AFEMTOCELL base station abbreviated as femto BS or. Load Balancing in Two-Tier Cellular Networks with Open and Hybrid Access Femtocells

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1 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 1 Load Balancing in Two-Tier Cellular Networks with Open and Hybrid Access Femtocells Dongmyoung Kim, Taejun Park, Hyoil Kim, and Sunghyun Choi arxiv: v1 cs.ni] 27 May 214 Abstract Femtocell base station BS) is a low-power, low-price BS based on cellular communication technology. It is expected to become a cost-eective solution or improving the communication perormance o indoor users, whose traic demands are large in general. There are mainly three access strategies or emtocell, i.e., closed access, open access and hybrid access strategies. While it has been generally known that open/hybrid access emtocells contribute more to enhancing the system-wide perormance than closed access emtocells, the operating parameters o both macro and emtocells should be careully chosen according to the mobile operator s policy, consumer s requirements, and so on. We propose long-term parameter optimization schemes, which maximize the average throughput o macrocell users while guaranteeing some degree o beneits to emtocell owners. To achieve this goal, we jointly optimize the ratio o dedicated resources or emtocells as well as the emtocell service area in open access emtocell networks through the numerical analysis. It is proved that the optimal parameter selection o open access emtocell is a convex optimization problem in typical environments. Then, we extend our algorithm to hybrid access emtocells where some intraemtocell resources are dedicated only or emtocell owners while remaining resources are shared with oreign macrocell users. Our evaluation results show that the proposed parameter optimization schemes signiicantly enhance the perormance o macrocell users thanks to the large oloading gain. The beneits provided to emtocell users are also adaptively maintained according to the emtocell users requirements. The results in this paper provide insights about the situations where emtocell deployment on dedicated channels is preerred to the co-channel deployment. Keywords Femtocell, two-tier cellular networks, load balancing, coverage control. I. INTRODUCTION AFEMTOCELL base station abbreviated as emto BS or BS is a small BS with low transmission power and low cost. Femtocells can be installed by the end users to enhance the cellular networking perormance at home, o which traic is transported via an Internet backhaul such as Digital Subscriber Line DSL) or cable modem. Two-tier cellular networks, consisting o a conventional macrocell network and underlaying short-range emtocells, have received considerable attention rom industry and academia as an eicient solution to deal with the exploding demand or wireless data communication. The emtocell technology has an advantage over other competing indoor wireless communication technologies, thanks to its high capacity and backward compatibility with existing cellular technologies. The history, current status o market and technology, research issues, and uture expectation o emtocell technology are well summarized in 1]. There are mainly three strategies or a emtocell access, namely, closed access, open access, and hybrid access strategies. A emtocell in a closed access mode can only be accessed by authorized emtocell users. On the other hand, i the owner o a emtocell installs it with the open access mode, any macrocell user might access the emtocell. Some previous researches 2] 4] have shown that the deployment o open access emtocells can improve the system-wide perormance by transerring some o the traic loads in congested macrocells to the emtocells. Hybrid access mode is a compromise between closed and open access, where an BS allows arbitrary nearby users to access it like open access mode but the subscribed emtocell owners can be prioritized over unsubscribed users. The prioritization can be implemented by using various vendor-speciic mechanisms. In 3GPP Release 8 speciication 5], only closed and open access modes are supported or emtocells while the hybrid access mode has been added in 3GPP Release 9 speciication 6]. Thereore, considering both the open and hybrid access strategies is important. In this paper, we numerically analyze and optimize the perormance o both open and hybrid access emtocell networks. We propose the load balancing schemes which properly balance the traic loads in macrocells and emtocells. Our load balancing schemes aim at maximizing the system-wide perormance, i.e., the average throughput o the users communicating with the macrocells, in two-tier cellular networks with open or hybrid access emtocells, while guaranteeing some beneits o the emtocell owners such that emtocell users can always achieve larger throughput than macrocell users. Such an approach not only improves the macrocell user s perormance via traic oloading rom macrocell to emtocell, but also promotes the deployment o emtocells via the guaranteed beneit to the emtocell owners. In our proposed ramework, we strike a balance between a macrocell and emtocells by controlling the service area o emtocells because the amount o traic loads is dominated by the number o associated users. In order to maximize the oloading eiciency, orthogonal deployment in which the whole wireless resources are divided into two parts, one dedicated to emtocells and the other reserved or a macrocell is considered, and we jointly optimize the amount o resources dedicated to the emtocells and the service area o emtocells. The optimization problem is irst studied or the open access case, and then extended to the hybrid access emtocell networks, where a variable portion o intra-emtocell resources is exclusively used by emtocell owners while remaining resources are shared with macrocell users associated with the emtocell. The contributions o this paper are summarized as ollows: 1) We numerically analyze the perormance o macrocell

