Cognitive radio channel allocation using

Cognitive Radio Channel Allocation Using Auction MechanismsBin Chen† , Anh Tuan Hoang‡ ←and Ying-Chang Liang‡ ← † Nanyang Technological University, Singapore ‡ Institute for Infocomm Res

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]

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 first-price or second-first-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

out-band sensing at the end of every frame according to their total

winning bids Figure 1 illustrates our proposed operating

sequence in a particular time frame of cognitive radio, where

T i.s and T o.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

out-band 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 T i.s before the auction begins We assume that T i.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:

(1 )

where λ is the packet arrival rate which is assumed to be fixed;

C i is Shannon’s capacity, and vi is user i’s valuation about his

strategic situation To elaborate:

2

log (1 i )

i

o

h p C

N

= +

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; N o is the mean channel noise power

The valuation can therefore be expressed as follows

Figure 1 Proposed operating sequence of a cognitive radio with m transmission slots for auction

2

1 log (1 )

i

i o

N

λ

= −

+

The valuation can be interpreted that user i uses the incoming packet arrival rate as a “ruler” to measure the ever-changing 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 v i 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 v i 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, {b 0 , b 1 , b 2 , … , b K}, to

represent the set of possible bids submitted In this set, b 0

represents the null bid, and we can simply normalize it to zero

without loss of generality b 1 represents the lowest admissible

bid, the reserve price The highest observed bid is b K 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 b i by π i, and

denote the probability of not participating at the auction by π 0

Thus the vector π, which equals (π 0 , π 1 , … , π k), denotes the

probability distribution over B where

0

K i

i= π

∑ equals one It is

assumed that, π is common knowledge to the potential bidders

.is

T m Transmission slots for auction

.

o s T

… …

(1)

The cumulative distribution function ∏ i, which equals

0

i j

is introduced to represent that a bidder bids bi or less All of

them are collected in the vector ∏ which equals (π 0 , ∏ 1 , … ,

∏ K-1 , 1)

The rational potential bidder with a valuation v i then faces

a decision problem of maximizing the expected profit from

winning the auction; i.e

b B v b winning b

< ∈ > −

For a particular bid b i, 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:

1 1

1, 2, ,

i

n −−

∏ − ∏

∏ − ∏

The numerator of the above equation is the probability that

the highest bid is exactly equal to b i, while the denominator is

the expected number of potential bidders submitting bid b i A

bidder’s best response is to submit a bid which satisfies the

following inequality:

(v i− Γ ≥b i) i (v i−b j)Γ ∀ ≠j j i

It means that the profit obtained from bid b i weakly

exceeds any alternative bid b j 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(v i ):

n f v n f v

where f(v i ) and F(v i ) 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:

1 1

( ) ( )

( )

i

r

i

F u du

F v

σ

−

−

For the first-price sealed-bid auction, the bidder i will

submit bid b i =σ(v i ) 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

second-highest bid Therefore, there is no incentive for him to bid

higher or lower than his true valuation as we do not include

the notion of budget here In this case, b i =v i 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 2 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 8 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

first-price and second-first-price sealed-bid auctions They perform

equally well and the reason behind that is: both auctions can

Figure 2 Packet loss percentage for three allocation schemes

Figure 3 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

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 7 The reason is that, at

Figure 4 Mean valuation and mean bid for the first-price auction and its improved version incorporating packet deadline checking algorithm

Figure 5 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 5 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 6 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 7 and 8 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

Figure 7 Throughput of user 1 for combined improvement schemes

Figure 8 Packet loss percentage for combined improvement schemes

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