On-Demand Spectrum Sharing By Flexible Time-Slotted Cognitive Radio Networks

Transcription

1 On-Demand Spectrum Sharing By Flexible Time-Slotted Cognitive Radio Network Shimin Gong, Xu Chen, Jianwei Huang, and Ping Wang Centre for Multimedia and Network Technology, Nanyang Technological Univerity Network Communication and Economic Lab, The Chinee Univerity of Hong Kong { gong, wangping}@ntu.edu.g; { cx8, jwhuang}@ie.cuhk.edu.hk. Abtract In thi paper, we preent a novel framework for pectrum haring in cognitive radio network. The econdary uer (SU) can hare the pectrum reource with primary uer (PU) in a cooperative manner, where PU trade their information and urplu reource, and SU acce the primary pectrum intelligently baed on SU heterogeneou demand and PU reource price. After paying PU a ubcription fee for the pectrum information, SU become pectrum-aware and avoid the overhead on pectrum ening. During SU channel acce, PU further charge SU baed on the amount of reource taken by SU. We model thi haring problem in a flexible time-lotted tructure, where SU deciion include the election of proper tranmiion channel and lot length to meet their demand. Thi joint deciion problem i tudied a a pectral temporal allocation game. We prove the exitence of a Nah equilibrium and deign a trategy update proce which can converge to an equilibrium. Index Term Cognitive radio, pectrum haring, potential game I. INTRODUCTION Spectrum-awarene in cognitive radio network i the baic requirement for harmonic pectrum haring between econdary uer (SU) and primary uer (PU). Due to the hardware contraint or the lack of an efficient ening algorithm, pectrumawarene through independent pectrum ening i rather difficult to implement epecially in dynamic environment. Another alternative i for PU or third partie to maintain a pectrum databae containing PU future activitie over pace and time, and thu relieve SU from the burden of pectrum ening. Compared with independent pectrum ening, the databaeaited pectrum-awarene can be more economic for cenario where the PU activitie do not change frequently. One example i the TV band, where the FCC ha made pectrum databae the default approach and pectrum ening optional []. A the pectrum databae predictively detail PU activitie in near future (e.g., TV program in 4 hour are cheduled in advance and reported to the pectrum databae), SU can query the databae and obtain neceary information to make intelligent deciion on channel acce [], []. In thi paper, we aume the exitence of a pectrum databae, and try to deign an efficient reource haring mech- Thi work i partially upported by the General Reearch Fund (Project Number CUHK47 and CUHK45) etablihed under the Univerity Grant Committee of the Hong Kong Special Adminitrative Region, China. anim that reolve the competition among different SU. We aume that SU have different demand requirement, and how how they compete and negotiate with each other to achieve a balance among their elfih puruit. The key challenge i to deign a pectrum haring mechanim tha ditributed and require only limited information exchange. A game theory i inherently trong at analyzing uer interaction, it become an important method of tudying the reource haring problem in cognitive radio network. A key difference between thi work and variou reuln literature i how the pectrum reource i characterized. Bandwidth haring among SU wa tudied in [4] a an auctionbaed game, where each SU make a bid for the bandwidth and the PU decide how to allocate it pectrum baed on all SU bid. In the mot recent work [5], the author further tudied the auction-baed pectrum allocation in both time and pectral dimenion. Conidering SU flexible requirement, each SU i allowed to ubmit a bid coniting of a bundle of time-frequency lot. Power conumption wa alo conidered in pectrum haring. The author in [6], [7], [8] conidered joint pectrum allocation and power control in a potential game with interference mitigation a the major target. Pricing cheme wa introduced to regulate SU behavior in [9], where bandwidth trading i modeled a a econdary market. A imilar pectrum leaing model i propoed in [], where the trading reource i viewed a the total tolerable interference at primary receiver. In thi paper, pectrum reource i conidered in term of channel and time lot of variable length, or more preciely, in pectral temporal block. Each SU elfihly maximize it atifaction by chooing the proper primary reource (i.e., a tranmiion lot of particular length on a particular primary channel), while conidering the concurred which contain two part: the firt par due to information ervice at the pectrum databae, and the other i related to channel uage. An SU channel uage i characterized by the length of time lot ued for it own tranmiion. A all SU and PU hare the primary channel, an SU channel uage co related to the length of it own time lot, and alo depend on other SU requet of time lot on the ame channel (i.e., congetion cot). We formulate the ditributed joint channel and lot length election problem among all SU a a pectral temporal allocation game with the following feature: Flexible Slotted Acce: We conider a time-lotted frame-

