An Efficient Quorum-based Rendezvous Scheme for Multi ... - Faculty

An Efficient Quorum-based Rendezvous Scheme for Multi-radio Cognitive Radio Networks AbdulMajid Al-Mqdashi, A. Sali, NK. NoorDin, Shaiful J. Hashim

Rosdiadee NorDin

Mohammad J. Abdel-Rahman

Dept. of Computer & Communication Systems Engineering, University Putra Malaysia, Malaysia

Dept. of Electrical, Electronic, & Systems Engineering, Universiti Kebangsaan Malaysia, Malaysia

Dept. of Electrical & Computer Engineering Virginia Tech, USA

Abstract—Rendezvous is an initial and vital process for establishing data communications between devices in cognitive radio networks. Channel hopping (CH) provides an effective method for achieving rendezvous without relying on a dedicated common control channel. Most of the existing rendezvous schemes are designed for single-radio devices. Due to the dropping cost of wireless transceivers, the use of multiple radios to significantly reduce the rendezvous delay becomes economically feasible. In this paper, we propose a deterministic multi-radio rendezvous scheme that exploits the combinatorial features of grid quorum systems. We refer to our proposed scheme as multi-grid-quorum channel hopping (MGQ-CH). Our scheme uses multiple overlapped grid quorums to map the available channels at each device to its radios. We derive the theoretical upper-bound of the maximum time-to-rendezvous of MGQ-CH. Furthermore, we conduct simulations to study the performance of MGQ-CH under various system parameters and compare it with the state-of-theart multi-radio rendezvous algorithms. The simulation results demonstrate the superior performance of MGQ-CH compared to previous schemes.

I.

I NTRODUCTION

Due to the traditional fixed spectrum assignment, a significant portion of the licensed spectrum (e.g., UHF) is underutilized. On the other hand, the unlicensed spectrum (e.g., ISM) is becoming over-crowded due to the growth of wireless devices and their huge demands for the wireless spectrum [1]. Accordingly, cognitive radio has been emerged as a promising solution for the spectrum under-utilization and scarcity issues. In cognitive radio networks (CRNs), the unlicensed users, a.k.a. secondary users (SUs) can use the licensed wireless bands in an opportunistic fashion while their use does not cause an interference to the bands licensed users, a.k.a. primary users (PUs). Rendezvous is a fundamental and an important process for initiating the SUs data communications. Due to the drawbacks of the common control channel rendezvous approach, channel hopping (CH) represents an alternative and more effective method for achieving a blind rendezvous. However, the majority of the existing CH rendezvous algorithms [2–12] schemes assume that each SU is only equipped with one radio, and hence each SU can only access one channel during each time slot. Due to the dropping cost of wireless transceivers, equipping CR users with multiple radios can significantly accelerate the rendezvous process and improve its performance with an acceptable increase in the cost [1]. In the literature, there are some proposed algorithms [1, 13– 16] that address the multi-radio rendezvous problem in CRNs.

