IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 9, SEPTEMBER 2008 639

Improved Policy for Resource Allocation inDecentralized Dynamic Spectrum Sharing Systems

Ivan Cosovic, Member, IEEE, Takefumi Yamada, Member, IEEE, and Koji Maeda

Abstract—In this letter, resource allocation in decentralizedspectrum sharing systems applying the existing policy rulereferred to as ”inequality-averse policy” is focused on. Theproblem related to the impact of inaccurate estimation of futuretraffic demands on the performance of such systems is addressed.To alleviate the problem, improved policy, which introducesadjusting factors and is resistant to such estimation errors, isproposed.

Index Terms—Spectrum sharing, decentralized resource allo-cation, inequality-averse, misallocation-averse.

I. INTRODUCTION

IT IS increasingly difficult to satisfy growing demands forspectrum with the conventional policy of fixed spectrum

allocation. To overcome this problem, cognitive radio anddynamic spectrum sharing methods that can significantlyimprove spectrum utilization of the spectrum have gainedincreasing interest recently e.g., see [1], [2].

In this letter, a decentralized approach for spectrum sharingamong wireless systems is focused on and the conventionalpolicy rule referred to as ”inequality-aversion model” [3]based on social anthropological studies is investigated. In [4]a decentralized algorithm based on this model is proposedto control inter-system fairness between wireless systems. Inthis model, the fairness control among the wireless systemsis done according to the estimated traffic demands. However,the effects of traffic estimation inaccuracies which can causeperformance degradations are not taken into account in [4].In order to address this problem, in this letter adjusting coef-ficients in the resource allocation control of the ”inequality-aversion model” are introduced to reduce such degradations.

II. CONVENTIONAL ”INEQUALITY-AVERSE” POLICY

In [4] a policy was proposed known as the ”inequality-aversion” model. This model is based on the aversion toinequality of wireless system payoffs in a spectrum sharinggame and was originally established by social anthropologystudies [3]. The inequality-aversion policy enables the wirelesssystems to act as altruists and their unselfish behavior enablesstable and sustainable community. The utility function basedon the inequality-aversion can be modeled as

ui =xi

Ai− αi

N − 1

∑xjAj

>xiAi

(xj

Aj− xi

Ai

)− βi

N − 1

∑xiAi

>xjAj

(xi

Ai− xj

Aj

)

(1)

Manuscript received May 2, 2008. The associate editor coordinating thereview of this letter and approving it for publication was G. Hong.

I. Cosovic is with DOCOMO Communications Laboratories Europe GmbH,Munich, Germany (e-mail: cosovic@docomolab-euro.com).

T. Yamada and K. Maeda are with NTT DOCOMO, Inc, Japan (e-mail:{yamadatak, maedakou}@nttdocomo.co.jp).

Digital Object Identifier 10.1109/LCOMM.2008.080697.

where ui is the utility of the i-th wireless system and eachwireless system behaves so as to independently maximizeit. Term xi indicates the payoff of the i-th wireless system,which represents the benefit of the wireless system, such asits profit, quantity, or other time-dependent measure. In thisletter the payoffs indicate the amount of spectrum used forthe signal transmissions. Term Ai is the priority level of i-thwireless system among all wireless systems and can be sete.g., in accordance with a wireless system’s traffic demand.N is the number of wireless systems sharing the spectrum.Parameters αi and βi indicate the reacting factor of the i-thwireless system against other wireless systems who receive ahigher payoff and against wireless systems who receive lowerpayoffs, respectively. Based on an anthropological study [3], itis shown that a sustainable community where wireless systemsreceive equal payoffs can be established by setting αi > βi.

Wireless systems could exchange their payoff values andthe priority levels by the information exchange via a backbonenetwork connected to all wireless systems. Alternatively, eachwireless system could individually measure payoffs by moni-toring all transmitted signals from users and by detecting, viasignal headers, to which wireless systems the users belong.

As an example for applying these spectrum sharing policiesto wireless communication systems, it is assumed that thesepolicies are implemented as a transmit probability control foreach wireless system. The transmit probability pi(t) for thei-th wireless system at the time t is given by [4]

pi(t)=max(0, min(1, pi(t − 1) + ΔPi(t))) (2)

where ΔPi(t) is the update to transmit probability of the i-thwireless system at time t. ΔPi(t) is calculated as

ΔPi(t)=αi

N − 1

∑xjAj

>xiAi

(xj

Aj− xi

Ai

)− βi

N − 1

∑xiAi

>xjAj

(xi

Ai− xj

Aj

)

(3)where Ai = Wiλi and λi is the estimated traffic demand forthe i-th wireless system and Wi is an optional discountingfactor selected according to possible further priority levels ofi-th system. By controlling the transmit probability of eachwireless system based on (2) and (3), the policy on spectrumsharing reflects the inequality-averse behavior of each wirelesssystem. Note, in a practical system the policy would need tobe implemented in machine understandable language, but weskip such details due to the space limitations of this letter.

