SUBSET: A Joint Design of Channel Selection and Channel Hopping for Fast Blind Rendezvous in Cognitive Radio Ad Hoc Networks

Transcription

1 SUBSET: A Joint esign of Channel Selection an Channel Hopping for Fast Blin enezvous in Cognitive aio A Hoc Networks Xingya Liu an Jiang Xie epartment of Electrical an Computer Engineering The University of North Carolina at Charlotte {xliu33, Lina.Xie}@uncc.eu Abstract Without a common control channel in cognitive raio a hoc networks CAHNs), two seconary users have to first hop on a common available channel before setting up their communication link. Existing papers on this blin renezvous process mainly focus on the sequence esign of channel hopping but o not consier the selection of available channels. Their time to renezvous TT) an operation complexity increase with the number of available channels, which is against the concept that cognitive raios shoul perform better when there are more unuse channels in primary networks. Thus, a new blin renezvous esign that can aress this paraoxical issue is esirable. In this paper, we propose a joint esign of channel selection an channel hopping for guarantee blin renezvous. For the first time, the TT is significantly reuce to O1) with a low operation requirement. An analytical moel of TT is also propose an valiate against the simulation. More importantly, uner our propose protocol, TT ecreases with the increasing number of available channels in the network. This is a very attractive feature in spectrum-uner-utilize scenarios which has not been achieve by any existing CAHN renezvous work. I. INTOUCTION In cognitive raio a hoc networks CAHNs) [1], seconary users SUs) are allowe to use channels if they o not cause harmful interference to license users, or, primary users PUs). We name these channels available channels for SUs. ue to PUs istribution an activities in the network, the available channel set ACS) of a SU may change with its location an time. Thus, unlike traitional wireless a hoc networks, it is ifficult or impractical to fin a channel which is commonly available for all SUs as their control channel. This requires SUs to work in a ecentralize way to communicate with each other. Uner such scenarios, an important issue is how they can fin each other on a common available channel without the knowlege of each other s available channels. This challenging process is calle blin renezvous. Channel-hopping CH) base technique recently emerges as a promising solution for blin renezvous which can guarantee the renezvous between any two SUs as long as they have at least one common available channel. In a typical CH process, time is ivie into time slots. All channels in the ACS of a SU This work was supporte in part by the US National Science Founation NSF) uner Grant No. CNS , CNS , an CNS /15/$31. c 215 IEEE are orere in a preefine sequence. Both source SUs i.e., SUs willing to renezvous) an listening SUs i.e., potential receivers) hop on to their available channels one by one accoring to their preefine sequences. Base on the Carrier Sense Multiple Access with Collision Avoiance CSMA/CA) mechanism in IEEE 82.11, a source SU broacasts a equest- To-Sen TS) message in each time slot on each channel it hops to check if its estination SU is on the same channel until a Clear-to-Sen CTS) message is receive. We efine TT time to renezvous) as the number of channels the source SU has hoppe on before a successful hanshake of an TS/CTS exchange. Thus, ETT expecte TT) an MTT maximum TT) are regare as two crucial metrics in CH performance. The rawbacks of current CH-base renezvous algorithms are threefol. Firstly, these algorithms raise an awkwar s- cenario: their TT increases with the number of available channels. If the total number of channels in the network is N, the state-of-the-art CH esign [2] [4] can achieve ETT an MTT at the orer of ON) an ON 2 ), respectively. This contraicts the original intention of cognitive raios which shoul perform better when there are ample unoccupie channels in primary networks. A metho to ownsize the large ACS of SUs uring the renezvous process is propose in [5], but the TT is still proportional to the new size of ACS. Only in [6], instea of N, the TT is proportional to the number of SUs, but every SU is preassigne a role source SU or listening SU) in each slot. In aition, the esign propose in neither [5] nor [6] is renezvous-guarantee. Seconly, the TT in existing effort is not short enough with respect to networking operations at higher layers. To get an acceptable successful hanshake rate, it is prove in [7] that the staying time on each hopping channel i.e., one time slot) shoul be 4 6 times longer than the T S + CTS) transmission uration, t T S+CTS. Consequently, the actual renezvous time is more than 4 t T S+CTS TT). Evenif the fastest CH algorithm is aopte, this long renezvous time can easily result in network congestion even uner moerate traffic conitions [8]. Lastly, in existing CH schemes, the energy consumption of a SU is high since it keeps hopping from one channel to another. Even if a SU oes not have packets to sen, in orer to provie the communication chance for potential source SUs, it /15/$ IEEE 426