The multi-radio rendezvous algorithms can be categorized into two categories, according to the channel set information used for constructing the CH sequences: global channels based (GC) and local channels based (LC) algorithms [13]. In the GC algorithms, the CH sequences are designed using all channels in the CRN, whereas in the LC algorithms only the locally available channels are used in constructing the CH sequences. The LC algorithms are more practical in distributed CRNs due to the dynamics in channel availability and the limitation of the sensing capability [1]. Furthermore, the LC algorithms can provide faster rendezvous than the GC algorithms due to the shorter CH sequence period. In [1], the authors proposed a GC algorithm, called role-based parallel sequence (RPS), in which they use one dedicated radio that stays for a while on a specific channel and (m − 1) general radios that keep hopping on different channels. In [16], the authors proposed another GC algorithm, called optimized waiting and hopping (OWH), in which they determine the proper number of dedicated radios among the m radios for each SU in order to optimize the rendezvous performance. In [14], the authors designed an LC algorithm, called enhanced adaptive rendezvous (EAR), in which they rank the available channels based on their qualities and divide them into m sets. Each set is assigned to one of the m radios, following jump-stay patterns that are similar to [5]. In [15], the authors proposed another LC algorithm, called general construction for rendezvous (GCR), in which each SU divides its available channel set into m/2 subsets. The m radios of each SU are divided into m/2 pairs, each pair follows a CH sequence that is based on one of the divided channel subsets. In [17], the authors proposed an LC algorithm, called adjustable multi-radio rendezvous (AMRR), that provides fast rendezvous and can adjust its best performance on either the maximum time-to-rendezvous (MTTR) or the average TTR by different allocations of the m radios. In AMRR, increasing the number of stay radios shorten the MTTR whereas increasing the number of hopping radios shorten the average TTR. Our Contributions–In this paper, we study the rendezvous problem in CRNs where each SU is equipped with multiple radios and different SUs could have different numbers of radios. We consider two network models that describe the channel availability: Symmetric and asymmetric. In the symmetric model, all SUs have the same set of available channels. In contrast, different SUs may have different sets of available channels in the asymmetric model.

We propose an LC quorum-based CH rendezvous scheme. Our scheme exploits the combinatorial features of the grid quorum system (GQS), which (i) provides deterministic guarantees on the intersection between the designed CH sequences and (ii) makes our CH sequences robust to synchronization errors. The main contributions of this paper are as follows: •

We propose a multi-grid-quorum CH scheme, called MGQ-CH, for pairwise rendezvous in multi-radio CRNs. Our scheme uses multiple overlapped grid quorums to map the available channels at each SU to its radios.

•

We derive the upper-bound of the MTTR under both the symmetric and asymmetric channel availability models.

•

We conduct simulations to study the performance of MGQ-CH under various system parameters and compare it with the state-of-the-art multi-radio rendezvous algorithms. Our results demonstrate the superior performance of MGQ-CH compared to previous schemes.

Paper Organization–The rest of this paper is organized as follows. The system model and problem formulation are presented in Section II. The proposed MGQ-CH algorithm is presented in Section III. In Section IV, we present the theoretical analysis of MGQ-CH. Using simulations, in Section V we evaluate the performance of MGQ-CH and compare it with the RPS [1] and AMRR [17] schemes. Finally, we conclude the paper in Section VI. II.

S YSTEM M ODEL AND P ROBLEM D EFINITION

A CRN consisting of different SUs operating over a licensed spectrum is considered. The licensed spectrum is divided into |L| non-overlapping channels, L = {L1 , L2 , . . . , L|L| } , in which Li denotes channel i. A channel is considered available to an SU for communication if the SU sensed the channel idle from any PU transmissions. We consider a time-slotted communication where time is divided into discrete slots that have fixed and equal durations. In this paper, we mainly focus on the pairwise rendezvous between any two SUs (say SU 1 and SU 2) in a multi-radio CRNs. Let |C1 | and |C2 | be the numbers of available channels of SU 1 |C | and SU 2, respectively. Let C1 = {C11 , C12 , . . . , C1 1 } ⊆ L |C | 2 and C2 = {C21 , C22 , . . . , C2 } ⊆ L be the two sets of available channels of SU 1 and SU 2, respectively. Also let m1 (m1 > 1) and m2 (m2 > 1) be the number of radios for SU 1 and SU 2, respectively. We note here that in multiradio CRNs m1 may not be equal to m2 . The CH sequence of each SU is denoted by a set of vectors. For example, the CH sequence of SU i for a period with length T time → − → − → − → − slots is represented by {S1i , S2i , S3i , · · · , STi }, where vector − → i i i i , · · · , Stm } indicates that SU i hops on Sti = {St1 , St2 , St3 i channel Stk using radio k during time slot t. The multi-radio rendezvous problem in CRNs is defined as: for any two SUs (say SU1 and SU2) that are equipped with m1 and m2 radios, respectively. We need to construct a CH sequence for each radio at each SU in order to achieve a guaranteed rendezvous between these two SUs on a commonlyavailable channel during the same time slot. The rendezvous

must be achieved within a bounded and short time despite any difference of their CH start times (i.e., asynchronous local clocks). III.

