Inefficiency of Bargaining Solution in Multiuser Relay Network

International Conference on Electrical and Computer Engineering ICECE'2015 Dec. 15-16, 2015 Pattaya Thailand Inefficiency of Bargaining Solution in Multiuser Relay Network Supenporn.Somjit, Pattarawit Polpinit, and Chatchai Khunboa Abstract This paper considers a multiuser single-relay network. The relay power allocation among the users and pricing problem are studied. We model the interaction between the relay and users as a Stackelberg game, where the relay is the leader who gets paid for helping users forward signal, and user is the followers who pay to receive relay service. For the relay power allocation, a bargaining game is deployed to model the negotiation among the users on relay power allocation. We propose the Kailai Smorodinsky Bargaining Solution KSBS of bargaining game in order to formulate the relay power allocation. The inefficiency of KSBS-based power allocation is investigated, compared with the sum-rate-optimal solution. Simulation results show inefficiency of KSBS-based power allocation under different relay power price. Keywords Inefficiency; Kailai Smorodinsky bargaining solution KSBS; multiuser relay network; power allocation; Stackelberg game. C I. INTRODUCTION OOPERATIVE communication is a promising concept to improve the performance of communication in wireless network [1]. The basic idea is to have some nodes help each other s transmission to achieve diversity and increase data rate. The cooperative strategy aim is to optimize the global network performance. Two main relaying schemes used cooperative strategies are amplify-and-forward AF and decode-and-forward DF [2]. For multi-user relay network, one prominent issue is resource allocation among the users. Recently, numerous works have investigated the relay power allocation as shown in [3-10]. Game theory was recently used in resource allocation in cooperative communication to optimize the global network performance. In [6] and [7], Stackelberg game model was proposed to perform power allocation in a multi-user relay network. In [8] and [9], Nash bargaining solution was applied in multiuser single-relay network in order to analyze the relay power allocation among the user. They consider the balance Supenporn. Somjit is with the Department of Computer Engineering, e-mail: s.supenporn@gmail.com. Pattarawit. Polpinit is with the Department of Computer Engineering, e-mail: polpinit@kku.ac.th. Chatchai. Khunboa is with the Department of Computer Engineering, e-mail: chatchai@kku.ac.th. between the network sum-rate and the user fairness. The work in [10] studies the relay power allocation and pricing problem, uses the KSBS of bargaining game to formulate the relay power allocation. The relay power allocation problem is considered to maximize the network sum-rate. However, research result presented in [10] was focused on efficiency of bargaining game, that the KSBS-based power allocation scheme achieves higher network sum-rate. Although, the KSBS-based solution cannot always achieve the network sum-rate optimal. This observation motivates this research in to investigate how much efficiency the KSBSbased power allocation compared with that of the sum-rateoptimal allocation. In this paper, we consider a multi-user single-relay network and use game theory to model and analyze the user and relay. We model the interaction between the relay and users as Stackelberg game model, in which the relay is the leader who set the unit power price for relay service and the user is the followers who pay to receive relay service. We consider the relay power allocation and pricing mechanism. The relay power allocation among users is model as a cooperative bargaining game. We propose the KSBS of bargaining game for fair allocation of relay. Based on the KSBS relay power allocation, we can find the optimal relay power price. This paper considers the KSBS-based power allocation to maximize network sum-rate. The problem under consideration is the inefficiency of KSBS-based power allocation under different relay power price, compared with the sum-rateoptimal power allocation. The reminder of paper is organized as follows: Section II describes the multi-user relay network. The relay power allocation and pricing solution are proposed and studied in section III. In section IV, we analyze the inefficiency of KSBS-based power allocation. Section V describe simple example multiuser single-relay network. Simulation results are shown in section VI. Section VII contains the conclusion. II. SYSTEM MODEL Consider multi-user single relay network in Fig.1. There are N users communicating with their destinations with the help of one relay. We employ the amplify-and-forward AF cooperation protocol in the system. Denote channel gain from user i to relay as f i, the channel gain from relay to destination i as g i and the channel gain from user i to destination i as h i Direct link 22