2 still nees to keep hopping. Most existing renezvous schemes ask every SU to follow the same CH algorithm no matter it is an active source noe or a passive listening noe. In [5], ifferent CH algorithms are esigne for the source SU an the listening SU, but the latter still has to hop on ifferent available channels frequently. From this point of view, there is no ile user in a seconary network when using current CH methos. To eliminate the above CH problems, we consier shortening the TT from the perspective of constructing esirable ACS for the renezvous-pair. We propose that the ACS of a listening SU shoul be a subset of a source SU s ACS. We use the following simple CH strategy to explain the salient feature of such renezvous pair no matter how the subset relationship of their ACS is forme. Assume that the listening SU keeps staying on an arbitrary channel in its ACS. The source SU keeps hopping on to every channel one by one in its ACS. ue to the subset relationship, the source SU can always meet the listening SU on one of its available channels eventually an thus renezvous is guarantee. As we can see, even in such a rough scheme, the operation of the listening SU is minimize since it only nees to keep listening on one channel an the orer of MTT is ON), which is alreay a breakthrough achievement in CH esign. Motivate by the above feature, we investigate the issue of available channel selection in orer to realize such ACS pair. In fact, as explaine in [9], the concept of available channels is imprecisely mentione in many CH-base renezvous papers as the channels that are not occupie by PUs. In this paper, we regar an available channel as the channel that can be use without generating unacceptable interference to PUs. By this efinition, whether a channel is available or not for a SU epens on the SU s interfering range an the locations of PUs on the same channel. Since the interfering range is variable uner ifferent transmission power of a SU [1] an the locations of PUs can be inferre from the sensing perio see etails in Section II), the number of available channels for a SU is controllable using appropriate transmission power. However, it is still very challenging to form the ACS subset relationship for a pair of renezvous SUs in practical CAHNs. For example, one challenge lies in the impact of the one-hop istance. In orer to inclue the listening SU s ACS, the source SU shoul limit its transmission power low enough to interfere less number of PUs an thus make more channels available. However, this may be a problem for the source SU s transmission to reach its estination SU when their istance is large. This issue is aresse in Section III-C. Other practical challenges are iscusse in Section II-B an taken into account in our propose esign. In this paper, we first analyze the relationships of several important parameters such as the transmission power of a SU, the interfering range of a SU transmitter, the istance between the renezvous pair, an the interference range of a SU receiver a ifferent concept from the interfering range of the source SU. See etails in Section II-A). Besies, we also consier practical issues incluing the sensing resolution of SUs, PU location erivation, role-exchange problem, an the interference among SUs. Then, base on these relationships an practical constraints, we propose a mechanism to construct the ACS of a pair of renezvous SUs. Moreover, two highly efficient CH algorithms are evelope base on such ACS pairs to eal with ifferent one-hop istances. Finally, we propose analytical moels an conuct simulations to valiate the analytical moels an evaluate the performance of the propose esign. The salient features of our propose protocol, SUBSET, are summarize as follows. 1) In Section IV, we prove that both the ETT an MTT of the SUBSET protocol are O1) with a 1% successful renezvous rate if the two renezvous SUs have at least one common available channel. To the best of our knowlege, this is the first protocol that can achieve guarantee blin renezvous in such a short time perio. 2) An inherent feature of our CH algorithms is that no matter what the primary network conition is even in ense high traffic volume networks) an what evice parameters PUs an SUs have, the ETT of our renezvous scheme will approach 1 monotonically ecreasing)asthe number of channels in the network increases. Therefore, SUs using our protocol can enjoy faster renezvous in spectrum highly unerutilize networks. 