Cognitive Radio Channel Allocation Using Auction Mechanisms Bin Chen† , Anh Tuan Hoang‡ ←and Ying-Chang Liang‡ ← † Nanyang Technological University, Singapore ‡ Institute for Infocomm Research, 21 Heng Mui Keng Terrace, Singapore 119613 ycliang@i2r.a-star.edu.sg Abstract - We adopt the auction mechanisms into the dynamic channel allocation of cognitive radio networks Under auction schemes, users bid the transmission time slots to gain access to the licensed channel Their bids accumulate throughout the repeated bidding process over time, and they pay the “bill” at the end of the time frame in the form of out-band sensing By doing so, we allocate the channel to the user who values it most, and impose a responsibility for out-band sensing which is split up among users according to their aggregate winning bids We study the allocation under both first and second price sealed-bid auctions and find that they yield similar outcomes in terms of throughput and efficiency We also develop two auction-based improvement schemes to address the traffic issue in secondary nodes, and the system performance receives a significant boost as a result I INTRODUCTION Cognitive radio networks make use of the under-utilized spectrum as the resource to exploit secondary usage by allowing opportunistic spectrum access from the secondary users The under-utilized spectrum is termed spectrum hole [1] While the detection of the spectrum hole has been analyzed very detailed in [2], how to use the spectrum hole efficiently remains a problem Due to the ever-changing characteristics of the channel quality and the traffic of secondary networks, an adaptive channel allocation algorithm is essential to address the dynamic spectrum management issue Game theory, a formal study of conflict and cooperation, has been applied extensively in communication The reason of popularity of game theory in communication networks is that it deals primarily with distributed optimization – individual users, who are selfish, making their own decisions instead of being controlled by a central authority [3] Game theory helps to solve many NP-problems in the communication system, and reduces the computational complexity especially when the system scales up Auction is an extremely useful tool in game theory It is a method for determining the value of a commodity that has an undetermined or variable price Most of the auctions are designed with the goal of allocating the limited resources more efficiently It has been used extensively in the mobile telecommunications industry to allocate rights to the use of bands of electromagnetic spectrum and additionally raised billions of dollars in the United States and Europe [5] 978-1-4244-1645-5/08/$25.00 ©2008 IEEE 1564 Recently, game theoretic concepts and auction-based algorithms have received much attention in communication network design In [6], game theory is applied to accommodate selfish nodes in CSMA/CA networks In [7], auction-based mechanisms are used to deal with the spectrum sharing problem subject to the interference temperature constraint In [4], a second-price auction mechanism is proposed to deal with wireless channel allocation Here, we apply the first-price and second-price sealed-bid auctions into the channel allocation and sensing problem of cognitive radio networks, modeling the out-band sensing time as the price that secondary nodes have to pay in order to obtain the transmission opportunities We test our auction models in the computer simulation to compare their performances The rest of the paper is organized in this way In section II, we describe the channel allocation and sensing problem of cognitive radio networks as well as the general system model In section III, we present our auction mechanisms In section IV, we introduce two schemes to improve the auction mechanisms In section V, simulation results are shown Finally we conclude the paper in section VI II PROBLEM DESCRIPTION AND SYSTEM MODEL For a cognitive radio network, a secondary (licensed) user has to sense the status of the primary (licensed) user from time to time in order to make sure that it does not collide with the primary user, thus the primary user’s right can be protected In [2], the operating time of a secondary user is divided into frames, and the secondary user carries out sensing at the beginning of every frame That sensing is also called in-band sensing, in which the secondary user keeps track of the availability of the channel that he is currently using For the dynamic spectrum management, out-band sensing is also an essential element The status of the backup channels also needs to be checked from time to time in case the secondary user has to vacate the current channel when the primary user wakes up Thus when he switches to the new channel, there would be minimal delay due to the “trial-and-error” process We expect different secondary users to view a channel differently due to fading and their ever-changing traffic conditions The issue of fairness induces the idea of allowing secondary users to compete for channels through either firstprice or second-price auction They take their own decisions to bid after evaluating the channel condition, traffic and other payoff-relevant information Then they commit to the outband sensing at the end of every frame according to their total winning bids Figure illustrates our proposed operating sequence in a particular time frame of cognitive radio, where Ti.s and To.s are the in-band and out-band sensing time respectively The rest of the time is divided into m slots for bidding Whenever a secondary node wins … the bid, a certain portion directly proportional to his bid would be registered at the outband sensing time slot After the total m transmission time slots in a particular frame have been sold out, users would pay the price (contribute to out-band sensing) at the