Double Hopping: A new Approach for Dynamic Frequency Hopping in Cognitive Radio Networks Daniel Willkomm, Mathias Bohge, Daniel Hollos, James Gross*, and Adam Wolisz Telecommunication Networks Group, Technische Universitat Berlin, Germany Email: {willkommlbohgelholloslgrosslwolisz}@tkn.tu-berlin.de Abstract-one of the major challenges in designing cellular find a frequency assignment such that, (a) two interfering cells Cognitive Radio (CR) networks is the avoidance of Secondary never use the same frequency at the same time, and (b) the User (SU) interference to so called Primary Users (PUs) oper­ total number of frequencies used in the network is minimized. ating in the licensed bands. Usually, SU operation has to be interrupted periodically in order to detect PU activity and avoid Reducing the number of frequencies increases the number of the respective frequencies. Recently, Dynamic Frequency Hop­ supportable cells and additionally reduces the probability of ping (DFH) mechanisms have been suggested to enable reliable interference with PUs. PU detection and continuous SU operation at the same time. The so called Frequency Assignment Problem (FAP) [3] is a Applying DFH in a multi-cell environment adds the challenge well investigated topic for frequency-static (Le. non-hopping) of mitigating Co-Channel Interference (CCI). In this paper, we introduce a new DFH approach for cellular CR networks to networks. Mathematically, the FAP can be expressed as a allow reliable PU detection and continuous SU operation while graph coloring problem with nodes (representing the cells) avoiding CCI: Double Hopping (DH). We present a distributed and edges between the nodes (representing their interference frequency assignment heuristic for DH and compare it to the relationships). Each node is assigned one (or multiple) color(s) optimal assignment. We show that the performance of the sub­ such that two connected nodes never own the same colors. optimal distributed assignment is only slightly worse than the optimal performance, and, thus, outperforms existing distributed Minimizing the total number of colors is - mathematically ­ approaches by far. similar to the list coloring problem, which is known to be np­ complete [4]. However, in non-hopping networks, distributed I. INTRODUCTION heuristics - such as the Distributed Largest First (DLF) Cognitive Radio (CR) has become a popular and promising algorithm [5] - have been shown to achieve remarkably good approach to overcome the artificial spectrum scarcity. The key results compared to the optimum for a wide set of graphs [6], idea of CR technologies is to allow the usage of temporarily while greatly reducing the computational complexity. unused licensed spectrum by so called Secondary Users (SUs) In this paper, we present a new concept for DFH called under the constraint that the spectrum has to be vacated, as Double Hopping (DH) and compare it to previously suggested soon as the owner of the band - referred to as Primary User DFH approaches. We introduce a distributed heuristic called (PU) - returns. To meet this constraint, the spectrum has to be Distributed Frequency Assignment (DFA) and compare it to sensed periodically - at least every t max - to detect potentially the Distributed Hopping Approach (DHA), introduced in [7]. appearing PUs. In order to perform reliable sensing on a Additionally, an optimal algorithm based on solving a Linear frequency, data transmission has to be interrupted. Depending Integer Program (LIP) called Optimal Frequency Assignment on the PU detection requirements and the sensitivity of the (OFA) is developed to serve as a lower bound for frequency sensing antenna, the sensing process can require up to hun­ usage. The remainder of this paper is structured as follows: dreds of milliseconds. Obviously, such interruptions in data Section II presents related work on frequency hopping. The transmission severely degrade the Quality of Service (QoS) ­ FAP and the system model is presented in Section III. The especially for real-time or streaming applications. general DH approach is introduced in Section IV and the To avoid periodic interruptions of the payload communica­ centralized and distributed algorithms in Section V. In Sec­ tion, Dynamic Frequency Hopping (DFH) has been proposed tion VI, we present the performance evaluation results. Finally, for cellular CR networks [1], [2]. The basic idea of DFH is in Section VII, we conclude the presented work. the following: A cell performs sensing on frequency Y in II. RELATED WORK parallel to data transmission on frequency X. After t max , the cell hops to frequency Y and performs sensing on frequency X A. Frequency hopping and so on. Obviously, this implies that sending and sensing in The idea of frequency