Distributed Power and Channel Allocation for Cognitive Femtocell Network using a Coalitional Game Approach

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1 1 Distributed Power and Channel Allocation for Cognitive Fetocell Network using a Coalitional Gae Approach Tuan eanh, Nguyen H. Tran, and Choong Seon Hong Departent of Coputer Engineering, Kyung Hee University, Korea eail: {latuan, nguyenth, cshong}@khu.ac.kr. Abstract The cognitive fetocell network (CFN) integrated with cognitive radio-enabled technology has eerged as one of the proising solutions to iprove wireless broadband coverage in indoor environent for next-generation obile networks. In this paper, we study a distributed resource allocation that consists of subchannel- and power-level allocation in the uplink of the two-tier CFN coprised of a conventional acrocell and ultiple fetocells using underlay spectru access. The distributed resource allocation proble is addressed via an optiization proble, in which we axiize the uplink su-rate under constraints of intra-tier and inter-tier interferences while aintaining the iniu rate requireent of the served feto users. Specifically, the aggregated interference fro cognitive feto users to the acrocell base station is also kept under an acceptable level. We show that this optiization proble is NPhard and propose a distributed fraework to axiize the surate of network based on coalitional gae in partition for. The proposed fraework is tested based on the siulation results and shown to perfor efficient resource allocation. Keywords Cognitive fetocell network, resource allocation, power allocation, subchannel allocation, coalitional gae, gae theory. I. INTRODUCTION In recent years, the nuber of obile applications deanding high-quality counications have treendously increased. For instance, high-quality video calling, obile high-definition television, online gaing, and edia sharing services always have connections with high-quality of services (QoS) requireents aong devices and service providers [1]. In order to adapt to these requireents, the Third Generation Partnership Project (3GPP) ong-ter Evolution Advanced (TE- Advanced) standard has been developed to support higher throughput and better user experience. Moreover, in order to accoodate a large aount of traffic fro indoor environents, the next obile broadband network uses the heterogeneous odel, which consists of acrocells and sallcells - This research was supported by Basic Science Research Progra through National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2014R1A2A2A ). *Dr. CS Hong is the corresponding author. [2], [3]. The sallcell odel (such as fetocells) is one way of increasing coverage in dead zones in indoor environents, reducing the transit power and the size of cells and iproving spectru reuse [4]. A two-tier fetocell network can be ipleented by spectru-sharing between tiers, where a central acrocell is underlaid with several fetocells [5]. This network odel is also called the cognitive fetocell network (CFN) [6], [7]. In this paper, we focus on the resource allocation in underlay CFN where the channel usages are based on the underlay cognitive transission access paradig [7], [8]. In the CFN deployent, interference is a ajor challenge caused by overlapping area aong cells in a network area and co-channel operations. The interference can be classified as: intra-tier (interference caused by acro-to-acro and fetoto-feto) or inter-tier (interference caused by acro-to-feto and feto-to-acro) [9]. In order to itigate interference, soe works have studied the downlink direction [10]. However, the CFN uplink using the underlay paradig is also an iportant challenge that needs to be considered [3], [4]. In the uplink direction, the uplink capacity and interference avoidance for two-tier fetocell network were developed by Chandrasekhar et al. [6]. In [11], an interference itigation was proposed by relaying data for acro users via feto users, based on the coalitional gae approach and leasing channel. The power control under QoS and interference constraints in fetocell networks was studied in [12]. However, ost of the above entioned works only focus on single-channel operation and do not ention the channel allocation to the feto users. In [13], the uplink interference is considered in OFDMA-based fetocell