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

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1 Distributed Power and Channel Allocation for Cognitive Fetocell Network using a Coalitional Gae in Partition For Approach Tuan LeAnh, Nguyen H. Tran, Meber, IEEE, Sungwon Lee, Meber, IEEE, Eui-Na Huh, Meber, IEEE, and Zhu Han, Fellow, IEEE, Choong Seon Hong, Senior Meber, IEEE, 1 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 average delay requireent for cognitive fetocell 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 NP-hard and propose an autonoous fraework, in which the cognitive fetocell users self-organize into disjoint groups (DJGs). Then, instead of axiizing the su-rate in all cognitive fetocells, we only axiize the su-rate of each DJG. After that, we forulate the optiization proble as a coalitional gae in partition for, which obtains sub-optial solutions. Moreover, distributed algoriths are also proposed for allocating resources to the CFN. Finally, 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 This research was supported by the MSIP(Ministry of Science, ICT and Future Planning), Korea, under the ITRC(Inforation Technology Research Center) support progra (IITP-15-(H ) supervised by the IITP(Institute for Inforation & counications Technology Prootion) *Dr. CS Hong is the corresponding author. Tuan LeAnh, N. H. Tran, C. S. Hong, S. Lee, and E.-N. Huh are with the Departent of Coputer Science and Engineering, Kyung Hee University, Korea (eail: {latuan, nguyenth, cshong, drsungwon, johnhuh }@khu.ac.kr). Z. Han is with the Electrical and Coputer Engineering Departent, University of Houston, Houston, Texas, USA (eail: zhan@uh.edu). adapt to these requireents, the Third Generation Partnership Project (3GPP) Long-Ter Evolution Advanced (LTE- 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 [], [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], [5]. In practice, a two-tier fetocell network can be ipleented by spectru-sharing between tiers, where a central acrocell is underlaid with several fetocells [6]. This network odel is also called the cognitive fetocell network (CFN) [7], [8]. The CFN can be deployed successfully and cost-efficiently via two different spectru-sharing paradigs: overlay and underlay [8] [1]. The overlay access paradig enables the cognitive fetocell user equipent (secondary user) to transit their data only in spectru holes where acrocell users (priary users) are not transitting. A fetocell user equipent (CFUE) vacates its channel if it detects an occupancy requireent of a acro user equipent (MUE). In the underlay access, CFUEs are allowed to operate in the band of the acrocell network, while the overall interference fro CFUEs occupancy on the sae channel should be kept below a given threshold. Moreover, in this paradig, entities in CFN are assued to have knowledge of the interference caused by transitters in the acrocell network [6], [9]. 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 [6], [8], [11]. 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) [1], [13]. Specifically, the inter-tier interference, which is caused by using the underlay spectru access, needs to be considered to protect the acrocell network [6]. In order to itigate interference, soe works have studied the downlink direction [1], [14] [16]. Suppression of intratier interference using the coalitional gae is studied in [1]. In [14], the authors eployed frequency division ultiple access

2 in ters of the area spectral efficiency and subjected to a sensible QoS requireent. The power and sub-carrier allocations for OFDMA fetocells based on underlay cognitive radios in a two-tier network are entioned in [15]. A selforganization strategy for physical resource block allocation with QoS constraints to avoid co-channel and co-tier interference is investigated in [16]. However, the CFN uplink using the underlay paradig is also an iportant challenge that needs to be considered [3] [5]. In the uplink direction, the uplink capacity and interference avoidance for two-tier fetocell network were developed by Chandrasekhar et al. [7]. In [17], 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 [18]. The distributed power control for spectru-sharing fetocell networks using the Stackelberg gae approach was presented in [6]. 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 [19], 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 [19] is not efficient where users can reuse the channels by power control, as in [6], [18]. In this paper, we study an efficient distributed resource allocation for the CFN uplink in two-tier networks to overcoe the drawbacks of the existing literature. The efficient distributed resource allocation in the ultiple channel environent is represented by solving an optiization proble. The objective of this optiization proble is the uplink surate. The intra-tier and inter-tier interference are considered with constraints in the optiization proble. Additionally, the guaranteed average delay requireents are at the iniu for the connected cognitive fetocell users, and the total interference at the MBS is kept under acceptable levels as well. We show that this optiization proble is an NPhard optiization proble. Motivated by the design of selfoptiization networks [4], [5], [8], [], we propose a selforganizing fraework in which CFUEs self-organize into disjoint groups (DJGs). By doing so, instead of axiizing the su-rate in whole cognitive fetocells, we only axiize the su-rate of each DJG where the coputation of the original optiization is decoposed to the fored DJGs. Then, in order to solve the optiization proble at each DJG, we forulate this optiization proble as a coalitional gae in the partition for, which obtains near-optial solutions along with efficient resource allocation in a distributed way. The coalitional gae is defined by a set of players who are the decision akers seeking to cooperate to for a coalition in a gae [1], [1]. One kind of gae expression is the coalitional gae in the partition for that captures realistic inter-coalition effects in any areas, particularly in wireless counication networks [1], []. In this paper, CFUEs can join and leave a coalition to obtain the axiu data rate (denoted by individual payoff). The joining and leaving of CFUEs have to satisfy soe constraints of the above entioned optiization proble. Specifically, the proposed gae is solved based on the recursive core ethod [1], []. Throughout this ethod, the stability of the coalition foration is a result of the optial channel and power allocation. The optial power allocation to CFUEs corresponding to the network partition is obtained fro sharing payoffs of CFUEs in a coalition. The geoetric prograing and dual-decoposition approaches, which are based on [18], [3] [5], are proposed to deterine the optial power allocation in the coalition. Siulation results show that the proposed fraework can be ipleented in a distributed anner with an efficient resource allocation. Furtherore, the social welfare of the usable data rate in CFN under our solution is also exained via our siulation results. In addition, we also estiate the gap between the global optial solution and the sub-optial solution using proposed cooperative approach. 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. The NP-hard optiization proble is siplified by dividing the network into DJGs. Then, it is solved by forulating 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 reainder of this paper is organized as follows: section II explains the syste odel and proble forulation. The optiization proble of the efficient resource allocation is forulated in section III, as is the DJGs foration. In section IV, we address the solutions to solve this optiization proble based on a coalitional gae in the partition for approach. Section V provides siulation results. Finally, conclusions are drawn in section VI. II. SYSTEM MODEL AND PROBLEM FORMULATION Firstly, we provide the syste odel followed by the proble forulation of priary network protection. Secondly, we consider the data transission odel in the uplink of CFUEs. Thirdly, we analyze a queuing odel of CFUEs. Finally, we discuss soe probles of licensed subchannel reuse aong CFUEs in the CFN. 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. Let N = {1,..., N} and M = {1,..., M} denote a set of all CFBSs and MUEs, respectively. A subchannel can be contain one resource block or a group resource with the single carrier frequency division ultiple access (SC-FDMA) technology in LTE syste [6]. Every CFBS n N is associated to the

