packet for rendezvous channel, a sensng perod s set to recognze the Copyrght c 2015 The Insttute of Electroncs, Informaton and Communcaton Engneers

2 TAKYU et al.: OPTIMIZATION OF LEARNING TIME FOR RENDEZVOUS CHANNEL 361 PS s average accessng rate, where the PS s average accessng rate s the channel occupancy rate (COR). The hoppng sequence s then modfed to access the channel of the low COR. Snce SS has a large enough sensor range, a common vew of the COR s easly obtaned by the SS. The resultng hoppng sequence provdes a lot of meetng tmes between master and slave and thus acheves a hgh speed rendezvous channel. The addtonal mert of ths technque s the realzaton of hgh throughput performance due to the many access opportuntes. Therefore, the scheme of rendezvous n Ref. [15] may be sutable for the spectrum sharng type of the CR but ts avalablty s only shown by computer smulaton under a smplfed system model. The optmal tme, n terms of mnmzng the tme to rendezvous, taken to estmate the COR has not been derved yet. Ths paper derves the optmal learnng tme for creatng hgh speed rendezvous channels. In the scheme of Ref. [15], the sensng perod s referred to as the learnng tme. Increasng the learnng tme ncreases the accuracy wth whch the low COR channel can be determned. Snce usng a low COR channel gves the SS more opportuntes to access the channel, the PS s quescent more often and thus the tme to exchange the packets for lnk connecton s reduced. We determne the optmal learnng tme for mnmzng the tme to rendezvous channel (TTR), where TTR ncludes the tme to exchange the packets between the master and the slave, unlke Ref. [15]. Our analyss confrms that selectng a low COR channel yelds hgh speed packet exchange. Ths s a heretofore unknown advantage of [15] s rendezvous scheme. Ths paper also assumes that actual sensng technques wll have some detecton errors. We clarfy the mpact of the msdetecton to the rendezvous channel. Ths paper s constructed as follows. Secton 2 descrbes the wreless communcaton system consdered here. Secton 3 detals the learnng-asssted rendezvous channel. Secton 4 derves TTR by a theoretcal analyss. In Sect. 5, numercal results are shown and our concluson s gven n Sect Overvew of Wreless Communcaton System Fgures 1(a) and (b) show the feld and tme envronments of the wreless communcaton system assumed here, respectvely. In ths envronment, there are three types of wreless termnals, the frst one belongs to the PS and s actve ntermttently, the second and thrd belong to the SS, where the second termnal has just joned ths wreless communcaton system and tres to construct the wreless communcaton lnk to the thrd termnal, where the second and thrd termnals are referred to as master and slave, respectvely. Ths paper consders the rendezvous channel between master and slave. Fgure 1(b) shows the status of PS access rate for each channel. In the wreless communcaton system assumed here, a tme slot s defned as the mnmum tme duraton and the slot-by-slot synchronzaton among all termnals s assumed to be deal. The PS decdes to access a channel Fg. 1 Wreless communcaton envronment. n each slot, ndependently. The channel access decson s consdered to be a stochastc process. The rate at whch the PS accesses the th channel s ρ,whereρ s referred to as the deal COR. The master and the slave detect PS actvty by carrer sensng. Ths paper assumes that carrer sensng s realzed by energy detecton [16]. In carrer sensng, there are two types of error, false alarm and msdetecton. To smplfy the analyss, we assume the decson threshold s set so hgh that the false alarm rate s neglgble [16]. The sensng result of each slot s recorded n the master and the slave n a frst-n frst-out (FIFO) memory. If the memory becomes full, the oldest result s popped to allow the latest one to be pushed. From the memory entres, each termnal calculates the COR for each channel. Each channel has one memory. To avod PS/SS collson, SS confrms PS quescence before attemptng channel access. Therefore, SS must be a carrer sense multple access system. 3. Learnng-Asssted Rendezvous Channel 3.1 Measurement Method of COR The carrer sensng process places a one bt result, occuped or vacant, n the memory for each channel. Therefore, the COR of a channel s calculated by each termnal as the total number of occuped results normalzed by the total number of results n that channel s memory. The master and the slave swtch between channels so as to evaluate the CORs of all channels. Fgure 2(a) shows the mage of COR measurement for each channel. Ths technque s referred to as the unform measurement because the connecton probabltes of each channel are equal. Fgure 2(b) shows the mage of learnng measurements. At the commencement of learnng measurement, the connecton probabltes to each channel

