Inter-Operator Spectrum Sharing in Future Cellular ... - IEEE Xplore

Globecom 2012 - Next Generation Networking and Internet Symposium

Inter-Operator Spectrum Sharing in Future Cellular Systems Yu-Ting Lin1 , Hamidou Tembine2 and Kwang-Cheng Chen1 , IEEE Fellow 1 Graduate

Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan. 2 SUPELEC, Gif-sur-Yvettes, France Email: [email protected], [email protected] and [email protected]

Abstract—Inter-operator spectrum sharing has been proposed to exploit spectrum efficiency in future communication system. By using game theory and learning algorithm, we design a partially distributed implementation method. Such a method is proven to reach the system equilibrium which improves spectrum efficiency between operators. Furthermore, by queueing analysis and robust potential game, we show that the convergence rate can be accelerated by incorporating more asynchronous operator systems. This distributed implementation method creates a low complexity solution for operators to realize inter-operator spectrum sharing for 3GPP LTE-A systems or similar.

I. I NTRODUCTION As the number of smart phones and tablet PCs explodes, systems that can support high data rate become more and more important in the next generation mobile communication system design. However, since spectrum resources are limited, efficient utilizing spectrum is one of the most important issues according to the FCC report [1]. Implementation of spectrum sharing is expected to improve the spectrum efficiency. Generally speaking, spectrum sharing can be categorized into three types, including spectrum sharing in one unlicensed band, one licensed band, and multiple licensed bands. In this paper, we focus on the third case by considering Inter-operator Spectrum Sharing, which has been less studied. In [2] and [3], it is demonstrated that the advantages of implementing Inter-operator Spectrum Sharing include reduction of latency and call dropping rate. They proposed methods to build Cognitive Radio (CR) networks to sense the spectrum hole or to build a centralized scheduler between multiple service operators. However, such implementations have concerned in complexity to realize. Therefore, our contribution here is to propose a practical distributed solution based on system mechanism of 3GPP Long Term Evolution Advanced (LTE-A) [4] standards to solve the difficulty of deployment cost and we also improve the convergence rate by using asynchronous system cooperation, which is one of the important benefits from introducing interoperator cooperation. Another contribution is to improve the overall spectrum efficiency and to provide load balancing function by using partially distributed learning algorithm for all users to choose their own service providers properly. As we mentioned, because building the centralized scheduler between each operator will be too costly, therefore, in future cellular

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system, our proposal assumes that there are little information exchange between the operators. To analyze the improvement of system performance, we compare the system benefits of global optimization and the thus introduce distributed game theory-based algorithm. Nash equilibrium can provide a decentralized solution (can be suboptimal) which is better than the outcome without using interoperator spectrum sharing but worse than the global optimum. The rest of paper is structured as follows. In section II, we mention some related works of inter-operator spectrum sharing and explain the initiatives of our design. In section III, queueing theory and 3GPP information broadcast mechanism are applied to model the independent operators. In section IV,V, we formulate a game due to the distributed property and interaction between users. Then we prove the existence of Nash equilibrium. Simulation results of the game- theory based algorithm and the benefit of asynchronous property are presented in section VI. Finally, we conclude the paper with section VII. II. R ELATED W ORKS Inter-operator spectrum sharing has been considered for a long time. In [2], [3], the benefits via implementation of interoperator spectrum sharing have been demonstrated. However, the proper implementation method is not clear, because the implementation methods in [2], [3] involve great complexity to operators. There are other possible implementation methods to achieve operators cooperation, for example, (i) Access Class Barring technique shown in [5], (ii) the technology Vertical Handover in [6], [7] or even (iii) the relay mechanism to assist [8]. The essence of vertical handover is pretty much the same as interoperator spectrum sharing. Both are implemented under the situation of no real-time information exchange between two systems (Cellular-Cellular, WiFi-Cellular) and two respective systems are deployed on the different frequency bands. The only difference is the RAT to be selected. In this paper, we apply the concept of vertical handover, which means that each user can attach to multiple operators but there is only one operator who serves the UE. The reason for doing that is to save the energy consumption for UEs. In addition, handover cost does not be considered in our works.