2 propoe the lotted tructure in Fig.. The firt ub-lo left for negotiation: PU negotiate with SU through updating the pectrum databae and offering the channel price. Then, SU compete for the tranmiion lot. When the negotiation proce tabilize, PU and SU tranmiion are cheduled equentially. We aume that the negotiation proce take much le time compared to the tranmiion time of PU and SU. Fig. : Sytem Model work in which SU channel acce i baed on the joint election of channel and time lot. Each SU chooe a proper time lot length to meet own tranmiion demand. Potential Function and Nah Equilibrium: We how that the pectral temporal allocation game i a potential game. According to the finite improvement property of potential game, we deign a ditributed trategy update proce that can converge to a pure Nah equilibrium. The remainder of thi paper i a follow. Section II introduce the ytem model. Section III tudie the game-theoretic reource haring problem and propoe the protocol deign. Numerical reult and concluion are preented in Section IV and V, repectively. II. SYSTEM MODEL We conider a cognitive radio network with N SU and M primary channel in equal bandwidth (e.g., the bandwidth of white-pace channel equal 6 MHz in U.S. and 8 MHz in EU). The et of SU and primary channel are denoted a N = {,,...,N} and M = {,,...,M}, repectively. Each SU i a dedicated pair of econdary tranmitter and receiver, and can only acce one PU channel at one time. With a lower priority, SU channel acce i ubject to the availability of primary channel. To ait SU channel acce, PU predict the pectrum uage and update thi information in a databae, which then provide information ervice for all SU and free the SU from the overhead of pectrum ening. Fig. give an illutration of pectrum haring model. Some notation are left for further explanation. We aume the information exchange among PU, pectrum databae, and SU are through dedicated control channel []. Due to the tochatic natural of PU traffic, tatically allocated pectrum reource i uually not fully utilized when PU experience the off-peak hour. To thi end, PU conider elling the unued pectrum reource to SU and to obtain ome additional revenue. We conider the pectrum reource a tranmiion opportunitie characterized by time lot, and A. Flexible Time Slot The major difference between our model and previouly propoed model i the flexibility of chooing tranmiion time lot length. The higher priority PU can et flexible primary lot t k p on each channel k for their excluive uage in the firt place. Thi etting of t k p hould adapt according to the fluctuation of PU traffic, uch that the probability of pectrum hortage i le than an acceptable level. The detailed procedure for PU to adjut t k p require further invetigation and i beyond cope of thi paper. Here we will aume a fixed primary lot length t k p on each channel k. For the eae of undertanding, we aume that all PU are erved by the ame primary bae tation (PBS), which et the price and reerve the primary lot on all channel. Given the channel price on channel k, each SU i chooe a time lot with length t k i T i [,min,,max ], which i alo flexible according to it tranmiion demand (ee Section II-C for detailed dicuion). Therefore the total length of the time lot on channel k i the ummation of two part, i.e., T k = t k p + t k where T k i defined a a uper lot and t k = i N k tk i denote the total tranmiion time purchaed by SU on channel k. In practice, the PBS can et an additional upper bound T k for the uper lot on each channel k. If there are ome SU with very high demand and requeting large time lot that exceed the length of a uper lot, their requet cannot be fulfilled and they get nothing. In thi cae, the PBS may change the channel price and retart the negotiation. We will dicu thi problem further in the protocol deign in Section III. However, a elfih player, the SU may not accept the channel elling price. To motivate SU payment for their channel acce, the PBS need to provide more than unguaranteed channel acce. In thi paper, we conider nonpreemptive PU, which will not preempt SU tranmiion in the middle of a uper lot. With thi aumption, SU are alo provided with excluive pectrum uage. Neverthele, SU privilege i limited, ince they are till required to upend tranmiion at the end of a uper lot T k whenever PU return during the uper lot. If the traffic demand of PU are high, the PBS can et a mall upper bound T k on the uper lot to improve PU througput. B. PU Pricing Policy A the licene holder, the PBS would like to charge a price on SU channel acce. We adopt a linear price cheme which Actually the pectrum databae can erve a the PBS.