M ULTI - GRID - QUORUM C HANNEL H OPPING S CHEME

In this section, we present the design of MGQ-CH rendezvous algorithm. Some preliminary definitions related to grid quorum systems are presented first to facilitate the understanding of the rest of the paper. A. Definitions and Basic Idea Definition 1: For a set Zn = {1, 2, . . . , n}, a quorum system Q under Zn is a group of non-empty subsets of Zn , each called a quorum, such that: ∀X and Y ∈ Q, X ∩ Y 6= ∅. Here, Zn is the set of non-negative integers less than or equal to n. 2: A GQS arranges the elements of Zn as a √ Definition √ n × n square grid array, where n must be a square of a positive integer. Hence, a quorum is formed as a union of the elements of one column and one row of the grid. There are n grid quorums in a GQS that√is constructed under Zn and each quorum has a size of (2 × n − 1). For example, a GQS Q under Zn = {1, 2, 3, 4} is Q = {Q1 , . . . , Q4 } = {{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}. Definition 3: For a given integer i and a grid quorum G in a GQS Q under Zn , we define rotate(G, i) = {(x + i) mod n, x ∈ G} to denote a cyclic rotation of quorum G by i. Definition 4: A GQS Q under Zn satisfies the rotation closure property T because ∀Gi1 , Gi2 ∈ Q and ∀j1 , j2 ∈ Zn , rotate(Gi1 , j1 ) rotate(Gi2 , j2 ) 6= ∅. Definition 5: Suppose two heterogeneous GQSs Q1 under Zn and Q2 under Zm , where n ≤ m and p = d m n e, This pair of the two heterogeneous GQSs satisfies the heterogeneous rotation closure property because ∀Gp ∈ Q1, H ∈ Q2, i ∈ {1, · · · m}, there is Gp ∩ (H + i) 6= ∅ or (G + i)p ∩ (H) 6= ∅. Although, GQSs have been proposed to construct sequences that achieve asynchronous communications because it satisfies the intersection as well as the homogeneous and heterogeneous closure properties [12, 18]. To the best of our knowledge, all proposed grid quorum CH sequences was constructed for a single transceivers. There is no work in the literature that addresses the GQS for multiple transceivers. In this paper, we propose a grid-quorum-based multi-radio rendezvous scheme for CRNs. Basically, when each SU has more than one radio, the CH-based sequences built based on GQSs can achieve rendezvous deterministically between any pair of SUs within a bounded time. The rendezvous is guaranteed between any pair of SUs when they have at least one common available channel. The basic idea of our scheme is to allow each SU to build its multi-radio CH sequence based only on its local available channels and the number of radios. For an SU i with |Ci | local available channels and m number of radios, a GQS is constructed based on |Ci | and m. The SU will then select |Ci | grid quorums from the GQS for mapping its |Ci | available channels into an m-radio CH sequence. The procedure steps of MGQ-CH (Algorithm 1) to construct the CH sequence of SU i is as follows:

Fig. 1: MGQ-CH sequence construction for two SUs. SU1 has m1 = 2 and C1 = {1, 2, 3, 4}, SU2 has m2 = 2 and C2 = {2, 5, 8, 9}, only one common channel.

