Channel Mobility Incurred Source Routing in Cognitive Radio Networks

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  Channel Mobility Incurred Source Routing inCognitive Radio Networks Yupeng  Li , Boya  Peng Department of Computer Science,University of Hong KongNovember 1, 2014 Abstract In Cognitive Radio Networks (CRN), Secondary users are allowed touse Primary Users’ (PUs’) idle channels for data transmission. However,PUs can reclaim their channels at any time and SUs must cease trans-mission immediately. Such a problem is known as the  spectrum mobility  ,and may further cause break of pre-established routes in multi-hop CRNswhere SUs act as relays. In this paper, we investigate a routing problemwhere channel switching and route re-selection are deployed to resolveSUs’ conflicts with PUs and further improve spectrum mobility. In par-ticular, we consider both protocol and physical interference models andform the routing game into a routing game which is proved to be a po-tential game with a pure Nash Equilibrium (NE). Finally, we present anefficient algorithm for finding the NE and analyze the  Price of Stability  of the proposed game. 1 Introduction Wireless spectrum is currently regulated by government and is assigned to li-cense holders and services on a long term basis. However, a large portion of the assigned spectrum is used sporadically, which leads to under utilization of frequency resources.The problem foresees the development of Cognitive RadioNetworks (CRNs) to improve spectrum efficiency. The idea of CRN is that unli-censed users (Secondary Users, SUs) can flexibly access licensed users’ (PrimaryUsers, PUs) idle channels without interfering with other PUs’ transmission.While such Dynamic Spectrum Access (DSA) improves spectrum utilization,new problems such as spectrum sensing, channel selection, MAC and routingprotocols design occurred with regard to the architecture of CRNs, and one of the major problems is  spectrum mobility  .In CRNs, due to higher priorities, PUs are allowed to reclaim their licensedchannels at any time, while SUs must cease their transmissions immediately.Therefore, for multi-hop CRNs where SUs act as relays, spectrum mobility may1  break pre-established routes as it disables data transmission over certain linkson those routes. To avoid conflicts with PUs and resume routing, each flowgenerator can either inform intermediate SUs to switch channels or select a newroute. However, there is no clear answer as for which approach is better. Whileswitching channels keeps the srcinal spacial routes which effectively reducerouting costs, frequent channel switching may cause significant switching costs.On the other hand, while re-selecting a spacial route can reduce switching costs,it may result in additional routing costs in the mean time. Therefore, due tothe trade off between channel switching and route re-selection, we combine thetwo approaches into a routing problem as a whole.In this paper, we construct the routing problem into a routing game, whereeach flow generator acts as a player and selects its route selfishly to minimizeits own cost, which results from both channel switching and route re-selection.In particular, we pay attention to the scenario where multiple flows can sharea common link which further improves spectrum efficiency but introduces con-gestion costs. Furthermore, we consider both protocol and physical interferencemodels, and construct the cost model and form the game accordingly.The contributions of this paper include the following: ã  We formulate the problem as the Route-Switching Game. ã  We construct the game in regards to both protocol and physical interfer-ence models. ã  We prove the existence of Nash Equilibria (NE) by applying the  Ordinal Potential Game   method ã  We simulate the  Fictitious Play Process   as the learning algorithm for thegame, prove its feasibility and efficiency, and analyze the  Price of Stability  (PoS).The rest of this paper is organized as following: We will first introduce somerelated works in section 2 and present the system model in section 3. Then insection 4, game formation for the Routing Game will be discusses. Next, weanalyze the learning strategy for the game and the Price of Anarchy in section5 and 6. At last, we present simulation results and conclusion in section 7 and8 respectively. 2 Related Works For routing problem in multi-hop CRN, the most relevant work would be thetwo dimensional routing game proposed by Qingkai [1], which also exploreda joint scheme of channel switching and routing re-selection in the context of spectrum-mobility incurred route-switching problem in multi-hop CRN. How-ever, his work failed to consider the scenario where multiple flows sharing acommon link, and he considered only the protocol interference model but notthe physical interference model. Most of the other works only considered either2  channel switching or spatial route selection. For instance, Qinghai [2] proposeda proactive channel selection scheme based on spectrum hole prediction. Heintroduced two two opportunistic channel selection algorithms to optimize thethroughput of the secondary user: minimum collision rate channel selection algo-rithm and minimum handoff rate channel selection algorithm. Besides, Zhao [3]provided a robust channel assignment scheme in the multi-hop CRN, while Cal-effi [4] proposed the criterion for an optimal