3 362 IEICE TRANS. COMMUN., VOL.E98 B, NO.2 FEBRUARY 2015 Fg. 2 COR measurement method. are equal and the CORs n all channels are roughly estmated durng one frame tme perod. As a result, the channel wth mnmum COR s found, where t s referred to as the superor channel. Ths s because t gves the more opportuntes to fnd the vacant of the channel and thus t s more sutable for the rendezvous channel than any other channel. The COR of the superor channel, ρ mn,sdefnedas ρ mn = mn ρ j, (1) j 1,2,...,N where N s the number of channels and ρ j s the estmated COR of the jth channel. The learnng measurement sets the larger connecton probablty to the superor channel than that to the other channel. The connecton probablty to the th channel s derved as { α, ρ = ρ mn 1 α, (2) N 1 ρ ρ mn where α s the prorty factor (0 α 1). As α becomes large, the connecton probablty to the superor channel becomes hgh. For example, n N = 3andα = 0.7, the connecton probabltes of the superor channel and the other channel are 70% and 15%, respectvely. Swtchng from unform measurement to learnng measurement s possble by controllng α. Ifα = 1/N, the measurement scheme becomes unform measurement, otherwse t s learnng measurement. The connecton probabltes are updated by the past estmated COR every frame tme perod. 3.2 Rendezvous Process We consder the stuaton n whch the master jons the wreless communcaton system and tres to establsh a lnk connecton to the slave. The handshakng type of rendezvous channel s used [5]. The master sends the request sgnal to the slave. If the slave successfully receves t, t sends the reply packet to the master. If the master successfully receve t, the rendezvous channel s completed. Therefore, the handshakng type of rendezvous channel s establshed by the packet exchange between the master and the slave. Snce the master has no pror nformaton of each channel s COR, ts COR memores are null before startng COR estmaton. We assume that the slave has full COR memory. In the learnng-asssted rendezvous channel, the master uses the unform measurement, whereas the slave uses learnng measurement as determned by the connecton probablty to each channel. Before sendng ts request packet, the master needs some tme to estmate COR. Ths s the learnng tme. After the learnng tme, the master selects the superor channel for sendng the request packet. Before sendng the request packet, carrer sensng s used to confrm PS quescence. Ths paper assumes that carrer sensng and packet transmsson take one slot to perform. When the slave receves the packet from the master, t also confrms PS quescence before sendng the reply packet to the master. If the slave s connected to a dfferent channel, t fals to receve the request packet. The master dscovers ths falure from the absence of a reply packet. After the confrmaton of falure to receve, the master sends the request packet agan. If PS occupes the channel after the master sends the request packet, the slave has to wat to send the reply packet. Snce the master also detects the PS s accessng, t also recognzes that the slave ntends to wat to send ts reply packet. Ths paper consders that the tme to rendezvous channel (TTR) ncludes the tme needed to confrm falure to receve reply packet. Once the master selects the superor channel, t contnues to use the same channel for subsequent attempts. One opton s to change the selected channel for subsequent connecton attempts. Ths paper consders an mportant future task s to determne the desrablty of swtchng the selected channel after falure to connect. 3.3 Impact of Msdetecton In carrer sensng, msdetecton trggers COR msunderstandng and collson between PS accessng sgnal and the request and reply packets. Collson causes the mss recepton of the packet, where the mss recepton of the packet means that not only the slave does not receve the request packet from the master, but also the master does not receve the reply packet from the slave. To compensate the mss recepton of the packet, retransmsson s necessary. As a result, TTR becomes large. Note that ths paper gnores false alarms; f the channel s vacant, the termnal surely sends the packet to the partner. 4. Theoretcal Analyss of TTR 4.1 Selecton Probablty of Mnmum COR s Channel The COR of th channel s defned as ρ = k /l, (3) where l and k are the number of slots taken for estmatng the COR of the th channel and the number of slots occuped by PS n the th channel, respectvely. From the defnton, the real COR of th channel, ρ, s derved as ρ = lm ρ l. (4) The real COR s equal to the average PS s accessng probablty n a slot. When the PS s access s modeled as the