International Conference on Electrical and Computer Engineering ICECE'2015 Dec. 15-16, 2015 Pattaya Thailand III. RELAY POWER ALLOCATION AND IT S OPTIMAL PRICE In this section we use Stackelberg game to model the interaction between users and relay, we use bargaining game to model interaction among independent users and formulate the relay power allocation problem. A. Stackelberg Game The stackelberg game model is a strategic game in which the leader take an action first and the follower observe the leader s action and act sequentially [11]. We consider relay as the leader who set the price of power in helping the user, the relay will set the price to maximize it revenue. We consider users as the followers who react in unit price of relay power by buying power from the relay. We model the interaction among the user as a bargaining game. The first step to formulate the power allocation problem as a bargaining game is to design the utility function from SNR of user i 3 we can define User i s utility function as Fig.1 Multi-user single-relay Network In this paper we consider Reylieigh flat-fading channel and assume the relay has global and perfect knowledge of channel state information CSI. Denote transmit power of User i as Qi and maximum transmit power of the relay as P. Half-duplex two step AF relaying protocol is used. In this paper we consider Reylieigh flat-fading channel and assume the relay has global and perfect knowledge of channel state information CSI. Denote transmit power of User i as Qi and maximum transmit power of the relay as P. Half-duplex two step AF relaying protocol is used. Let si be information symbol of user i. It can be normalized as Esi2 = 1 where E stands for the average. In the first step: The user to transmit the originated information is divided in to to two parts. Part I: The user i transmits information and 2 where is the noise at the destination i in the second step. We assume all noise in different channels are i.i.d. additive circularly symmetric complex Gaussian with zero-mean unit variance. After combining the direct path and relay path the signal to noise ratio SNR of user i at the destination i is 7 Given the unit price of relay power, the ideal power demand of User i that maximizes its utility is 3 { If the user i s transmission is not helped by the relay and uses direct transmission only the SNR at the destination i is 6 B. Relay Power Allocation We use bargaining game to model interaction among independent users and find the relay power allocation. We look for KSBS to formulate relay power allocation, which guarantees fairness in the sense of equal penalty. First step, to find KSBS-based power allocation, we calculate User i s ideal to maximize its utility. User i s ideal of given utility utility can be found using Lemma 1[10] Lemma 1 [10]: Define the price above which User i will not purchase any relay power as 1 5 where and are the noise at the relay and the destination in the first step. In the second step, the relay amplifies and forward it with power to destination i. Denote as power the relay uses in helping user i. We assume that the relay has perfect knowledge of CSI. The received signal at destination i is It represents the received quality-of-service of user because is directly related to the performance of the communication. If user does not purchase any relay power and uses the direct transmission only, i.e., its utility is minimum utility that User i expects as relay. Part II: The user i transmits information to destination by direct link. The received signal at relay and destination i are The ideal utility of user i is 4 23 8

International Conference on Electrical and Computer Engineering ICECE'2015 Dec. 15-16, 2015 Pattaya Thailand { From Lemma 1 the ideal power demand when the price is too high, in case 1 8, User i will not buy any power from the relay. When the price is too low, in case 3 8, User i wants to buy all power from the relay. When the price range in case 2 8 User i will buy part of relay power that give ideal power between its SNR and the cost. To find the KSBS-based power allocation of user, let L be the number of user satisfying, assume and of users are sorted in descending order as follows 10 With the given price, for users as shown in Lemma1, their ideal power is 0; thus, they do not enter the game. The first Lλ user will participate in the bargaining game and buy the relay power, to find the KSBS-based power allocation of Lλ user is equivalent to the following problem, whose proof can be found in [12] and 11 where k is constant