3 3 CFUE 11 CFUE 1 CFUE L MUE CFUE L ' CFBS 1 CFUE CFBS n CFUE MUE 1 Data transission Interference CFUE 1 MBS CFBS n' CFUE L CFUE MUE CFUE 1 CFUE L MUE CFBS N MUE M CFUE Fig. 1: Syste architecture of a cognitive fetocell network. sae L nuber of CFUEs. Let L n = {1,..., L} denote the set of CFUEs served by a CFBS n N. Furtherore, cognitive odules are added to CFUEs and CFBSs to support selforganization, self-optiization as in [8]. Moreover, CFUEs 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 CFUEs, as in [7] [9]. The protection on subchannel at the MBS is addressed as follows: αh,p ζ, M, (1) l L n,n N where α is a subchannel allocation indicator defined as { α 1, if l L = n is allocated to subchannel,, otherwise, () h, denotes the channel gain between CFUE l L n and the the priary MBS, P is the power level of CFUE l L n using subchannel, and ζ 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 CFUEs is affected by the interference fro the MUE and other CFUEs in other fetocells. Each CFUE is assued to be assigned to one subchannel for a given tie. The transission rate of CFUE l L n on subchannel follows the Shannon capacity as follows: R = B w log (1 + Γ ), (3) where B w is the bandwidth of subchannel, M, and Γ is the Signal-to-interference-plus-noise ratio (SINR) of the CFUE l L n using subchannel as follows: Γ = h P I n + n. (4) In (4), In denotes the total interference at CFBS n on subchannel : In = h l np l n + h,np, (5) l L n,n N where n n; h, h l n and h,n are the channel gains between CFUE l and CFBS n, CFUE l L n and CFBS n, and MUE and CFBS n, respectively; n is the noise variance of the syetric additive white Gaussian noise; h,np is the inter-tier interference at CFBS n fro MUE ; and h l n P l n is total intra-tier interference l L n,n N fro CFUEs at the other CFBSs that use the sae subchannel. In order to successfully decode the received signals at the CFBS of the CFUE transission, the SINR at CFBS n fro CFUE l L n has to satisfy [3]: Γ γ, (6) where γ is the SINR threshold to decode received signals at the CFBS, n N, M. Because the transission on the CFUE-CFBS link can be dropped due to a certain outage event, the successful transission of CFUEs can be coputed based on the probability of aintaining the SINR above a target level γ, given by: ξ = Pr (Γ > γ). (7) This outage value can be reduced by eployent of the Hybrid Autoatic-Repeat-Request protocol with Chase Cobining at the ediu access layer [31]. According to this protocol, packets will be re-transitted if they have not been successfully received at the receiver. This re-transission can occur up to K ax ties until the successful data transission. Hence, if arrivals to CFUE l L n follow a Poisson process with arrival rate λ, the effective arrive rate λ with a axiu of K ax re-transissions is coputed as follows: Kax λ = λ k=1 ξ (1 ξ ) k 1, (8) where (1 ξ ) is the error packet transission probability of the connected link CFUE l L n to CFBS n, which is calculated based on (7), and Kax k=1 ξ (1 ξ ) k 1 is the successful transission probability of a data packet of CFUE l with a axiu of K ax re-transissions. Clearly, through (8), congestion at the queue of the CFUE occurs when the departure rate or data rate on the CFUE-CFBS link is lower than the acceptable threshold. This congestion leads to delaying data packets in the queueing odel of the CFUE data transission. The queueing odel for CFUEs will be discussed in the next subsection.

4 4 Data packets Re-transission IR 11 IR 1 IR 13 R l n CFBS l n Services rate on wireless link = 1 = 1 = 1 CFUE l n CFBS n CFBS 1 CFUE 1 CFUE 1 CFUE 1 CFBS 3 Fig. : The M/D/1 queueing odel for data transission of CFUEs. D. Queuing odel analysis for guaranteeing the CFUE deands In this subsection, we address the data transission of the CFUE using the M/D/1 queuing odel [3], as shown in Fig.. In this queueing odel, the arrival rate λ depends on the data rate fro the upper layer of CFUE l. Based on Little s law, the average waiting tie of a packet in CFUE l can be calculated as follows: D = R λ (R λ ), (9) where R is considered as the service rate in the M/D/1 queuing odel deterined by (3). Assuing that, at the beginning of each tie slot, the axiu delay requireent for each CFUE l L n is given by D Dax, the condition R in = R R th (1) has to be guaranteed. Fro (9) and the axiu delay value requireent D = Dax, the data rate requireent Rin is calculated as follows: ( ( D ax λ ) ) 1/ + D ax λ + D ax λ D ax. (11) Fro (3), (4) and (1), we have the constraint of total interference to guarantee the iniu delay requireent of each CFUE as follows: In + n h P χ, (1) ( ) where χ = Rin Bw 1. Intuitively, fro (3) and (1), in order to satisfy the iniu average delay requireent, the CFUE needs to increase its power greater than a power level threshold. However, this increase ay produce harful interference to other CFUEs, which leads to a reduced data rate of other CFUEs using the sae subchannel, as in (3). Additionally, the increasing power level at the CFUEs using the sae subchannel will increase the overall interference at the MBS, as entioned in (1). Therefore, when the power allocation to CFUEs cannot satisfy constraints (1), (3), and (1), CFUEs have an incentive IR: interference range Fig. 3: The interference odel for reusing a licensed subchannel aong CFUEs. to find another opportunity for selecting the subchannel fro a set of subchannels. E. Channel reuse in the CFN In the CFN, a subchannel that allocated to a CFUE n can be reused at other CFUEs if it overcoes the intratier interference constraints as considered in [16]. Certainly, in order to allocate a subchannel efficiently, the unlicensed subchannels need to be reused aong CFUEs that are based on paraeter α as follows: { αl, if l n = L n, n T, M, 1, if l L n, n / T, M, (13) where T is a set of the CFBSs lying within the interference range of CFUE l L n on subchannel. The CFBS n T if and only if: IR,n γ, (14) where the interference range IR,n is deterined based on the SINR level fro observing the surrounding CFBSs of CFUE l L n as follows: IR,n = h,ax P h n P + n, (15) and P,ax is the axiu transit power of CFUE l L n that can be allocated on subchannel. In order to illustrate the reuse of subchannels aong CFUEs and to for table T, we present a siple exaple as follows. Exaple 1: Let us consider reusing a licensed subchannel = 1 aong three CFUEs as shown in Fig. 3, in which each CFBS serves one CFUE. The table T of each CFUE is constructed by considering the interference range of the CFUEs based on (14), (15). Then, the CFBSs that belong to the table of CFUEs 11, 1 and 13 are T11 1 = {1, }, T1 1 = {} and T13 1 = {, 3}, respectively. Fro (13), if subchannel = 1 is allocated to CFUE 11, then α11 1 = 1, α1 1 =, and α13 1 = 1. This eans that subchannel 1 cannot be reused at CFUE 1 fro CFUE 11 but CFUE 13 can reuse this subchannel. Siilarly, we consider principles for CFUEs 1 and 13, respectively. The detail of the table T foration is discussed in section III.B.