1) Determine the size of the square grid array dimension needed to construct the GQS based on |Ci | and m. The dimension is denoted as Ci0 and it is determined by Algorithm 2 where we provide valid formulas for majority of the Ci and m combinations. For example, in Fig.1, SU 1 has 4 available channels and 2 number of radios. Hence,  4 e = 4. on the other hand, C30 for SU C10 = d 2−(d2/2e) 3 in Fig.2 who has same number of channels |C3 | = 4 and has 3 radios is C30 = 4 − 2 = 2. 2) Construct a GQS Q under Z(Ci0 )2 from the Ci0 × Ci0 grid array. 3) Select |Ci | grid quorums from Q for the purpose of assigning them with the |Ci | channels. Put the selected quorums in a Quorum Channel Mapping array QCM. The selection method in lines 12 − 20 ensures that each column or row in the grid array will not be selected more than m times. This is important since if the grid quorums are selected randomly or in non appropriate way, this may cause assignment failures. Specifically, for any t ∈ {1, · · · , (Ci0 )2 }, the random selection of quorums may results in assigning more than one channel to the same − → i i slot in Sti = {St1 , · · · , Stm }. The selection method is valid for any combination values of Ci0 and m. 4) Assign each channel from the |Ci | available channels to the time slots that correspond to their selected quorums in QCM. The assignment of the channels into − → − → − → −− −→ i the CH sequence {S1i , S2i , S3i , · · · , S(C 0 )2 } is done vec− →i i i i tor by vector. For each vector St = {St1 , · · · , Stm }, 0 2 t ∈ {1, · · · , (Ci ) }, we map each quorum-row element of each channel into a slot on one radio from the {1, · · · , d m 2 e} radios. And also each quorum-column element of each channel is mapped into on one radio from the {d m 2 e + 1, · · · , m} radios. 5) Randomly assign a channel to each empty un-assigned cell (the white slots) if they exist in each vector. However these channels are selected from the Ci available channels that are not mapped in any other cell in the same vector.

Fig. 2: MGQ-CH sequence construction for two SUs. SU3 has m3 = 3 and C1 = {1, 2, 3, 4}, SU4 has m4 = 4 and C2 = {2, 3, 4, 5, 7, 9}, 3 common channels.

This guarantee that during the same slot, each radio of the SU m radios is assigned with a different channel and hence a full use of the radio resources is achieved. As can be seen in Figures 1 and 2, each segment of Ci0 slots over all radios (we call it sub-frame) in the CH sequence of each SU contains all the Ci available channels assigned to the multiple radios. Each SU stays for a sub-frame of Ci0 consecutive time slots on d m 2 e number of channels from its Ci channels using its first d m e 2 and then switch to another channel. These stay slots are assigned based on the row elements of each quorum. For example SU 1 stays using its radio R1 on ch2 for 4 consecutive slots and then switch to ch1 and stays on it for another 4 consecutive slots, and so on. Similarly, SU 4 stays on ch2 and ch7 using its R1 and R2 radios, then switch to another channels (ch3 and ch5 ) on the next 3 slots, and so on. On the other hand, during each sub-frame, one column based element from the quorum of each channel is assigned into one slot in the sub-frame, except the channels that are assigned in the first radios using its full quorum row elements. For example, SU 1 has channels (ch3 , ch4 , and ch1 ) assigned to the three slots on R2 during the first sub-frame while ch2 is assigned to the first radio based on its quorum full row elements. The non-quorum slots (white slots in the figures)are assigned randomly from the available channels that are not assigned to any other radio during the same time. IV.

S CHEME A NALYSIS

In this section, we analyze our MGQ-CH scheme theoretically by deriving the upper-bounds of MTTR of the scheme under both the symmetric and the asymmetric models. A. Symmetric Model Theorem 1: Under the symmetric model (C1 = C2 ), let m1 and m2 indicate the numbers of radios of two SUs, respectively. If m1 = m2 , the MTTR of the MGQ-CH scheme is upper bounded by either C20 or C10 . If m1 6= m2 , the MTTR of the MGQ-CH scheme is upper bounded by (2 × max{C10 , C20 }) − 1.