networks with partial co-channel deployent without the fetocell users power control. Additionally, channel allocations are based on an auction algorith for acrocell users and fetocell users. Clearly, the channel allocation in [13] is not efficient where users can reuse the channels by power control. In this paper, we study a distributed resource allocation for the CFN uplink in two-tier networks to overcoe the drawbacks of the existing. The ain contributions of this paper are suarized as follows: We investigate an efficient resource allocation for the underlay CFN uplink that is addressed via a NP-hard optiization proble /16/$ IEEE 251 BigCop 2016

2 n MUE CFBS 1 n ' l 1 CFBS n l n MUE 1 Data transission Interference MBS 0 1 n' CFBS n' n' MUE 1 N l n ' MUE 2 CFBS N N MUE M l N Fig. 1: Syste architecture of a cognitive fetocell network. We forulate the optiization proble as a coalition gae in a partition for. We propose algoriths to allocate resources in a distributed way, in which the CFN ipleentation is selforganized and self-optiized. The rest of the paper is organized as follows. In section II, we explain the syste odel and proble forulation. In section III, we address the solutions to solve this optiization proble based on a coalitional gae in the partition for approach. Section IV provides siulation results. Finally, conclusions are drawn in section V. II. SYSTEM MODE AND PROBEM FORMUATION Firstly, we provide the syste odel followed by the proble forulation of priary network protection. Then, we consider the data transission odel in the uplink of s. Next, we present s QoS deand. Finally, we forulate the resource allocation as an NP-hard optiization proble. A. Syste odel We consider an uplink CFN based on the underlay spectru access paradig, in which N CFBSs are deployed as in Fig. 1. These CFBSs are under-laid to the acrocell frequency spectru and reuse the set of licensed subchannels of the uplink OFDMA acrocell. In the priary acrocell, there exist M subchannels which are correspondingly occupied by M acrocell user equipents (MUEs) in the uplink direction. et N = {1,..., N} and M = {1,..., M} denote a set of all CFBSs and MUEs, respectively. Every CFBS n N is associated to the sae nuber of s. et n = {1,..., } denote the set of s served by a CFBS n N. s and CFBSs are integrated cognitive odules that support selforganization, self-optiization and estiating channel state inforation (CSI) as in [7]. Moreover, s and CFBSs exchange inforation via dedicated reliable feedback channels or wired back-hauls. B. Priary network protection In the underlay CFN, the MBS of the acrocell needs to be protected against overall interference fro s, as in [14], [15]. The protection on subchannel at the MBS is addressed as follows: αh,0p ζ0, M, (1) l n,n N where α = {0, 1} is a subchannel allocation binary indicator; h,0 denotes the channel gain between l n and the the priary MBS, P is the power level of l n using subchannel, and ζ0 is the interference threshold at the priary receiver MBS on subchannel. C. Data transission odel in uplink In our considered odel, the data transission of s is affected by the interference fro the MUE and other s in other fetocells. Each is assued to be assigned to one subchannel for a given tie. The transission rate of l n on subchannel follows the Shannon capacity as follows: R = B w log (1+ h P ) In, (2) + n 0 where B w is the bandwidth of subchannel, M; In denotes the total interference at CFBS n on subchannel : I n = l n,n N h l np l n + h np 0, (3) where n n; h, h l n and h n are the channel gains between l and CFBS n, l n and CFBS n, and MUE and CFBS n, respectively; n 0 is the noise variance of the syetric additive white Gaussian noise; h np0 is the inter-tier interference at CFBS n fro MUE ; and l n,n N h l n P l n is total intra-tier interference fro s at the other CFBSs that use the sae subchannel. D. s QoS deand Assuing that, at the beginning of each tie slot, the iniu data rate requireent for each l n for running high quality of services is given by R th, the condition R R in (4) has to be guaranteed. Fro (2) and (4), we have the constraint of total interference to guarantee the iniu data rate requireent of each as follows: I n + n 0 h P χ, (5) where χ = (2 Rin Bw 1). In order to illustrate the subchannel and power allocation efficiently and optially, we address an optiization proble in the next subsection. 252