5 5 In order to illustrate the subchannel and power allocation efficiently and optially, we address an optiization proble in the next section. DJG III. OPTIMIZATION PROBLEM AND DJG FORMULATION In this section, we first discuss an optiization proble that represents an efficient resource allocation for the underlay CFN uplink. Secondly, we address the network partition into DJGs to decopose the coputation of the optiization proble into distributed coputations at DJGs. CFUE CFUE CFUE CFUE CFUE CFUE CFUE Selforganization into DJGs DJG Partitions into stable coalitions Coalition 1 Coalition M DJG Algorith 1 Algorith,3 Coalition A. Optiization 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 average delay requireents for connected CFUEs. Specifically, the total interference at the MBS is also kept under acceptable levels. Moreover, the subchannels are efficiently reused aong CFUEs. Fro the discussion of our considered probles in section II, the optiization proble is forulated as follows: OPT1: axiize (α,p ) M n N l L n α R (16) subject to: (1), (1), (13), α 1, n N, l L n, (17) M α = {, 1}, M, n N, l L n, (18) P,in P P,ax,, n, l. (19) The purpose of OPT1 is to allocate the optial subchannels and power levels for CFUEs in order to axiize the CFN uplink su-rate. The constraints (1), (6), (1), (13) are addressed in section II. Moreover, soe conditions of subchannel allocation indicator α are represented in (17), (18) and (19). Constraint (17) shows that each CFUE l L n is only assigned one subchannel at a given tie, and (18) is represented as in (). Constraint (19) represents the power range of each CFUE l L n, which has to be within the threshold range. The thresholds P,ax and P,in indicate the liitations of the power range of CFUE l L n on each licensed subchannel. Clearly, OPT1 is an NP-hard optiization proble because, in order to find the optial solution, we ust allocate subchannels with ixed integer variable α and non-integer variable along with ixed linear and nonlinear constraints [33], [34]. The NP-hard optiization proble along with the huge nuber of CFUEs akes it infeasible to find an optial solution. In order to solve OPT1, we propose a solution that is based on the DJGs foration and coalitional gae in the partition for approach. A sketchy suary of the proposed solution is illustrated in Fig. 4. Firstly, CFUEs in the network self-organize into DJGs using Algorith 1 (to be discussed in section III.B), in which the interference fro P Fig. 4: The proposed structure for solving OPT1 based on the DJGs foration and coalitional for in the partition for. CFUEs transission in a DJG is not affected by CFUEs transission aong other DJGs. The purposes of this division are to reduce feedback aong network entities and decopose the coputation in OPT1 into distributed coputations at DJGs. Secondly, CFUEs in DJGs will be considered as players in the coalitional gae. CFUE cooperates with other CFUEs to choose subchannel and power levels in order to for stable coalitions using Algoriths and 3 (described in section IV.C). In the next subsection, we siplify the optiization proble OPT1 by addressing DJGs foration. B. DJGs foration In the CFN deployent, depending on the ais of network designers and obile user equipents, the locations of CFBSs and CFUEs are distributed randoly in a network area. Soe fetocells less be affected by interferences fro others fetocells. Thus, CFUEs can self-organize into DJGs as addressed in Algorith 1. At the beginning of each period, the CFBS broadcasts a essage that contains CFBS identification (ID) and interference fro MUEs (line 1). The CFUE decodes the received essages (line,3) and detects the surrounding CFBSs within the interference range (IR) using (14) and (15). The detected CFBSs are stored in table T and then for table T = {t } M Nl (line 4); here, t = 1 if n T, else t =, and N l is the set of CFBSs detected by CFUE l. Then, the CFUE sends its inforation T to its CFBS n (line 5). The CFBS n collects inforation T of all its CFUEs and constructs table T n = {t l,n } M ax( N l ) L n (line 6). Here, {t t } equals to 1 if n T l,n ; otherwise, it equals to. Siultaneously, the CFBSs exchanges inforation the table T n with the CFBSs n T n to for a disjoint group g (line 7). Then, the CFBSs build a subchannel reuse table aong CFUEs based on (13) (lines 8, 9). For convenience, let denote T g = {α } ( M the reuse table of CFUEs at DJG g. Here, denoting by = n Ng L n is the set of CFUEs in DJG g, and N g is the set of CFBSs belonging group g. Clearly, soe CFUEs can be self-organized into disjoint group g. After CFUEs for DJGs, CFUEs only exchange inforation for group foration if and only if the network has new events such

6 6 IR 11 IR 1 IR 13 IR 14 IR 15 CFBS CFBS 5 = 1 = 1 = 1 = 1 = 1 CFBS 1 CFUE 1 CFUE 1 CFUE 1 CFBS 3 CFBS 4 OP1 G CFUE 1 CFUE 1 DJG-1 DJG- IR: interference range Fig. 5: The DJG forulation in exaple. Algorith 1 : The self-organization of CFUEs into DJGs 1: Initially, T =, P = P,ax, M, n N, l L n. The CFBSs broadcast TxCFetoBS-ID essages based on pilot channels as discussed in [16]. * At the CFUE, l L n, n N, do: : decodes TxCFetoBS-ID essage of the surrounding CFBSs. 3: estiates h, n n based on received RSSIs. 4: constructs table T based on (14). 5: sends table T to its CFBS. * At the CFBS n, n N, do: 6: collects T fro its CFUEs. 7: constructs table T n based on table T, l L n. 8: exchanges T n T n, n T n. 9: self-organizes into groups. 1: constructs tables T g based on condition (13), then sends it to the network coordinator. as the CFUEs location or new joining CFUEs. In addition, exchanging inforation aong CFBSs in the DJG foration can be processed via asynchronous inter-cell signaling [35], [36]. A fetocell signals its status inforation to neighbor fetocells periodically and updates its CFUEs local inforation upon reception of the other fetocells signaling. For clear understanding of DJG foration, we provide Exaple as below. Exaple : Let us consider a CFN odel consisting of five CFBSs, as shown in Fig. 5, in which each CFBS contains an CFUE. Assue that the interference ranges (IRs) of CFUEs are deterined and exist as shown in Fig. 5 (Steps 1-3). Intuitively, table T is constructed as in Table I (Step 4), where 1 indicates the CFBS belongs to the CFUE s IR, represents the CFBS does not belong to the IR of the CFUE, and indicates that the CFUE does not receive the CFBS s pilot signals. Because we only consider one subchannel, the tables T 1, T, T 3, T 4 and T 5 are also represented as T 1 11, T 1 1, T 1 13, T 1 14 and T 1 15 as in Table II, respectively. In order to obtain databases of tables of the surrounding CFBSs, the CFBS n exchanges table T n with other CFBSs n T n. By doing so, the CFUEs {11}, {1} and {13} have the sae database as in Table II and for a disjoint group, naely DJG-1. Moreover, DJG- is fored by CFUEs {14} and {15}. After finishing disjoint group foration, subchannel reuse tables for DJGs are TABLE I: The table T forulation of all CFUEs. Table T CFetoBS ID CFBS-1 CFBS- CFBS-3 CFBS-4 CFBS-5 T T 1 1 T T T 15 1 TABLE II: The subchannel reuse talbe T g aong CFUEs. Channel = 1 CFUEs CFUEs fored based on (13) and exist as shown in Table II. Here, 1 denotes two CFUEs that can reuse subchannel 1, denotes two CFUEs that cannot reuse subchannel 1, and the denote two CFUEs belonging to different DJGs. After establishing DJGs, without loss of generality, we find the local optial solution of OPT1 by finding an optial solution of OPT1 g in each DJG g, which is taken fro OPT1 as follows: OPT1 g : ax. (α,p ) s.t. M n N g l L n α R () l L n,n N g α h,p ζ, M, (1) I n,g + n h P χ, n,, l, () { αl, if l n = L n, n T, M, 1, if l L n, n / T, M, (3)