3) Both analytical an simulation results show that the TT of our SUBSET protocol is only 1 or 2 time slots in most cases. Such a fast renezvous can significantly reuce the network congestion in practical scenarios, as compare to existing renezvous algorithms. 4) Our propose SUBSET protocol oes not require ile SUs to keep hopping from a channel to another. Most of the time, they just stay on one channel. Simulation results show that SUBSET requires fewer operations uring a long renezvous time. The rest of this paper is organize as follows. The system moel an parameter analysis are escribe in Section II. In Section III, both the channel selection an channel hopping issues in SUBSET are aresse with etails. In Section IV, TT analysis is presente. Simulations results of our protocol are shown in Section V, followe by the conclusions in Section VI. II. SYSTEM MOEL AN PAAMETE ANALYSIS The system consiere in this paper consists of finite number of PUs an SUs which can operate over a set of orthogonal channels enote by C {c 1,c 2,c 3,..., c N }. Each time when a PU wants to transmit, a channel c i is ranomly selecte for the PU. Both the source SUs an listening SUs utilize SUBSET to form appropriate ACSs an follow CH algorithms in SUBSET. This process shoul be one perioically to avoi channel status change ue to PU activities. Note that time-slotte synchronization is not a necessary requirement, because the listening SU in SUBSET stays on one channel most of the time. 427

3 A. Important elationships We first analyze the relationships that parameters must satisfy in our esign. In [11], the relationship between a sener s transmission range an a receiver s interference range is stuie in a hoc networks. Similar relationship in cooperative sensing in CAHNs is use in [12]. In this paper, we erive specific relationships of parameters in renezvous scenarios in CAHNs. Interfering i_st Interference i_s Primary Tx Primary x Seconary Tx Seconary x Fig. 1. Two ranges of the renezvous pair. Interfering ange Interference ange As mentione in Section I, the ACS of a SU epens on its interfering/interference range. In particular, in this paper, we consier seconary transmitter ST) interfering range an seconary receiver S) interference range, as illustrate in Fig. 1. Interfering ange i ST ) is the range centere at a source SU. Any PU receiver P) within this range has the possibility of failing to ecoe a packet sent from its PU transmitter PT) ue to the interference signal from the ST. In other wors, for any P outsie this range, its SI the ratio of the receive signal power from a PT to the receive interference power from a ST) shoul be greater than a certain threshol Γ sir PU ) which is usually set to be 1B as in the 82.11b specification. Let P r PT be the receive signal power from the PT an P i ST be the receive interference power from the ST. Then, P r PT P i ST Γ sir PU. 1) Accoring to the path loss moel [13] commonly use in wireless networks, when a transmitter propagates a signal to a receiver, the receive signal power at the receiver is P r P t G t G r h 2 t h 2 r, where P t is the transmission power, G t an G r are antenna gains of the transmitter an receiver, respectively, h t an h r are the height of the antennas, an is the transmitter-receiver istance. is the path loss exponent reflecting the signal attenuation rate which is equal to 4 in the two-ray groun reflection moel an is equal to 2 within the Freznel zone. About faing: since our esign explaine in etail in the next section) only requires the existence of ifferent receiving power from ifferent channels, we o not nee to establish a very accurate path loss moel to estimate the exact location of each PU. Instea, only the closest possible Ps on each channel nee to be estimate. Thus, we suppose that each receive signal sent by a PU propagates with the largest possible faing, i.e., the receive signal power can be represente as P r kpt, 2) where k is a known constant for the worst possible faing case. Let P t PT an P t ST be the transmission power from the PT an ST, respectively. From 1) an 2), the relationship between P t ST an i ST is given by P r PT P i ST kp t PT kp t ST i ST P t ST i ST Γ sir PU, 3) where is the longest possible PT-P istance i.e., the raius of the PU s transmission range). Interference ange i S ) is the range centere at a S. Any PT within this range may cause the S failing to receive a packet correctly ue to the PT s raio interference. Let Γ sir SU be the SI threshol of a SU, P r ST an P i PT be the receive signal power from the ST an PT, respectively, an is the ST-S istance. The relationship between P t ST, i S, an is: P r ST P i PT kp t ST kp t PT i S P t ST P t PT