independent of user. The constraint in 11 is due to the total relay power and the last constraint ensures the user can not request relay power larger than User i s ideal power. We call solution of equation 11 the KSBS-based power allocation and only first Lλ user whose s are larger than the unit price of relay power participate in bargaining game. The remaining N - Lλ does not request any relay power and uses the direct transmission only. The problem KSBS-based power allocation under consideration of the relay power constraints, for given unit price of relay power, the total power demand by the user does not exceed the relay power constraint. If total ideal power demand by the user exceeds the relay power constraint, KSBS-based power allocation will allocate all relay power to the user fairly, shown in following Lemma 2, whose proof can be found in [10] Lemma 2 [10]: For a fixed, let the ideal power allocation of User i be, the KSBS-based power allocation be. When, we have ; when, where is the relay power allocation to User i s based on the KSBS for the given price.we have find from 11., of second case can be C. Optimal Relay Power Price The relay modeled as the service provider who sets the unit power price for relay service and maximize relay revenue. When the unit price of the relay power λ and by using the KSBS-based power allocation in section B, the revenue of the relay is, The relay pricing problem can be formulated as 12 To find the optimal relay power price, we first show the following Lemma3 [10] Lemma 3[10]: The optimal price is inside the interval, where price at which the total ideal power demands of user is P. To find in Lemma3, we need to solve the following equation: 13 Note that in 13 monotonically decreases from to 0 as increases from 0 to. To find the value of. To find the value of, we can first find the M such that and. Thus [ ]. We can calculate following equation: 14 From ordering of users based on their value in 10 and M is index such that. Define γ for and γ and define and for as the price range where i user purchase the relay power. Can divided the price range into the following M intervals From Lemma 2, we can rewritten the price optimization problem in 12 as 15 16 In 16, we have decomposed the optimization problem into M subproblems, where the ith subproblem is to find the optimization problem in 16 are solved in following theorem, the proof of which can be found in [10] Theorem 1 [10]: Define following equation, for, 24

International Conference on Electrical and Computer Engineering ICECE'2015 Dec. 15-16, 2015 Pattaya Thailand We set the relay power to be optimal according to Theorem 1. We consider two schemes for the relay power allocations based on KSBS power allocation and optimal solution. To compare the network performance of two schemes, we show in Table I, the network sum rate the two power allocation schemes at the relay power price 0.5 time of optimal price. As can be seen from Table I, the KSBS-based schemes achieve a smaller network sum-rate than that of the sum-rate optimal solution. 17 The solution to subproblem i is { 18 Note, the value of optimal price can be obtained using TABLE I SYSTEM SUM RATE IN THREE USER RELAY NETWORK With the subproblems solved, to find the optimal relay power price following equation is used: { } Network Sum-Rate x10-4 19 IV. INEFFICIENCY OF RELAY POWER ALLOCATION BASED ON KSBS w, W In this section, we analyze and compare the network sum rate of the KSBS-based power allocation with sum-rateoptimal solution. We look at different price range of relay power price. The network sum-rate formulate from the received SNR, thus it can be shown the network performance. From the expression 5 we can formulate the network sum rate as follows: [13] KSBS-Based 7906 7900 Algorithm 1. From Lemma 3, the optimal price is in the. If the optimal price is the total power interval demand by user does not exceed the relay power constraint., from Lemma 2, thus, the sum rate Therefore, of KSBS-based to have the same performance as that of the sum-rate optimal. Therefore, to show the performance of power allocation in KSBS when relay set the price too low. In the simulation we consider the relay power price 0.5 time of optimal price. where is optimal relay power price We can find the optimal price for the relay power price by solving the M subproblem in 16 and then find the optimal price among the M subproblem solutions that result in the maximum relay revenue. Sum-Rate Optimal energy density N, D VI. demagnetizing factor SIMULATION RESULT 1 erg/cm3 10 1 J/m3 1 1/4 In this section we shown via the simulate inefficiency of KSBS-based power allocation. The inefficiency of KSBSbased can be shown via performance of KSBS-based power allocation compared with that of the sum-rate-optimal solution. We consider a network with 5 users. The transmit power of the user are set to be 10 db and the relay power constrain P is 20 db. We set the relay power price to be optimal according to Theorem 1. 