3 and channel acce cot a follow: π i (k, t) =u i (, d i ) α ki j N k i t j β ki β d, () Fig. : Slotted tructure i commonly aumed in literature []: c i (k i, )= β ki + β d () where k i and are the operating channel and lot length of SU i, repectively. Here β ki denote the unit uage price on channel k i, and β d i a contant ubcription fee for the information ervice which i charged by the PBS for the pectrum databae intallation and maintenance, and for the information retrieve for SU trategy update in negotiation tage (pleae refer to Section III-B). A we conider nonpreemptive PU in thi model, we need to have a mechanim that hold PU tranmiion and cache the incoming traffic. Therefore, PU performance will be very enitive to the ize of uper lot. A larger uper lot mean a higher probability of holding PU traffic and a longer waiting time. Although the cot of cache (buffer) i not high today, PU delay performance may be ignificantly affected by a larger uper lot. Thi conideration urge u to redeign the pricing function in (). Beide the unit uage price β ki and contant fee β d, we add a new pricing term tha proportional to the ize of uper lot, i.e., c i (k i, )=α ki T ki + β ki + β d. () Here α ki T ki i the unit price that reflect PU enitivity to tranmiion delay on channel k i, and reflect the delay cot charged to SU i baed on it contribution. For implicity, we define the new unit price a θ ki (T ki )=α ki T ki + β ki, and denote γ ki =(α ki,β ki ) a the pricing parameter on channel k i. Such parameter may be different on different channel. Then we can write the new pricing model a c i (k i, ) = θ ki (T ki ) +β d. When PU traffic are in the peak, the PBS et a higher α ki in order to preerve the primary channel for PU tranmiion. During the off-peak time, the PBS will chooe a maller coefficient α ki, and thu will reduce the impact of the uper loze on SU activitie. C. SU Strategy An SU i problem i to chooe a channel k i A i and a lot length T i to maximize it payoff, where ubet A i M lit all primary channel available for SU i. Thi et repreent the local pectrum map retrieved from the pectrum databae. We define SU payoff a the difference between SU utility where k =[k,..., k N ] and t =[t,..., t N ] denote the channel and lot length election of all SU, repectively. Subet N ki denote the SU chooing the ame channel k i. The utility u i (, d i ) decribe how uer demand d i i atified by the choen time lot. A imple illutration i the quadratic demand function, i.e., u i (, d i )= ( d i ). In thi demand model, SU are rational ince they only puruit the tranmiion opportunitie that exactly meet their demand. A more aggreive demand model i baed on the α-fairne utility function []: { u i (, d di i )= ω t ω i ω<, (4) d i log( ) ω =. When SU are charged with the ame unit price θ k (T k ) on channel k, their optimal lot length are proportional to their demand, i.e., t i (θ k(t k )) = arg max ti u i (, d k ) θ k (T k ) β d =( d i ) ω /θ k (T k ) ω. When primary reource i ufficient, each SU will puruit the lot length a longer a poible. However, beide SU elfih puruit, thi demand model alo conider proportional fairne between competing SU, which i an appealing property in congetion control. A illutrated in Fig., the PBS can et different price for primary channel, reulting in different trategie of 4 SU. Due to the heavy primary traffic load on channel, the PBS et a high price on that channel and drive SU to channel and with light primary traffic load. A a reult, PU tranmiion take up the complete uper lot on channel, i.e., t p = T (here T can be viewed a the maximum length of the uper lot on channel ), while SU and tranmit on channel with a lot length t and t, repectively. III. GAME ANALYSIS AND PROTOCOL DESIGN In thi paper, we focu on the analyi of SU activitie given PBS deciion on channel price (α k,β k ) and primary lot t k p. Then, each SU make independent deciion on channel and lot length election to maximize the individual payoff, by taking into account SU competition, PU channel availabilitie, and channel price. We expre the conflicting goal of all SU into a pectral temporal allocation game G =(N, M, J, Π). Specifically, each player (i.e., SU) i N chooe one available channel k i from it local pectrum repoitory A i M, and purchae a tranmiion lot T i on the choen channel. We denote the joint trategy pace a J = i N J i A T, where A i N A i and T i N T i. SU payoff are defined a Π {π i } i N : J R N where π i i given in (). We are intereted in characterizing the Nah equilibrium (NE) of thi game, where SU independent and elfih behavior may reach a table point where no SU ha an incentive to deviate from it current trategy unilaterally.