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Game theory has also been proposed as a solution for interoperator spectrum sharing. In [9], authors have proposed a game model between operators and introduces an existence of meta-operator to coordinate the spectrum sharing. Here we consider a strategic decision making problem among users. Although our study is mainly on the interoperator spectrum sharing scenario, however, it is not difficult to imagine the similarity to use this method in the scenario of femto-cell and macro-cell cooperation, where the femto-cells do not have fast backhauling signaling and they are deployed on non-overlapping frequency bands. III. S YSTEM M ODEL A ND A SSUMPTION Shown in Fig. 1, in order to improve the spectrum efficiency we assume that NOP operator systems share their spectrum with each other by allowing users to switch between NOP systems. We assume that each user can connect to one base station of different operators. Therefore, the total number of base stations that a user can connect to is NBS = NOP . For UEs that are out of the coverage still have NOP base station to connect. However, the channel condition will be very bad shown in Remark 1. And total NUE user equipments exist in the system model.

B. 3GPP system information broadcast According to the specification of LTE, physical broadcast channel (PBCH) is responsible for system information broadcasting by system information block (SIB). We assume that information λ, µi , ci , and Ni are periodically broadcasted in an information block with period T in future system. In specs LTE [4], the period of SIB transmission are categorized from 80ms to 320ms which may be too long compared to fast fading coherence time but enough for slow-fading channel.

Fig. 2.

Asynchronous base station information broadcasting

The information update mechanisms are shown in Fig. 2. Generally broadcasting is not synchronized between systems like shown in Fig. 2. Here we consider both of the cases when base station queues information are synchronous and asynchronous. C. Global Optimum View We first describe the problem with pure strategies. From regulator’s view, we want to find out {aj , ∀j} which can maximize equation (3) with the constraints. N UE X

max (aj ,a−j )

Inter-Operator Spectrum Sharing Scenario

A. Queueing system model Consider a finite number of base stations NBS . For the ith base station, we model it as an M/G/c/c queue with each user arriving rate λ, service rate µi and ci servers. Each server represents one Resource Block (RB). Although simulation scenario has finite number of users (different from the assumption of MG/c/c), however, each user still can generate multiple service requests to base stations. Therefore, we model a base station as a Markovian process for arrival, general distribution and c servers, which is denoted as M/G/c/c queue in Kendall’s notation. Assume that each base station has Ni users attached, then we can get the server utilization of BSi , ci ci X X λNi k π0i ρi = jπki = ( ) (1) µi (k − 1)! k=0 ci X

(3)

j=1

aj ∈ Aj , ∀j

subj Fig. 1.

uUE j (aj , a−j )

where aj index the base station chosen by user j, and a−j = (a1 , . . . , aj−1 , aj+1 , . . . , aNUE ) denotes the set of others’ actions, the cardinality of the set Aj is NBS . Each user j has a payoff function uUE which is a function of aj j and a−j which is decided by ρi and Ni ,

uUE j (aj , a−j )

=

N BS X

1l{aj =BSi }

i=1

ρi (Ni , λ, ci , µi ) i Rj Ni

(4)

i ,µi ) where ρi (Ni ,λ,c represents the server number that the jth Ni PNUE user can access from ith base station, Ni = h=1 1l{ah =BSi } stands for the users served by ith base station. 1l{ah =BSi } = 1 means that the user h selects the ith BS. Based on the channel qualities of each links ij, theoretical data rate Rji is shown below,

k=1

ci λNi k 1 λNi k 1 −1 X ) ) ( ) (2) =( ( µi k! µi (k − 1)! k=0 k=1 Pci λNi k 1 −1 where π0i = ( k=0 ( µi ) k! ) . After knowing ith BS parameters λ, µi , ci , and Ni , each user can predict the server efficiency it can get from base station i.