Algorithm 1 MGQ-CH Input: Ci , m. Output: the CH sequence of i 1: Invoke algorithm 2 to determine C 0 2: Construct a GQS Q under C 0 × C 0 3: Define QCM = array [|Ci |][2 × C 0 − 1] 4: if m is even then 5: index=C 0 6: else 7: index=1 8: end if 9: for j = 1 : |Ci | do 10: QCM [j][:] = Qindex 11: index=(index+(C 0 − 1))%(C 0 )2 12: end for 13: for t = 1 : (C 0 )2 do − → i i 14: Sti = {St1 , · · · , Stm } 15: for x = 1 : |Ci | do 16: if t is a row element in QCM [x][:] then 17: for r = 1 : dm/2e do i 18: if Str is empty then i 19: Str = Cix 20: end if 21: end for 22: else 23: if t is a column element in QCM [x][:] then 24: for r = dm/2e + 1 : m do i 25: if Str is empty then i 26: Str = Cix 27: end if 28: end for 29: end if 30: end if 31: end for − → 32: if there exist some un-assiagned slots in Sti then − → 33: h = Ci \ { the assigned channels in Sti } − →i 34: Assign each empty slot in St with a unique channel from h 35: end if 36: end for

Algorithm 2 Determining the grid array dimension Input: |Ci |, m. 1: if |Ci | ≤ m then 2: C0 = 2 3: else 4: if m is even then 5: if |Ci | > m  AND |Ci |< m + (dm/2e + 1) then |Ci | 0 6: C = b m−(dm/2e) c 7: else   |Ci | e 8: C 0 = d m−(dm/2e) 9: end if 10: else 11: if m = 3 then 12: C 0 = |Ci | − 2 13: else 14: if |Ci | > m  AND |Ci |< m + (dm/2e + 1) then |Ci | 15: C 0 = b m−(dm/2e) c−1 16: else   |Ci | e−1 17: C 0 = d m−(dm/2e) 18: end if 19: end if 20: end if 21: end if

Proof: In Figure 3, the four cases of rendezvous under the symmetric model are presented. These four cases are happened according to the two SUs starting times (i.e., asynchronous local clocks). Figure 3(a) occurs when m1 = m2 while Figures 3(b), 3(c), and 3(d) occur when m1 6= m2 . For the three later cases, without loss of generality, we assume m1 < m2 (i.e., C10 > C20 ). For simplifying the understanding of analysis, we differentiate the radios that are assigned based on the quorum row elements only as the quorum row-based radios while we call all radios that are assigned based on the quorum (both row and column) elements as the quorum radios. This is applicable to the slots as well. 1) Case 1: Figure 3(a), C10 = C20 , the rendezvous can happen between the row-based slots of SU2 and the quorum slots of SU1 from the start point of SU2. So the rendezvous occur within C20 . 2) Case 2: Figure 3(b). l indicates the clock difference of start time and l0 denotes the remaining time slots of relative longer row-based sub-frame except l . l0 ≥ C20 implies that rendezvous is possible during l0 because the m2 quorum radios of SU2 hop on all SU2 available channels before the (dm1 /2e) quorum row-based radios of SU1 transfer to the next (dm1 /2e) channels. TTR in this case is ≤ C20 . 3) Case 3: in Figure 3(c), l0 < C20 means that SU2 does not have enough time slots to hop on all its available channels before the quorum row-based radios of SU1 transfer to the next (dm1 /2e) channels. So, the rendezvous is only guaranteed between the quorum slots of SU2 and the quorum row slots of SU1 during the next C20 sub-frame of time slots after the row-based radios of SU1 transfers to the next (dm1 /2e) channels. Hence,T T R ≤ 2×C20 −1. 4) Case 4: in Figure 3(d), SU2 starts earlier than SU1, the rendezvous can be achieved during SU2 sub-frame of the grid row slots from the start point of SU1. So, T T R ≤ C20 . When we exchange the roles of the two SUs in our above analysis, we can get similar bounds but with replacing C10 instead of C20 in each case. Above all, we approved that MTTR is achieved no later than the first C20 or (C10 ) time slots for the case when m1 = m2 and no later than (2 × max{C10 , C20 }) − 1 slots when m1 6= m2 . B. Asymmetric Model Theorem 2: Under the asymmetric model (C1 6= C2 ), let m1 and m2 indicate the numbers of radios of two SUs, respectively. C10 and C20 is the square grid dimension sizes by which the two SUs construct their CH sequences. Let G indicates the number of common available channels between the two SUs. If C10 = C20 , the MTTR of  the MGQ-CH scheme is upper  |C2 |−G bounded by C20 ( or C10 ) × min{b |Cd 1m|−G 1 e c, b d m2 e c} + 1 . 2 2 If C10 6= C20 , the MTTR upper bound is (max{C10 , C20 }×β +2) ( |C1 |−G b d m1 e c if C10 > C20 2 β= b |Cd 2m|−G if C20 > C10 2e c 2