i S Γ sir SU. 4) B. Practical Constraints In a CAHN, the esign of blin renezvous shoul also consier the following practical issues. Sensing resolution: ue to the limitation of SU s antenna sensitivity, there is usually a sensing range ) of a SU within which any PT can trigger SU s carrier sense etection. The etection threshol P SU ) is thus given by k P SU. 5) Since the activities of PUs outsie this sensing range cannot be etecte by a SU, i ST is require to avoi interfering possible PUs outsie the sensing range. On the other han, for a successful renezvous, P r ST P SU is necessary, which inicates P t ST P t PT. 6) P location erivation: When a source SU etermines its interfering range i ST on a channel, i ST shoul exclue the closest possible P in orer not to cause interference to any nearby PUs. However, a P cannot be sense immeiately by the ST since it oes not generate any power while receiving, which is the hien primary receiver problem. Nevertheless, the ST can still recognize a P inirectly. For example, if the primary network is in the half-uplex moe, a PU will sen an acknowlege ACK) back to its communication user after each reception. Hence, a hien P s location can be erive from a long-term sensing. In CNs, the long-term sensing can be substitute by mining a SU s own sensing history or cooperative sensing [12], [14]. If the primary network is in the full-uplex moe, the locations of the communication PU pair can also be inferre from their combine signals [15], [16]. In this paper, since we only aim to estimate the location of the closest possible P to a ST, a simpler yet effective metho is propose. 428

4 Let the aggregate receive power at the ST from all PUs on c i be P r ci for the full-uplex moe. In the half-uplex moe, the maximum P r ci from the ST s recent sensing history is chosen. For easy explanation, we use P r ci uniformly for both moes. Then, n kp t PT P r ci, 7) j j1 where n is the number of PUs on c i an j is their istance to the ST. The interfering range on this channel, ci i ST, shoul satisfy ci i ST Minimum{ 1, 2,..., n }, n 1. Thus, P r ci n j1 kp t PT j nkp t PT ci i ST ) ci i ST ) nkp t PT. P r ci Consier the closest P case: when n 1, the relationship between ci i ST an P r c i is: ) 1 c i i ST kpt PT. 8) P r ci ole-exchange problem: After the listening SU receives a TS or a ata packet on the renezvous channel, a CTS or ACK is expecte to sen. Consequently, the listening SU also nees to consier the transmission interfering issue. Let P t ST be the transmission power of the listening SU who just receive a correct TS or ata packet. Now, the interference range of this SU becomes its interfering range since the closest PU may be just outsie this range. To avoi interfering this potential PU when sening CTS/ACK, by 3), P t PT P t ST i S Γ sir PU. 9) Interference among SUs: The interference among SUs can be avoie by limiting SU s transmission power. For example, if a SU s maximum transmission power is higher than a PU s transmission power i.e., Pt max ST >P t PT), replace P t PT in an the interference range may not be able to prevent the interference from an outsie ST. Hence, we shoul set P t ST P t PT. On S s sie, if its minimum receive signal power is lower than that of a PU i.e., Pr min ST <P r PT), replace P r PT in 3) 4) with P max t ST an the interfering range may still affect an outsie kp t ST is require. Combining the above two requirements together, the transmission power of a SU shoul have the following constraint to avoi interference among SUs themselves, with Pr min ST S s reception. Therefore, kp t PT which is a practical setting in CAHNs. Pt ST P t PT 1, 1) III. POPOSE SUBSET ESIGN In this section, we establish the esign of SUBSET from channel selection to channel hopping. The main goal of SUB- SET is to achieve blin renezvous in CAHNs as quickly as possible. Motivation: A short TT of current CH algorithms is base on two requirements: more common available channels an less uncommon available channels in the ACSs of the renezvous pair. Motivate by this observation, a funamental step in our esign is to buil esirable ACSs for the CH algorithm, i.e., the ACS of a listening SU is the largest possible subset of the ACS of a source SU. c 7 c 1 c 5 c 8 c 7 c 3 c 8 c 2 c 4 PU Source SU Listening SU Sensing ange Interfering ange Fig. 2. An illustration of esirable ACSs for the renezvous pair. Example: We illustrate the subset relationship in Fig. 2. In existing CH-base renezvous papers, both the source SU an the listening SU only use the channels not occupie by PUs for constructing the CH sequence. In practice, these are the channels not being use in their sensing range. Thus, the ACSs of the source SU an the listening SU in Fig. 2 are {c 2,c 4,c 6 } an {c 1,c 5,c 6 }, respectively. They