Rji

= log2

|hij |2 Qij 1+ N0 WRB

! (5)

which depends on the channel fading between ith UE and jth BS, |hij |2 , WRB standing for the bandwidth of one resource block and transmission power Qij .

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IV. G AME FORMULATION

is the set N BS X

As the optimization problem of (3) has a global optimal solution, however, a centralized optimizer who needs to know all the channel information ∀i, j, Rji and base station loading information ∀i, λ, µi , ci should be set up. Game Theory is suitable, because each UE distributedly and spontaneously decides its own optimal selection strategy aj that is influenced by the others decision. Denoting Aj as the action space of UEs, then we can form a strategic game Gpure = hNUE , {Aj }, {uUE j (aj , a−j )}i in pure strategies.

is the expected payoff (utility) of user j. The resulting game Gmixed has at least one equilibrium. Moreover, any equilibrium of Gpure is also an equilibrium of Gmixed .

A. Existence of equilibrium in pure strategies

Theorem 1. Nash’s Theorem [12] Every finite strategic game has a mixed strategy NE.

This is a congestion game in the sense of Rosenthal (1973, [10] if the channel gains are fixed. Rosenthal has shown that for this type of games, there is at least one Nash equilibrium in pure strategies. We apply this result in our mathematical formulation. Since congestion game with complete information can be seen as a potential game (see also Monderer & Shapley 1996 [11]), our game is a finite potential game if the channel gain are fixed. However, there exists difference between the game proposed here and the classical potential game formulation. The difference is mainly due to the uncertainty on the channel gain. Thus, we have a potential game with uncertainty, called robust potential games. Remark 1. Note that if hij = 0 or Qij = 0 then Rji = 0 and the utility of user j to BS i is zero. This means that if all the channel gains are 0 then the payoff functions are 0 and any strategy profile reachs an equilibrium and also a global optimum. Here we provide a simple game example to show the existence of NE with only two BSs and two UEs and assuming that c1 = 5, c2 = 2, µλ11 = µλ22 = 1 and R11 = R21 = 1, R12 = 1.3, R22 = 1.25. We can get the following Table. I, which shows the multiple NEs (BS1,BS2) and (BS2,BS1). Although there is no unique NE but Ni = (1, 1) is unique like shown in this example. TABLE I S TRATEGIC FORM OF PURE STRATEGY GAME

UE1,UE2 Payoff BS1 BS2

BS1 (0.9633, 0.9633) (1.04, 0.9969)

{pj = [pij ]i=1,··· ,NBS ,

pij = 1, pij ≥ 0}

i=1

i.e the set of probability distribution over {1, 2, . . . , NBS }, and UE u ¯UE j (pj , p−j ) = Epj ,p−j uj (aj , a−j )

Theorem 2. Existence of Mixed Nash Equilibrium [12] A strategic game hNUE , {Pj }, {¯ uUE j (pj , p−j )}i has a NE if, ∀j ∈ N , the set Pj of player j is a nonempty compact convex set of an Euclidian space, and the utility function u ¯j is continuous and quasi-concave on pj . C. Learning equilibria in a partially distributed manner [13] Let Gmixed = hNUE , {Pj }, {¯ uUE j (pj , p−j )}i. To reach the ∗ fixed point [pj ]j=1,...,NUE , we design a dynamic game to adapt the access probability. In addition, αj represents the learning rate for user j designed as learning rate in [14]. i i pij (t + 1) ∈ (1 − αj )pij (t) + αj [arg max u ¯UE j (pj (t), p−j (t))] i pj

(7) When fixed points reach, then the selection probability will not be updated anymore. ∗ ∗ u ¯UE p∗j = (1 − αj )p∗j + αj [arg max j (pj , p−j )] i pj

= (1 −

αj )p∗j

+

αj p∗j

(8)

However, how to properly select the learning rate requires further considerations. V. M ODIFIED P OTENTIAL GAME BasedPon our broadcast mechanism, the number of users NUE i Ni = h=1 ph representing the others’ strategies will be broadcasted by base station. We transform equation (6) into a modified potential game given by the following, so that partially distributed learning algorithm can be applied.