3 3 E. Proble forulation The objective is to axiize the uplink su-rate of the whole CFN. The constraints include iniization of the intratier and inter-tier interference levels with siilarly inial rate requireents for connected s. Specifically, the total interference at the MBS is also kept under acceptable levels. Moreover, the subchannels are efficiently reused aong s. Fro the discussion of our considered probles in section II, the optiization proble is forulated as follows: OPT1: ax. (α,p ) s.t. (1), (5), 0 M M n N l n α R (6) α 1, n N, l n, (7) α = {0, 1}, M,n N,l n, (8) P,in P P,ax,, n, l. (9) The purpose of OPT1 is to allocate the optial subchannels and power levels for s in order to axiize the CFN uplink su-rate. The constraint (1) are addressed in section II. Moreover, soe conditions of subchannel allocation indicator α are represented in (5) and (7). Constraint (8) shows that each l n is only assigned one subchannel at a given tie. Constraint (9) represents the power range of each l n, which has to be within the threshold range. Clearly, OPT1 is a ixed integer linear progra, which is NP-hard in general [16]. In order to solve OPT1, we propose a distributed solution that is based on the the coalitional gae approach. cooperates with other s to choose subchannel and power levels in order to for stable coalitions using 1 (described in section III.C). III. RESOURCE AOCATION BASED ON COAITIONA GAME IN PARTITION FORM. Herein, the proble OPT1 is solved based on coalition gae approach where s are players as follows. Firstly, the OPT1 is forulated as a coalitional gae in partition for in which s are players. Secondly, we present the recursive core ethod to solve the proposed gae. Thirdly, we address an ipleentation of the recursive core ethod to deterine the optial subchannel and power allocation in a distributed way. Finally, we consider the convergence and existence of the Nash-stable coalitions in the gae. A. Forulation OPT1 as a coalitional gae in partition for The coalitional gae is a kind of cooperative gae that is denoted by (,U), in which individual payoffs of a set of players = n N n are apped in a payoff vector U. The players have incentives to cooperate with other players, in which they seek coalitions to achieve the overall benefit or worth of the coalitions. The coalitional gae in partition for is one such gae expression, which is studied and applied in [17], [18]. The worth of coalitions depend on how the players outside of the coalition are organized and on how the coalitions are fored. In the coalitional gae, the cooperation of players to for coalitions is represented as the non transferable utility (NTU) gae which is defined as follows [17]: Definition 1: A coalitional gae in partition for with NTU is defined by the pair (,U). Here, U is a apping function such that every coalition S, U (S,φ ) is a closed convex subset of R S, which contains the payoff vectors available to players in S. The apping function U is defined as follows: { } U (S,φ )= x R S x (S,φ )=R(S,φ ), (10) where x (S,φ ) is the individual payoff of player l n, which corresponds to the benefit of a eber in S in partition for φ ; R (S,φ ) is data rate of FUE in coalition S of network partition φ. The l n belongs to coalition S depending on the partition φ in a feasible set Φ of players joining coalitions. The singleton set U (S,φ ) is closed and convex [19]. In suary, the players ake individual distributed decisions to join or leave a coalition to for optial partitions that axiize their utilities and bring the overall benefit of coalitions. Based on the characteristics and principles of this gae, we odel the OPT1 as a coalitional gae in partition for. Instead of finding the global optial that cannot be solved directly, s will cooperate with other s to achieve sub-optial solution of the optiization proble OPT1. Proposition 1: The optiization proble OPT1 can be odeled as a coalitional gae in partition for (,U). Proof: l n and its data rate R in are considered as player l n and individual payoff x (S,φ ) in the gae, respectively. A set of s is represented as. The data rate R is apped in a payoff vector U as in (10). In order to address foration of a certain coalition S, we assue that there are only M +1 candidate coalitions