only have one common available channel c 6 an four uncommon available channels, c 2, c 4, c 1, an c 5. However, in SUBSET, whether a channel is available epens on the interfering/interference range. In Fig. 2, assume that the interference range is equal to the SU s sensing area. Then, the ACS of the listening SU is still {c 1,c 5,c 6 }. In orer to have this set be the source SU s largest possible subset, the interfering range of the source SU shoul be the re soli circle in Fig. 2. Now, the ACS of the source SU is {c 1,c 2,c 4,c 5,c 6 }, which makes all channels in the ACS of the listening SU, c 1, c 5, an c 6, common available channels. At the same time, this set has the least number of uncommon available channels, c 2 an c 4. A smaller interfering range such as the ash-ot circle may harm the renezvous by increasing the number of uncommon available channels an ecreasing the reception power at the listening SU. A. ACS Construction Next, we show how to construct the esirable ACS with the subset relationship step by step. 1) ACS for the listening SU: For a listening SU, in orer to generate minimum interference to all potential source SUs signal, from 4), we prefer a listening SU to stay on the channel with the largest interference range i max S ). Base on the analysis in the role-exchange problem in Section II, after a packet is correctly receive, the interference range will 429

5 become the listening SU s interfering range which is. Thus, we have i max S. Those sense-ile channels thus can be chosen into its ACS: ACS listening {c i P r ci P SU,i1, 2,..., N}. 11) 2) Transmission power of the listening SU: A listening SU sens a CTS with the maximum transmission power it can use, because the location of the source SU is unknown. Since the interfering range is, base on 3), this transmission power P t ST ) shoul be: P t ST Γ sir PU, 12) which is the upper boun of the constraint 9). 3) ACS for the source SU: To ensure that the ACS of the listening SU is the largest possible subset of the ACS of the source SU, the source SU s minimum interfering range of the selecte channel shoul be inclue in the interference range of the listening SU as shown in Fig. 2. Suppose that the istance between a source SU an its estination SU is. Then, the source SU s maximum interfering range Γ shoul satisfy Γ+. 13) Any ile channel or channel occupie by PUs locate farther than this range Γ can be selecte to the source SU s ACS. From the relationship in 8), this means that any channel with receive power lower than P γ can be selecte, where P γ k Γ. 14) Then, the ACS for the source SU can be forme by: ACS source {c i P r ci P γ,i1, 2,..., N}. 15) 4) Transmission power of the source SU: For those channels with ci i ST Γ, from 3), the maximum transmission power of the source SU on such channels shoul be: P c i c i t ST i ST. 16) Γ sir PU However, since there is an interfering range limit to form the subset relationship 13), the source SU shoul only use the limit transmission power: P t ST Γ sir PU Γ. 17) 5) erivation of the maximum : So far, for a given, the source SU can form a esirable ACS from 15). However, when becomes large, the transmission power from 17) may not be enough for the istant listening SU to ecoe. To guarantee the renezvous, we require an upper boun of that can satisfy the relationship for ecoing in 4) as well as other necessary constraints in Section II. We list them as follows: P t ST Γ sir PU Pt min ST P t PT Γ sir SU. 18) Pt min ST P t PT Finally, we erive the upper boun of as r 19) + Γ sir SUΓ sir PU 1 with the conition Γ sir SU 1. 2) Or r 21) 1+Γ sir PU ) 1 with the conition Γ sir SU 1. 22) We enote this upper boun as the renezvous range r ) for SUBSET. Since the source SU oes not know how far away the estination SU is uring renezvous, it shoul limit its interfering range for the worst case r in orer to form the subset relationship with any listening SU that is locate within r istance. Thus, 2 Γ r; 23) Since homogeneous antennas are consiere in this paper, we assume that the sensing range ) of SUs an PUs is the same an their SI threshols are also the same, i.e., Γ sir PU Γ sir SU 1. In esign, > is require [17], [18]. Particularly, we aopt the efault setting 2.2 in ns-2 [19]. Thus, the left-han sie of both 2) 1 an 22) is 2.2).If 2, 2) hols an r.4. Similarly, if 4, 22) hols an r.8. B. CH Algorithm After forming such an ACS pair, we propose a specific CH algorithm which can further reuce the TT. Algorithm 1 an Algorithm 2 give the pseuo coe for the renezvous pair. For a source SU, it orers the channels in its ACS by their inexes low to high) an hops on to them one by one in a cyclic way until renezvous. For a receiver, it also arranges its ACS by the inexes of channels low to high) an keeps staying on the first orere channel until a correct TS is receive. If the first orere channel becomes busy i.e., a power above the etection threshol is sense), it hops on to its next orere channel an stays there. Algorithm 1: The CH algorithm for the source SU Input: ACS an P t ST ; 1: Orer channels by their inex: {c k1,c k2,..., c km k1 <k2 <... < km}; 2: i 1; 3: Hop on to c ki an sen TS with P t ST ; 4: while not renezvous o i i +1; j i 1) mo +1; /* next orere channel */ Hop on to c kj an sen TS with P t ST ; Base on our CH esign, the listening SU stays on the first orere channel most of the time, which saves the energy consumption of SUs. 43