2 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 2 and emtocell users in two-tier cellular networks where open and hybrid access BSs are deployed in an unplanned manner. 2) Multiple essential parameters in the open and hybrid access emtocell networks are jointly optimized to enhance the perormance o both the macrocell and emtocell users. 3) Our results show that the orthogonal spectrum dedication or open and hybrid access emtocell can be more beneicial than co-channel deployment in some aspects. The conditions that emtocell deployment on dedicated channel can be preerred are also discussed. 4) It is proved that the joint optimization o the amount o dedicated resources and the service area o emtocells is a convex optimization problem in typical environments. The rest o the paper is organized as ollows. Section II presents the related work. In Section III, we introduce the system model and our load balancing problem ormulation in the open and hybrid access emtocell based two-tier cellular networks. We analyze the average throughput o each type o users in Section IV to complete the problem ormulation. In Section V, we obtain the optimal parameters o open access emtocell networks and some theorems or optimal parameter selection are discussed. By extending the optimization ramework o open access emtocell networks, system parameters o hybrid access emtocell are also optimized in Section VI. In Section VII, our proposed schemes are evaluated based on both numerical analysis and computer simulations. Finally, we conclude the paper in Section VIII. II. RELATED WORK Many resource allocation schemes have been proposed or the two-tier cellular networks, but most o the proposed schemes are heuristic or locally optimized schemes 7] 16]. On the other hand, some previous work conducts optimization based on ull channel inormation 17] 19] or game theoretic model 2] 23]. Thereore, the previous researches are dierent rom our work which optimizes the system-wide perormance based on the long-term system inormation o the two-tier cellular networks where BSs are deployed in an unplanned manner. Our long-term parameter optimization ramework is not incompatible with but complementary to the short-term resource allocation schemes in the sense that the long-term optimization ramework can provide good guidelines or the parameter coniguration considering the system-wide average perormance. Recent papers 12], 24] are the most relevant previous work in the literature. Coverage control schemes have been proposed in 12], 25]. The authors in 12] proposes an adaptive transmit power control scheme to control the shape and the size o emtocell coverage. In closed access emtocell networks, which is the system model o the above mentioned papers, the objective o coverage control is minimizing the intererence leakage rom BSs to the outdoor macrocell region while the expected service area or the subscribed users is guaranteed. Service area adaptation in this paper is dierent because the strong signal received rom a emtocell is considered a good serving signal in open and hybrid access emtocell networks, which allow the macrocell users to access them. In 24], the authors propose a bandwidth division scheme in the two-tier cellular networks composed o the closed access emtocells. The objective and constraints o 24] are dierent rom our work since ours utilizes the traic oloading gain in the open and hybrid access emtocell networks. Furthermore, we optimize some other control parameters, such as target service area o a emtocell and intra-emtocell resource dedication ratio or a emtocell owner, together with the bandwidth division ratio to enhance the system perormance. III. A. System Model SYSTEM MODEL AND OUR FRAMEWORK We assume a single circular macrocell region with the radius o D m and the area o A m = πd m 2, where a macrocell BS mbs) is located at the center o the circular region. Multiple BSs are randomly distributed within the macrocell region according to a homogeneous Spatial Poisson Point Process SPPP) 26] with intensity λ. In an SPPP, the number o points in a given region ollows Poisson random variable with the mean o λa, where λ and A are the intensity o the points and the area o the given region, respectively. We assume that each BS is owned by a emtocell mobile station MS), and the BS is located at the center o the indoor circular home region with the radius o D h. The MS o each BS is randomly located within the circular home region, and the indoor home area and outdoor area are partitioned with a wall. It is possible that the BSs ollowing SPPP are located closer than 2D h to each other thus resulting in overlapping home areas. Although this should not happen in practice, we argue that the