S that s can join, M {0}. Here, S 0 eans that s in this coalition are not allocated to any subchannel. Furtherore, each joining or leaving coalition of s has to satisfy the constraints of the optiization proble OPT1. The total data rate of s using the sae subchannel bring the overall benefit or worth of a coalition. In order to find a suboptial value in OPT1, s have incentives to cooperate with other s. The cooperation inforation consists of the subchannels and power levels allocated to s. Intuitively, if s do not exchange their inforation with other s, the syste perforance will be degraded due to unsatisfied constraints in OPT1. Hence, in order to iprove the individual payoff value of s, incentives to cooperate aong s are necessary [17], [20]. Therefore, the OPT1 can be solved based on odeling as a coalitional gae in partition for. Then, we apply the recursive core ethod that is introduced in [18] to solve this proposed gae as following subsections. B. Recursive core solution Herein, we apply the recursive core ethod to solve our proposed gae. In order to overcoe the challenge of the 253

4 4 NTU gae in partition for, we transfor the NTU gae into a transferable utility (TU) gae, as discussed in [18]. In the TU gae, the benefit of a coalition is captured by a real function. Because (10) is a singleton set, we define an adjunct coalitional gae as (,v). When S belongs to φ, the function value v(s,φ ) v is deterined as follows: { v(s,φ )= S x (S,φ ), if S 1, 0, otherwise. (11) We can see that the apping vector of the individual payoff value of s in (10) is uniquely given fro (11) and the core in TU gae is non-epty [18]. Thus, we are able to exploit the recursive core as a solution concept of the original gae (,U) by solving the gae (,v) while restricting the transfer of payoffs according to the unique apping in (10). Here, the value v(s,φ ) is the su-rate of s allocated to the sae subchannel in partition φ. Through cooperating and sharing the payoff aong s in the coalition, s achieve their optial power allocation to axiize each coalition S to which they belongs. Then, based on the results in each coalition, the optial subchannel allocations are deterined by finding the core of the gae using the recursive core definition. Before describing the recursive core definition, we define a residual gae that is an iportant interediate proble. The residual gae (R,v) is a coalitional gae in partition for that is defined on a set of s R = \S. s outside of R are deviators, while s inside of R are residuals [18]. The residual gae is still in partition for and can be solved as an independent gae, regardless of how it is generated [17]. The residual gae of s fors a new gae that is a part of the original gae. s in the residual gae still have the possibility to divide any coalitional gae into a nuber of residual gaes which, in essence, are easier to solve. The solution of a residual gae is known as the residual core, which can be found by recursively playing residuals gaes, which are defined as follows (entioned in [18], definition 4): Definition 2: The recursive core C (,v) of a coalitional foration gae (,v) is inductively defined as follows: 1) Trivial Partition. The core of a gae with is only an outcoe with the trivial partition. 2) Inductive Assuption. Proceeding recursively, consider all s belonging to, and suppose the residual core C(R,v) for all gaes with at ost -1 s has been defined. Now, we define A(R,v) as follows: A(R,v) = C(R,v), if C(R,v) ; A(R,v) = Ω(R,v), otherwise. Here, let Ω(R,v) denote a set of all possible outcoes of gae (R,v). 3) Doinance. An outcoe (x,φ ) is doinated via coalition S if at least one (y \S,φ \S ) A(\S,v) there exists an outcoe ((y S, y \S ),φ S φ \S ) Ω(,v), such that (y S, y \S ) S x. The outcoe (x,φ ) is doinated if it is doinated via a coalition. 