6 Algorithm 2: The CH algorithm for the listening SU Input: ACS an P t ST ; 1: Orer channels by their inex: {c k1,c k2,..., c km k1 <k2 <... < km}; 2: i 1; j i; 3: Stay on c ki ; 4: while no correct TS is receive o if not ile then i i +1; j i 1) mo +1; Stay on c kj ; 5: Sen CTS on c kj with P t ST ; C. Long-istance SUBSET Motivation: We consier a special issue namely longistance renezvous. In this scenario, the transmission range ofasu ST ) is longer than the require renezvous range in SUBSET. Then, the istance ) between the renezvous pair may excee the renezvous guarantee range, r << ST. Note that to have a successful transmission, a minimum interfering range Γ is generate given a transmission istance. From 4) an 5), i ST Γsir SU Γ sir PU, which implies Γ4.54 when 2or 1.44 when 4in our setting. Therefore, when >.4, +Γ >. The same relationship hols when >.8. Thus, our subset relationship no longer exists. Example: As illustrate in Fig. 3, if the renezvous pair still follows Algorithm 1 an 2, the renezvous is unsuccessful: the listening SU keeps staying on c 1 an the source SU keeps hopping on c 2 an c 3. c 1 c 3 c 2 PU Source SU Listening SU Sensing ange Interfering ange Fig. 3. An illustration of long-istance renezvous. Metho: To solve this problem, we propose to moify Algorithm 1 for the source SU. Instea of only hopping on to the selecte channels with fixe transmission power, the source SU sens an TS with the maximum allowable transmission power on each channel in the network. Thus, when it hops on to the channel where the listening SU stays, the transmission power require on this channel may not be enough for the listening SU to ecoe the TS signal. However, the receive power may be more than the etection threshol an trigger the listening SU carrier sense. Then, accoring to Algorithm 2, the listening SU will choose the next orere channel in its ACS to stay. As the process continues, the listening SU has to keep changing channels until the channel it stays on can receive the correct TS. In this way, the renezvous can be guarantee as long as the renezvous pair has at least one common available channel. For example, in Fig. 3, by running the new algorithm, the source SU starts to hop from c 1. The listening SU etects that c 1 is not ile an chooses c 3 to stay. Finally, they will renezvous on c 3. New renezvous range: We erive the new renezvous guarantee range r. The worst case is that a P is locate at the ege of the listening SU s sensing range an meanwhile, it is the closest PU to the source SU. Uner this circumstance, the minimum allowable interfering range of the source SU, i ST. Then, the corresponing transmission power shoul satisfy 3): P t ST 1. 24) On the other han, the maximum allowable transmission power shoul be able to trigger the listening SU s carrier sense. From 6) an 24), P t PT P t PT. 25) 1 Using the same setting 2.2 in 25), {.9, 2 r 1.2, 4. 26) enezvous guarantee: Note that when.48 in the 2scenario, the interfering range excees the sensing range, Γ Hence the transmission range cannot be set over.48 when 2. On the other han, <is require in 1). Therefore, the new esign can satisfy long-istance renezvous uner both 2an 4.. Protocol etails Algorithm 3: The SUBSET protocol for SU Input: k, P t PT,,, ST an Γ sir; 1: if conition 2) hols) Calculate r using 19); 2: if conition 22) hols) Calculate r using 21); 3: Sense all channels an obtain P r ci i 1, 2,..., N); 4: if source SU then Calculate P t ST using 17) an 23); Calculate P γ using 14) an 23); if ST r then Calculate ACS using 15); un Algorithm 1; if ST r then /* long-istance */ ACS {c i,i1, 2,..., N}; i 1; Calculate Pt ci ST using 8) an 16); Hop on to c i an sen TS with Pt ci ST ; while not renezvous o i i +1; j i 1) mo +1; Hop on to c j an sen TS with P cj t ST ; 5: if listening SU then Calculate P SU using 5); Calculate ACS using 11) an P t ST using 12); un Algorithm 2; 431