proposed SPPP model still well captures the reality because it is highly unlikely to have such overlapping BSs with the practical range o λ and D h. Suppose we denote by P overlap the probability that two or more BSs overlap with each other. Since P overlap is identical to the probability that two or more BSs exist in the area o π2d h ) 2, we have P overlap = 1 e λ 2 4πD h λ 4πD h2 e λ 2 4πD h {.79, in US, =.81, in Korea, where the values o λ and D h are obtained rom 27], 28]. Hence, we henceorth assume that there exists only one BS per home, i.e., the distance between any two BSs is larger than 2D h. In Section VII, it will be veriied that such an approach approximates typical environments with a reasonably small analytical error less than 1 %) as shown in Fig. 6a). Note that in our simulation, we generate BSs according to SPPP and drop a new BS located closer than 2D h to any o the previously-generated BSs. Similarly to BSs, macrocell users are randomly distributed according to an SPPP with intensity λ u in the whole macrocell area. Because some macrocell users can associate with a nearby emtocell in the open and hybrid access emtocell networks, the macrocell users are categorized into two types,

3 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 3 TABLE I. TRANSMISSION RATE SET Rate index, l Spectral eiciency, b l SINR region db) bps/hz) , ) , 4) , 8) , 12) , 16) , ) Fig. 1. Resource dedication in hybrid access emtocells ρ and β). i.e., macrocell mobile station mms) and open access mobile station oms). We reer to the macrocell user who associates with mbs as mms, while the macrocell user who associates with an BS thanks to the open or hybrid access policy is reerred to as oms. The downlink channel gain between a BS and an MS is characterized by a pathloss and ading. When the distance between a transmitter and a receiver is d, the channel gain o the link is modeled by ΨZd) α, where α is the pathloss exponent and Z represents a ixed loss which is dependent on the type o the link. Dierent Z and α values, i.e., Z 1 to Z 5 and α 1 to α 5, are deined or dierent types o links as shown in Table III. Ψ exp1) is a Rayleigh ast ading component which has a unit average power. We consider multiple discrete transmission rates, where the rate is adaptively determined according to the Signal to Intererence plus Noise Ratio SINR) value at the receiver. Rate index l 1,L] corresponds to the case when the SINR lies in Γ l,γ l+1 ), where Γ L+1 =. and the spectral eiciency o rate index l is modeled as the ollowing based on the variable rate M-QAM transmissions: b l = log 2 1+ Γ ) l, 1) G wheregdenotes Shannon Gap introduced in 29]. The speciic rate set used in the simulations are summarized in Table I. Furthermore, Table II provides the deinitions and deault values o all notations requently used in this paper. In this paper, we consider a ully loaded network environment where the BSs always have packets to transmit. Furthermore, we assume that the scheduler in the mbs or the open access BS allocates the resource blocks in a roundrobin manner so that the whole wireless resources in the cell are equally distributed to the associated users in a long-term. The basic level o airness, i.e., intra-cell resource airness, is guaranteed rom this assumption. In the hybrid access BS, the scheduler reserves some amount o resources or the MS while the remaining resources are allocated using a roundrobin manner. We assume that the transmission power spectral densities, i.e., power per Hz, o the mbs and BSs are ixed as P m and P, respectively, and the noise power density is given by P N. B. Our Framework In this section, we introduce our load balancing ramework or open and hybrid access emtocell networks. As shown in Fig. 1, our schemes divide the whole available resources into two orthogonal sub-parts, and the two parts are dedicated to Fig. 2. Femtocell service radius d ) and user associations. the macrocell and emtocells, respectively. We reer to the ratio o resources dedicated to the emtocells among the whole available resources as ρ, 1], and we optimize ρ to properly balance the traic loads in the macro and emtocells. We assume that the wireless resources can be divided either in time domain or requency domain or both. Our ramework allocates the separate resources to the emtocells because the resource separation not only limits the side eect to the existing macrocell users due to the emtocell deployment but also maximizes the oloading capability in the two-tier cellular networks by increasing the maximum cell coverage. Though it has been generally said that open access emtocell networks preer the co-channel deployment option, the results o this paper show that algorithms based on separate bandwidth can be more beneicial in some aspects thanks to the enhanced oloading gain and the increased lexibility to control the perormance o MSs, mmss, and omss. Appendix C summarizes the beneits and preerred conditions o orthogonal deployment. A hybrid access BS allows the macrocell users to access like open access BS, but the intra-cell resource scheduler gives priority to the MS. It is dierent rom the intra-cell resource allocation policy o the open access emtocell where the resources are equally allocated to all the users without distinguishing the MS rom the other macrocell users. As shown in Fig. 1, we assume that β raction o intra-emtocell resources are dedicated to the MS, and the remaining resources are equally shared by the MS and omss. Open access emtocell is a special case o hybrid access emtocell where β =. Our load balancing scheme in the open and hybrid access emtocell networks jointly optimizes the average service area o a emtocell as well as the amount o bandwidth dedicated to emtocells and the amount o intra-emtocell resource dedicated to an MS. We optimize the service coverage o a emtocell because the cell selection based on the strongest