4) Core Generation. The recursive core of a gae of is a set of undoinated partitions, denoted by C(,v). Corresponding to each network partition, the individual payoffs of all s in the gae are uniquely deterined and undoinated. Furtherore, the coalitions in the recursive core are fored to provide the highest individual payoffs or data rates of s, as detailed in Step 4. C. Ipleentation of the recursive core at each coalitional gae foration in partition for We address ipleentation of the recursive core ethod to solve the proposed gae. According to the transforation fro a NTU gae into a TU gae, the coalition S in a partition φ is represented by a real function v(s,φ ) as in (11). Corresponding to the subchannel allocation of s, soe s can be allocated into the sae subchannel, which fors a coalition S. Then, s optiize their individual payoffs by sharing with other s in the sae coalition S. In this case, s cooperate with others in coalition to axiize the individual payoff and value v(s,φ ). Sharing is achieved by finding optiu power values of each in the following optiization proble: OPT1 S,φ : ax. v(s,φ ) (12) P s.t. h,0p ζ0, (13) S Zn h np0 + n 0 h P χ, l n, S, (14) P,in P P,ax, S,l n. (15) The constraint (14) is taken fro (5) in which Z n = l n,n N h l n P l n denote the intra-tier interference fro other s to CFBS on subchannel. When l n belongs the coalition S, α is set to 1, otherwise is set to 0. Therefore, without loss of generality, we ignore paraeter α in OPT1 S,φ. By finding the optial power allocation to s, they will achieve an optiu individual payoff value that axiizes the worth of coalition S. The optial solution of OPT1 S,φ can be found in a centralized or distributed way. We find the optial solution in a distributed way. We solve the optiization proble by odeling as a geoetric convex prograing proble [21]. Corresponding to the optial transit power levels in OPT1 S,φ, in general, coalition S guarantees the optial sharing payoffs aong ebers s. Siultaneously, we also find the optiu worth v(s,φ ) of coalition S. Based on the steps in the Definition 2, we propose Algorith 1 to find recursive core which leads to the distributed subchannel and power allocation. The algorith is repeated until convergence to stable partitions φ (k), which results in a set of undoinated partitions in the recursive core. Whenever undoinated partition φ (k) is updated at tie k, the network coordinator updates allocation subchannel to s (Step 9). In addition, observing value v(s,φ ) are done by network coordinator such as the fetocell gateway [20]. We note that, in our algorith, subchannel and power allocation of s are updated whenever network partition is transfered fro partition (k 1) to partition (k), 254

5 5 Algorith 1 Distributed algorith for subchannel and power allocation in cogntive fetocell network. * Initialization: 1: φ (0) = {{1}, {2}..., { }} in which s are randoly allocated subchannel and transit power with non-cooperative aong FUEs. * Coalition foration: 2: s operate in cooperative ode and join into potential coalitions φ = {{0}, {1}..., { M }}. 3: for player {nl} do 4: for S {φ (k 1) \{nl}} do 5: Set φ (k) := {φ(k 1) \S, S,g = S {nl}}. 6: Calculate v(s,g,φ (k+1) ). 7: if v(s,g,φ ) > v(s,φ ), then: M {0} 8: Set φ (k) = φ (k) 9: Update α, P.. M {0} 10: end if 11: end for 12: end for * Output: Output the stable core of gae (,v) consisting of both the final partition φ, subchannel allocation decision α and transit power level P., which produces Pareto doinates S (k). The convergence and Nash-stable coalition in Algorith 1 are discussed in the next subsection. D. Convergence and stability analysis of the proposed gae The convergence of the proposed gae through four steps of the recursive core ethod is guaranteed as follows: Propriety 1: Starting fro any initial partition φ, using the Algorith 1, coalitions of s erge together by Pareto doinance, which results in network partition stable and lies in the non-epty recursive core C(,v). Proof: Every transfer operation fro partition (k 1) to partition (k) is an inductive step, which produces Pareto doinates S (k) as follows: S (k) φ (k) v(s (k),φ (k) ) > S (k 1) φ (k 1) v(s (k 1),φ (k 1) ). (16) We note that, each s gradually selects the coalitions based on conditions (7) and (8). Hence, the value of coalition will set to zero if conditions of the fored coalition is violated, and the value of other coalitions reains unchanged. Therefore, given any two successive algorith steps k 1 and k, we have v(φ (k) )= S (k) φ (k) v(s (k),φ (k) ) is Pareto doinated by φ (k). Therefore, the Algorith 1 ensures that the overall network utility sequentially increases by Pareto doinance. In addition, the su of values of the coalitions in each group g increases without decreasing the payoffs of the individual s and the whole network as well. The nuber