4 TAKYU et al.: OPTIMIZATION OF LEARNING TIME FOR RENDEZVOUS CHANNEL 363 random varable, the recognton of PS s access by the master or the slave s also the random varable. Therefore, the probablty that the master or the slave recognzes the occupancy of the th channel by PS s access n the slot, ˆρ,s ˆρ = ρ (1 ε), (5) where ε s the mss detecton probablty of carrer sensng (0 ε 1). The mss detecton probablty depends on the locaton of PS and the channel propagaton between sensor and PS. For smple analyss, ths paper assumes the accuracy of carrer sensng s unform and thus the mss detecton probablty of carrer sensng s also unform for all the channels. Note that ths paper assumes the false alarm s gnored. Therefore, t does not occur that the sensor decdes the occupancy of the channel even n no PS s accessng. Snce the ρ defned by Eq. (3) s composed of some decson results of PS s access, t s stochastc process. Therefore, the occurrence probablty of ρ, f (ˆρ, l, k ), s defned as f (ˆρ, l, k ) = l C k ˆρ k (1 ˆρ ) l k, (6) where a C b s the number of combnaton patterns possble n selectng b from a. Ths paper assumes the tme for estmatng each channel s COR s unform. Therefore, l = l 1 = l 2 =...= l N. In the proposed learnng asssted rendezvous channel, the channel of the smaller COR s more superor for rendezvous channel and that of the smallest COR among all the channels s the superor channel. When the estmated COR of the th channel s smaller than that of jth channel, the master or the slave selects the th channel as the more superor channel. If the former s as large as the latter, t decdes the th channel as the more superor channel by flppng con. Therefore, the probablty that the master or the slave chooses the th channel as the more superor channel than the jth channel s l l g, j (l) = f (ˆρ, l, k ) f (ˆρ j, l, k j ) k =0 k j =k { f (ˆρ, l, k )} 2. (7) Therefore, the probablty that the master or the slave chooses the th channel as the more superor channel than any other channel, that s a superor channel, s N g (l) = g, j (l). (8) j=1, j The normalzed probablty that the master or the slave chooses the th channel as the superor channel from the learnng tme of l slots s N G (l) = g (l)/ g j (l). (9) j=1 4.2 Tme to Exchange the Request Packet and the Reply Packet In the packet exchange of the rendezvous channel, after the master emts the request packet, t hears the request packet. If the request packet s receved, the rendezvous channel s completed, otherwse the master emts the request packet, agan. In ths secton, the consecutve protocol of emttng the request packet and hearng the reply packet s defned as a one tral th Tral We consder that the master selects the th channel as the superor channel for sendng the request packet. We also consder that the master must wat for m 0 slots (m 0 = 0, 1,...) untl the PS releases the th channel. After m 0 slots, the probablty that the master can transmt the request packet through the th channel s h (m 0 ) = (1 ˆρ )ˆρ m 0 1. (10) Smlarly, after the slave must wat for n 0, (n 0 = 0, 1,...) slots, the probablty that the slave obtans the opportunty of transmttng the reply packet n the th channel s I (n 0 ) = (1 ˆρ )ˆρ n 0 1. (11) From Eqs. (10) and (11), the probablty that t takes m 0 + n 0 slots to exchange them, J (m 0, n 0 ), s J (m 0, n 0 ) = (1 ˆρ ) 2 ˆρ m 0+n 0 2. (12) We derve the probablty of avodng the collson between the PS s access and the request packet or the reply packet. We consder the two events. Event A: The master or the slave decdes that the channel s vacant. Event B: The channel s truly vacancy because of no PS s access. The probablty of Event B under the Event A s that of avodng the collson between the PS s access and the request packet or the reply one. Ths s the condtonal probablty P(B A) and s defned as P(B, A) P(B A) = P(A), (13) where P(B, A) andp(a) are the jont probablty of