7 7 M α 1, n N g, l L n, (4) =1, α = {, 1}, n N g, l L n, M, (5) P,in P P,ax, n,, l, (6) where let N g denote the set of CFBSs that belong to the DJG g. Constraint (3) is taken fro (13), and n, n N g. Herein, the network size is decreased, but OPT1 g is still an NP-hard optiization proble. In the next section, we discuss in detail how to find the optial solution of OPT1 g. We note that, the intra-tier interference In,g in () is deterined based on (3) as follows: I n,g = Z n,g + Z n,g + h,np, (7) where Zn,g = l L n,n N g h l n P l n is the intra-tier interference fro CFUEs inside DJG g to CFBS on subchannel ; Zn,g = l L n,n N \N g h l n P l n is the intra-tier interference fro CFUEs outside DJG g to CFBS n on subchannel. IV. RESOURCE ALLOCATION BASED ON COALITIONAL GAME IN PARTITION FORM. Herein, the proble OPT1 is solved based on coalition gae approach where CFUEs are players as follows. Firstly, the OPT1 g of each DJG g is forulated as a coalitional gae in partition for. 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 g as a coalitional gae in partition for The coalitional gae is a kind of cooperative gae that is denoted by ( ), U Lg, in which individual payoffs of a set of players are apped in a payoff vector U Lg. 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 [1], [37], [38]. 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 [38]: Definition 1: A coalitional gae in partition for with NTU is defined by the pair (, U Lg ). Here, U Lg is a apping ( function ) such that every coalition S,g, U Lg S,g, φ Lg is a closed convex subset of R S,g, which contains the payoff vectors available to players in S,g. The apping function U Lg is defined as follows: ( ) U Lg S,g, φ Lg = { ( ) x R S,g x S,g, φ Lg = R (S,g, φ Lg ) }, (8) ( ) where x S,g, φ Lg is the individual payoff of player l L n, which corresponds to the benefit of a eber in S,g in partition for φ Lg of group g. The CFUE l L n belongs to coalition S,g depending on the partition φ Lg in a feasible set Φ Lg of players joining coalitions. ( ) Reark 1: The singleton set U Lg S,g, φ Lg is closed and convex [3]. 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 g as a coalitional gae in partition for. Instead of finding the global optial that cannot be solved directly, CFUEs will cooperate with other CFUEs to achieve sub-optial solution of the optiization proble OPT1 g. Proposition 1: The optiization proble OPT1 g can be odeled as a coalitional gae in partition for ( ), U Lg. Proof: CFUE l L n and its data rate R in a certain DJG( g are considered ) as player l L n and individual payoff x S,g, φ Lg in the gae, respectively. A set of CFUEs that belong to DJG g is represented as. The data rate R is apped in a payoff vector U Lg as in (8). In order to address foration of a certain coalition S,g, we assue that there are only M + 1 candidate coalitions S,g that CFUEs can join, M {}. Here, S eans that CFUEs in this coalition are not allocated to any subchannel. Furtherore, each joining or leaving coalition of CFUEs has to satisfy the constraints of the optiization proble OPT1 g. The total data rate of CFUEs using the sae subchannel bring the overall benefit or worth of a coalition. In order to find a sub-optial value in OPT1 g, CFUEs have incentives to cooperate with other CFUEs. The cooperation inforation consists of the subchannels and power levels allocated to CFUEs. Intuitively, if CFUEs do not exchange their inforation with other CFUEs, the syste perforance will be degraded due to unsatisfied constraints (1)-(6), as entioned in III.A. Moreover, fro (7), the individual payoff of each CFUE depends on CFUEs belong to using the sae subchannels. In addition, the individual payoff of CFUEs depend on using subchannels of CFUEs at other DJGs. Hence, in order to iprove the individual payoff value of CFUEs, incentives to cooperate aong CFUEs are necessary [1], [38], [39]. Therefore, the OPT1 g can be solved based on odeling as a coalitional gae in partition for. In order to solve this gae, we siplify the coalition foration by assuing the value of the coalition depends on the outside coalitions, which is intra-tier interference fro other DJGs. Then, we apply the recursive core ethod that is introduced in [], [37] to solve this proposed gae. Different fro the core of Shapley value in the characteristic for, recursive core allows odeling of externalities for gaes in partition for []. The details of the solution are discussed in the following subsection. B. Recursive core solution As discussed in [], [37], the NTU gae in partition for is very challenging to solve. However, we can use the concept

8 8 of a recursive core to solve the proposed gae []. Norally, the recursive core is defined for gaes with transferable utility (TU), where a real function captures the benefit of a coalition instead of apping [], [37]. Moreover, since the apping function in (8) is a singleton set, we can define an adjunct coalition gae as (, v) for the proposed gae in which the benefit of each coalition S,g is captured over a real line v(s,g ). By doing so, the original gae (, U Lg ) is solved via the adjunct coalition gae (, v) that is siilar to gaes with transferable utility as studied in [1], [17], [39]. Whenever a CFUE detects a coalition S,g that it can join, it copares its payoff in the current coalition and payoff in coalition S,g. If the payoff in S,g is greater than the current then CFUE will join it; otherwise will stay in the current coalition. In the NTU gae, payoffs are a direct by product of the gae itself due to power allocation of CFUEs on subchannel to avoid violation of MBS protection (1) and providing guaranteed QoS to CFUEs in coalition as in (). However, the payoff values of players are not deterined solely by the data rate that CFUEs can achieve because of the CFUEs are the subscribed users of the wireless service providers. Meanwhile, the wireless service providers are the operators of the networks, so they can control the payoffs of the players via network coordinator fro two aspects. First, service providers can physically provide different services to cooperative and non-cooperative users using rewards and punishent. Second, the CFUEs are stiulated to act cooperatively and iprove the overall perforance of the fored coalition S,g or network while guaranteeing the MBS protection and CFUEs QoS, which can be obtained via division of the single TU value v(s,g ) [], [37]. Whenever S,g belongs to φ Lg, the function value v(s,g, φ Lg ) v of the our gae is deterined as follows: { x, if (1), (), and S,g 1, v(s,g, φ Lg ) = S,g, otherwise. (9) We can see that the apping vector of the individual payoff value of CFUEs in (8) is uniquely given fro (9) and the core in TU gae is non-epty [37]. Thus, we are able to exploit the recursive core as a solution concept of the original gae (, U Lg ) by solving the gae (, v) while restricting the transfer of payoffs according to the unique apping in (8). Here, the value v(s,g, φ Lg ) is the su-rate of CFUEs allocated to the sae subchannel in partition φ Lg. Through cooperating and sharing the payoff aong CFUEs in the coalition, CFUEs achieve their optial power allocation to axiize each coalition S,g to which they belongs (details are discussed in Algorith of section IV.C). 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 CFUEs R = \S,g. CFUEs outside of R are deviators, while CFUEs inside of R are residuals [], [37]. The residual gae is still in partition for and can be solved as an independent gae, regardless of how it is generated [38]. For instance, when soe CFUEs are deviators that reject an existing partition, they have incentives to join another coalition that satisfy (3), (4), (5) and subchannel reuse table T g. Naturally, their decisions will affect the payoff values of the residual CFUEs. Hence, the residual gae of CFUEs fors a new gae that is a part of the original gae. CFUEs 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 [], [37], which is a set of possible gae outcoes, i.e. possible partitions of R. The recursive core solution can be found by recursively playing residuals gaes, which are defined as follows (entioned in [], definition 4): Definition : 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. ) Inductive Assuption. Proceeding recursively, consider all CFUEs belonging to the DJG g, and suppose the residual core C(R, v) for all gaes with at ost -1 CFUEs 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 Lg ) is doinated via coalition S if at least one (y Lg\S,g, φ Lg\S,g ) A( \S,g, v) there exists an outcoe ((y S,g, y Lg\S,g ), φ S,g φ Lg\S,g ) Ω(, v), such that (y S,g, y Lg\S,g ) S,g x. The outcoe (x, φ Lg ) 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). In Step 1, the core of a trivial partition is initialized with CFUEs belonging to coalition. Step is an inductive assuption that establishes the doinance for a gae of - 1 CFUEs through inductive steps of the fored coalitions. For instance, subchannel allocation perits assigning subchannels to CFUEs to bring doinance. Step 3 is the ain step for checking and finding doinant coalitions, which captures the value of a coalition depending on partitions. We define x as the payoff vector of players and φ S,g as the partition of the user set. The payoff vector x is an undoinated coalition if there exists a way to partition that brings an outcoe ((y S,g, y Lg\S,g ), φ S,g φ Lg\S,g ) that achieves greater reward to CFUEs of S,g, copared to x. Corresponding to each DJG partition, the individual payoffs of all CFUEs 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 CFUEs, as detailed in Step 4. C. Ipleentation of the recursive core at each coalitional gae foration in partition for at DJGs We address ipleentation of the recursive core ethod to solve the proposed gae, which is sketched in Fig. 6.