4 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 4 TABLE II. DEFINITION OF PARAMETERS AND DEFAULT VALUES Symbol Description Deault value D m, A m Radius and area o a macrocell region 8 m, πd 2 m D h, A h Radius and area o a home region 2 m, πd 2 h c Carrier requency 2 MHz W System bandwidth 5 MHz P N Noise power density 174 dbm/hz P m Macrocell transmit power density 46/W dbm/hz P Femtocell transmit power density 23/W dbm/hz W L Wall penetration loss 1 db Ψ Rayleigh ading component N/A α, Z α Pathloss exponent and ixed loss value See Table III b l,γ l Spectral eiciency and SINR threshold or rate index l See Table I N,λ Average number and intensity o BSs in a macrocell area 3, 3/A m N u,λ u Average number and intensity o macrocell users mmss + omss) 2, 2/A m ρ Ratio o emtocell resources to the whole bandwidth, ρ, 1] N/A d, D max Service radius o a emtocell region and maximum value o d, respectively N/A x Average service area o a emtocell region, x X min,x max] N/A θ Resource usage probability in OA/HA-Thin, θ, 1] N/A β Ratio o resources reserved or an MS to the whole resources o a hybrid access BS, β,1] N/A T, T m, T o Average throughput o MS, mms, and oms N/A M K) Required ratio between average throughput o MS oms) and mms 1, 1 O max Maximum average outage rate allowed or an oms.15 RSS value is not eicient to promote the load balancing. Fig. 2 describes the system model or the service coverage optimization. We reer to the service radius o a emtocell as d, and the emtocell and macrocell users who are located closer than d associate with the emtocell rather than the macrocell. Each BS is required to ully cover the indoor home area, i.e., d D h. The maximum service radius, i.e., D max, is constrained by the physical limitation to support wireless communications. In our work, D max is deined by the maximum distance where the average outage probability o an oms is less than or equal to O max while the lowest transmission rate is used. The service radius is chosen in the range o d D h,d max ] to properly balance the traic loads in macro and emtocells. The service coverage adaptation is implemented by using a simple MS initiated Cell Selection MSCS) scheme. In MSCS, the RSS threshold or emtocell association, which is reerred to as P cs, is determined, and an MS measures the average RSS values o transmitted signals rom the neighboring mbss and BSs. I the MS inds some BSs providing the average RSS larger than P cs, the MS associates with the best BS among them regardless o the RSS values rom the mbss. Thereore, the target emtocell radius d is directly related to P cs by P cs = P Zd ) α, 2) where P is the ixed transmission power density o the BS. We optimize d instead o P cs in this paper to simpliy the presentation. Then, we ormulate our parameter optimization problem or load balancing in hybrid access emtocell networks. The same ramework can be applied or the open access emtocell networks by setting β =. Deployment o open and hybrid access emtocells has an advantage that it can improve the perormance o the macrocell users as well as the emtocell owners by transerring the traic load in the congested macrocells to the emtocells. Though the open access is allowed, the MSs expect a dierentiated experience when they use their emtocells at home. Guaranteeing the beneits o MSs is very important to motivate the consumers to buy and install the emtocells. Thereore, we aim at maximizing the average perormance o mmss by controlling ρ, d, and β hybrid access only), while guaranteeing the relative beneits o emtocell owners. Speciically, it is assumed that MSs expect that their average emtocell throughput should be at least M times larger than the average throughput o mmss though they allow the open access. Denoting the average throughput o an MS, mms, and oms byt ρ,d,β),t m ρ,d,β), andt o ρ,d,β), respectively, our optimization problem is ormulated as: max ρ,d,β T mρ,d,β) 3) s.t. T ρ,d,β) MT m ρ,d,β), 4) T o ρ,d,β) KT m ρ,d,β), 5) D h d D max, 6) ρ 1, 7) β 1. 8) The macrocell users might not want to associate with BSs i the perormance is degraded by the open access with BSs. Thereore, the constraint 5) is additionally introduced to guarantee the minimum perormance o omss. Because omss are not the subscribed users,k is conigured as a value smaller than M, and we basically assume that K = 1. Our optimization ramework is a long-term parameter optimization based on the average system-wide perormance metric. Though a short-term local resource allocation scheme might improve the perormance o the local system eiciently, our long-term optimization is very meaningul in the ollowing aspects. First, the parameter optimization involving both the macrocells and emtocells is generally perormed at a long-term interval due to the system architecture o the two-tier cellular