Events B and A, and the probablty of Event A, respectvely. We can consder Event A s the sum event between the followng two events. In frst event, when the PS s accessng to the channel, the master or the slave decdes that t s vacant due to the msdetecton. In second event, when the PS s not accessng to the channel, t does. Note that we assume the false alarm s gnored. When PS s not accessng to the channel, the master or the slave can perfectly detect that the channel s vacant. Therefore, the probablty of Event A to the th channel, P (A) s P (A) = ρ ε + (1 ρ ). (14) In addton, snce Event A ncludes Event B, B A, P (B, A) = P (B) = 1 ρ [17]. Therefore, the probablty of avodng the collson between PS and the request packet or the reply packet n the th channel s

5 364 IEICE TRANS. COMMUN., VOL.E98 B, NO.2 FEBRUARY ρ P (B A) = ρ ε + (1 ρ ) = 1 ρ. (15) 1 ˆρ Next, when the master and the slave decde the th channel and the jth one as superor channels, respectvely, the successful probablty of exchangng the request and reply packets between the master and the slave, V(, j), s derved from Eq. (2) as α ( ) 1 ρ 2 1 ˆρ V(, j) = = αβ, j = ( 1 α 1 ρ ) 2 (16) N 1 1 ˆρ = 1 α N 1 β, j ( ) 2 1 ρ β =. (17) 1 ˆρ Therefore, n 0th tral, the probablty of completng the packet exchange wthn m 0 + n 0 slots, K, j (0, m 0, n 0 ), s K, j (0, m 0, n 0 ) = J, j (m 0, n 0 )V(, j) = (1 ˆρ ) 2 ˆρ m 0+n 0 2 V(, j). (18) When the total slots for the packet exchange are p 0 (= m 0 + n 0 = 2, 3,...), the number of combnatons of m 0, n 0 for satsfyng p 0 = m 0 + n 0 s p0 1C 1. Therefore, K, j (0, m 0, n 0 ) s reformed as K, j (0, p 0 ) = p0 1C 1 (1 ˆρ ) 2 ˆρ p 0 2 V(, j). (19) st Tral In the 1st tral, we assume that t takes m 1 slots and n 1 slots to send the request packet to the slave and the reply packet to the master, respectvely. The cumulatve requred slots for completng the packet exchange n the 1st tral s r = p 0 + p 1 = m 0 + n 0 + m 1 + n 1. Therefore, the probablty of completng the packet exchange wthn r slots, K, j (1, r), s derved as follows. K, j (1, r) = p0 +p 1 1C 3 J, j (p 0 ){1 V(, j)} J, j (p 1 )V(, j) = r 1 C 3 (1 ˆρ ) 4 ˆρ r 4 V(, j){1 V(, j)}. (20) S th Tral Smlarly, we can derve the probablty of successfully completng the exchange of the request packet and the reply one, when the master and the slave fal to exchange the packet n S 1 attempts but do so at the S th attempt, where S = 0, 1,... The total number of tme slots, r, sdefnedas follows. r = S p s = s=0 S (m s + n s ), (21) s=0 where m s and n s are the number of slots for sendng the request packet and the reply packet at the sth attempt, respectvely. The number of combnatons of m 0, n 0,...,m S, n S s r 1C 2S +1. Therefore, we derve the probablty of completng the packet exchangng wthn r slots, K, j (S, r), as K, j (S, r) = (1 ˆρ ) 2(S +1) r 2(S +1) ˆρ V(, j) {1 V(, j)} S r 1C 2S +1. (22) In = j, we can rewrte K, j (S, r)as P (S, r) = (1 ˆρ ) 2(S +1) r 2(S +1) ˆρ αβ (1 αβ ) S r 1C 2S +1. (23) Smlarly, n j, we can rewrte K, j (S, r)as Q (S, r) = (1 ˆρ ) 2(S +1) r 2(S +1) ˆρ 1 α N 1 β ( 1 1 α N 1 β ) S r 1C 2S +1. (24) 4.3 Success Probablty of Rendezvous Channel If the master and the slave select the same channel as the superor channel, the probablty of successfully exchangng packets s Eq. (23). Each tral needs at least two slots. Therefore, when the total slots for completng the packet exchange are u = (2, 3,...), the maxmal number of trals s u/2 1, where s the floor functon. The probablty of completng the packet exchange wthn u slots n the th channel, C (u), s C (u) = u r=2 r/2 1 S =0 P (S, r). (25) Smlarly, f the master and the slave select dfferent superor channels, the probablty of successfully exchangng packets s gven by Eq. (24). Therefore, the probablty of successfully completng packet exchange wthn u slots n the th channel, D (u), s D (u) = u r=2 r/2 1 S =0 Q (S, r). (26) We assume that the slave has been actve long enough to have flled ts COR memores before the master starts estmatng COR. In addton, for smplcty, we assume that COR remans constant. Therefore, the probablty that the slave consders the th channel as the superor channel s gvenbyeq.(9)wthl = M, wherem s memory sze for each channel. If the master and the slave decde the th channel as the superor channel, the probablty of completng the packet exchange wthn u slots s C (u)g (l)g (M), (27) where l s the tme for estmatng the COR per one channel and thus ln s referred to as Learnng tme. If the master decdes the th channel as the superor channel but the slave decdes the other channel as t, the probablty of completng the packet exchange wthn u slots

