Ring-Walk Based Channel-Hopping Algorithms with Guaranteed ...

2010 IEEE/ACM International Conference on Green Computing and Communications & 2010 IEEE/ACM International Conference on Cyber, Physical and Social Computing

Ring-Walk Based Channel-Hopping Algorithms with Guaranteed Rendezvous for Cognitive Radio Networks Hai Liu1, Zhiyong Lin1,2, Xiaowen Chu1, and Yiu-Wing Leung1 Dept of Computer Science, Hong Kong Baptist University, Hong Kong 2 Dept of Computer Science, GuangDong Polytechnic Normal University, GuangZhou, China {hliu, zylin, chxw, ywleung}@comp.hkbu.edu.hk 1

licensed spectrum, the vulnerability of CCC to jamming attack, and so on. Therefore, blind rendezvous systems without any centralized controller and CCC are preferable in practice. A representative approach for blind rendezvous is to use channel-hopping (CH) technique, in which each user of a CRN selects a set of available channels and hops among them for rendezvous with its potential neighbors. If all users have the same available channels, we call it symmetric model. We call it asymmetric model otherwise, i.e., different users might have different available channels. Several CH algorithms have been proposed in the recent literature for rendezvous of users in CRNs [2, 4, 5, 9]. The generated orthogonal sequence algorithm (GOS) [5, 9], the modular clock algorithm (MC) and its modified version (MMC) [9] are notable ones. However, all the existing CH algorithms have one or more of the following limitations: i) without guaranteed rendezvous; ii) demand on timesynchronization of the systems; iii) not applicable to asymmetric model; iv) not applicable to rendezvous of multiuser and multi-hop scenarios. In this study, we focus on the design of CH algorithms for blind rendezvous. We propose two ring-walk based CH algorithms, namely RW1 and RW2, which guarantee rendezvous of two or multiple users in timeslotted CRNs without the need of time-synchronization. The most important metric to evaluate CH algorithms is time-torendezvous (TTR), which is defined as the number of time slots that it takes for users to achieve rendezvous. Table I highlights the performance of our algorithms and other representative algorithms, where MTTR and E(TTR) denote the maximum TTR and the expected TTR, respectively.

Abstract—Rendezvous is a fundamental and essential operation for users of cognitive radio networks (CRNs) to meet and establish a link on a common channel, so that information exchange and data communication can be carried on. This work addresses the problem of blind rendezvous, i.e., rendezvous without the help of any central controller and dedicated common control channel. We propose two ring-walk (RW) based channel-hopping (CH) algorithms. The basic idea is to represent each channel as a vertex in a ring. Users “walk” on the ring by visiting vertices of channels with different velocities. Rendezvous is achievable since the user with lower velocity will eventually be “caught” by the user with higher velocity. Compared with the existing solutions, our algorithms achieve the following advances: i) guaranteed rendezvous without the need of time-synchronization; ii) applicability to rendezvous of multi-user and multi-hop scenarios. We derive the maximum time-to-rendezvous (TTR) and the expected TTR of our algorithms in both 2-user and multi-user scenarios (shown in Table I). Simulation results show superior performance of our algorithms. Keywords-cognitive radio; rendezvous; channel hopping.

I. INTRODUCTION Cognitive radio networks (CRNs) have been proposed as a new way to allow unlicensed users (or secondary users, SUs) to access the spectrum of licensed users (or primary users, PUs) opportunistically [1]. The unlicensed users in CRNs are also referred to as cognitive users (CUs). Equipped with cognitive radios, CUs can dynamically identify idle channels in the spectrum of PUs and hop among them adaptively without causing interference to the PUs. Unless otherwise stated, the users mentioned hereafter in this paper refer to CUs by default. Users in a CRN should detect the presence of each other and establish communication links, so that information exchange, spectrum management and data communication can be carried on. The process of two or more radios of users to meet and establish a link on a common channel is referred to as “rendezvous”. Rendezvous is a fundamental and essential operation in CRNs. However, implementation of rendezvous is a challenging problem since users are even not aware of presence of one another before rendezvous and available channels of users are usually different and change dynamically. Most of existing works on rendezvous either utilize centralized controller [3] or employ global/local common control channel (CCC) [6, 7, 8] to facilitate the rendezvous. These strategies usually suffer from problems including the low scalability and flexibility of centralized systems, the difficulty or even infeasibility in establishing a CCC in the

978-0-7695-4331-4/10 $26.00 © 2010 IEEE DOI 10.1109/GreenCom-CPSCom.2010.30

TABLE I.