9 9 Algorith 3 The partition of the DJG-g into coalitions under partition. 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 [18], [4], [9]. Then, the optiu values can be found using Karush Kuhn Tucker (KKT) conditions [18], [3], [4], [4], as follows: no Each coalition corresponds to the partition finds optiu P g power level through Algorith to axiize OP1. Check convergence based on conditions of recursive core. yes Optial values, P * * Fig. 6: The deterination of the optial solution of OPT1 g based on the coalitional gae in partition for. S, g P = e y = 1 + µ βh, + η ς, (34) where [a] + = ax{a, }; the Lagrange ultipliers β, µ, η, ς and the consistency price ϑ for all CFUE S,g are updated as (35), (39), (36), (37) and (38), respectively. β(t) = β(t 1) + s 1 (t) h,e y S,g ζ +, (35) η (t) = [η (t 1) + s 3 (t) (y (t) log P,ax )] +, (36) [ ( )] +, ς (t) = ς (t 1) + s 4 (t) y(t) + log P,in (37) [ ( +. ϑ (t) = ϑ (t 1) + s 5 (t) Zn,g e n,g)] z (38) As discussed in the above subsection, the gae (, U g ) is solved via the gae (, v). According to this alternative, the coalition S,g in a partition φ Lg is represented by a real function v(s,g, φ Lg ) as in (9). Corresponding to the subchannel allocation of CFUEs, soe CFUEs can be allocated into the sae subchannel, which fors a coalition S,g. Then, CFUEs optiize their individual payoffs by sharing with other CFUEs in the sae coalition S,g. In this case, CFUEs cooperate with others in coalition to axiize the individual payoff and value v(s,g, φ Lg ). Sharing is achieved by finding optiu power values of each CFUE in the following optiization proble: OPT1 S,g,φ Lg : axiize P subject to: v(s,g, φ Lg ) (3) S,g h,p ζ, (31) Z n,g + Z n,g + h,np + n h P χ, l L n, S,g, (3) P,in P P,ax, S,g, l L n. (33) The constraint (3) is taken fro () and (7). When CFUE l L n belongs the coalition S,g, α is set to 1, otherwise is set to. Therefore, without loss of generality, we ignore paraeter α in OPT1 S,g,φ Lg. By finding the optial power allocation to CFUEs, they will achieve an optiu individual payoff value that axiizes the worth of coalition S,g. The optial solution of OPT1 S,g,φ Lg can be We use the changing logarith of the variables y = log P. The paraeter s i(t) represents the step size satisfying s i (t) <, and s i (t) =, i = 1,, 3, 4, 5, t= t= (4) which leads to the convergence of algoriths [3]. Additionally, the variable zn,g is also calculated fro the KKT necessary conditions as follows: ( ) ϑ Z e z n,g n,g + h,np + n =, (41) 1 ϑ + µ where zn,g = log(zn,g). The details of finding the optiu value P and ez n,g in OPT1 S,g,φ Lg is expressed in [41]. The updating of values e z n,g and P are expressed in Algorith. In Algorith, the inforation being exchanged aong CFUEs and CFBSs is based on feedback, such as ACK/NACK. This inforation can be exchanged in fors such as wired back-hauls, dedicated control channels, or pilot signals. The CFBS easures the intra-tier interference and inter-tier interference on subchannel (Step ). Then, the CFBS updates the value e z n,g (t + 1) (Step 3). The Lagrange ultiplier µ (t + 1) and consistence price ϑ (t + 1) are updated (Step 4). After that, the CFBS transits µ (t + 1) to CFUE l (Step 5). CFUE l L n estiates channel gain h, and the aggregated interference at the MBS (Step 6). Siultaneously, CFUE l L n gets updated values of β (t + 1), ϑ (t + 1) fro CFBS n. We note that the value threshold ξ is updated fro MBS via a weighted interference vector depending on the fored coalition. Then, the reaining Lagrange ultipliers