6 TAKYU et al.: OPTIMIZATION OF LEARNING TIME FOR RENDEZVOUS CHANNEL 365 s D (u)g (l) (1 G (M)). (28) When we take the probabltes of the packet exchange for all the channels, fnally, the probablty of completng the packet exchange, n other words the probablty of successfully establshng the rendezvous channel, wthn u slots s Table 1 Channel model. Name Number of COR for Each Channel Channels N Case 1 3 ρ 1 = 0.2,ρ 2 = 0.6,ρ 3 = 0.8 Case 2 3 ρ 1 = 0.7,ρ 2 = 0.8,ρ 3 = 0.9 Case 3 3 ρ 1 = 0.1,ρ 2 = 0.2,ρ 3 = 0.3 Case 4 3 Random Model of Unform Dstrbuton ρ = Case 5 8 Random Model of Unform Dstrbuton ρ = R(u) = N [C (u)g (l)g (M) =1 + D (u)g (l) {1 G (M)}]. (29) 5. Numercal Results Table 1 shows the channel model, where the numbers of channels, N, are3forcases1,2,3,4and8forcase5, respectvely. In Cases 1, 2, and 3, the COR of each channel s fxed. Snce the COR of the 1st channel s mnmum, the 1st channel s consdered as the superor channel. In Cases 2 and 3, the dfferences n CORs between 1st and 2nd channels and between 2nd and 3rd ones are both 0.1. The CORs of Case 2 are much larger than those of Case 3. In Cases 4 and 5, for confrmng the effect of the constructed rendezvous channel scheme n varous channel model, the COR of each channel follows an ndependent unform dstrbuton wth range of [0.0,0.8]. The msdetecton probabltes, ε, are 0.0 and 0.1 for all fgures except Fg. 8. The prorty factor, α, s 0.7 for all fgures except Fgs. 5 and 6. Memory sze, M, s 50 slots. 5.1 TTR n Fxed COR Channel Envronment Ideal Carrer Sensng Fgure 3 shows the learnng tme versus the TTR, where TTR s defned as the tme, u, taken to satsfy R(u) = 0.99 n Eq. (29) plus the learnng tme. Therefore, TTR means the tme taken to successfully establsh the rendezvous channel n 99% of all attempts. The channel models are Cases 1 to 3. From ths fgure, n Cases 1 and 2, the performance exhbts a concave tendency. As the learnng tme becomes large, the accuracy of COR estmaton s mproved and thus the hgh speed exchange of request and reply packets through the superor channel s acheved. However, as the learnng tme ncreases further, t, rather than packet exchange, becomes the domnant component of TTR. When the learnng tme exceeds a certan value, TTR ncreases. Wth ε = 0.0, the mnmum TTRs are acheved for Cases 1 and 2 when the learnng tmes are 38 and 80 slots, respectvely. To clarfy the reason for ths, Fg. 4 shows the mpact of learnng tme on the selecton probablty for each channel. In Case 1, when the learnng tme s 38 slots, the selecton probabltes of ρ = 0.8 andρ = 0.6 channels are approxmately 0.0 and , respectvely. Therefore, n Case 1, the superor channel s certanly selected and a hgh Fg. 3 Impact of learnng tme on TTR n Cases 1 to 3. speed rendezvous channel s thus formed. In Case 2, when the learnng tme s 60 slots, the selecton probabltes of ρ = 0.9 channel s However, that of ρ = 0.8 s Snce the dfference n COR between ρ = 0.8 and ρ = 0.7 s not so large, the channels cannot be dstngushed by the roughly estmated COR. In addton, TTR s not sgnfcantly reduced because of the slght dfference n COR between the superor channel and ρ = 0.8 channel. In Case 2, the worst channel s excluded by COR estmaton and then the master starts packet exchange through the superor channel or the second superor channel. Ths s a sutable strategy for formng the hgh speed rendezvous channel. In Case 3, Fg. 3 shows TTR s smallest wth 0 learnng tme. There are a lot of access opportuntes for any channel n Case 3, so the packets are quckly exchanged. In addton, as ndcated, the dfference n COR between the superor channel and the others s so small that the superor channel cannot be dstngushed from the others by the roughly estmated COR. To form the hgh speed rendezvous channel, the zero learnng tme strategy s sutable Carrer Sensng wth Msdetecton Event In cases 1 and 2 of Fg. 3, the optmal learnng tmes wth ε = 0.1 are larger than that wth ε = 0.0. From Fg. 4, when msdetecton may occur, the requred tme for selectng the superor channel at the certan probablty becomes large. In other words, the degradaton of selecton probablty to the superor channel can be compensated by enlargng the learnng tme. However, n Case 2, when ε becomes large, the