hopping has gained lots of attention parallel is possible, e.g. by using two antennas. Having a whole in the context of Global System for Mobile Communications network of mutually interfering cells, mitigating Co-Channel (GSM), Bluetooth@, and Wireless Local Area Networks Interference (CCI) becomes crucial. The question is, how to (WLANs). The main objective to apply frequency hopping in these systems is to mitigate fast fading and CCI. Hopping *Since January 2008, James Gross is with the Mobile Network Per­ formance Group, UMIC Research Centre, RWTH Aachen University, sequence design for GSM is studied in [8], [9]. Dynamic [email protected]. frequency hopping in GSM is studied and compared to random 978-1-4244-2644-7/08/$25.00 ©2008 IEEE hopping in [10]. Here, the frequency hopping pattern of a mo­ In [18] and [19] two different approaches are made to use bile is adapted based on measurements made at the base station graph coloring in CR networks. However, note that in both and the mobile. In Bluetooth®, each cell chooses one out of papers, "frequency-static" networks are considered. In [18], in several pre-specified pseudo-random hopping sequences. Re­ contrast to our approach, each node in the graph represents cently, a non-cooperative Adaptive Frequency Hopping (AFH) one CR terminal, which is subject to an individual PU inter­ method has been proposed to combat the so called frequency­ ference. According to the experienced interference level, the static interference that originates e.g. from WLAN systems or frequencies differ in the reward accredited to the terminal in microwave ovens [11], [12]. In [13], Mishra et al. propose case of an assignment. In addition, power control is used to to assign each WLAN of a large, uncoordinated network a control interference. The objective in [18] is the maximization hopping pattern, such that the performance degradation of ofthe network utility subject to reward and fairness constraints interference is somewhat spread over all cells in the network for a given number of terminals and available frequencies. over a longer time span, leading to an increased system-wide Recall that, in contrast to that, our goal is to minimize the cell-level fairness. number of necessary frequencies. In [19], the maximization In contrast to the application of frequency hopping in non­ of the network utility is considered as well, but, in contrast, CR related networks as described above, the scope of applying all terminals experience the same interference from PUs. In frequency hopping in CR networks is to allow continuous data conformity with our approach, the total number of frequencies transmission and at the same time to assure the unimpaired op­ used in the network is minimized. However, since there is eration of the PU. To the best of our knowledge, so far, among a different graph coloring I network relation, and since the existing frequency hopping applications solely Bluetooth®'s channels might differ in bandwidth, a different optimization Adaptive Frequency Rolling (AFR) approach [14] is somewhat problem is formulated. related and could be modified for CR operation. APR tries to avoid frequencies occupied by WLAN systems (which could III. SYSTEM MODEL be seen as PUs) and at the same time also avoids CCI between We consider a spectrum range of B MHz, divided into Ftot different Bluetooth systems. However, since AFR has been frequency bands of equal size, indexed from 1 to Ftot• Each of developed under non-CR related assumptions, a high number the frequency bands is owned by a PU. The total number ofCR of modifications would be necessary to support CR operation. cells in the investigated network is denoted by IV I. Each cell Frequency hopping in CR networks has been first consid­ consists of one Base Station (BS) and a number of associated ered within the IEEE 802.22 standardization process [15]. terminals. We assume that user data sent under the impact of Based on that standard, we have been the first ones to introduce interference is lost. Two CR cells are interfering ifboth operate the general concept of Dynamic Frequency Hopping (DFH) in the same frequency band at the same time (referred to as in 802.22 [1], [2]. In these papers, we present phase-shifted working frequency) and are within each others interference operation for interference-free sensing and collision-free hop­ range. In the following, we refer to these cells as neighboring ping in combination with a cooperative hopping approach cells. Neighboring cells have means to exchange control for neighboring cells referred to as Revolver Hopping (RH). information using a control channel. The control channel can Additionally, the concept of Dynamic Frequency Hopping be physically separated from the data transmission channel