10 1 µ (t) = [ ( e y ( ) ) + µ (t 1) + s (t) log h e z n,g + Z n,g + h,np + n log(χ )], (39) Algorith Distributed power allocation for CFUEs in the coalition S,g φ Lg * Initialization: 1: Initialize t =, β ()[ >, µ () >, ] η () >, ς () >,, ϑ () >, P () P,in, P,ax, χ, S,g. * At CFBS n, n S,g: : Measures the interference In,g. 3: Calculates the variable e z n,g as in (41). 4: Updates the Lagrange ultiplier µ (t + 1) and consistency price ϑ (t + 1) using (39) and (38), respectively. 5: Transits µ (t + 1) to CFUE l L n. * At CFUE l L n, S,g: 6: Estiates channel gain h, and copute the total interference at the MBS; Receives the updated value µ, ϑ. 7: Updates the Lagrange ultipliers β, η, and ς fro (35), (36), and (37), respectively. 8: Calculates the power value P (t + 1) as in (34). 9: Sends power value P (t+1) and h,(t+1) to other CFUEs in the coalition S,g. * Output: Optial transit power level P and optial value v(s,g, φ Lg ) of the fored coalition. are updated via (35), (36), (37) (Step 7). After that, the CFUE updates the power value at tie t + 1, as in Step 8. Then, the CFUE sends its the newest power value P (t + 1) and newest channel gain h, (t + 1) to other CFUEs that belong to coalition S,g (Step 9). OPT1 S,g,φ Lg is transfored to the convex optiization proble, the optial duality gap is equal to zero, and step-sizes satisfy (4). Therefore, the solution P will converge to the optial solution under Algorith. After finishing Algorith, in general, coalition S,g guarantees the optial sharing payoffs aong ebers CFUEs. Siultaneously, we also find the optiu worth v(s,g, φ Lg ) of coalition S,g. Based on the steps in the Definition, we propose Algorith 3 to find recursive core which leads to the distributed subchannel and power allocation. To obtain a partition in the recursive core, the CFUEs in use Algorith 3. In the initial step, the inforation on subchannel reuse table T g of DJG g is fored at the network coordinator (Step 1). The network coordinator akes decision to allocate subchannel to CFUEs with the assurance to protect MBS and provide guaranteed QoS to CFUEs. The individual payoff values of CFUEs in (8) are apped to the fored coalitions via (9). Then, in the coalition foration, the value of whole gae in group g ( M {} v(s,g, φ Lg )) is captured at the network coordinator. Network partitions of DJG g are controlled by network coordinator that akes a decision to assign CFUEs into coalition S,g, M {} (Step ). Additionally, network partitions of DJG g have to satisfy the principles in the subchannel reuse table T g and Steps 3, 4 and 5. After that CFUEs find the optial transit power and individual payoff value based on Algorith in order to Algorith 3 Distributed algorith for subchannel and power allocation in cogntive fetocell network. * Initialization: 1: CFUEs and CFBSs for DJGs Algorith 1; Fors table T g; φ () = {{1}, {}..., { }} in which CFUEs are randoly allocated subchannel and transit power with non-cooperative aong FUEs. * Coalition foration at each DJG g: : CFUEs operate in cooperative ode and join into potential coalitions φ Lg = {{}, {1}..., { M }} that satisfy the table T g. 3: for player {nl} do 4: for S,g {φ (k 1) \{nl}} do 5: Set φ (k) := {φ (k 1) \S,g, S,g = S,g {nl}}. 6: Find v(s,g, φ (k+1) ) based on (9) and Alg.. 7: if v(s,g, φ ) > v(s,g, φ Lg ), M {} then 8: Set φ (k) = φ (k). 9: Update α, P. M {} 1: end if 11: end for 1: 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. adopt their delay requireent and the MBS protection (Step 6). The network coordinator updates the undoinance partition via Step 3 of Definition (Steps 7 and 8). The algorith is repeated until it converges to the stable partition φ (k), which results in an undoinated partition in the recursive core. Whenever undoinated partition φ (k) is updated at tie k, the network coordinator updates subchannel allocation to CFUEs (Step 9). CFBS of each fetocell shares the resource usage inforation aong each other when they get the updated inforation fro its CFUEs. Sharing of these confiration causes overhead in the syste. However, we have itigated the aount of essages exchange by foring DIGs. By doing this, only CFUEs inside a DJG are peritted to exchange inforation. In addition, observation of the value v(s, φ Lg ) is done by network coordinator such as the fetocell gateway [39]. We note that the subchannel and power allocation of CFUEs are updated whenever a network partition is transferred fro partition (k 1) to partition (k), which produces Pareto doinates S,g. (k) The convergence and Nash-stable coalitions in Algorith 3 are discussed in the next subsection. D. Convergence and stable analysis of the proposed gae, Convergence of the proposed gae through four steps of the recursive core ethod is guaranteed as follows:

11 11 Propriety 1: Starting fro any initial partition φ Lg, using the Algorith 3, coalitions of CFUEs erge together by Pareto doinance, which results in a stable network partition and lies in the non-epty recursive core C(, v). Proof: Let φ (k) be the fored partition at iteration k that is based on principles of residual gae (Steps 4 and 5 of Algorith 3). The individual payoff of CFUE l L n via a function v (k) (S,g, (k) φ (k) ) as (9) is denoted by x (k) (S,g, (k) φ (k) ). Therefore, each distributed decision ade by the CFUE in Algorith 3 can be seen as a sequential transforation of the coposition of the network partition as follows: φ () φ (1) φ ()... φ (k)..., (4) where the decision of aking a partition is anaged by the network coordinator; and φ (k) is the network partition in DJG g after k transfers. Every transfer operation fro partition (k 1) to partition (k) is an inductive step, which produces Pareto doinates S,g (k) as follows: φ (k 1) S (k),g φ (k) Lg φ (k) v(s (k),g, φ (k) ) > S,g (k 1) φ (k 1) Lg v(s,g (k 1), φ (k 1) ). (43) We note that, each CFUE gradually selects the coalition based on reuse table T g and conditions (3), (4) and (5). Hence, the value of coalition will be set to zero if any condition of the fored coalition is violated, and the value of other coalitions reains unchanged. Therefore, in Algorith 3, when any two successive steps k 1 and k are successful, then we have v(φ (k) ) = S (k),g φ (k) Lg v(s (k),g, φ (k) ) is Pareto doinated by φ (k). Therefore, Algorith 3 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 CFUEs and the whole network as well. Since the nuber of partitions of CFUEs into M + 1 coalitions is a finite set given by the Bell nuber [37], thus the nuber of transission steps in (4) is finite. Hence, the sequence in (4) will terinate after a finite nuber of inductive steps and will converge to a final partition. After DJG g partition converges to a final partition φ Lg, it is still not guaranteed analytically that the partition is Nash-stable. A partition φ Lg is Nash-stable if no player can get benefit in transferring fro its coalition (S,g, φ Lg ) to another existing coalition S, which can be atheatically forulated based on [4] as follows: Definition 3: The partition φ Lg is Nash-stable with Pareto doinance if, such that S,g, S,g φ Lg ; thus, (S,g, φ Lg ) (S {}, φ ) for all S φ Lg { } with φ = (φ Lg \{S,g, S } {S,g \{}, S {}). Hence, the stability of partition φ Lg in the proposed gae can be considered as below. Proposition : Any final partition φ Lg belongs to the core C(, v) of the DJG in Algorith 3 and always converges to a Nash-stable partition. Proof: Consider a partition φ c belongs to core C(, v), that is found according to the four steps in Definition. If this partition is not Nash-stable, then there exists a CFUE with S,g, S,g φ c, and a coalition S φ c such that y(s {}, φ ) x(s,g, φ Lg ), and CFUE l L n can ove to coalition S. Here, φ = (φ Lg \{S,g, S } {S,g \{}, S {}}). However, this contradicts with the final partition φ Lg in Propriety 1. On the other hand, after finishing the recursive core foration, we can see that CFUEs have no incentive to abandon their coalitions, because any deviation can be detriental. As a result, a partition φ Lg in the recursive core is also stable since it ensures the highest possible payoff for each CFUE with no incentive to leave this partition, as studied in [43]. Thus, any partition φ Lg that belongs to the core of Algorith 3 is Nashstable. With respect of coputational coplexity, related to centralized solution, it is worth entioning that finding a partition is strongly challenged by the exponentially growing nuber of required iterations and the signaling overhead traffic which would rapidly congest the backhaul and dedicate channels. Moreover, fetocell does not have reliable centralized control due to unreliable backhaul [9]. Due to these characteristics, fetocell deployent needs distributed solutions with autoatic channel selection, power adjustent for autonoous interference coordination and coverage optiization. In our distributed solution, the coplexity can be significantly reduced by considering follows aspects. First, in our gae, the network partition is anaged by network coordinator of each DJG. Moreover, cooperation is established only aong those CFUEs who are using the sae subchannel in their DJG is often sall. Further, the network partition foration does not depend on the order in which the CFUEs in coalition are evaluated, the nuber of iterations is further reduced. Second, the network partition is obtained by running residual gaes in each DJG with checks in subchannels reusing table, significantly reducing the search space and aount of exchanged inforation. Obviously, the recursive core ethod applied to our proposed gae always converges to a final DJG partition. Moreover, the network partition based on residual gae always converges to a Nash-stable partition. V. SIMULATION RESULTS As shown in Fig. 7, we siulate an MBS and 16 CFBSs with the coverage radii of 5 and 3, 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 = 36 khz (by using two sub-carriers for each licensed subchannel) and a fixed power level of 5 W. Moreover, the interference threshold at the MBS for each licensed subchannel equals to -7 dbw. Each CFBS has two CFUEs, a pilots signal with power equals to 5 W. Each CFUE has an arrival