MTTR AND E(TTR) OF DIFFERENT ALGORITHMS 2-user

multi-user multi-hop

Algorithms

RW1

SM

AM

SM

AM

(M−1)(N2−N)

2(M+1−G)(M −1)(N2−N) unknown 2(M+1−G)(M −1)N unknown x

(M−1)(N+1−K)[2D+( N−K)(1+lnD)] unknown

unknown x

2(M+1−G)(M −1)(N2−N)D unknown 2(M+1−G)(M −1)ND unknown x

x

x

x

O(MNlnN) RW2

(M−1)N (M−1)(lnN+1/2) M(M+1)

GOS [5, 9]

M 4 + 2M 2 + 6M − 3 3M 2 + 3M

(M−1)N(1+lnD)

2P x x x (not guaranteed) x x x 2P2⁄ (P−1) x unknown x x MMC [9] x unknown x x Remarks: i) MTTR and E(TTR) are shown in unshadowed rows and shadowed rows, respectively. ii) SM and AM denote Symmetric Model and Asymmetric Model, respectively. iii) “x” means that the algorithm cannot be directly applied; “unknown” means that the algorithm is applicable but its performance is unknown. iv) GOS, MC and MMC are short for Generated Orthogonal Sequence, Modular Clock and Modified Modular Clock algorithm, respectively. v) M is the size of the whole potentially available channel set; P is the smallest prime number that is greater than or equal to M; G is the number of common available channels of users; D is the network diameter in terms of number of hops; N is the network size. MC [9]

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maximum TTR (MTTR) and expected TTR (E(TTR)) are usually adopted to evaluate the performance of CH algorithms. If a CH algorithm has a finite MTTR, then it is said to be with guaranteed rendezvous. In this study, we seek CH algorithms with guaranteed rendezvous for both symmetric and asymmetric models. III. RING-WALK BASED RENDEZVOUS ALGORITHMS

Contributions of this work are summarized as follows. i) New algorithms with guaranteed rendezvous: two ringwalk based CH algorithms are proposed to achieve guaranteed rendezvous without the need of timesynchronization under both symmetric and asymmetric models. ii) Generalized rendezvous for multi-user and multi-hop scenarios: RW1 and RW2 are both applicable to rendezvous of multiple users within 1-hop and even multihop neighborhood. iii) Solid theoretical analysis: we derive the MTTR and the expected TTR of new algorithms in 2user and multi-user multi-hop scenarios. II. SYSTEM MODEL AND PROBLEM FORMULATION We consider a CRN consisting of K, K ≥ 2, users, who coexist with one or more PUs in the same geographical area. We assume that each user has an unique ID and knows the largest possible ID of users, i.e., the network size N. The PUs are the holders of some licensed spectrum, which can be divided into M, M>1, non-overlapping channels. We assume that these channels are indexed uniquely as 1, 2, , M and the indices are known to every user in the network. The whole set of potentially available channels for the users is denoted by C={c1, ,cM}, in which ci denotes the ith channel and usually is called channel i for convenience (i=1, 2, , M). Each user in the CRN is equipped with one cognitive radio, which can access the idle channels in C opportunistically. Let Ci ⊆ C denote the set of available channels of user i, i=1, , K, where a channel is said to be available to a user if the user can communicate on the channel without causing interference to PUs. Let G denote the number of common available channels of all users, i.e.,