BS2 (0.9969, 1) (0.78, 0.75)

N BS X

ρi (Ni , λ, ci , µi ) i Rj Ni i=1 PNUE i N BS X ρi ( h=1 ph , λ, ci , µi ) i = pij Rj PNUE i h=1 ph i=1

u ˜UE j (pj , p−j ) =

B. Existence of equilibrium in mixed strategies Because mixed extension formulation will be useful when using dynamic game to find the equilibrium. We form a mixed extension of the above game here and propose a learning algorithm in next section. Since our game is a finite game, by Nash theorem, we know that there is at least a Nash Equilibrium (NE) in mixed strategies i.e. in the game Gmixed = hNUE , {Pj }, {¯ uUE j (pj , p−j )}i where Pj = ∆(Aj )

(6)

pij

(9)

i ,µi ) where ρi (Ni ,λ,c represents the server number that jth user Ni can access from ith base station. We now focus on the Nash equilibria of the modified game. As the example we showed in pure strategy game, there may be multiple NEs, however the total number of users attached to each BS Ni will be unique. The uniqueness can be straightforwardly proved by Theorem 3, 4 from [15].

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Theorem 3. Uniqueness Property [15] In a two-terminal network, for any assignment of (strictly increasing) cost functions, the flow on each arc is the same in all Nash equilibria if and only if the network is nearly parallel or it consists of two or more nearly parallel networks connented in series. Theorem 4. Uniqueness of Equilibria [15] If the users utility functions are identical up additive constants then for every two Nash equilibria, the number of each user through each base station in the first equilibrium is equal to that in the second, and the same is true also the equilibrium utility. After the proof of uniqueness of Equilibria, we show the details of learning process of this Nash equilibria like (7). In order to optimize the utility function of each u ˜UE j , we need to solve the following optimization problem. According to [16], concave optimization problem like standard convex optimization problem has an unique solution, where pj  1 denotes ∀i, pij ≤ 1. max

u ˜UE j (pj , p−j )

subj

0  pj  1,

pj

1T pj = 1.

(10)

Concavity of function u ˜UE : j From equation (9), it is not difficult to prove that i i i u ˜UE j (pj , p−j ) is an increasing function corresponding to pj . Because both of

ρi (pij )

and

pij

PNUE h=1,h6=j

pij ,

pih +pij

are increasing

functions with therefore with another condition 0 ≤ ρi ≤ i i ci , limpij →∞ ρi = ci , we can prove that u ˜UE j (pj , p−j ) is at least a quasi-concave function. To show the strict concavity, we should show that equation (11) is less than 0. Because of the complexity, we can only use numerical result. ∂2u ˜UE j ∂pij

2

=

ci ci ∂ 2 Rji pij X λNi k 1 −1 X λNi k 1 ( ) ( ( ) ) 2 N i µ k! µ (k − 1)! i i i ∂pj k=0

=

k=1

ci ci X X Rji k k 1 −1 i Ni h pj ( ) Ni k−1 hk 2 k! (k − 1)! ∂pij k=0 k=1

∂2

Fig. 3.

sent back to BS and optimal pij have to be transmitted to UEs, which will cost a lot information exchange to get the global optimum. However, based on the derivation in this section, if base station can broadcast the proper loading information to the UEs, then UEs’ strategies can converge to a fix value that can achieve the better spectral efficiency. VI. S IMULATION R ESULT In this section, we compare the results of global optimization and game implementation. First we show our game theory based algorithm in the case of synchronous system information broadcasting and then we demonstrate in asynchronous system deployment. By comparing the two scenario results, we show that convergence rate can be accelerated if we implement the asynchronous case. Here, we set NOP = 3, because three operators scenario is more common in the present. A. Synchronous System Information Update As shown in Fig. 1, all the parameter configurations for three operators inter-operator spectrum sharing are listed in the Table. II. TABLE II S IMULATION C ONFIGURATION