Proof: We will provide the proof for the case when C10 = 0 C2 because of the limited space in this paper. Figure 4 shows the rendezvous case when C10 = C20 that may happen under

(a) TTR ≤ C20

(b) l ≤ C10 − C20 , l0 ≥ C20 , TTR ≤ C20

40 MGQ−CH AMRR RPS

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Fig. 5: Comparison of the algorithms under the symmetric model when m1 = m2 = 4 and θ = 0.4.

(c) l > C10 − C20 , l0 < C20 , TTR ≤ 2 × C20 − 1

(d) TTR ≤ C20

Fig. 3: Rendezvous cases for MGQ-CH under the symmetric model.

Fig. 4: Rendezvous case when C10 = C20 for MGQ-CH under the asymmetric model.

the asymmetric model in which SU1 start earlier than SU2. In our scheme, the multiple quorum row based radios of each SU can achieve multiple rendezvous over its stay channels during each sub-frame. These multiple rendezvous times are expected to occur with the quorum based radios of its partner. For the MTTR upper bound under the asymmetric case, we consider the worst cases. If the number of channels of SU1 is larger than those of SU2 (|C1 | > |C2 |), then the worst case is when all the c × d m22 e potential rendezvous fails first consecutive b |Cd 2m|−G 2 2 e because the channels assigned to the d m22 e radios based on the quorums row elements are not commonly-available channels to both of SUs. However, during the next C20 subframe, the d m22 e row-based radios of SU 2 will hop definitely on one common available channel between SU 2 and its partner SU 1. Accordingly, therendezvousis achieved and the TTR here  |C2 |−G 0 is ≤ C20 + C20 × b |Cd 2m|−G ce = C × 1 + b ce . m 2 2 d 22 e 2 e If (|C1 | < |C2 |), the worst case is on the failure of all first b |Cd 1m|−G ×d m21 ec potential rendezvous because the d m21 e radios 1 2 e are staying on quorum row assigned channels that are not common between the two SUs. After that, the quorum row radios of SU 1 will definitely hop into at least one common channel in the next C10subframe and occurs. Hence,  rendezvous   TTR |C1 |−G |C1 |−G 0 0 0 ≤ C2 + C2 × b d m1 e ce = C2 × 1 + b d m1 e ce . Above 2 2  |C2 |−G all, TTR ≤ C20 × min{b |Cd 1m|−G c, b c} + 1 . m 1e d 2e 2

2

V.

S IMULATION R ESULTS

In this section, we evaluate the performance of MGQ-CH and compare it with two multi-radio rendezvous algorithms, RPS [1] and AMRR [17], through simulations using MATLAB. RPS is selected from the GC algorithms category while AMRR is the state of art in LC algorithms category that provides the shortest MTTR. AMRR algorithm is simulated for the case where dm/2e among the m radios of each SU are adjusted as stay radios and the remaining as hopping radios. This adjustment provides AMRR best performance in terms of the MTTR [17]. We consider both the symmetric and the asymmetric models for our simulations where we compare the algorithms based on the average TTR and the MTTR. TTR is the number of time slots needed for achieving a successful rendezvous between the two SUs. In our simulations, we vary the number of channels in |L| from 10 to 100. Also, we introduce a parameter θ(0 < θ ≤ 1) to indicate the ratio of number of local available channels to the number of all channels. For each SU, we select θ × |L| channels randomly from the whole channel set. For each set of the simulation parameter values, the simulation results in each figure are obtained by 10, 000 independent runs where we accordingly compute the average TTR and the MTTR for each figure results. A. Symmetric Model In this simulation scenario, we compared the rendezvous performance when each SU have m1 = m2 = 4 radios and C1 = C2 . We let θ = 0.4×|L| and hence the numbers of local available channels of the two SUs are |C1 | = |C2 | = 0.4×|L|. In Figure 5(b), we can see that MGQ-CH provides the smallest MTTR. For example, when there are 100 channels, the MTTRs of MGQ-CH, AMRR, and RPS are 18, 20, and 30. For the average TTR in Figure 5(a), RPS has a slight smaller average TTR than our AMMR and our MGQ-CH as the number of available channels increase because it dedicates only one radio as stay radio while the remaining radios keeps hopping in different channels. This will provides smaller average TTR but at the cost of longer MTTR. B. Asymmetric Model We consider two simulation settings for measuring the performance of our MGQ-CH with the compared algorithms. In the first setting, we let m1 = m2 = 4 and the number of