7 Algorithm 3 gives the entire protocol showing our joint esign of channel selection an channel hopping. As we can see, our propose SUBSET is very easy for implementation, yet very efficient base on the analysis in Section IV). IV. TT ANALYSIS In this section, we first propose two analytical moels for calculating ETT an MTT of our CH algorithm with ACSs of any subset relationship. Then, we erive the ETT an MTT of our SUBSET protocol using these moels. A. Analytical Moels Let n be the number of channels in the source SU s ACS an m be the listening SU s. Since they share the subset relationship, n m. Fig. 4 illustrates a possible istribution of the paire ACSs. Assume that channels are alreay orere by their inexes from low to high. The ACS of the listening SU ACS 2 ) is a subset of m channels ranomly chosen from the ACS of the source SU ACS 1 ). ACS 1 ACS 2 C k1 C kj C kn Fig. 4. An illustration of subset istribution. MTT: The largest possible inexe first-channel in ACS 2 is the n-m+1)th channel in ACS 1, i.e., the m channels in ACS 2 are exactly the last m channels in ACS 1. Therefore, in SUBSET, MTTn, n m +1 27) which is only relate to n an m. ETT: The total number of the istribution cases of ACS 1 an ACS 2 is n. If the source SU renezvous on the jth channel in its ACS, then TT j. In this case, the first channel in ACS 2 must be the same channel an other channels can be chosen from the channels after it. As shown in Fig. 4, the number of possible cases becomes to n j m 1). Let Pj be the probability of TT j. Then, P j n j m 1) / n. The ETT in SUBSET can be erive by n 1 m 1 +2 n 2 m 1 + +n m +1) m 1 ) m 1 ETT n. 28) We first analyze the expression ) n k m m 1 fk) m 1 m 1 m 1 Using m 1) m an the combinatorial law p q p 1 q 1) + p 1 q to the last two items, m m 1 + m 1 m 1 m m 1) + m m+1 ) m. Then, keep applying the law to the last two items of the new forme equation iteratively, fk) n k m 1) + + m+1 m 1 + m+1 m n k m m+2 m n k+1 ) m. Thus, the numerator of 28NUM) can be rewritten as NUM f1) + f2) + + fn m +1) ) n n 1 m +1 m , m m m m m which has the same pattern as fk). Using the same metho, we can erive NUM n+1 m+1). Therefore, ) ETTn, n +1 m +1 / n m n +1 m +1, 29) which also only epens on two variables n an m. B. Normal SUBSET To analyze the performance of SUBSET, we only nee to know the average n an m in a network. Assume that PUs are evenly istribute. enote K as the number of PUs in a unit area. If the active rate of a PU is ρ, then the average number of channels occupie by PUs in a listening SU s sensing range is Kρπ 2. Then, the average number of available channels for the listening SU is m N Kρπ 2. Using the same way, we can erive that n N KρπΓ 2. Therefore, the estimations of ETT an MTT in the normal case are: N +1 Kρπ r)2 ETT N +1 Kρπ 2, 3) MTT Kρπ r2 r)+1 both of which are O1). Note that lim N ETT 1, which means that ETT approaches 1 when there are more channels in the network no matter what the primary network conition is an what the PU an SU evices are K, ρ,, an r ). C. Long-istance SUBSET In the long-istance esign, the listening SU will eventually stay on a common available channel of the source SU an the listening SU. Therefore, the TT is the inex number of their first common available channel since the source SU hops on every channel one by one. Thus, the problem is similar to the normal case shown in Fig. 4, where ACS 2 is the common available channel set an ACS 1 is the set of all channels. C B A O Source SU Listening SU Sensing ange Interfering ange Fig. 5. Changing interfering range with a known. In this way, we have n N. Let m be the number of channels in the common available channel set. Note that when r, Γ+, which means that the renezvous pair still shares the subset relationship an thus m m1 N π 2. When > r, they o not own the subset relationship an m m2 N KρS U, where S U represents the size of the union area of the renezvous pair. Using Fig. 5, we erive S U as a function of. erivation of S U : To erive S U, we first nee to know the size of the intersection area S I in Fig. 5. By observation, S I is equal to the interfering area of the source SU minus the crescent area S C : S I πγ 2 S C, where S C 2S BAC S BA ). Meanwhile, we know S BA S BO S BOA. Since,, 432

8 an Γ are known Γ 1.44), we erive θ cos Γ 2 2, β π cos 1 Γ Γ, an S BOA 1 2 sin θ. Then S BO π 2 θ 2π an S BAC πγ 2 β 2π. Then, S U πγ 2 + π 2 S I. After calculating m, the ETT an MTT for the longistance SUBSET are r N +1 ST ETT l m1+1 + N +1 r m ) MTT l MTTN,m )N m +1 To get the maximum value of MTT l, m shoul be as small as possible. The extreme value can be erive when the union area is the largest, i.e., when ST. ue to the space limit, the final expression is not shown here. Notice that both ETT l an MTT l in 31) have the same forms as in the normal case. Therefore, the ETT an MTT in long-istance SUBSET are also O1). V. PEFOMANCE EVALUATION In our simulation, 1) PUs an SUs are evenly istribute in the simulation area; 2) Each PU is ranomly assigne a channel when a new packet nees to be