end of the frame according to their accumulated lengths of out-band sensing time System Model 1) Cognitive Network Model: We consider a secondary network with N users and S available channels For a particular channel s, there are n users interested in To protect the primary user, secondary users have to carry out in-band sensing Ti.s before the auction begins We assume that Ti.s and the frame size have been predetermined to meet the requirements for the detection of primary user At each time instance, there is only one secondary user can access the channel s To exclude the confounding variables, we assume that that channel is always available and no misdetection would occur when the primary user is actually not present 2) Traffic Model: We assume that data packets that randomly arrive to the buffers of secondary nodes follow a Poisson distribution with mean λ All data packets have the same size of L bits and same deadline of D seconds If a packet is not transmitted by its deadline, it is dropped and considered lost It is also assumed that the buffers of all secondary nodes are long enough so that no buffer overflow would occur 3) Channel Model: The channel coefficient between the secondary transmitter and receiver is assumed to be randomly distributed on the interval [h_min, h_max] We assume that the channel coefficient is unchanged during each time slot Secondary users are assumed to know their channel state information at the beginning of each slot III AUCTION MECHANISMS To reflect a particular user i’s valuation about the channel condition, a simple valuation function is proposed: λ = Ci (1 − vi ) where λ is the packet arrival rate which is assumed to be fixed; Ci is Shannon’s capacity, and vi is user i’s valuation about his strategic situation To elaborate: Ci = log (1 + hi p ) No where hi is the channel coefficient between user i’s transmitter and receiver; p is the transmit power and is also assumed to be a constant for simplicity; No is the mean channel noise power 1565 The valuation can therefore be expressed as follows Frame Frame K Frame … Ti.s m Transmission slots for auction To.s Figure Proposed operating sequence of a cognitive radio with m transmission slots for auction vi = − λ log (1 + hi p (1) ) No The valuation can be interpreted that user i uses the incoming packet arrival rate as a “ruler” to measure the everchanging channel state condition with the objective of clearing newly arriving packets The valuation here measures a secondary user’s (if he wins the auction) willingness and capability to sacrifice the corresponding portion of his capacity while still achieving the objective stated earlier Putting in this way, we assume that the user always has packets to transmit We observe that when the channel condition is good, the user would be more willing and affordable to sacrifice As a result, a higher bid would be expected from him and vice versa Note that we design the auction in such a way that vi does not represent the real price that a secondary user has to pay during the transmission; it is merely an interpretation of the strategic situation that a user is facing vi truthfully reflects a user’s channel condition In addition, since the channel coefficient h is a continuous random variable with a known distribution, the distribution of v is also known due to their relationship shown in (1) v lies in the interval [v_min, v_max] We design a discrete bid space B, {b0, b1, b2, … , bK}, to represent the set of possible bids submitted In this set, b0 represents the null bid, and we can simply normalize it to zero without loss of generality b1 represents the lowest admissible bid, the reserve price The highest observed bid is bK The bid increment between two adjacent bids is taken to be the same in the typical case In the event of ties, the object would be allocated randomly to one of the tied bidders For the first-price sealed-bid auction, a theoretical model is borrowed from Harry J Paarsch and Jacques Robert’s paper [8] We denote the probability of observing a bid bi by πi, and denote the probability of not participating at the auction by π0 Thus the vector π, which equals (π0, π1, … , πk), denotes the probability distribution over B where ∑ K π i equals one It is i =0 assumed that, π is common knowledge to the potential bidders The cumulative distribution function ∏i, which equals ∑i π j , j =0 is introduced to represent that a bidder bids bi or less All of them are collected in the vector ∏ which equals (π0, ∏1, … , ∏K-1, 1) The rational potential bidder with a valuation vi then faces a decision problem of maximizing the expected profit from winning the auction; i.e max (vi − bi ) Pr( winning | bi ) For a particular bid bi, we denote Гi as the equilibrium probability of winning, these probabilities are collected in Г, (Г0, Г1, … , ГK) Using π, the elements of the vector Г can be calculated Intuitively, the element Г0 is known to be zero because when someone submits the null bid, he is not going to win For the remaining elements of Г, one can directly verify that the following constitute a symmetric, Bayes-Nash equilibrium of the auction game: (∏i ) n − (∏ i −1 ) n Γi = ∀i = 1, 2, , K n(∏i − ∏ i −1 ) The numerator of the above equation is the probability that the highest bid is exactly equal to bi, while the denominator is the expected number of potential bidders submitting bid bi A bidder’s best response is to submit a bid which satisfies the following inequality: (vi − bi )Γ i ≥ (vi − b j )Γ j ∀j ≠ i It means that the profit obtained from bid bi weakly exceeds any alternative bid bj The above inequality is the discrete analogue to the equilibrium first-order condition for expected-profit maximization in the continuous-variation model which takes the form of the following ordinary differential equation in the strategy function σ(vi ): σ '(vi ) + σ (vi ) (n − 