A Resource Allocation Algorithm in Cognitive

A Resource Allocation Algorithm in Cognitive Radio Networks Based on Cooperative Game Theory Approach Zehui Qu, Deng Wei and Zhiguang Qin

A Resource Allocation Algorithm in Cognitive Radio Networks Based on Cooperative Game Theory Approach Zehui Qu, Deng Wei and Zhiguang Qin School of Computer science and Engineering University Electronic Science and Technology of China Chengdu, China 611731 {quzehui,dengwei,qinzg}@uestc.edu.cn doi: 10.4156/jdcta.vol4.issue5.13

Abstract In cognitive networks, the parameters of radios were adapted to achieve end-to-end or network objectives such as spectral or energy efficiency, reliability, or throughput maximization. In these networks, the licensed spectrum and dynamic spectrum sharing based on opportunistic communication play an important role of resource allocation. Since the resource allocation networks always cooperate and coexist in cognitive, Game theory has been employed to analysis that. In really case, the cooperator only have partial or no information concerning in advance to making decision. However, the current game theory models in cognitive radio networks always regard they have enough information. In this paper, we take Incomplete Information into account and propose an algorithm base on game theory to resource allocation. Compare traditional algorithms, this one can improve the in the cognitive radio networks as the simulations showing.

Keywords: Cognitive radio, Game theory, Incomplete information 1. Introduction As the continuously increasing of services and radio resources demand, the traditional communication systems which means a priori allocation of the frequency band, the service assigned to it and the used technology, should be more flexible, efficient and easy-to-use dynamic systems able to deal with the requirements and constraints of the environment and the users. Cognitive radio (CR) technology has considered with excellent prospects and suitable solution to solve this problem. The definition of cognitive radio was introduced in [1] with reference to a communication system able to observe and learn from the surrounding environment as well as to implement and adapt its own transmission modalities to cope with users’ requirements. The idea of CR is stemmed from the contrast between growing demand of broadband services and the inadequacy of radio resources. Current researches of the Federal Communications Commission of U.S. (FCC) Spectrum Policy Task Force demonstrate that a large amount of licensed bands are under-utilized [2], i.e. a lot of spectral resources are reserved for specific services, but, actually, they remain unused for most of the time or unused in several locations. From these researches, the potentiality of a CR is envisaged, i.e. a system can sense the electromagnetic environment (spectrum sensing), detect the spectral resources actually occupied in a in a given location and given temporal interval, and take the free bands (holes) for its own communication. The spectrum sensing for available resources is not limited to spectrum portions dedicated to unlicensed communications, but is also included to licensed bands. Many researchers use game theory to adoption of a cognitive radio strategy to the coexistence problem. For simplify, these game theory models in cognitive radio networks always ignore the players in game have not enough information in advance. Here, we take deficient information into account and propose an algorithm base on game theory to resource allocation. In this paper we use the same Scenario with [6]. The paper is organized as follows: in Sect. 2 the Coexistence Environment description. In the Sect.3, Game theory with Incomplete Information will be introduced while in Sect. 4 the resource allocation methods will be introduced. The Sects. 4 the achieved results for the method and the comparison with traditional methods in reference [6] will be presented. Finally, some concluding remarks will be given in last sec 5.

2. The Coexistence Envisaged Scenario

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International Journal of Digital Content Technology and its Applications Volume 4, Number 5, August, 2010

The considered environment of the project is established by a primary licensed system and a secondary system. The terminals of the later are Cognitive Radio based network which implement cognitive resource allocations. Specially, it has been considered a mobile satellite system compatible with DVB-SH standard [3] as primary system in the envisaged scenario. We consider a wireless terrestrial network in secondary system that means all the secondary terminals communicate with a local base station. The main radio resource in the two systems is the L band frequency spectrum (0.39– 1.55 GHz). The Fig. 1 demonstrates the proposed environment. A complex vector of length K represents the frequency domain of the transmitted OFDM symbols for both primary and secondary systems which is the real number of subcarriers used to transmit the signal. Here K has been set to 853 in the DVB-SH standard.