12 1 1 Y() DJG 6 = (16) DJG 1 = CFBS (1) MUE 1 DJG 5 = (6,7,8,9,1) MBS DJG = (,3,1,14) X() DJG 4 =(5,11,13) DJG 3 = (4,15) Fig. 7: Self-organization of CFUEs in the CFN to six DJGs according to Algorith 1. DJG-1, DJG-, DJG-3, DJG-4, DJG-5 and DJG-6 are coposed of CFUEs belonging to the groups CFBS {1}, {, 3, 1, 14}, {4, 15}, {5, 11, 13}, {6, 7, 8, 9, 1} and {16}, respectively. rate equals to 1.5 Mb/s, and the delay ust be less than or equal to 1 s. In addition, each CFUE has a axiu power level constraint (P ax ) of 1 W. We assue that distance-dependent path loss shadowing according to the 3GPP specifications [44] affects the transissions. After the network is initialized, the CFBS and MBS periodically broadcast the pilot signal to CFUEs. CFUEs easure RSSI of the pilot signals and estiate channel gain to the surrounding CFBSs. Additionally, the CFUE also estiates its channel gain to the MBS based on the essages broadcast fro the MBS. Independently, the CFUE estiates the axiu power level for each licensed subchannel based on its own observed channel gain to the MBS and (1), in which the axiu power level on each licensed subchannel is deterined by P,ax = [in(p ax, ζ /h, )]+, {1,, 3}. The axiu power level of CFUEs on licensed subchannels are shown in Fig. 8. CFUEs in CFBS-16 have the highest axiu power level because the distance to MBS is too far fro CFUEs where the MBS lies outside the interference threshold range. In order to find DJGs, we run Algorith 1. The selforganization DJGs are shown in Fig. 7, in which CFUEs selforganize into six DJGs. Siultaneously, the subchannel reuse tables aong CFUEs of DJGs are also fored. The subchannel reuse tables of all DJGs are depicted in Fig. 9, in which value eans two CFUEs cannot be reused, else it has a value equal to 1. In Fig. 1, we copare our proposal to a rando subchannel allocation schee. Specifically, we consider DJGs 1 and 5. Intuitively, by using Algorith 3, DJG-5 needs tie steps, and DJG-1 needs 5 tie steps to converge to the optiu value. 15 Power level (W) channel channel 1 channel CFUEs CFBSs Fig. 8: The axiu power levels of CFUEs on three licensed subchannels. : not reused, 1: reused DJG 1 DJG DJG 3 DJG 4 DJG 5 DJG , 15,14 CFUEs 5 3 5,11 6,7,8,9, CFUEs 16 13,11 16 Fig. 9: The subchannel reuse tables aong CFUEs in DJGs of the CFN. The value eans two CFUEs cannot be reused the subchannels, else it has a value equal to 1. The su rate of the CFUEs in the DJGs (Mb/s) Optial solution 4 Optial channel allocation in DJG 1 Rando channel allocation in DJG 1 Optial channel allocation in DJG 5 Rando channel allocation in DJG Tie steps Fig. 1: The optial subchannel allocation in DJG-1 and DJG-5. On the other hand, by randoly allocating the subchannels, the su-rate of each DJG-1 and DJG-5 is not stable and are 3

13 13 Su rate (Mbps) DJG 1 6 DJG Foration a new DJG 3 4 partition in DJG 5 DJG 4 DJG 5 DJG Tie steps Fig. 11: The convergence of each disjoint group. Power (W) CFUE 1 CFUE Maxiu power allocation no subchannel and power level allocation The indexes of the CFBSs Fig. 13: The optial power allocation of CFUEs. Subchannel indexes 3 1 CFUE 1 in CFBS 6 is assigned to subchannel 3 CFUE of CFBS 6 is assigned to subchannel 1 CFUE 1 CFUE The indexes of the CFBSs Fig. 1: The optial subchannel allocation of CFUEs. lower than the optiu value. This exaination is the sae for all DJGs in the network. We also see that the su-rate in each DJG using our schee is greater than that of the rando subchannel allocation schee. Therefore, our schee is ore efficient than the rando subchannel allocation schee. The convergence of DJGs after applying coalitional gae approach via Algorith 3 is shown in Fig. 11. By using the coalitional gae, in each tie step, all CFUEs will cooperate with other CFUEs in its fored coalition and for DJGs with joining and leaving principles to axiize the su-rate of DJGs. Clearly, using the coalitional gae approach, we can achieve a local optiu. We also see that the convergence of Algorith 3 is achieved after around 18 tie steps, as shown in Fig. 11. The results of the subchannel and power allocation based on the core of the gae are shown in Figs. 1 and 13, respectively. In each group, soe CFUEs ay not be allocated to any subchannel because these allocations do not satisfy the constraints of the iniu delay and protection at the MBS. Additionally, the power of CFUEs in CFBS-16 are allocated with the axiu power level because the MBS is outside of the interference range of CFUEs in CFBS 16. Furtherore, this group is not affected by interference fro other CFUEs Social welfare (Mb/s) Our proposal CA+axiu power allocation CA + rando power allocation Tie periods Fig. 14: The social welfare of CFUEs in OPT1 with different power allocation schees. in other DJGs or by interference fro the MUEs. To leverage subchannel variations and network stochastic realizations, the results are averaged over a large nuber of siulations. We consider our proble in 3 periods, and we estiate ( the social welfare of CFUEs by the utilitarian 1 L ) N easure N L l=1 n=1 R for each period. There are three schees considered: our proposal given in Algorith 3, subchannel allocation using Algorith 3 with the fixed axiu power level of CFUE (CA + axiu power allocation), and subchannel allocation using Algorith 3 with rando power level allocation to each CFUEs (CA + rando power allocation). The results are shown in Fig. 14. Intuitively, our proposed schee always achieves a higher social welfare utilities for all CFUEs copared to the other ethods. Hence, sharing the individual payoff aong CFUEs using Algoriths is necessary to find the optial solution of OPT1. ( Next, we estiate the social welfare of CFUEs L ) N l=1 n=1 R with respect to different interference thresholds of the MBS. Fig. 15 shows that for any interference threshold at the MBS, the social welfare of the proposed approach is always higher than those of the (CA + axiu