1) f (vi ) ( n − 1) f (vi ) = vi F (vi ) F (vi ) where f(vi ) and F(vi ) are the probability density and cumulative distribution functions of bidder’s valuation respectively We assume that they are common knowledge to bidders along with n, the number of potential bidders We denote the reserve price by r, and the above differential equation has the following solution: ∫ σ (v ) = v − vi F (u )n−1 du (2) F (vi ) n−1 For the first-price sealed-bid auction, the bidder i will submit bid bi=σ(vi ) in equilibrium and pay a price proportional to his bid if he wins For each user, the total payment will be calculated after each frame The payment is made in the form of out-band sensing, but as we confine the out-band sensing time to a fixed slot, a normalization process is required In the end, out-band sensing time slot of the frame will be split up and each user carry out out-band sensing according to the calculated ratio of their total winning bids For the second-price sealed-bid auction, the bidder i will submit his valuation truthfully, because the price he has to pay if he wins the auction is not the winning bid but the secondhighest bid Therefore, there is no incentive for him to bid i i r 1566 higher or lower than his true valuation as we not include the notion of budget here In this case, bi=vi The payment process is the same as in the first-price auction IV IMPROVEMENT SCHEMES FOR THE AUCTION The mechanisms mentioned in the previous section have yet to take the traffic into account for the valuation The valuation of a secondary user should be higher if he has more packets in the buffer, thus he might want to submit a higher bid to win the auction so as to prevent the deadline violation of the packets in the buffer However, inserting this variable directly into the valuation function is a bit difficult as the buffer length varies stochastically, and the distribution of the packets which will expire over time is unknown In order to deal with this problem, a methodology of packet deadline checking is integrated into the auction mechanisms Before submitting the bid, a secondary user checks the amount of packets that would expire if he fails to win the following transmission slot Then he adds a corresponding amount of bid increments to the quantized equilibrium bidding solution of (2) if it is the first-price auction, or it adds the increments directly to the quantized valuation of (1) if it is the second-price auction Furthermore, we also consider the possible packet loss due to the randomization created by the “tie breaking rule” and the variation of the channel coefficient A loser bonus scheme is thus incorporated into the auction mechanisms In this scheme, a secondary node who fails to win a transmission slot will automatically gain one bid increment in the next auction The “bonus” will accumulate until he finally wins an auction The combined effect of these two improvement schemes has also been studied V SIMULATION RESULTS In this section, we test the auction mechanisms and the improvement schemes in the simulation We consider a cognitive radio network with one available channel, one base station and multiple secondary users (more than 2) The state of the primary user is initially set to be idle and its mean idle time is sufficiently large so that it is not going to wake up during the running time We set the mean packet arrival rate λ to be 0.1 packet/ms, and the packets length to be 1000 bytes with deadline of 40 ms We assume that the bandwidth of the channel is 1MHz, all secondary nodes use mW of transmit power and the channel coefficients between the secondary transmitters and receivers are drawn from a uniform distribution on the interval [0.05, 1] The frame size of the sensing time is 100ms Each time frame is divided into 10 slots, with in-band and out-band sensing time occupying one slot each while the remaining slots in the middle are used for auction The channels are static during each slot of time After calculation, the valuation v is found to be in between 0.2 and 0.82 For simplicity, the reserve price is set to be 0.2 and the bid increment is 0.005 In Fig 2, the overall packet loss rate is plotted against the different population sizes of secondary users for both firstprice and second-price sealed-bid auctions They perform equally well and the reason behind that is: both auctions can Figure Packet loss percentage for three allocation schemes incorporate the packet deadline checking in to the first-price auction, the convergence is even faster We notice that the gap between the two “mean bid” curves remains almost constant after the number of users grows up to The reason is that, at Figure Mean valuation and mean bid for the first-price auction and its improved version incorporating packet deadline checking algorithm Figure Throughput of a particular user for three allocation schemes allocate the resource to the party possessing the highest valuation of the object In our system, both auctions allocate the transmission slots to the secondary nodes with the best channel state conditions In second-price auction, the true valuation is revealed, so the outcome is not surprising This might not be so obvious in the first-price auction, as the bidder is trying to maximize the profit from winning by lowering the bid below his true valuation However, in equilibrium, as every bidder adopts the same strategy, the bidder with the highest valuation still stands out Comparing with random allocation scheme, we can observe that the auction-based schemes are significantly better The system efficiency increases due to the auction mechanisms and the positive impact on the individual can be seen in Figure 3, where the throughput of a particular user is plotted again the population size In Figure 4, the mean valuation and bid of a particular bidder is plotted against the population size for the