A. Basic idea Our basic idea is to represent each channel as a vertex in a ring, so that generating a CH sequence is equivalent to visiting vertices in the ring. For simplicity, we let indices of channels equal the corresponding indices of vertices. Each user “walks” on the ring by visiting vertices with a preassigned velocity in either clockwise or anticlockwise direction (clockwise direction is adopted in our algorithms). In each time slot, a user stops at a vertex (channel). In the next time slot, the user either stays at the current vertex or jumps to next vertex which is dependent on velocity of the user. A CH sequence is generated when the user continuously walks on the ring. All users walk on the ring in the same direction. Intuitively, any two users with different velocities can eventually meet at a vertex since the user with lower velocity will be “caught” by the user with higher velocity. That is, CH sequences of the two users will meet at a common channel in the same time slot and thus the rendezvous is achieved. Note that each user has an unique ID which could be used to design its distinct velocity. In this way, rendezvous is guaranteed since users walk on the ring with different velocities. In the following, we consider two designs of velocity based on the user ID. 1) Ring-walk scheme 1 In this scheme, the user with ID v, 1 ≤ v ≤ N, stays at each vertex for v time slots before it advances one vertex. It implies that the user with smaller v will walk faster. For instance, suppose that there is a ring with 4 vertices (i.e., M=4). A user with v=2 starts at vertex 1 and walks on the ring. The CH sequence generated by the user is: 1, 1, 2, 2, 3, 3, 4, 4, 1, 1, 2, 2, 3, 3, 4, 4, The CH function of this scheme is formally described as follows.

K

G =| ∩ C i | . We consider the following two models. i =1

i) Symmetric model. All users have the same available channels if their geographical locations are close. That is, for any 1 ≤ i, j ≤ K, we have Ci=Cj. For simplicity, we assume Ci=Cj=C. ii) Asymmetric model. Different users might have different available channels if their geographical locations are far. We assume that at least one common channel is shared by all users in the network, i.e., G≠0. This is a necessary assumption since there is no feasible solution, otherwise, for rendezvous of the users. We assume that the rendezvous of K, K ≥ 2, users is said to be successful if all the users hop on a common available channel in the same time slot [2, 4, 9]. The rendezvous problem studied in this paper is formulated as follows. Rendezvous problem: Given a multi-hop CRN consisting of K, K≥2, users, the problem is to design CH algorithms to generate the CH sequences for the users, such that all users are guaranteed to hop on a common available channel in the same time slot, regardless of different time when the users start their CH sequences. TTR is an important metric to evaluate CH algorithms. It is defined as the number of time slots that it takes for users to achieve rendezvous once all users have begun their hopping. The TTR of a CH algorithm is usually not constant due to random starting time of CH sequences of the users. Thus,

Function RW1Hopping 1: Input: M, v, i0, t 2: Output: channel c 3: n=⌊t/v⌋; 4: i=(i0+n−1)％M+1; 5: RETUEN c=ci; In line 1, variable i0 represents the starting channel-index and t represents the time slot counter which starts from zero. 2) Ring-walk scheme 2 In this scheme, each user with ID v advances v vertices in the ring for every N time slots. Correspondingly, CH sequence of the user is generated in a periodical way and each period lasts for N time slots. Suppose that the user stops at vertex i at the end of a period. The CH sequence in the next period is: i％M+1, (i+1)％M+1, , (i+v−1)％M+1, (i+v−1)％M+1 , , (i+v−1)％M+1.

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takes at most (⌈(v1−1)/(v2−v1)⌉+2)v1 time slots for user 1 to catch up with user 2 if they perform RW1_2_SM. Proof. As mentioned before, one feature of RW1_2_SM is that the user with ID v should stay for v time slots at the current vertex before it moves to the next vertex. So, we denote by Γj(t) the remaining amount of time slots (including time slot t) that user j should still stay at the current vertex before it moves to the next vertex, and let Γ(t)=Γ1(t)−Γ2(t). Obviously, we have 1≤Γj(t) ≤ vj (j=1, 2) and Γ(t) ≤ v1−1