5 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 5 TABLE III. PATHLOSS PARAMETERS Environment Exponent Fixed loss db) Outdoor α 1 = 4 Z α 1 1 = 3log 1 c 71 Indoor α 2 = 3 Z α 2 2 = 37 Outdoor-to-indoor α 3 = 4 Z α 3 3 = 3log 1 c 71 + WL Indoor-to-outdoor α 4 = 4 Z α 4 4 = 3log 1 c 71 + WL Indoor-to-indoor α 5 = 4 Z α 5 5 = 3log 1 c WL by sel-coniguration may be updated by the localized seloptimization algorithms in the operational phase. Fig. 3. SON architecture o 3GPP LTE system. networks. In 3GPP LTE system, automatic parameter coniguration and optimization are conducted based on Sel Organizing Network SON) procedures. Fig. 3 illustrates the SON architecture o 3GPP LTE system, where macrocell and emtocell base stations are reerred to as Home enodeb HeNB) and enodeb enb), respectively 3]. SON algorithms can be implemented either in the end devices, i.e., HeNBs or enbs, and/or Device Management and/or Home enodeb Management System, and/or Network Management NM). However, it is natural that the joint optimization o macrocell and emtocell parameters is perormed by NM in a centralized manner, because no direct interace between enb and HeNB exists. Shortterm parameter optimization in the centralized entity, e.g., NM, is almost impossible due to the limited processing power and the limited Operations, Administration and Maintenance bandwidth on the interaces among the entities. Consequently, the joint parameter optimization involving both macrocells and emtocells need to be perormed in the centralized entity at a long-term interval. Second, short-term resource allocation schemes cannot generally consider the network-wide perormance due to the excessive overhead and lack o inormation. On the other hand, long-term optimization can consider the network-wide perormance thanks to the relatively small overhead per unit time and relaxed time constraint. Thereore, our long-term optimization is not incompatible with but complementary to the short-term resource allocation schemes in the sense that the long-term optimization ramework can provide good guidelines or the parameter coniguration considering the system-wide average perormance. Finally, our long-term parameter selection schemes have the strength in the sense that they can be utilized in both the sel-coniguration and/or sel-optimization phases. Note that SON algorithms can be categorized into sel-coniguration and sel-optimization 6] according to the unctionality and phases. Sel-coniguration presents pre-operational procedures including the initial parameter selection. Though an initial parameter coniguration is essential, an initial parameter selection based on the local instantaneous optimization is not generally recommended because the inormation is very insuicient and unreliable. On the other hand, our algorithm which does not require the instantaneous local inormation can be used or initial parameter selection. The parameters determined IV. NUMERICAL ANALYSIS OF TWO-TIER CELLULAR NETWORKS A. Average Throughput o MS In this section, we analyze the average throughput perormance o MSs. Let us consider an MS who is located at r away rom its serving BS. As explained in Section III, we simply assume that the distribution o BSs ollows pure SPPP in numerical analysis. Due to the characteristics o homogeneous Poisson point process 26], the intererence measured by a typical MS is representative o the intererence seen by all other MSs. Then, similarly to the SINR models in 31], 32], the complementary cumulative distribution unction CCDF) o an MS s SINR is given by F Γ r ) = PrSINR Γ r ] = exp sp N )exp 2π2 λ Z 2 5 sp ) 2/α5 α 5 sin2π/α 5 ) where s = ΓZ 2 r ) α2 P 1. The pathloss parameters in the above equation, i.e., Z 2, α 2, Z 5, and α 5, are properly chosen rom Table III by considering that the MSs are always located inside the buildings in our system model. The detailed derivation or 9) is given in Appendix A-A. The probability density o the distance between an MS and its serving BS is r is given by 2r D 2 h ), 9). Hence, the average spectral eiciency o an MS, denoted by B, is calculated as B = L l=1 Dh b l F Γ l r ) F Γ l+1 r )] 2r Dh 2 dr, 1) where b l, Γ l, and L are the spectral eiciency o rate index l, the SINR threshold to utilize the rate index, and the number o available rate sets, respectively. At a given average spectral eiciency value, the average throughput o an MS is degraded when the emtocell resources are shared with other macrocell users i.e., omss, in the hybrid and open) access mode. Let us denote the random variable or the number o omss who are associated with an BS as N o. Then, the average throughput T is given by