III. IMPROVED ”MISALLOCATION-AVERSE” POLICY

In the conventional inequality-averse policy rule, the prob-lem of falsely estimated traffic demand λi is not consideredand it is assumed that future traffic demand is always perfectly

1089-7798/08$25.00 c© 2008 IEEE

640 IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 9, SEPTEMBER 2008

known. However, in a realistic case the traffic demand whichis estimated long in advance does not match with the actualtraffic demand. The closer the transmission frame is, the bettera wireless system can estimate its actual traffic demand at aspecific place. However, signaling of estimated traffic demandsamong wireless systems on a very short-term basis is notfeasible due to the related signaling overhead. This means thatit is not viable to re-broadcast estimated traffic demands evenif the estimation error is afterwards found by some wirelesssystems. Thus, it is reasonable to assume that in a realistic casewireless systems exploit only the estimates of traffic demandof other wireless systems obtained on longer-time basis. Onthe other hand, prior to actual transmission each wirelesssystem has very accurate estimation of its traffic demand. Inthe following, a problem which occurs in such a realistic caseis described by using an example.

We observe situation in which two systems, termed S1 andS2, share the spectrum. We define: their actual traffic demandsa1 and a2, the estimated upcoming traffics λ1 and λ2, acquiredchannel resources x1 and x2, and transmit probabilities p1 andp2. The estimated traffic amounts λ1 and λ2 are broadcastedon long-term basis to S1 and S2 and shared by them. Asmentioned, it is reasonable to assume that it is not viable tore-broadcast on short-time basis even if the estimation errorscan be found afterwards, due to the related signaling overhead.According to the broadcasted information of λ1 and λ2, S1 andS2 attempt to acquire the channels based on the inequality-averse policy.

In Fig. 1(a) an ideal situation is shown in which λ1 =a1 and λ2 = a2. If there is enough spectrum available, bothsystems can acquire enough spectrum resources by controllingp1 and p2, so that a perfect fairness, that is x1/λ1 = x2/λ2

(e.g., x1/λ1 = x2/λ2 = 1) can be achieved. In this situationthere is no channel over-consumption and no channel shortage.Consequently, misallocation, which we define as |λi −xi|/λi,equals zero.

As shown in Fig. 1(b), which is a more realistic scenario,we assume the estimated traffic amount of S1, λ,

1, has anerror such as λ,

1 > λ1 = a1. This error decreases the ratioof the acquired channel resource x1 to the estimated amountof upcoming traffic λ,

1. Hence, S1 attempts to acquire morechannel resources than needed up to x,

1(x,1 > a1) so as to

keep fairness against S2. At the same time, S2 attempts todecrease channel resources down to x,

2(x,2 < a2) for keeping

the fairness, i.e., so as to satisfy x,1/λ,

1 = x,2/λ,

2. Because x,1

is larger than the correct value a1, S1 has unused channels,resulting the misallocation performance for S1 will worsen.Also, the misallocation for S2 will worsen due to the channelshortages.

In summary, overall misallocation performance will beworsening due to the S1 overestimation of upcoming trafficvolume. To significantly reduce the negative impact on theperformance of the problem described above, we adopt thefollowing strategy: We adjust transmission probability of thewireless systems which establish its own estimation error bylocally exploiting the knowledge of this error. In our improvedpolicy, termed misallocation-averse, transmission probability

Fairness control

x1’/λ

1’ = x

2’/λ

2

Fairness control

x1/λ

1= x

2/λ

2=1

S1

S2

x1λ

1=a

1

λ2=a

2x2

channel

shortage

channel over-

consumption

S1

S2

x2’

λ2=a

2

x1’

a1

λ1’

(a) (b)

Fig. 1. Effect from inaccurate estimation of future traffic demand for theconventional inequality-averse policy: (a) ideal and (b) realistic case.

pMA,i(t) is adapted by introducing weights Ci and Di

pMA,i(t)=max(0, min(1, CiDi(pMA,i(t − 1) + ΔPi(t))))(4)

where

Ci =Call − γCcoll,i∑Nj=1 xj + Ccoll,i

=Call − γCcoll,i

Call − Cblank,i(5)

and

Di =

{ai/λi, λi > ai

1, otherwise.(6)

In (5), Call is the total amount of shared spectrum, Cblank,i

indicates the amount of unused spectrum measured by thei-th wireless system, Ccoll,i is the amount of spectrum losscaused by signal collisions, and γ reflects the sensitivity for thespectrum loss over the unused spectrum. In the paper we con-sider that all systems share the common pool of frequencies,so ideally these values are common for all wireless systems.However, they may be different for each wireless system dueto the measuring errors that occur if each wireless systemmeasures individually Cblank,i, Ccoll,i and xj by sensing theirsurrounding radio environment.