MGQ−CH AMRR RPS

8

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100 MTTR(slots)

Average TTR(slots)

algorithms. Our results showed the superior performance of MGQ-CH under both the symmetric and asymmetric channel availability models.

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ACKNOWLEDGMENT

40 20

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Fig. 6: Comparison of the algorithms under the asymmetric model when m1 = m2 = 4, θ = 0.4, and G = 0.2|L|.

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Fig. 7: Comparison of the algorithms under the asymmetric model when m1 = m2 = 4, θ = 0.1, and G = 1.

available channels to the two SUs be |C1 | = |C2 | = 0.4 × |L| where (C1 6= C2 ). Also we set G = 0.2 × |L| as the number of common available channels between the two SUs. Figure 6 shows that our MGQ-CH provides the best performance in terms of both the average and the maximum TTR. This is due to the deterministic rendezvous guarantee provided by the grid quorums where at least two intersections between each common channel. In the second setting, we let |C1 | = |C2 | = 0.1 × |L| and we set G = 1 in order to evaluate the performance when there is only one common available channel between the two SUs which suppose to invoke the MTTR upper bound. As depicted in Figure 7, MGQ-CH provides the shortest MTTR and average TTR. This is due to the small constructed CH period of MGQ-CH that guarantee rendezvous within a smaller and bounded time. For example, when the number of channels L is 100 and hence |C1 | = |C2 | = 10, each SU will construct its CH sequence based on 5 × 5 grid array and the period will be 25 slots. This will ensure that rendezvous occurs within the fifth sub-frame as the worst case (specifically on the earlier 21-23 time slots). VI.

C ONCLUSIONS

We proposed an efficient pairwise rendezvous scheme, called MGQ-CH, for multi-radio CRNs, which uses only the locally available channels to construct the CH sequences. MGQ-CH guarantees rendezvous within a bounded and short time. We derived the upper-bound of the maximum TTR, and conducted simulations to evaluate the performance of MGQCH as compared to the state-of-the-art multi-radio rendezvous