20 We consider the inefficiency of KSBS-based power allocation at different price ranges. The comparison the sumrate of KSBS and sum rate optimal solution, from 20, can be use to formulate the inefficiency of KSBS-based power allocation as 21 Note that the sum rate optimal solution aim to maximize network sum rate, thus,. We would like to investigate the bounding the inefficiency of KSBS-based power allocation, that can be guarantee the network performance of KSBS-based power allocation not less the lower-bound. V. KSBS-BASED IN SIMPLE RELAY NETWORK In this section, we describe a simple example of multiuser single-relay network. The network has three users, one relay, and three destinations. We use Rayleigh flat-fading channels model, channel gain generated as i.i.d random variables following the distributed. The transmit power of the user is set to be 10 db and the relay power is set to be 15 db. Fig 2. Inefficiency of KSBS under different price in five user relay network 25

International Conference on Electrical and Computer Engineering ICECE'2015 Dec. 15-16, 2015 Pattaya Thailand [13] Qian Wang; Yindi Jing "Power Allocation and Sum-Rate Analysis for Multi-User Multi-Relay Networks", Vehicular Technology, pp. 1 5 Fig. 2 shows the inefficiency of KSBS under different relay power price. It shows that when the relay power price is optimal price, the inefficiency is 1. It can be shown that the network sum-rate of KSBS-based and the sum-rateoptimal give the same performance. We can see that when the relay power price decreases from optimal price, is the inefficiency of KSBS-based decreases. This is because when the relay power price low, all users ask for high ideal power. But they cannot request more than power constraint P thus, based on Lemma 2, when we have KSBS based power allocation where. Thus, all users cannot reach their ideal power that makes the inefficiency of KSBS-based decreases when relay power price decreases. VII. CONCLUSION In this paper, we consider a multiuser single-relay network, we investigated the inefficiency of KSBS-based power allocation under different relay power price, compared with that of the sum-rate-optimal. Simulation results show the inefficiency of KSBS-based power allocation is 1 at optimal price. It can be shown that network sum-rate of KSBSbased and sum-rate-optimal give the same performance, and when relay power price decreases from optimal price trend inefficiency of KSBS-based decreases. REFERENCES A. Nosratinia, T. E. Hunter, and A. Hedayat, Cooperative communication in wireless networks, IEEE Commun. Mag., vol. 42, no. 10, pp. 74 80, Oct. 2004 [2] L. N. Laneman, D. N. C. Tse, and G.W.Wornell, Cooperative diversity in wireless networks: Efficient protocols and outage behavior, IEEE Trans.Inf. Theory, vol. 50, no. 12, pp. 3062 3080, Dec. 2004. [3] K. T. Phan, L. Le, S. A. Vorobyov and T. Le-Ngoc "Centralized and distributed power allocation in multi-user wireless relay networks", IEEE Intl. Conf. Commun., 2009 [4] K. Phan, T. Le-Ngoc, S. Vorobyov and C. Tellambura "Power allocation in wireless multi-user relay networks", IEEE Trans. Wireless Commun., vol. 8, no. 5, pp.2535-2545 2009 [5] Y. Shen, G. Feng, B. Yang, and X. Guan, Fair resource allocation and admission control in wireless multiuser amplify-and-forward relay networks, IEEE Trans. Veh. Technol., vol. 61, no. 3, pp. 1383 1397, Mar. 2012. [6] B. Wang, Z. Han, and K. J. R. Liu, Distributed relay selection and power control for multiuser cooperative communication networks using Stackelberg game, IEEE Trans. Mobile Comput., vol. 8, no. 7, pp. 975 990, Jul. 2009. [7] H. Al-Tous and I. Barhumi Resource Allocation for AF Cooperative Communication Using Stackelberg Game, IEEE Trans. Signal Processing and Commun, pp. 1-6, Dec. 2012 [8] Q. Cao, Y. Jing, and H. V. Zhao, "Power bargaining in multi-source relay networks, " in Proc. IEEE Commun. Conf., Jun. 2012, pp. 39053909. [9] Q. Cao, Y. Jing and H. V. Zhao "Power allocation in multi-user wireless relay networks through bargaining", IEEE Trans. Wireless Commun., vol. 12, no. 6, pp.2870-2882 2013 [10] Q. Cao, H. V. Zhao, and Y.D. Jing, "Power Allocation and Pricing in Multiuser Relay Networks Using Stackelberg and Bargaining Games," IEEE Trans. Vehicular Technology, vol.61, no.7, pp.3177-3190, Sep.2012. [11] D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA: MIT Press,1991. [12] E. Kalai and M. Smorodinsky, Other solutions to Nash s bargaining problem, Econometrica, vol. 43, no. 3, pp. 513 518, May 1975. [1] 26