7 366 IEICE TRANS. COMMUN., VOL.E98 B, NO.2 FEBRUARY 2015 Fg. 5 Impact of prorty factor α on TTR n Case 1. Fg. 6 Case 1. Impact of the probablty of completng rendezvous on TTR n Fg. 4 1to3. Impact of learnng tme on channel selecton probablty n Cases TTR acheved by the optmal learnng tme s sgnfcantly ncreased. Snce the CORs of all the channels are large, the collsons between the PS and the reply or request packets caused by the msdetecton frequently occur. Therefore, a lot of retrals consume tme Effect of Prorty Factor, α Fgure 5 shows the mpact of prorty factor, α, on TTR, where the channel model s Case 1, ε = 0.0, and TTR s obtaned by the R(u) = 0.99 of Eq. (29). The prorty factor decdes the access probablty of the slave to the superor channel. From ths fgure, the TTR of α = 0.33 s 4 slots smaller than that of α = 0.7. Snce α = 0.33 means unform measurement s used, the advantage of learnng measurement s not obvous. For understandng ths effect, Fg. 6 shows the mpact of the probablty of completng rendezvous, R(u), n Eq. (29) on TTR, where α = 0.33 and 0.7. The learnng tme s optmzed for each probablty. From ths fgure, when the probablty les n the range 0.4 to 0.9, the TTR wth α = 0.7 s 2 to 5 slots smaller than that wth α = Reference [15] ndcates that the average TTR wth learnng measurement s smaller than that wth random hoppng, where the random hoppng scheme s the same as unform measurement. Therefore, our results match those of Ref. [15]. However, n R(u) = 0.99, the TTR wth α = 0.33 s 4 slots smaller than that wth α = 0.7. As we explaned n Fg. 4(a), the access probablty of ρ = 0.6s InR(u) = 0.99, t s not neglgble that the slave selects the channel wth

8 TAKYU et al.: OPTIMIZATION OF LEARNING TIME FOR RENDEZVOUS CHANNEL 367 Fg. 7 Impact of learnng tme on TTR n Case 4 - part 1. Fg. 8 Impact of learnng tme on TTR n Case 4 - part 2. ρ = 0.6. In α = 0.7, the probablty of accessng the channel wth ρ = 0.6 s Therefore, the master has more dffculty n reachng the slaves wth α = 0.7 than wth α = 0.3. It takes more tme to complete rendezvous. Nevertheless, f t s accepted that the rendezvous channel s completed wth long TTR at 1%, we admt α = 0.7 s slghtly superor to α = Snce the weak pont of learnng measurement s found n the worst cases, n the followng evaluaton, the TTR for R(u) = 0.99 s also evaluated. 5.2 TTR n Unform Model of COR Fgure 7 shows the mpact of the learnng tme on TTR n Case 4, where the COR of each channel s modeled by a random varable wth unform dstrbuton. There are two varants, fxed and adaptve learnng tme. In fxed learnng tme, the learnng tme s fxed regardless of the actual COR. In adaptve learnng tme, as the mnmum TTR s acheved, the learnng tme for each COR s adaptvely, and deally, changed. Ths fgure ndcates that TTR wth adaptve learnng tme s constant. From ths fgure, when ε = 0.0 and the learnng tme s 18 slots, the mnmum TTR wth fxed learnng tme s acheved. The dfference n mnmum TTR between fxed learnng tme and adaptve learnng tme s 7 slots. If the slght degradaton n TTR s accepted, t s not necessary to adaptvely change the learnng tme followng the actual COR. When ε = 0.1, the TTRs wth fxed and adaptve learnng tmes become larger than those when ε = 0.0. In addton, Fg. 8 shows the mpact of learnng tme on TTR for varous msdetecton rates. From ths fgure, as ε becomes large, the optmal learnng tme for mnmum TTR becomes large. Ths s because a longer learnng tme s necessary to compensate the msdetecton. However, as ε becomes large from 0.0 to 0.4, the optmal learnng tme becomes large from 20 slots to 35 slots but the mnmum TTR sgnfcantly becomes large from 85 slots to 140 slots. Therefore, the longer learnng tme does not compensate the msdetecton, perfectly. Ths s because as we descrbed n Case2, the Fg. 9 Impact of learnng tme on TTR n Case 5. longer learnng tme s not effectve for avodng the packet collson between PS and SS caused by the msdetecton. In Fg. 7, the dfference n TTR between fxed and adaptve learnng tmes at ε = 0.0 s as large as that at ε = 0.1. If the constant degradaton n TTR s accepted, t s also not necessary to adaptvely change the learnng tme to sut the actual COR even wth practcal carrer sensng. Fgure 9 shows the performance between learnng tme and TTR n Case5. The dfference between Cases 4 and 5 s the number of channels, where the number of channels s 8. The model of COR s the same as that of Case 4. In Fg. 9, we can see the performance tendency and the performance gap between fxed learnng tme and the adaptve one are smlar to those of Case 4. However, when ε s changed from 0.0 to 0.1, the TTR s sgnfcantly degraded. The TTRs n ε = 0.1 s about 95 slots larger than that n ε = 0.0. Ths reason s as follows. From Eq. (2), the connecton probabltes of the superor channel and the other one are 0.7 and 0.15 n N = 3 but 0.7 and n N = 8, respectvely. If the master does not select the channel whch the slave selects as the superor channel, the slave can hardly receve the request packet, so a lot of trals are necessary for completng the rendezvous channel. As we descrbed, the msdetecton