4 A. Exitence of Nah Equilibrium Definition : A trategy profile q J i a Nah equilibrium for the game, if and only if π i (q i, q i) π i (q i, q i ), q i J i, i N, where (q i, q i) denote the trategy profile when player i change it trategy to q i, while other player keep their previou trategie (q j,j N,j i) unchanged. Definition : Given the current trategy profile q, trategy update q i i a better repone of SU i if π i (q i, q i) > π i (q i, q i ). Next, we how that our game fall into the cla of potential game [], which alway admit a Nah equilibrium due to ome appealing mathematical propertie in uer payoff function. In a potential game, any change in player payoff function can be reflected by the change of a global potential function Φ( ). Moreover, we will have an exact potential game (EPG) if the unilateral payoff change i the ame a the change in the potential function, i.e., Φ(q i, q i ) Φ(q i, q i )=π i (q i, q i ) π i (q i, q i ). (5) For our pectral temporal allocation game, the change of trategy profile from (q i, q i ) to (q i, q i) implie that uer i unilaterally change it trategy to q i =(k i,t i ). Propoition : The pectral temporal allocation game G poee a potential function in the form of Φ(k, t) = i N Φ i(k, t), where Φ i (k, t) =u i (, d i ) α ki t j + β ki. j i,k j=k i Proof: Given other uer action (k, t ) unchanged, the potential function before uer deviate from it current trategy (k,t ) to (k,t ) i repreented in (6) on the next page. Since Q(k, t ) i irrelevant with the trategy change and will not effect the potential, we can prove that Φ(k, t) i an exact potential function a follow: Φ(k, t ) Φ(k, t) = u (t, d ) t j,k j=k α k t j + β k u (t, d )+t α k t j + β k j,k j=k α k t + α k t i>,k i=k i>,k i=k = u (t, d ) t α k t j + β k j N,k j=k u (t, d )+t α k t j + β k j N,k j=k = π (k,t ) π (k,t ). The nice property in (5) implie that the potential function will be monotonically increaing if uer equentially play their better repone. Therefore, a determinitic trategy profile q J i a pure Nah equilibrium for the potential game if and only if Φ(q) Φ(q i, q i ), q i J i for every player i. Thi implie that finding the Nah equilibrium in a potential game i equivalent to maximizing it potential function. Theorem : Spectral temporal allocation game G poee a pure Nah equilibrium. Proof: Since the potential function Φ(k, t) i finite, there i alway a maximal point q for the potential function. If q i not a NE point and an SU i ha incentive to deviate, then Φ(q i, q i) Φ(q) =π i (q i, q i) π i (q) >, which contradict with the aumption. In order to achieve a Nah equilibrium, we deign a equence of trategy update I {q i,...,q in,...}. Here q in indicate that, in the n-th trategy update, player i n update it trategy. If each trategy update in the equence I trictly increae the payoff function of the correponding player, we call I an improving equence. Propoition : In a potential game, any improving equence I converge to a Nah equilibrium within finite tep. Propoition preent the finite improvement property of a potential game []. Since our potential function Φ(k, t) i finite, any improving equence will maximize it within finite tep and achieve a Nah equilibrium. B. Protocol Deign Baed on the finite improvement property, we now deign a ditributed protocol for the channel negotiation in Fig.. Suppoe that an SU i currently chooing trategy (k, t). Then we can rewrite it cot function a c i (k, t) =α k t + β k t + α k p i k t + β d, where p i k = j N k,j i t j repreent the congetion level SU i experienced on channel k. The firt two term in the cot function relate to PBS pricing parameter on channel k. The third term relate to uer-pecific channel experience. And the lat term i the contant ubcription fee for all SU. Therefore, we define an information et {p i k,γ k} k Ai to characterize the channel quality perceived by SU i. Note that the pricing parameter γ k =(α k,β k ) i channel pecific, and