6 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 6 ] 1 β)ρwb T ρ,d,β) =EβρWB ]+E N o +1 =βρwb +1 β)ρwb E 1 N o +1 ], 11) where W is the system bandwidth and B is the spectral eiciency o an MS. In Eq. 11), the dedicated resources to MS contribute to the irst term while the second term is due to the shared resources between MS and oms. In addition, the equality holds because the spectral eiciency o an MS, i.e., B, is independent o the number o N o. I we reer to the service area o a given emtocell as y, the number o omss in the emtocell s service area ollows Poisson random variable with the mean λ u y, and the probability mass unction pm) o N o y) is given by Noy)k] λ uy) k e λuy, 12) k! and we obtain the expectation value as ] 1 E N o y)+1 y λ u y) k e λuy = = 1 e λuy. k +1)k! λ u y k= 13) Let us denote the average service area o a emtocell as x = Ey]. From 11) and 13), we obtain the approximated value or the average throughput o an MS as ollows: 1 e λ uy] T ρ,d,β) = βρwb +1 β)ρwb E y λ u y = βρwb + 1 β)ρwb ) 1 e λ ux. λ u x 14) The average throughput o an MS in open access emtocell is obtained by setting β =. Here, we obtain the average service area, i.e., x, which is a unction o the target service radius d. A macro user associates with an mbs only when no BS exists within d meters rom the user. According to the property o SPPP, the probability that the distance R between a speciic mms and its nearest BS is larger than r 1 is given by PrR > r 1 ) = PrNo BS closer than r 1 ) = e πλ r ) Thereore, the probability that a macrocell user is covered by an BS is given by 1 e πd2 λ, and it is equivalent to) the act that the BSs cover the area o A m 1 e πd2 λ on average. Because the average number o BSs in a macrocell area is A m λ, the average area o a emtocell region can be approximated by xd ) = 1 e πd2 λ λ. 16) Because d and x have an one-to-one relationship, we use x as the control parameter instead o d in the rest o the paper or the simplicity o presentation. B. Average Throughput o mms In this section, we model the average throughput perormance o an mms, where mms is deined by the macrocell user who is currently associated with the mbs. Let us reer to the distance between an mms and its serving mbs as r m. From the assumption that each BS ully covers its indoor home area, SINR CCDF o an mms or a givenr m is obtained by ) ΓP N ) F m Γ r m ) = exp. 17) P m Z 1 r m ) α1 As shown in Table III, Z 1 and α 1 are the ixed pathloss value and the pathloss exponent in outdoor environments, respectively. The detailed derivation or the above equation is shown in Appendix A-B. The probability that a macrocell user becomes an mms, which is reerred to as p mms, is given by p mms = e πλ d 2 = 1 λ x, 18) where x is the average service area o a emtocell derived in 16). As shown in 18) that p mms is independent o the location o the macrocell user, i.e., the distance between the user and the mbs, due to the random distribution o BSs. Thereore, i we reer to the distance between an mms and its serving mbs as r m, the probability density unction PDF) o r m is also given by Rm r m ) = 2r m Dm 2. 19) From 17) and 19), the average spectral eiciency o an mms is given by Dm L B m = b l F m Γ l r m ) F m Γ l+1 r m )] 2r m l=1 Dm 2 dr m, 2) where Γ L+1 =. In order to calculate the above equation, we calculate Dm F m Γ l r m )r m dr m = Dm r m e β lr α m drm, 21) where β l is deined by P N Γ l Z α1 1 P 1 m. By substituting β l r α1 with y, the above equation is obtained by βl D α 1 m 1 α 1 β l y β l 2 α 1 e y dy = β α 1 ) 2 G,β l Dm lα α1, 1 α 1 ) 2 α 1 22) where Ga,b) = b ta 1 e t dt is the incomplete gamma unction. Although emtocell deployment does not change the average spectral eiciency o an mms, the average throughput o an mms can be improved by deploying the emtocells, because the number o mmss sharing the macrocell resource is reduced by relocating some macrocell users, i.e., omss, to the emtocells. In our system model, the average number o macrocell users is given by N u = A m λ u. Let us reer to the number o mmss in a macrocell area or a given x as N m. From 18), the

7 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 7 expectation o N m is given by N m x) = A m λ u 1 λ x). We approximate N m as a Poisson random variable with the mean o N m, and hence, the average throughput o an mms is given by 1 ρ)wb m n Nm n] T m ρ,x) = n n=1 k Nm k] k=1 = 1 ρ)wb ) m 1 e A mλ u1 λ x). 23) A m λ u 1 λ x) C. Average Throughput o oms In order to complete the load balancing problem ormulated in 3), we analyze the average throughput o an omss and the maximum service radius o emtocells, i.e., T o and D max, respectively. When the target emtocell service radius is conigured as d, a macrocell user associates with its nearest BS i the distance between the user and BS is equal to or smaller than d. From 18), the probability that a macrocell user becomes an oms is given by λ x. Let us reer to the distance between an oms and its serving BS as r o. Then, the conditional probability density unction o r o is given by { 2πλ r oe πλ r2 o λ x ln1 λ x) πλ, Ro r o x) =, r o, otherwise. 24) When r o is given, the SINR CCDF o an oms is given by: F o Γ r o ) = exp πλ sp ZI 2 π )) 2 tan 1 Z I 2 r2 o sp sp N ), where ) Z 4,P 1 ΓZ 4 r o ) α4, r o D h, Z I,s) = ) Z 5,P 1 ΓZ 2 r o ) α2, otherwise. 25) 26) The detailed derivation or the above equation is ound in Appendix A-C. Then, we obtain the average spectral eiciency o an oms. I we reer to the probability that an oms chooses the rate index l as L l r o ] = F o Γ l r o ) F o Γ l+1 r o ), the average spectral eiciency o an oms is given by B o x) = L l=1 d x) b l L l r o ] Ro r o x)dr o, 27) where Ro r o x) is shown in 24). We reer to the random variable representing the number o omss in a emtocell area as N o. As done or the average throughput analysis o an MS in 14), we approximately assume that N o is a Poisson random variable with the mean o λ u x. Because N o +1 users including an MS equally share the emtocell resources in the open access mode and only 1 β raction o intra-emtocell resources are allowed to the omss, the average throughput o omss is expressed by ρ1 β)wb o x) n o No n o ] T o ρ,x,β) = n n o +1, 28) o=1 k No k] k=1 where n No n] = 1 n 1) Nn oe No = λux+e λux 1. n+1 N n=1 o n! λ n=2 ux 29) From 28) and 29), T o is obtained by T o ρ,x,β) = 1 β)ρwb ox) λ u x+e λux 1 ) λ u x) 2. 