Figure 1. The envisaged scenario

3. The Proposed Game Approaches The Game Theory based resource allocation method in the secondary network implies the definition of a proper framework. These approaches succeed in resource allocation based on assume all the equipments (player in the game theory model) have the complete information about others. However, in mostly real case, the equipments (player in the game theory model) could not know the complete information. So we proposal the resource allocation algorithm of cognitive network here, it is differently from the exits approaches since it based on Incomplete Information assume. In our case, the players involved in the game are M cognitive radio terminals. The definitions of strategies are the actions each player can choose the best resources differently from the operating environment and the opponent players choices. The actually played strategies can be represented Π

through a resource allocation matrix, Q containing all the amounts of resource the terminals allocated. The resource allocation matrix has some mandatory constraints to respect. In fact each cognitive radio terminal has to keep into account two constraints per subcarrier plus a general one due Π

to the maximum resource available for transmission, Qmax . The constraint on the maximum resource for the i -th user can be stated in the following way: K

∑Q

Π

i

Π (k ) ≤ Qmax

k =1

(1)

Π

where the term Qi ( k ) is the amount of power the i-th cognitive user is allocating on the k-th subcarrier. The constraints on each subcarrier, 1) the minimum amount of resource to allocate in order to respect the secondary system target BER (i.e. the lower bound); 2) in order to guarantee and protect the primary system functioning and it establishes the maximum amount of resource on a certain

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subcarrier (i.e. the upper bound). The lower bound relative to the k-th subcarrier for the i-th terminal is given by: Π SINRmin

Π

Q (k ) ≥

(∑

P j =1, j ≠i

hΠj (k ) pΠj (k ) + u Ι→Π (k )PΙ (k ) + N (k )

)

Π i

i

h (k )

(2)

Π where hi ( k ) is the channel coefficient between the i-th terminal and the base station of the secondary P ∑ j =1, j ≠i hΠj (k ) pΠj (k )

is the interference on the k-th subcarrier due to the other terminals of

network,

Ι→Π

Ι

(k ) P (k ) is the disturb due to the transmission of the satellite system on the secondary network, u the k-th subcarrier, and N(k) is the noise power on the k-th subcarrier. The former constraints define a multidimensional real subspace within the available strategies stay. Given such particular constraints the subspace is also compact and convex. The k-th subcarrier for the i-th terminal has an upper bound. It is given by:

hΙ ( k ) P Ι ( k )

Π

Q (k ) ≤ i

Π min

SINR u

Ι→Π

(k )

∑ −

P j =1, j ≠i

u

u Ι→Π pΠj (k ) j

Ι→Π

(k )

−

N (k ) u

Ι→Π

(k )

(3)

Ι

where h ( k ) is the coefficient of the channel between the satellite and nearest to the i-th secondary Ι user, P (k ) is the resource of the primary system satellite is transmitting on the k-th subcarrier, Π hΙ (k ) P Ι (k ) is the channel coefficient with the impairment effects of the resource allocation p j (k )

on the primary receiver nearest to the j-th terminal. In the case inequalities (2) and (3) do not have a common interval of real values, it is clear no resource will be allocated on that subcarrier. The utility function for the i -th player is so defined: K M ⎛ ⎞ ui (Q Π ) = ∑ ⎜ B log 2 ⎡⎣1 + SINRi ( Q Π ( j ) ) ⎤⎦ − ∑ μmΠ→Ι ( j ) pmΠ ( j ) ⎟ j =1 ⎝ m =1 ⎠ (4) Where

SINRi (QΠ (k)) =

∑

hiΠ (k) piΠ (k)

P

Π j =1, j ≠i i

Π i

h (k) p (k)

+ μΙ→Π (k) pΙ (k) + N(k) (5)

from the reference [8-11], we know that:

[

ui (Q ) = maxmin Πi ( pi , pj , wi , wj ) +Πj ( pi , pj , wi , wj ) Π

pi , pj wi , wj

= maxmin [ p ( β − γ p ) − w ( β − γ p ) + p ( β − γ i

p ,p i

j

w ,w i

i

i

i

i

i

i

i

j

j

j

]

p ) − w (β −γ p j

j

j

j

j

)] ,

j

(6)

and from reference [12] and [13] we have

∂ ⎡⎣ Π i + Π j ⎤⎦ ∂pi

∂ 2 ⎡⎣ Π i + Π j ⎤⎦

= 2 β i − 2γ i pi = 0

∂pi 2

,

∂ ⎡⎣ Π i + Π j ⎤⎦ ∂p j

= −2γ i ,

∂ ⎡⎣ Π i + Π j ⎤⎦ = −2γ j ∂p j 2 2

= 2 β j − 2γ j p j = 0 ,

.