can be broadcated by the PBS when SU enter the network. While the congetion level need to be informed by PBS during the negotiation. The cot of information broadcat by PBS can be integrated into the information ervice fee. We denote SU better repone a a et BR i (k, t) {(k,t ) A i T i π i (k i,k, t i,t ) > π i (k, t)} given the current trategy profile (k, t). Finite improvement property require aynchronou trategy update, which can be achieved through the PBS coordination. Before the competition among SU reaching a Nah equilibrium, the PBS equentially poll SU to update their trategie and pae them the information et. After receiving SU trategy update, the PBS then update the information et and pae it to the next SU. Thi proce iterate until no SU i willing to update it trategy any more. In the tranmiion tage, all SU will be cheduled to tranmit within 4

5 Φ(k, t) = u (t, d )+ i u i (, d i ) t i>,k i=k α k t j + β k j,k j=k α ki t j + β ki i,k i=k j i,k j=k i,k i=k = u (t, d ) t α k t j + β k + Q(k, t ) j,k j=k α k t j + α kt + β k j i,j, k j=k α ki i>,k i=k i, k i k,k j i,k j=k α k α ki t j + β ki j i,j, k j=k t j + β ki j i,k j=k i t j + β k. (6) their own time lot. We propoe the aynchronou trategy update proce in Algorithm. However, there i till a poibility that the um of SU required time opportunitie at the equilibrium exceed PU acceptable lot length (i.e., the length of uper lot on a channel k i greater than the pre-defined upper bound T k ). We leave thi to the PBS dicretion a hown in Fig.. More pecifically, if the converging equilibrium by Algorithm doe not atify the total time length contraint, the PBS reject thi equilibrium. Baed on the time lot purchaed by different SU on different channel, the PBS predict the demand of SU. Then the PBS update the channel price accordingly, and initiate another round of negotiation proce. When the negotiation reache a feaible equilibrium, all PU and SU are cheduled to tranmit according to the converging pectral temporal allocation. Algorithm Spectral Temporal Allocation : initialization: : SU chooe initial trategy (k, t) : PBS broadcat the pricing information 4: end initialization 5: loop until convergence 6: PBS poll an SU to update trategy 7: PBS pae information et {p i k,γ k} k M to SU 8: SU i update trategy (k,t ) from et BR i (k, t) 9: end poll : end loop Once the context (i.e., pectrum environment) ha been changed, the PBS will upend the periodic tranmiion and tart another around of negotiation at the end of the previou uper lot. For TV band, the change of pectrum environment i uually due to prearranged program hifting in a larger time cale. In thi cae, thi protocol can provide long time table operation for SU with mall negotiation overhead at a Nah equilibrium. Fig. : Flowchart of the competition and negotiation proce. IV. SIMULATION RESULTS In the imulation, we conider N = SU haring M = primary channel. We ue the α fairne utility in (4) and et ω = for all SU. SU demand requirement are characterized by different parameter d = [,, 4, 5, 6, 55, 45, 5, 5, 5]. Each SU choice of lot length i limited to the interval et T =[.5, 5]. We conider the PU in the peak hour, thu the unit price β k i mall compared to α k T k. According to PU traffic demand, we aume that the PBS et the pricing parameter for channel a α =[.5,.5,.5] and β k =for k =,,. We alo aume that the ubcription fee for the pectrum databae i negligible and hence et β d =. Fig. 4a how the dynamic of SU election on their time lot during the algorithm iteration. Initially, we et all SU tranmit on channel with the unit lot length. Due to evere congetion and the high price on channel (α =.5), SU obtain mall payoff initially a hown in Fig. 4b. After ome iteration (around 5), SU choice of lot length coincide with their demand. Note that SU 4, 5, and 6 are high 5