3) Furthermore, we analyze the maximum service radius o a emtocell, i.e., D max, to complete the problem ormulation in 3). D max is an important parameter which determines the range o our design parameter d or x). As described in Section III-B, we deine D max as the maximum target service radius where the average outage rate o an oms is less than or equal to O max. We assume that an outage occurs when the instantaneous SINR is less than the threshold or the lowest transmission rate, i.e.,γ 1 in Table I. From the deinition, average outage rate o an oms with the given target service radius d is calculated by O o d ) = d 1 F o Γ 1 r o )) Ro r o d )dr o, 31) which looks very similar to 27). D max is obtained rom the equation O o D max ) = O max. Though D max cannot be given in a closed orm, the near-optimal solution or 31) can easily be obtained by using the simple binary search algorithm because O o d ) is a monotonically increasing unction o d. Because any mobile stations which are in the emtocell coverage should attached to emtocell, SINR o the oms is likely to worse as the service radius o a emtocell, d, is larger when it is larger than threshold, i.e., the radius that a reerence signal received power rom the nearest BS and mbs are about the same. The detailed description or the binary search algorithm is omitted due to the space limitation. V. OPTIMIZATION IN OPEN ACCESS FEMTOCELL NETWORKS A. Optimization o Parameters in Open Access Femtocell Networks In this section, we prove that our optimization problem in open access mode becomes a single variable convex problem in some typical environments, and the optimal parameters are obtained. In this section, β = because we consider the open access emtocells. I we deine t m x) and t o x) as t m x) = T mρ,x,β = ) W 1 ρ) 32)

8 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 8 and T ρ,x,β = ) t o x) = min, T ) oρ,x,β = ) MWρ KWρ the optimization problem 3) is rephrased by 33) max mx) ρ,x) 34) s.t. ρt o x) 1 ρ)t m x), 35) X min x X max, 36) ρ 1, 37) where X min = xd h ) and X max = xd max ) rom 16). Proposition 1: The optimal ρ which maximizes the objective in 34) is given by ρ t = mx ), where t o x )+t mx ) x is the optimal value o x. Proo: See Appendix B-A. As inerred by 33) and 35), the perormance o our load balancing algorithm is always limited by the throughput requirement o an MS i KT ρ,x,1) MT o ρ,x,1) or all x X min,x max ]. We deine such cases by the MS s requirement-limited environments. Then, the ollowing proposition holds. Proposition 2: In the MS s requirement-limited environments, the optimization problem 34) is a convex optimization problem. Proo: See Appendix B-B. From the above proposition, the optimal solution o x can be eiciently obtained by using the standard methods used or solving the convex optimization 33] i the given environment is the MS s requirement-limited environment. We expect that the two-tier cellular networks mostly operate in the MS s requirement-limited environments, because the oms s throughput requirement is easily satisied with the reasonably large MS s beneit requirement, i.e., M. However, i the given environment is not the MS s requirement-limited environment, we should obtain the near-optimal solution o x using the ineicient exhaustive search algorithm. To check whether a given environment is the MS s requirement-limited environment, the ollowing proposition could be useul. ) Proposition 3: I we deine Cx) = 1 e λux and 1) = λux+e λux B CX min) λ ux Dx), M λ ux) 2 B ox max)dx min) K is the suicient condition that a given environment is the MS s requirement-limited environment. Proo: See Appendix B-C. From the near) optimal value x, the service area control is implemented by setting P cs according to 2) and 16). The optimal ρ is conigured according to Proposition 1. The optimal solution x has the ollowing property. Proposition 4: N B > 1, wheren MB is the average number m o BSs in a macrocell area, is a suicient condition that the optimal solution o the problem 34) is given by x = X max in the typical MS s requirement limited environments where the average number o users in a macrocell is larger than that in a single emtocell. Proo: See Appendix B-D. Proposition 4 can be interpreted as ollows. The expansion o the emtocell service area is encouraged i the average spectral eiciency o an MS is much larger than that o an mms, and the expansion o the emtocell service area is also encouraged i there are many emtocells in the system because the sum o perormance gain in the system is approximately proportional to the number o emtocells. On the other hand, large beneit requirements rom MSs, i.e., M, can limit the service area expansion to guarantee the perormance o emtocell owners who are the premium users. B. Extension Considering Intererence Thinning Thin) As described in Proposition 4, the optimal perormance o our load balancing scheme is determined by the physical limitation D max in many cases. Thereore, we expect that the eiciency o our load balancing scheme can be enhanced i the maximum coverage o emtocell is increased by applying an intererence thinning scheme, which reduces the intererence by limiting the resource