14 14 Social welfare (Mbps) 1 1 Optiality gap =4.56% Optiality gap =4.96% Centralized solution Our proposal CA + rando power allocation CA + axiu power allocation Interference power theshold, dbw Fig. 15: The social welfare of CFUEs in OPT1 versus the interference threshold at the MBS. Social welfare (Mb/s) saturation point 1 Our proposal.5 CA + axiu power allocation CA + rando power allocation Nuber of subchannels Fig. 16: The average data rates of CFUEs follow nuber of the subchannels. subchannels, the social welfare is increased because ore CFUEs are allocated to subchannels. The saturation point is achieved when the nuber of subchannels is greater than or equal to 11 because, at this point, all CFUEs are allocated to the optial subchannel and power level fored in the core of the proposed gae. The schee Optial CA + rando power allocation always has the sallest value because soe CFUEs which are allocated with rando power level do not satisfy the conditions to protect MBS or the iniu delay requireent of each CFUE. In such cases, the subchannel is not allocated to these CFUEs, which draatically decreases the su rate of all CFUEs, as well as the the social welfare in the network. VI. CONCLUSIONS 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 CFUEs 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 axiu delay requireent of the connected CFUE are kept under the acceptable level. In order to solve the optiization proble, we siplified the CFN by foring DJGs and suggested a forulation optiization proble as a coalitional gae in partition for in each fored disjoint group. The convergence of algoriths was also carefully investigated. Siulation results showed that the CFUEs can be self-organized into DJGs. Additionally, the surate in the proposed fraework is achieved by the optial subchannel and power allocation policy with all CFUEs average delay constraints being satisfied. Moreover, the efficient resource allocation is tested, with the su-rate of the proposed fraework always being close to optial solution and better than those of the other fraeworks. power allocation) and (CA + rando power allocation) schees. Further, in Fig. 15, we have nuerically copared the proposed approach with the optial solution, in which CFUEs are allocated subchannel and transit power in a centralized fashion. The social welfare of all the schees grows with the increase in interference thresholds at the MBS. The coparison shows that perforance of the proposed is close to centralized solution. In addition, gaps between the proposed approach and centralized solution are 4.56% and 4.96% when the interference thresholds are of -7 dbw and -4 dbw, respectively. In order to see the social welfare versus the nubers of licensed subchannels, we fix the positions of CFUEs and CFBSs. Then, we increase the nuber of licensed subchannels that are allocated to CFN in the uplink direction. We exaine OPT1 with different ethods, as shown in Fig. 16. When the nuber of subchannels is less than or equal to 11, the social welfare of CFUEs in our schee is higher than that of the other two schees. With increasing nuber of licensed 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. 11. [] J. Hoadley and P. Maveddat, Enabling sall cell deployent with hetnet, IEEE, Wireless Counications Mag., vol. 19, no., pp. 4 5, Apr. 1. [3] T. Nakaura, S. Nagata, A. Benjebbour, Y. Kishiyaa, T. Hai, S. Xiaodong, Y. Ning, and L. Nan, Trends in sall cell enhanceents in LTE advanced, IEEE, Counications Magazine, vol. 51, no., pp , Feb. 13. [4] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, Fetocell networks: a survey, IEEE, Counications Magazine, vol. 46, no. 9, pp , Sep. 8. [5] J. Zhang, G. De la Roche et al., Fetocells: technologies and deployent. Wiley Online Library, 1. [6] X. Kang, Y.-C. Liang, and H. K. Garg, Distributed power control for spectru-sharing fetocell networks using Stackelberg gae, in IEEE, International Conference on Counications (ICC), Kyoto, Jun. 11. [7] V. Chandrasekhar and J. G. Andrews, Uplink capacity and interference avoidance for two-tier fetocell networks, IEEE Transactions on Wireless Counications, vol. 8, no. 7, pp , Jul. 9.

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16 16 Tuan LeAnh received the B.Eng. and M.Eng. degrees in electronic and telecounication engineering fro Ha Noi University of Technology, Vietna, in 7, and 1, respectively. Since 7, he was an engineer with the Vietna Posts and Telecounications Group (VNPT), Ha Noi, Vietna. Since 11, he has been working the PhD degree at Departent of Coputer Science and Engineering, Kyung Hee University, South Korea. His research interest include queueing, optiization, control and gae theory to design, analyze and optiize the cutting-edge applications in counication networks, including cognitive radio, heterogeneous, sall-cell, and content centric networks. sall-cell networks. Nguyen H. Tran (S 1M 11) received the BS degree fro Hochiinh City University of Technology and Ph.D degree fro Kyung Hee University, in electrical and coputer engineering, in 5 and 11, respectively. Since 1, he has been an assistant professor with Departent of Coputer Science and Engineering, Kyung Hee University. His research interest is to design, analyze and optiize the cuttingedge applications in counication networks, including cloud, obile-edge coputing, datacenters, sart grid, Internet of Things, and heterogeneous, Zhu Han (S 1M 4-SM 9-F 14) received the B.S. degree in electronic engineering fro Tsinghua University, in 1997, and the M.S. and Ph.D. degrees in electrical and coputer engineering fro the University of Maryland, College Park, in 1999 and 3, respectively. Fro to, he was an R&D Engineer of JDSU, Gerantown, Maryland. Fro 3 to 6, he was a Research Associate at the University of Maryland. Fro 6 to 8, he was an assistant professor at Boise State University, Idaho. Currently, he is a Professor in the Electrical and Coputer Engineering Departent as well as in the Coputer Science Departent at the University of Houston, Texas. His research interests include wireless resource allocation and anageent, wireless counications and networking, gae theory, wireless ultiedia, security, and sart grid counication. Dr. Han received an NSF Career Award in 1, the Fred W. Ellersick Prize of the IEEE Counication Society in 11,the EURASIP Best Paper Award for the Journal on Advances in Signal Processing in 15, and several best paper awards in IEEE conferences. Currently, Dr. Han is currently an IEEE Counications Society Distinguished Lecture. Sungwon Lee received the Ph.D. degree fro Kyung Hee University, Korea. He is a professor of the Coputer Science and Engineering Departent at Kyung Hee University, Korea. He was a senior engineer of Telecounications and Networks Division at Sasung Electronics Inc. fro 1999 to 8. He is a editor of the Journal of Korean Institute of Inforation Scientists and Engineers: Coputing Practices and Letters. His research interests include obile broadband networks and counication protocols. He is a eber of IEEE, KIISE, KICS and KIPS. Eui-Na Huh he has been a Professor with the Departent of Coputer Science and Engineering, since 11. He is also founding Director of Realtie Mobile Cloud Research Center (RCRC) and Chair ISOC Asia Pacific Advanced Network (APAN). He did his PhD fro The Ohio University, in. His MS was fro University of Texas, in 1995, while he did his BS fro Busan University, in 199. His research interest lies in Cloud Coputing, Internet of Things, Wireless Sensor Networks, HPC, and Real-tie Mobile Cloud Coputing. He is serving several highly reputed journals as Editor, including, but not liited to KSII Transactions on Internet and Inforation Systes, International Journal of Distributed Sensor Networks. He is a Meber IEEE, Meber ACM, Meber Korea Inforation Processing Society (KIPS), and several other technical coittees. Choong Seon Hong (AM 95M 7SM 11) received the B.S. and M.S. degrees in electronic engineering fro Kyung Hee University, Seoul, South Korea, and the Ph.D. degree fro Keio University, Tokyo, Japan, in 1983, 1985, and 1997, respectively. In 1988, he joined KT, where he worked on broadband networks as a Meber of the Technical Staff. In Septeber 1993, he joined Keio University. He had worked for the Telecounications Network Laboratory, KT as a Senior Meber of Technical Staff and as a Director of the Networking Research Tea until August Since Septeber 1999, he has been a Professor with the Departent of Coputer Science and Engineering, Kyung Hee University. His research interests include future Internet, ad hoc networks, network anageent, and network security. He has served as a General Chair, TPC Chair/Meber, or an Organizing Coittee Meber for International conferences such as NOMS, IM, APNOMS, EEMON, CCNC, ADSN, ICPP, DIM, WISA, BcN, TINA, SAINT, and ICOIN. Also, he is now an Associate Editor of the IEEE TRANSACTIONS ON SERVICES AND NETWORKS MANAGEMENT, International Journal of Network Manageent, Journal of Counications and Networks, and an Associate Technical Editor of the IEEE Counications Magazine. He is a eber of ACM, IEICE, IPSJ, KIISE, KICS, KIPS, and OSIA