9 368 IEICE TRANS. COMMUN., VOL.E98 B, NO.2 FEBRUARY 2015 causes the packet collson between PS and SS, so a lot of retrals consumes TTR. 6. Concluson Ths paper ntroduced a theoretcal analyss to derve the optmal learnng tme for the learnng-asssted rendezvous channel. The analyss took the mpact of carrer sensng errors nto account. The numercal results ndcate that f the dfference n COR among channels s large, the optmal learnng tme for mnmum rendezvous exsts and can be found from the convex plot of TTR versus learnng tme. However, f t s not, t s dffcult to dstngush among the low COR channels, and a small learnng tme s the most sutable strategy for hgh speed rendezvous. In the unform random model envronment of COR, the TTR acheved wth the certan learnng tme s near to that wth the optmal learnng tme for actual COR. In addton, the mpact of msdetecton to the rendezvous channel s evaluated. As the number of channels becomes large, t becomes harder. The causes of ths are the dffculty of fndng the superor channel and the packet collson between prmary system and secondary one. It s mportant future work to recover these problems. In practcal wreless envronment, the propagaton models, such as fadng, shadowng, and propagaton loss, are necessary for determnng the model of msdetecton. Reference [18] clarfes the mpact of the propagaton loss to the rendezvous channel, where the problem of mssng PS s access s referred to as hdden node termnal. The analyss of the hdden node termnal problem n practcal wreless envronment s also mportant future work. Acknowledgement A part of ths research project s sponsored by Mnstry of Internal Affars and Communcatons n Japan under the project name of Strategc Informaton and Communcatons R&D Promoton Programme (SCOPE ) and KAKENHI ( ). References [1] J. Mtola and G.Q. Magure, Cogntve rado: Makng software rados more personal, IEEE Pers. Commun., vol.6, no.4, pp.13 18, Aug [2] H. Harada, T. Baykas, S. Chn-Sean, H. Murakam, K. Ishzu, S. Fln, Y. Alemseged, T. Ha Nguyen, S. Chen, M. Azzur Rahman, W. Juny, L. Zhou, P. Chang-Woo, G. Vllard, S. Chuny, R. Funada, and F. Kojma, Research, development, and standards related actvtes on dynamc spectrum access and cogntve rado, Proc. IEEE DYSPAN 2010, pp.1 12, Aprl 2010 [3] S. Haykn, Cogntve rado: Bran-empowered wreless communcatons, IEEE J. Sel. Areas Commun., vol.23, pp , Feb [4] E. Hossan, D. Nyato, and Z. Han, Dynamc spectrum access and management n cogntve rado networks, Cambrdge unversty press [5] K.C. Chen and R. Prasad, Cogntve rado networks, Wley, [6] J.J. Pl and Y. Myungsk, Resource-aware rendezvous algorthm for cogntve rado networks, Proc. IEEE The 9th Internatonal Conference on Advanced Communcaton Technology, vol.3, pp , Feb [7] J. Le and F.Y. L, A sngle rado based channel data rate-aware parallel rendezvous MAC protocol for cogntve rado networks, Proc. IEEE Conference on Local Computer Networks, 2009, pp , Oct [8] M. Jeonghoon, H.-S.W. So, and J. Walrand, Comparson of multchannel MAC protocols, IEEE Trans. Moble Comput., vol.7, no.1, pp.50 65, Jan [9] S. Jongmn, Y. Dongmn, and K. Cheeha, A channel rendezvous scheme for cogntve rado networks, IEEE Commun. Lett., vol.14, no.10, pp , Oct [10] D. Yang, J. Shn, and C. Km, Determnstc rendezvous scheme n multchannel access networks, Electron. Lett., vol.46, no.20, pp , Sept [11] S. Hang and Z. X, Channel-hoppng based sngle transcever MAC for cogntve rado networks, Proc. IEEE Conference on Informaton Scences and Systems, 2008, pp , March [12] N.C. Thes, R.W. Thomas, and L.A. DaSlva, Rendezvous for cogntve rados, IEEE Trans. Moble Comput., vol.10, no.2, pp , Feb [13] L.A. DaSlva and I. Guerrero, Sequence-based rendezvous for dynamc spectrum access, Proc. IEEE DySPAN 2008, p.7, Oct [14] S. Ho, W. So, J. Walrand, and M. Jeonghoon, McMAC: A parallel rendezvous mult-channel MAC protocol, Proc. IEEE, Wreless Communcatons and Networkng Conference, 2007, pp , March [15] C. Cormo and K.R. Chowdhury, An adaptve multple rendezvous control channel for cogntve rado wreless ad hoc networks, Proc. IEEE Internatonal Conference on Pervasve Computng and Communcatons Workshops, pp , March-Aprl [16] S.M. Kay, Fundamentals of statstcal sgnal processng, Prentce hall, [17] A. Papouls, Probablty, random varables, and stochastc process, McGraw-Hll, 2nd edton, [18] O. Takyu, K. Knoshta, T. Fuj, and Y. Umeda, A study of channel dentfcaton method based on channel occupancy rato for multchannel wreless access, IEICE Techncal Report, SR , May (n Japanese) Osamu Takyu receved the B.E. degree n Electrcal Engneerng from Tokyo Unversty of Scence, Chba, Japan, n 2002 and the M.E. and Ph.D. degrees n Open and Envronmental Systems from Keo Unversty, Yokohama, Japan n 2003 and 2006, respectvely. From 2003 to 2007, he was a research assocate n the Department of Informaton and Computer Scence, Keo Unversty. From 2004 to 2005, he was vstng scholar n the School of Electrcal and Informaton Engneerng, Unversty of Sydney. From 2007 to 2011, he was an assstant professor n the Department of Electrcal Engneerng, Tokyo Unversty of Scence. He was an assstant professor from 2011 to 2013 and has been an assocate professor from 2013 n the Department of Electrcal & Electronc Engneerng, Shnshu Unversty. Dr. Osamu TAKYU s a recpent of the Young Researcher s award of IEICE 2010 and 2010 Actve Research Award n Rado Communcaton Systems from IEICE techncal commttee on RCS. Hs current research nterests are n wreless communcaton systems and dstrbuted wreless communcaton technology. He s a member of IEEE.

10 TAKYU et al.: OPTIMIZATION OF LEARNING TIME FOR RENDEZVOUS CHANNEL 369 Takayuk Yamakta receved the B.E. and M.E. degrees n the Department of Electrcal & Electronc Engneerng, Shnshu Unversty n 2012 and 2014, respectvely. Hs current research nterests are n cogntve rado technologes. Takeo Fuj was born n Tokyo, Japan n He receved the B.E., M.E., and Ph.D. degrees n electrcal engneerng from Keo Unversty, Yokohama, Japan, n 1997, 1999, and 2002, respectvely. From 2000 to 2002, he was a research assocate n the Department of Informaton and Computer Scence, Keo Unversty. From 2002 to 2006, he was an assstant professor n the Department of Electrcal and Electronc Engneerng, Tokyo Unversty of Agrculture and Technology. Snce 2006, he has been an assocate professor n Advanced Wreless Communcaton Research Center, The Unversty of Electro-Communcatons. Hs current research nterests are n cogntve rado and wreless dstrbuted networks. He receved Best Paper Award n IEEE VTC Fall, 2001 Actve Research Award n Rado Communcaton Systems from IEICE techncal commttee on RCS, 2001, Ercsson Young Scentst Award and Young Researcher s Award from the IEICE n He s a member of IEEE. Shro Handa receved B.E. and M.E. degrees from Shnshu Unversty n 1978 and 1980 respectvely, and the Dr.Eng. degree from Kobe Unversty n From 1982 to 1988, he was a Research Assocate at Kobe Unversty. From 1988 to 1994, he was wth Nagano Natonal College of Technology. He has been wth the Department of Electrcal and Electronc Engneerng, Shnshu Unversty, snce 1994 as an Assocate Professor and snce 2005 as a professor. In 1996, he was at the Unversty of Calforna, Davs, as a vstng researcher. Hs research nterests nclude satellte and moble communcaton systems, modulaton and codng, and vsble lght communcatons. He s a member of IEEE and SITA. Ma Ohta receved the B.E., M.E. and Ph.D. degrees n electrcal engneerng from The Unversty of Electro-Communcatons, Tokyo, Japan, n 2008, 2010 and 2013 respectvely. Snce 2013, she has been an assstant professor n the Department of Electroncs Engneerng and Computer Scence, Fukuoka Unversty. Her research topcs are cooperatve sensng and channel selecton for cogntve rado systems. She receved Young Researcher s Award from the IEICE n She s a member of IEEE. Fumhto Sasamor receved the B.E., M.E. and Dr.Eng. degrees from Waseda Unversty, Tokyo n 1994, 1996 and 2000, respectvely. Snce 2000, he has been wth the Department of Electrcal and Electronc Engneerng, Shnshu Unversty, frst as a Research Assocate and snce 2006 as an Assocate Professor. Hs current research nterests nclude dgtal moble communcaton systems. He receved the IEICE Young Engneer Award n He s member of IEEE.