first-price auction It shows that the gap between the mean valuation and the bid is decreasing with the increasing population size It is a reasonable behavior for the first-price bidder because when the competition becomes more intense, the winning chance declines, they will try to raise their bids closer to their true valuations to maintain a certain winning probability When we 1567 Figure Revenue of auctioneer represented by mean out-band sensing time for first-price and second price auctions large enough population sizes, the packets in the buffer of each user would accumulate to the extent that the packet loss rate is almost constant over time A bottleneck of the channel capacity has been met that the packet clearing rate under the average channel capacity is unable to catch up with the packet expiring rate Therefore even with the packet deadline checking, we hit the ceiling of the improvement due to the constraint of the channel capacity and the limited resource In Figure 6, we study the revenue gained by the auctioneer in the original first-price and second-price auctions The revenue in this case is the out-band sensing time committed by the secondary users We observe that when the population size exceeds 6, the revenues created by both auctions become virtually the same It can be explained by Revenue Equivalence Principle (REP) and Figure In REP, it states that any auction that allocates the object to the bidder with the highest value, provided that this value exceeds v*, yields the same expected revenue v* is the revenue maximizing reserve price [9] When the population size exceeds 6, the first-price bidder raises his average bid value closer to his true valuation as shown in Figure 5, so his average bid value exceeds the revenue maximizing reserve price v* and REP applies In Fig 6, the proposed improvement schemes are studied in terms of packet loss It is not surprising to find that both schemes enhance the system performance In contrast, both schemes implemented in the second-price auction perform Figure Throughput of user for combined improvement schemes Figure Packet loss percentage for different schemes including improved schemes with loser bonus or packet deadline checking algorithm better than that in the first-price auction It can be attributed to the masking of bids in the first-price auction The strategic bidding function not only lowers the bid, it also reduces the discrete bid space, and thus enlarges the randomization effect especially when the there are more users in the network That is not the case for second-price auction as the bonus is built directly upon the true valuation of the users We also observe that the packet deadline checking scheme is more effective than the loser bonus scheme for both types of auctions The reason behind it is: the packet deadline checking scheme is a more direct way to account for the packet deadline violation We incorporate both schemes in the auctions and the performance is illustrated in Figure and We refer it to both system efficiency and individual performance When comparing with the random allocation scheme, we see that the improved auction mechanisms outperform it by as much as 50% at the larger population sizes VI CONCLUSION In this paper, we implement the auction-based mechanisms into the dynamic channel allocation problem of cognitive radio networks We have found that two types of auctions, namely first-price and second-price sealed-bid auctions yield similar performances in terms of revenue and efficiency They distribute the resource to the party who value it the most and thus boost the system efficiency and individual satisfaction We understand that the auction mechanisms in our environmental set-up are quite different from the conventional economic auctions where bidder’s valuation about an object does not change so frequently and randomly To fit the mechanisms into our system, we develop two improvement schemes and level up the efficiency of the auction significantly as a result 1568 Figure Packet loss percentage for combined improvement schemes REFERENCES [1] S Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications 23 (2), 2005 [2] Y.-C Liang, Y Zeng, E Peh and A T Hoang, “Sensingthroughput tradeoff for cognitive radio networks,” in Proc of IEEE ICC’2007 [3] Allen B MacKenzie, Stephen B Wicker, “Game Theory in Communications: Motivation, Explanation, and Application to Power Control,” Global Telecommunications Conference, 2001 [4] J Sun, L Zheng and E Modiano, “Wireless Channel Allocation Using an Auction Algorithm,” IEEE Journal Selected Areas in Communications, Volume 24, Issue 5, May 2006 [5] Theodore L Turocy and Bernhard von Stengel, “Game Theory,” Encyclopedia of Information Systems, Academic Press, 2002 [6] M Cagalj, S Ganeriwal, I Aad, and J.-P Hubaux, "On selfish behavior in CSMA/CA networks," in Proc IEEE INFOCOM 2005 [7] J Huang, R Berry, and M Honig, “Auction-based Spectrum Sharing,” ACM/Kluwer MONET special issue on WiOpt’04, 2004 [8] Harry J Paarsch and Jacques Robert, “Testing Equilibrium Behaviour At First-Price, Sealed-Bid Auctions,” CIRANO Working Papers series with number 2003s-32 [9] E Maasland and S Onderstal, “Auction Theory,” Medium Econometrische Toepassingen, Volume 13 Issue 2005 ... CONCLUSION In this paper, we implement the auction-based mechanisms into the dynamic channel allocation problem of cognitive radio networks We have found that two types of auctions, namely first-price... occur 3) Channel Model: The channel coefficient between the secondary transmitter and receiver is assumed to be randomly distributed on the interval [h_min, h_max] We assume that the channel coefficient... auction mechanisms and the improvement schemes in the simulation We consider a cognitive radio network with one available channel, one base station and multiple secondary users (more than 2) The state