routing metric in CRNs based onthe diversity effects of spatial routes.As for game formation, Roughgarden [5, p. 461- 487] discussed selfish routinggame in general, and analyzed the existence and uniqueness of a Nash Equilib-rium (NE) in the game. He then introduced the potential function method forfinding NE, and brought up the concept of the Price of Stability (PoS) whichcompare the best NE to the socially optimal result to analyze the efficiencyof self routing games. Furthermore, Ragavendran [6] discussed the ’hourglass’architecture for game-theoretic control, which allowed a diverse set of possibleutility and learning designs, with an constrained interface connecting the two.In this paper, we construct players’ utility function in terms of routing costs,and deploy the famous  Fictitious Play   (FP) process [7] as the learning rulefor each player to update its strategy during the game. Additionally, the class potential game   is chosen to be the constrained interface, which requires utilitydesigns to guarantee that the resulting game is a potential game and requiredlearning rules to guarantee to provide desirable behavior. In a potential game,a pure Nash Equilibrium will be reached where no player can further reduce itsown cost under the specific utility and learning design. 3 System Model What we consider is the channel-mobility-incurred source routing problem inthe multi-flow multi-hop Cognitive Radio Networks (CRNs). In this section, wepresent the formal definitions of our system model. 3.1 Cognitive Radio Networks (CRNs) A CRN can be characterized by a potential directed graph  G  = ( V,E  ), where  V   is the set of all active secondary users in the network and  E   denotes the set of all potential links. Here, potential links mean that not all the links in this graphcan be established simultaneously. Similar to other recent works on CRNs, weonly consider  unicast   in the communication, and assume that each node hasalready had a stable power level 1 . Therefore, with a known power level, we canget the wireless transmission range of each node and establish all the potentiallinks. Formally, an edge  e ci ( u,v )  ∈  E   from SU u  to SU v  is established if and onlyif SU v  is within the transmission range of SU u , which is a potential link andtherefore corresponds with a channel  c . We assume that a node can be equipped 1 Broadcast and power allocation is beyond our consideration here. 3  with multiple antennae 2 , so multiple wireless links can be established betweentwo nodes. Two links are called opposite if they differ from each other only bythe direction, and are denoted  e  and ¯ e . 3.2 Channel In CRNs, each secondary user (SU) is able to sense the licensed channel stateto avoid colliding with any PU who has the priority to occupy channels. Eachuser 3 can establish a link with any SU within its own transmission range on anychannel they have sensed. We denote C   =  { 1 , 2 ,...,C  } as the potential availablechannel set, and  C  SU i  is the available 4 channel set of the  i th SU at a time. Sincemost channels in CRNs are occupied by PUs,  C   is a small number, and we canassume that the number of antennae of each wireless node is enough to supportall its potential links working on different available channels simultaneously.Since different SU may collide with different PUs,  C  SU i  and  C  SU j  can be notequal given that  i   =  j  at a time. 3.3 Flow There are  N   flows indicated by  i  ∈ N   =  { 1 , 2 ,...,N  }  being injected into thenetwork concurrently, each of which can be considered being generated by anunique fictitious flow generator. That is to say, no two flows are from the samegenerator. Each flow corresponds to a source-destination pair ( s,t ) and has anumber of information (packets) to transmit. For example, flow  i  has to routeits  α i  information from  s i  to  t i  in one period of time 5 . We assume that 1) theinformation can be divided into equal size to transmit no matter which flowthey belong to; 2) each flow generator chooses only one path to route all itsinformation; 3)the buffer at each node is large enough to sustain the wholeprocess. 3.4 Interference and Congestion We deploy a linear interference measurement to generalize different kinds of interference model. We use a matrix  I   to characterize the influence of thetransmission on one link on a transmission of another link. For links  e ci ( u,v )  and e c  j ( u  ,v  ) ,  I  ( i,j ) shows to what extent link  e ci ( u,v )  is interfered by link  e c  j ( u  ,v  )  at atime. Note that only the link pairs assigned with the same channel ( c  =  c  ) caninterfere with each other, for the ones assigned with different channels ( c   =  c  ),the corresponding entries are set to zero. After normalization, 0  ≤ I  ( i,j )  ≤  1 2 i  stands for link’s (or edge’s) identity;  u,v  stand for the nodes; and  c  stands for a channel.We will use  e ci ,  e i  and  e  for denoting simplicity according to the context, all of which areliterally equivalent to  e ci ( u,v ) . 3 We will use secondary user, user, SU and node interchangeably in this draft. 4 ”Available” means that the channel is sensed idle, and can be used by the user. 5 In this paper, we consider the concurrent flows. Each generator will choose a routeperiodically. In each period of time,  α i  information are expected to route. 4
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