of partitions of s into M +1 coalitions is a finite set given by the Bell nuber [18], the nuber of transission steps is finite. Hence, Su rate (Mbps) optiality gap = 5.6% Centralized solution Proposed cooperative approach Rando SCA with power control SCA without power control Interference power theshold, dbw Fig. 2: Average throughput in uplink CFN versus interference threshold at MBS when N = 4 FBSs, K = 3 subchannels. the sequence of step transissions will terinate after a finite nuber of inductive steps and will converge to a final partition. Obviously, the recursive core ethod applied to our proposed gae always converges to a final network partition. Moreover, the network partition based on residual gae always converges to a Nash-stable partition. IV. SIMUATION RESUTS We siulate an MBS and a group of 4 CFBSs with the coverage radii of 500 and 30, respectively. In order to allocate subchannels to the fetocells, we utilize three SC- FDMA licensed subchannels, which are allocated to uplink transission of three MUEs, each with bandwidth B w = 360 khz (by using two sub-carriers for each licensed subchannel) and a fixed power level of 500 W. Moreover, the interference threshold at the MBS for each licensed subchannel equals to -70 dbw. Each CFBS has two s, a pilots signal with power equals to 500 W. Each has a iniu data rate equals to 2 Mb/s. In addition, each has a axiu power level constraint (P ax ) of 100 W. We estiate the su rate of s versus the interference threshold at the MBS. As shown in Fig.2, the average throughput in our proposed approach increases with the interference threshold value of each subchannel at MBS increase. However, this value is saturated as the interference threshold value becoes sufficiently large (-50 db). Moreover, we copare the average throughput under two other ethods, i.e., SCA without power control and Rando SCA with power control. The SCA without power control approach perforance is based on the algorith 1 given fixed transit power levels. For the Rando SCA with power control approach, s are randoly allocated subchannels. Fig.2 shows that for any interference threshold at the MBS, the su rate of the proposed approach is always higher than those of the (Rando SCA with power control) and (SCA without power control) schees. Further, in Fig.2, we have copared the proposed approach to 255

6 6 Su rate (Mbps) optiality gap = 5.6% Proposed cooperative approach Centralized solution Nuber of steps Fig. 3: The optiality gae between the proposed approach and centralized solution. an optial solution, in which s are allocated subchannel and transit power in a centralized fashion. The coparison shows that the proposed approach is close to centralized solution. In Figure 2 and Figure 3, we show the optiality gap between the optial centralized approach and proposed cooperative approach, with a gap of 5.6% for a network with value -50dBW of interference threshold at MBS. Moreover, in Figure 3, our algoriths converge after around 14 tie steps. V. CONCUSIONS In this paper, we investigated an efficient distributed resource allocation schee for uplink underlay CFN. The efficient resource allocation is characterized via an optiization proble. We identified the optial subchannels and power levels for s to axiize the su-rate. The optiization proble guaranteed the inter-tier and inter-tier interference thresholds. Specifically, the aggregated interference fro fetocell users to the MBS and the iniu rate requireent of the connected are kept under the acceptable level. In order to solve the optiization proble, we suggested a forulation optiization proble as a coalitional gae in partition for. The convergence of algoriths was also carefully investigated. The efficient resource allocation has tested via siulation results, with the su-rate of the proposed fraework has closed to optial solution and better than those of the other fraeworks. REFERENCES [1] I. Z. Kovács, P. Mogensen, B. Christensen, and R. Jarvela, Mobile broadband traffic forecast odeling for network evolution studies, in IEEE, Vehicular Technology Conference (VTC Fall). San Francisco, CA, Sep [2] J. Hoadley and P. Maveddat, Enabling sall cell deployent with hetnet, IEEE, Wireless Counications Mag., vol. 19, no. 2, pp. 4 5, Apr [3] T. Nakaura, S. 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