(11) In Fig. 3, the numerical analysis demonstrates the utility i i function u ˜UE j (pj , p−j ) with different parameter configuration. PNUE i In analysis, ci = 5 and l=1,l6=j pl = 0.1, which are all concave functions, no matter how much is the h = µλii . When h → 0,

i i ∂2u ˜UE j (pj ,p−j ) ∂ 2 pij

i i Numerical Analysis of u ˜UE j (pj , p−j )

Configuration Parameter Subcarrier No. Ratio Arrival/Serving Rate Fading Channel Variance Learning Rate αi Total Users Number Initial Users Distribution

→ 0− .

By observing the function u ˜UE j (pj , p−j ), the solutions

Parameter Values c1 = 5, c2 = 3, c3 = 10. λ1 λ2 λ3 = µ = µ = 1. µ1 2 3 σ=1 0.1 100 (80, 10, 10), (10, 80, 10), (10, 10, 80)

∂u ˜UE

of optimization appear either at the ∂pji = 0 or at the j boundary of constraints functions. Therefore, the best response is obtained by calculation the optimization problem. p∗j ∈ BRj (p∗−j )

(12)

With equations (12) from j = 1 to j = NUE , we can solve all the values of pij . However, all information Rji need to be

In Fig. 4, we can easily find out that Nash Equilibrium solutions are sub-optimal compared to global optimum and the final convergence users number are different. Additionally, no matter which initial users distribution system starts from, user number finally converges to the unique Ni Nash Equilibrium (NE). Here we assume the channel is slow fading. If the channel conditions are the same, users will converge

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Fig. 5.

Convergence with different learning rate.

needed. Therefore, our distributed method is suitable in the case of slow fading channel such as the scenario of sensor networks which are low-mobility. B. Asynchronous System Information Update In the case of synchronous system information update, we assume that three base stations loading information are broadcasted at the same time. However, in general as shown in Fig. 2, system information are not synchronized. Fig. 4. Comparison between Global Optimum and Nash Equilibrium Solution

and finally fix their strategies, including the pure strategies. Total spectral efficiency can be calculated by the utilization of servers. In the simulation configuration total 18 servers serve in the scenario, which represents all the capacity of three operators. In case of Global Optimal solution it can be seen that equivalent uglobal = 25.5 servers exist. And game theory approach can provide approximately uNE = 24.5 servers. On average only uav = 18.92 servers are obtained without deployment of Inter-Operator Spectrum Sharing. This shows that with enough convergence time cooperation between operators can exploit the channel diversity gain. In the worst case when all the user are only subscribed to operator 2, uworst = 4.94 happens, which emphasizes the importance of introducing inter-operator spectrum shairng which can provide a solution to achieve load balancing. With different settings of channel fading variance we have almost the same gain sourced from the channel diversity. The average gain we can get is equal to 29.49%, which is less than the global optimum, 40%. In Fig. 4, learning rate 0.1 is chosen for all users. However, different learning rate will result in different convergence rate. In Fig. 5, learning rate 0.1, 0.2 can converge to NE, which means users will fix a particular strategy. However, when learning rate is equal to 0.3, some oscillations will appear, which shows that UEs will not fix at a strategy. We can observe that to reach the NE, tens of iterations are

Fig. 6.