The coefficient Ci from (4) addresses the case where thespectrum is not fully utilized with the conventional policyrule, because the conventional policy controls the fairnessfor shared spectrum usage without considering the wirelesssystem payoff. By weighting the utility function ui from (1)by Ci, wireless systems act more actively to get their payoffwhen there is a relatively large amount of unused spectrum.Also, they act more passively when there is a relatively largeamount of spectrum loss.

The coefficient Di from (4) performs self-adjustment ofwireless system transmit probabilities according to the estab-lished falsely estimated traffic. The correction factor Di isactive only if the wireless system has overestimated its actualneeds. In this way, the i-th wireless system exploits knowledgeof its own upcoming traffic estimated on short-term basis. Thisknowledge is inherently available at the i-th wireless systemfrom the queue size of the downlink transmission buffer.

Coefficients Ci and Di generate a complementary interac-tion: Ci promotes wireless systems that want more resourcesto use available channel resource generated by introducing Di.That is, even if Di can reduce the resource misallocation sothat unused resources can be released, none of the systems

COSOVIC et al.: IMPROVED POLICY FOR RESOURCE ALLOCATION IN DECENTRALIZED DYNAMIC SPECTRUM SHARING SYSTEMS 641

TABLE ISIMULATION PARAMETERS

Number of shared channels 100Number of wireless operators 8

(α, β, γ) (1.0, 0.2, 0.9)Wi 1 (for all operators)

can successfully utilize the resources without introducing Ci.The proposed approach does not introduce additional signalingoverhead as own traffic data estimated on the short-term basisis not transmitted to other wireless systems.

IV. NUMERICAL RESULTS

Simulation assumptions: To evaluate the feasibility of theimproved policy, we conduct simulations considering resourceallocation in one cell with the parameters shown in Table1. In each simulation round, we first draw initial trafficdemands for each wireless system from independent, butequally parameterized Poisson processes and then perform40 steps in which demands change from one to the nextstep by means of a random walk. We assume that trafficestimations obtained on longer-time basis do not correspond toactual traffic demand. In particular, we assume that deviationbetween estimated λi and the actual traffic demand ai equalsδi = λi−ai = niai where ni is a normally distributed randomvariable with zero mean and 0.3 standard deviation. Note, ni

is obtained new for each operator and simulation run. Thus,in about 68% and 95% of the simulated cases the operatorsunder-/over-estimate the actual traffic demand by less than30% and 60%, respectively. The rest of the assumptions isbased on assumptions from [4]: Each system accesses allchannels with the same transmit probability at the same timeand initial transmit probabilities are set to 1; All systemsare synchronized and their transmission duration is the same;Parameters α, β and γ are determined heuristically; Carriersensing works ideally and no hidden terminal is present. Also,sensing error caused by propagation time difference and byswitching time lag from sensing mode to signal transmit modeis small enough to neglect.

Simulation results: To evaluate proposed policy from thefairness point of view, the fairness index (FI) [5] is used. Thecloser to one FI is, the fairer the spectrum sharing is. Also,overall resource usage as a function of average overall resourcedemand is evaluated. The overall resource usage and FI forsystems applying the conventional and the improved policiesare depicted in Fig. 2 and Fig. 3, respectively. The improvedpolicy outperforms the conventional policy and significantlyimproves the overall resource usage and FI. E.g., at an overalldemand of 120 resources, the performance gains by theimproved policy rule are 12% and 30% for the overall resourceusage and for FI, respectively. For reference, performances ofa system applying the conventional or improved policy, butwithout estimation errors are also shown.

V. CONCLUSIONS

We consider an existing policy for decentralized spectrumsharing and propose a method to improve its robustness to

Fig. 2. Overall resource usage performance.

Fig. 3. Fairness performance among wireless systems.

inaccuracies in traffic demand estimation. The policy is basedon game-theory and implemented as an adaptive transmitprobability control algorithm. The proposal is evaluated bynumerical simulations. The results show that the improvedpolicy outperforms conventional in terms of the fairness,the overall throughput and the misallocation performance byreducing the amount of unused resources.

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[5] R. Jain, G. Babic, B. Nagendra, and C. Lam, “Fairness, call establishmentlatency and other performance metrics,” Tech. Rep. ATM Forum/96-1173, ATM Forum Document, 1996.