The authors would like to thank Malaysian Ministry of Higher Education to fund this study under the Fundamental Research Grant Scheme (FRGS) entitled On the Cogitation of Primary User Reappearance in Cognitive Radio Network (Project code: MOHE: FRGS/1/2015/TK10/UPM/02/2, UPM:03-0115-1626FR, Vote No.:5524731). R EFERENCES [1] L. Yu, H. Liu, Y. W. Leung, X. Chu, and Z. Lin, “Multiple radios for fast rendezvous in cognitive radio networks,” IEEE Transactions on Mobile Computing, vol. 14, no. 9, pp. 1917–1931, September 2015. [2] K. Bian, J.-M. Park, and R. Chen, “Control channel establishment in cognitive radio networks using channel hopping,” IEEE Journal on Selected Areas in Communications, vol. 29, no. 4, pp. 689–703, April 2011. [3] M. J. Abdel-Rahman, H. Rahbari, and M. Krunz, “Adaptive frequency hopping algorithms for multicast rendezvous in DSA networks,” in Proc. of the IEEE DySPAN Conf., October 2012, pp. 494–505. [4] M. J. Abdel-Rahman, H. Rahbari, M. Krunz, and P. Nain, “Fast and secure rendezvous protocols for mitigating control channel DoS attacks,” in Proc. of the IEEE INFOCOM Mini-Conf., April 2013, pp. 370–374. [5] H. Liu, Z. Lin, X. Chu, and Y.-W. Leung, “Jump-stay rendezvous algorithm for cognitive radio networks,” IEEE Transactions on Parallel and Distributed Systems, vol. 23, no. 10, pp. 1867–1881, October 2012. [6] Z. Gu, Q.-S. Hua, Y. Wang, and F. Lau, “Nearly optimal asynchronous blind rendezvous algorithm for cognitive radio networks,” in Proc. of the IEEE SECON Conf., June 2013, pp. 371–379. [7] M. J. Abdel-Rahman and M. Krunz, “Game-theoretic quorum-based frequency hopping for anti-jamming rendezvous in DSA networks,” in Proc. of the IEEE DySPAN Conf., April 2014, pp. 248–258. [8] Z. Lin, H. Liu, X. Chu, and Y.-W. Leung, “Enhanced jump-stay rendezvous algorithm for cognitive radio networks,” IEEE Communications Letters, vol. 17, no. 9, pp. 1742–1745, September 2013. [9] G.-Y. Chang, W.-H. Teng, H.-Y. Chen, and J.-P. Sheu, “Novel channelhopping schemes for cognitive radio networks,” IEEE Transactions on Mobile Computing, vol. 13, no. 2, pp. 407–421, February 2014. [10] M. J. Abdel-Rahman, H. Rahbari, and M. Krunz, “Multicast rendezvous in fast-varying DSA networks,” IEEE Transactions on Mobile Computing, vol. 14, no. 7, pp. 1449–1462, July 2015. [11] M. J. Abdel-Rahman and M. Krunz, “CORE: A combinatorial gametheoretic framework for coexistence rendezvous in DSA networks,” in Proc. of the IEEE SECON Conf., June 2015, pp. 10–18. [12] M. J. Abdel-Rahman, H. Rahbari, and M. Krunz, “Rendezvous in dynamic spectrum wireless networks,” University of Arizona, Department of ECE, TR-UA-ECE-2013-2, Tech. Rep., May 2013. [Online]. Available: http://www2.engr.arizona.edu/∼krunz/publications by type.htm#trs [13] B. Yang, W. Liang, M. Zheng, and Y. C. Liang, “Fully distributed channel-hopping algorithms for rendezvous setup in cognitive multiradio networks,” IEEE Transactions on Vehicular Technology, 2015. [14] R. Paul, Y. Z. Jembre, and Y. J. Choi, “Multi-interface rendezvous in self-organizing cognitive radio networks,” in Proc. of the IEEE DySPAN Conf., April 2014, pp. 531–540. [15] G. Li, Z. Gu, X. Lin, H. Pu, and Q.-S. Hua, “Deterministic distributed rendezvous algorithms for multi-radio cognitive radio networks,” in Proceedings of the ACM International Conference on Modeling, Analysis and Simulation of Wireless and Mobile Systems, 2014, pp. 313–320. [16] K. y. Cheon, C. j. Kim, and J. K. Choi, “Rendezvous for self-organizing MANET with multiple radio,” in International Conference on Information and Communication Technology Convergence (ICTC), October 2015, pp. 906–911. [17] L. Yu, H. Liu, Y. W. Leung, X. Chu, and Z. Lin, “Adjustable rendezvous in multi-radio cognitive radio networks,” in Proc. of the IEEE GLOBECOM Conf., December 2015, pp. 1–7. [18] S. Lai, B. Ravindran, and H. Cho, “Heterogenous quorum-based wakeup scheduling in wireless sensor networks,” IEEE Transactions on Computers, vol. 59, no. 11, pp. 1562–1575, November 2010.