Three BS loading users number received by UE

In Fig. 6, each asynchronous iteration represents an update of only one base station information. In asynchronous case, we adapt learning rate to be equal to 0.2, which originally needs at least 15 iterations to converge shown in Fig. 7, now it can converge in 5 iterations (five times of T ). Multiple operator systems create more update points in an information broadcast period T . By observation from Fig. 7, for asynchronous case the real convergent time is N3T which is three times faster than N T in synchronous case. N denotes the iteration times for convergence and T is the period of information broadcast.

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Therefore, we can improve equilibrium convergence rate by introducing more operators cooperation. This rate acceleration will enable operators to find out the solution to get better spectral efficiency faster than synchronous case.

Fig. 7.

[8] P.-Y. Chen, W. C. Ao, S.-C. Lin, and K.-C. Chen, “Reciprocal spectrum sharing game and mechanism in cellular systems with cognitive radio,” GlobeCom Workshops, 2011. [9] H. Kamal, M. Coupechoux, and P. Godlewski, “Inter-operator spectrum sharing for cellular networks using game theory,” IEEE Personal, Indoor and Mobile Radio Communications, pp. 425–429, 2009. [10] R. W. Rosenthal, “A class of games possessing pure-strategy nash equilibria,” International Journal of Game Theory, vol. 2, no. 1, pp. 65–67, 1973. [11] D. Moderer and L. S. Shapley, “Potential games,” Game and Economic Behavior, vol. 14, pp. 124–143, 1996. [12] M. J.Osborne and A. Rubinstein, A Course in Game Theory. The MIT Press, 1999, cambridge, MA. [13] H. Tembine, Distributed Strategic Learning for Wireless Engineers. CRC Press, Taylor & Francis, 2012. [14] D. Niyato and E. Hossian, “Competitive spectrum sharing in cognitive radio networks: A dynamic game approach,” IEEE Trans. Wireless Communications, vol. 7, no. 7, July 2008. [15] I. Milchtaich, “Topological conditions for uniqueness of equilibrium in networks,” Mathematics of operations Research, vol. 30, no. 1, pp. 225– 244, February 2005. [16] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, Mar. 2004.

Convergence of Benefit

VII. C ONCLUSION Cooperation between operators remains an open issue from the aspects of regulators for enhancing spectrum efficiency in the design of future cellular system. According to the current standards, communication system still does not apply any spectrum sharing techniques, because of the complexity of system information exchange. However, there are obvious benefits on executing load balancing and improvement of spectrum utilization by inter-operator spectrum sharing. Therefore, providing a low-complexity solution which can reduce the cost of infrastructure will facilitate operators to implement. Our works give an insight on the possible future solution that gives UEs the right to select its own connection among operators. With the aid of convergence rate acceleration, UEs can reach an equilibrium even faster so that it can converge at least in the coherence time of slow fading channel. This can guarantee the operator systems to exploit the slow-fading diversity gain by introducing cooperation between them. R EFERENCES [1] FCC, “Federal Communication Commission std.” First Report and Order, pp. 02–48, 2002. [2] G.Middleton, K.Hooli, A.Tolli, and J.Lilleberg, “Inter-operator spectrum sharing in a broadband cellular network,” IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications, 2006. [3] X. Li and S. Zekavat, “Spectrum sharing across multiple service providers via cognitive radio nodes,” IET Communication, 2010. [4] E. Dahlman, S. Parkval, and J. Skold, 4G LTE/LTE-Advanced for Mobile Broadband. ELSEVIER, 2009. [5] S.-Y. Lien, T.-H. Liau, C.-Y. Kao, and K.-C. Chen, “Cooperative access class barring for machine-to-machine communications,” IEEE Transaction of Wireless Communication, pp. 02–48, 2011. [6] W. Song, W. Zhuang, and Y. Cheng, “Load balancing for Cellular/WLAN integrated networks,” IEEE Network, February 2007. [7] S. Busanelli, M. Martalo, G. Ferrari, and G. Spigoni, “Vertical handover between WiFi and UMTS networks: Experimental performance analysis,” International Journal of Energy, Information and Communications, vol. 2, February 2011.

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