6 SU SU SU SU 4 SU 5 SU 6 SU 7 SU 8 SU 9 SU SU SU 4 SU SU 4 SU 5 SU 6 SU 7 SU 8 - SU 9 SU CH CH CH (a) Slot allocation (b) Uer payoff Fig. 4: Dynamic of lot length election, uer payoff, and channel price (c) Channel price 4 Channel 4 5 Secondary uer (a) Nah equilibrium (b) Potential function Fig. 5: Convergence to Nah equilibrium demanding uer (higher value in vector d), therefore they chooe longer time lot and their final payoff tabilize on the top of Fig. 4b. Meanwhile, the lot length and payoff of low demanding SU, 9, and converge to maller value. The initial high price on channel urge competitive SU to deviate from evere congetion, therefore raie the price on other channel. When price on different channel become cloe enough to each other a hown in Fig. 4c, there will be no incentive for any SU to deviate. Fig. 5a plot the channel acce map at an NE point, where every SU channel acce trategy i the bet repone of other SU trategie. The Nah equilibrium i further verified by the maximum point of it potential function a hown in Fig. 5b, which gradually increae a different SU aynchronouly update their trategie. V. CONCLUSION In thi paper, we tudy the joint channel and lot election problem for competitive SU with primary pricing. Thi problem i modeled a pectral temporal allocation game which i hown to be a potential game. We prove the exitence of a pure Nah equilibrium, and deign a trategy update proce that converge to a Nah equilibrium. A an extenion, we may conider the interaction between PBS pricing and SU trategy change, and thu model the whole ytem uing a multi-tage dynamic game. REFERENCES [] FCC unlicened operation in the tv broadcat band - final rule, Federal Regiter, vol. 75, no., December. [] R. Southwell, J. Huang, and X. Liu, Spectrum mobility game, in Proceeding of the th IEEE International Conference on Computer Communication (INFOCOM ), March. [] X. Chen and J. Huang, Game theoretic analyi of ditributed pectrum haring with databae, in Proceeding of IEEE International Conference on Ditributed Computing Sytem (ICDCS ), Macau, China, June. [4] X. Wang, Z. Li, P. Xu, Y. Xu, X. Gao, and H.-H. Chen, Spectrum haring in cognitive radio network - an auction-baed approach, IEEE Tranaction on Sytem, Man, and Cybernetic, Part B: Cybernetic, vol. 4, no., pp , June. [5] M. Dong, G. Sun, X. Wang, and Q. Zhang, Combinatorial auction with time-frequency flexibility in cognitive radio network, in roceeding of the IEEE International Conference on Computer Communication (INFOCOM ), March, pp [6] N. Nie and C. Comaniciu, Adaptive channel allocation pectrum etiquette for cognitive radio network, in Proceeding of IEEE Sympoium on New Frontier in Dynamic Spectrum Acce Network (DySPAN 5), Nov. 5. [7] I. Mutika, K. Yamamoto, H. Murata, and S. Yohida, Spectrum haring with interference management for ditributed cognitive radio network: A potential game approach, in Proceeding of the 7t IEEE Vehicular Technology Conference (VTC ), May. [8] M. Canale, J. R. Gallega, and R. Ciria, Ditributed channel allocation and power control in cognitive radio network uing game theory, in Proceeding of IEEE Vehicular Technology Conference (VTC Fall ), September. [9] D. Niyato and E. Hoain, Competitive pectrum haring in cognitive radio network: a dynamic game approach, IEEE Tranaction on Wirele Communication, vol. 7, no. 7, pp , July 8. [] G. El-Howayek and S. Jayaweera, Ditributed dynamic pectrum leaing (d-dl) for pectrum haring over multiple primary channel, IEEE Tranaction on Wirele Communication, vol., no., pp. 55 6, Jan.. [] K. Chowdhury and I. Akyldiz, OFDM-baed common control channel deign for cognitive radio ad hoc network, IEEE Tranaction on Mobile Computing, vol., no., pp. 8 8, Feb.. [] L. Yang, H. Kim, J. Zhang, M. Chiang, and C. W. Tan, Pricing-baed pectrum acce control in cognitive radio network with random acce, in Proceeding of the th IEEE International Conference on Computer Communication (INFOCOM ),, April. [] D. Monderer and L. S. Shapley, Potential game, Game and Economic Behavior, vol. 4, no., pp. 4 4,