transmitte; 3) Packet arrivals follow the Poisson istribution; an 4) Each SU ranomly chooses a SU within its transmission range as its estination SU when it has a new packet to transmit an becomes a source SU. The parameters use in our simulation are liste in Table I. TABLE I SIMULATION PAAMETES The antenna relate constant B The minimum require SI for PU/SU 1 B The path-loss factor 2 The transmission power of a PU 2w Sie length of the simulation area L 5 m Channel ata rate 2 Mbps PU/SU packet size 5 slots The size of TS+CTS) bits b/g) Simulation time 1 slots Power etecte Source SU estination SU Channel Fig. 6. etecte power on each channel. Fig. 6 illustrates the spectrum conition etecte by a potential renezvous pair 8 in a moment uring simulation. If there are only five channels in a primary network, as shown in the top figure, uner the SUBSET protocol, the listening SU will stay on channel 2 an the hopping sequence for the source SU is {c 1, c 2, c 5, c 4, c 3 }. Then, TT is 2. When the number of channels increases, the number of common available channels also increases, which expeite the renezvous process an both SUs hop on channel 5 with 1 time slot. A. Analysis Valiation Fig. 7 shows the analytical an simulation results of the ETT uner ifferent number of channels. The analytical results are calculate using our analytical moel propose in Section IV where K 1, ρ.375. ETT Near SUBSET simulation) istant SUBSET simulation) Near SUBSET analytical) istant SUBSET analytical) Number of Channels N) Fig. 7. ETT vs. N. From Fig. 7 we summarize: i) The ETT of both SUBSET esigns approaches 1 as the number of channels in the network increases. This feature truly accors with the goals of cognitive raios to perform better in spectrum-uner-utilize scenarios; ii) The ifference between the simulation an analytical results is 4.3% with.7 stanar erivation, which valiates our analytical moels; iii) Near-SUBSET performs better than the long-istance SUBSET because the source SU in the esign has to hop on every channel before renezvous; an iv) The average number of unavailable channels is about Kρπ When N 1, the network is in spectrum scarcity. Even uner this scenario, our propose SUBSET protocols can still achieve renezvous within 2 slots. B. ETT an MTT The ETT an MTT of both the near- an istant- SUBSETs are compare with the state-of-the-art CH protocol Enhance Jump-Stay ) [3]. All these protocols can achieve a 1% successful renezvous rate. The near-subset protocol is use when ST r ) an istant-subset is applie when ST > r ). ETT SUBSET Number of Channels N) Number of Channels N) a) ST.8. b) ST 1.2. Fig. 8. ETT vs. N in ifferent protocols K 1an ρ.37) ETT SUBSET From Fig 8, when the number of channels in the network increases, the ETT of increases with ON), while our SUBSET protocol maintains the same performance ue to our O1) esign. 433

9 From Fig 9, when the number of PUs increases, the ETT performance of all the protocols oes not change much. However, the ETT of SUBSET is still less than 2 time slots even in high-ensity high-traffic-volume primary networks. ETT SUBSET ETT Number of PUs Number of PUs a) ST.8. b) ST 1.2. Fig. 9. ETT vs. K in ifferent protocols N 3an ρ.52) SUBSET The performance of MTT is shown in Table II. The results well reflect our O1) avantage of MTT, which is significantly lower in SUBSET. TABLE II MTT VS. NUMBE OF CHANNELS Number of channels Near enezvous SUBSET istant enezvous SUBSET A high MTT can easily cause network congestion. In a recent stuy [8], a renezvous threshol is erive for avoiing network congestion uner similar parameters. This threshol is aroun 1. The MTT of SUBSET shown in the table is lower than this threshol, which inicates that SUBSET can support a congestion free network. C. Energy Consumption of Ile SUs Consumption ate S Near S Far Number of Channels Number of PUs a) C vs. N K 1). b) C vs. K N 3). Fig. 1. Ile SU consumption rate uner ifferent conitions in CAHNs. We efine a metric C to evaluate the energy consumption of an ile SU in CAHNs. Let nl) be the number of channels a listening SU hoppe in a CH process. Then, C nl) TT which represents the consumption rate of a listening SU uring the renezvous time. Fig. 1a) shows the impact of spectrum scarcity on C an Fig. 1b) illustrates C in ifferent PU istributions. It is obvious that SUs with SUBSET can enjoy a longer battery life ue to less activities uring renezvous, especially when the renezvous may take a longer time SUBSET-far), a worse spectrum conition smaller N as in a)), or a worse network conition higher K as in b)). Consumption ate S Near S Far VI. CONCLUSION In this paper, an efficient an aaptive protocol, SUBSET, is propose by joint esign of channel selection an channel hopping. 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