Combined (2), (3), (4), and (6) , we can get potential function that:

V(QiΠ) = max ⎡⎣pi ( βi −γi pi ) + pj ( βj −γ j pj ) −λcsi ( βi −γi pi ) −λcsj ( βj −γ j pj )⎤⎦ p , p ,w ,w i

j

K

(

i

j

)

= ∑ Blog2 ⎡⎣αi (k) + hiΠ (k) piΠ (k)⎤⎦ − μiΠ→Ι ( j) pΠ ( j) − βi ( j) − N( j) j=1

(7)

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where β i is the coefficient of the channel between the satellite and nearest to the i-th secondary user,

P Ι (k ) is the resource of the primary system satellite is transmitting on the k-th subcarrier, Π h ∏ (k ) P Π (k ) is the channel coefficient with the impairment effects of the resource allocation p j (k ) on the primary receiver nearest to the j-th terminal. In the case inequalities (2) and (3) do not have a common interval of real values, it is clear no resource will be allocated on that subcarrier.

4. Simulation and Result Obviously, in the Fig.1 the two communication systems require two distinct channel models. For the satellite based primary system at L band, it has been modeled by the Lutz propagation model [4]. This model is based on a two state, i.e. good and bad. The model uses Markov chain for the fading process and both slow fading and fast fading are kept into account. Due to large obstacles, slow fading events are modeled as a finite state machine. But fast fading events, caused by irregular obstacles (e.g. vegetative shadowing) and multipath phenomena, have been superimposed as a random variation with a given probability density function (PDF) for each state of Markov chain. The propagation model describes a flat frequency reaction. A term of path loss l has been also considered in the primary system propagation model. It is modeled by:

l = 10α log10 (

4π d

λ0

)

dB

(8) where d is the distance between the transmitter and the receiver, α is the attenuation varying by d, and λ0 is the wave-length at central frequency of the given frequency band. In the propagation channel model of the terrestrial secondary system, we take two mainly phenomena into account: path loss and multipath fading. The Eq. (8) above is an expression about the channel model for the primary system. As for the multipath fading, due to the operating environment, it has been considered through a tapped delay model with Rayleigh distributed coefficients. The square of delay is an exponential function as follows:

σ n2 = e − μ n

(9)

2 where σ n stands for the n-th coefficient and μ is a normalized mean power response. Take these

parameter into consider, we comparison the SSNR of our approach and the tradition one called MultiLevel QAMI(MQAMI) in the reference [5]. We do the SINR and RATE comparisons by Matlab 2008a on a computer which with an AMD turionX2-64bits CPU and 4G DDR. Fig. 2 is the result about Signal-to-noise-interference ratio (SINR) vs. frequency when primary system working at 20 dB. The figure Fig.3 demonstrates the RATE variation in give frequencies.

Figure 2. Signal-to-noise-interference ratio vs. frequency. Primary system working at 20 dB

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Figure 3. Comparison between the two methods in terms of rate achieved

From Fig.2 and Fig.3, we come to a conclusion that the current method which is proposed here has a better performance both on SINR and trace rate. The reason for that is in our approach we use incomplete information assume and consider the whole system utility instead the player ‘self.

5. Conclusions and Discussion In this paper we have developed a resource allocation approach in the Cognitive network based on incomplete information theory of Game Theory. Two different resource allocation methods have been introduced. In particular for the our method it has been presented the mathematical formulation as well. As far as it concerned the MQAMI method, the iterative allocation algorithm has been presented. The results have shown that our method achieves higher rates, although it cannot be implemented in a distributed way like MQAMI based allocation. This result was expected since our algorithm of allocation is the optimal one, even if the practice is not usable due to the complexity rising exponentially with the number of users.

6. Acknowledgment This work was support by NSFC 60903157. We should thank Xinggao He, Feng li Zhang and other colleague. They give us great suggestions about this

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[10] Brandenburger, Adam, “Cooperative Game Theory: Characteristic Functions, Allocations, Marginal Contribution. Stern School of Business”, New York University, 2007. [11] Branzei, R., Dimitrov, D., Tijs, S., “Models in Cooperative Game Theory. Crisp, Fuzzy and Multi-Choice Games”, Springer, Berlin Heidelberg 2005. [12] Cachon, G., Lariviere, M., “Supply Chain Coordination with Reveneu-Sharing Contracts: Strengths and Limitations”, Management Science 51, 30-44 ,2005. [13] Cantisani M., Marchi E., “The Weighted Core with Distinguished Coalition. International Games Theory Review” 6 (2), 239-246, 2004.

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