usage in BSs while all the BSs ully utilize the given resources in our basic model. In our intererence thinning scheme, the probability that an BS uses a speciic resource block is limited to θ, to reduce the intererence among emtocells. The channel condition is improved by using θ < 1, but using small θ can reduce the aggregate throughput by decreasing chances or packet transmissions. Our proposed scheme including the intererence thinning scheme is reerred to as OA-Thin. The objective and constraints o OA-Thin is the same as those o the original problem ormulation in OA scheme, but we optimize the new control parameter, i.e., θ, as well as ρ and d to maximize our objective while satisying the constraints. Some parameters in our analytic model are updated by considering θ. The SINR distribution o an MS and an oms, i.e., F Γ r m ) in 9) and F o Γ r o ) in 25), are updated by replacing λ in the equations with θλ. Furthermore, D max in is also updated considering θ. It is diicult to show that inding the optimal solution o OA- Thin scheme is a convex problem in the MS s requirementlimited environments as described in Proposition 2. However, i θ is given, Proposition 2 holds, and we can ind the optimal x θ) and ρ θ) eiciently in the typical environments where the operation is dominated by the beneit requirement o MSs. Thereore, we repeatedly solve the convex optimization problems with various candidate θ values, and θ which minimizes the objective unction is chosen as the suboptimal θ. C. Analysis o Optimal Parameters In this section, we show the optimal parameters o the proposed schemes based on our analytic model. The basic parameters shown in Table II are used in the evaluations unless mentioned otherwise, and we obtain the results with various M values, where MSs require M times higher average throughput than the average throughput o mms. Fig. 4a) shows the optimal service radius d given by the optimization o OA and OA-Thin schemes. The straight lines

9 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 9 Optimal Femtocell Coverage, d * m) N = 1 OA) N = 1 OA Thin) 6 N = 3 OA) N = 3 OA Thin) 4 N = 5 OA) 2 N = 5 OA Thin) Required Beneit o MS, M db) a) Optimal emtocell coverage d ). Partial Resource Access Rate, q * N = 1 OA) N = 3 OA) N = 5 OA) Required Beneit o MS, M db) b) Optimal resource utilization ratio θ ). Optimal Resource Division Ratio, r * N = 1 OA) N = 3 OA) N = 5 OA) Required Beneit o MS, M db) c) Optimal amount o resources dedicated to emtocells ρ ). Fig. 4. Optimal parameters. in the igure represent D max with the given average number o BSs which is reerred to as N. As N increases, D max value decreases due to the increased intererence. For all N values, OA scheme determines to use D max as the service radius o emtocells when M is not very large. I M exceeds some threshold, the optimal emtocell radius becomes smaller than D max, because sharing the emtocell resources with many omss is not an eicient method to provide a large relative beneit to the MSs. In the sense o N, D max is preerred in the wider range o M values when N is large, because the oloading gain o using emtocells is more signiicant with the large number o BSs. These results are the same results which are inerred by Proposition 4. The optimal resource utilization ratio o emtocells, i.e., θ, in OA-Thin scheme is shown in Fig. 4b). The needs or intererence management is larger in the environments where many BSs exist. Thereore, Fig. 4a) shows that OA-Thin scheme chooses to expending the maximum service radius by applying θ < 1 when there are 3 or 5 BSs in average. In the mean time, the intererence thinning is not eective when M is very large, because it is diicult to satisy the requirement o M i BSs use the partial resources in the emtocells. Accordingly, Fig. 4b) shows that the emtocells are required to ully utilize the dedicated emtocell resources when M is large. The optimal ratio o resources dedicated to emtocells, i.e., ρ, is shown in Fig. 4c). For the region where d is ixed, ρ proportionally increases as M increases. However, in the middle region where d increases, ρ decreases to properly maximize the average throughput o mmss while meeting the requirements or the MS s perormance. VI. OPTIMIZATION IN HYBRID ACCESS FEMTOCELL NETWORKS In hybrid access emtocell networks, we optimize β as well as x and ρ. The analysis results or the open access emtocell networks in the previous section are used in the optimization procedures or the hybrid access emtocell networks. Proposition 5: When the target emtocell service area x is given, the optimal ρ and β which maximize the objective in Fig. 5. Ratio between Avg. Throughput o oms and mms Open Access Hybrid Access K=1) Hybrid Access K=2) Hybrid Access K=4) Required Beneit o MS M) Ratio between the average throughputs o oms and mms. 3) are given as ollows: { Cx)+Dx) β x) = Bx) Cx)+Dx), Dx) Cx),, otherwise, and ρ x) = Ax) Bx)Dx) Bx) Cx)+Dx) 38) Dx) Cx), +Ax), Ax) Dx)+Ax), otherwise, 39) 1 e Amλu 1 λ x) ) whereax) = Bm A mλ u1 λ x),bx) = B M,Cx) = B 1 e λux ) Mλ ux, and Dx) = Box)λux+e λux 1). Kλ ux) 2 Proo: See Appendix B-E. From Proposition 5 and the original problem ormulation in 3), the load balancing problem in hybrid access emtocell can be treated as the single variable optimization with the control parameter x. Unortunately, the above optimization problem is not a convex optimization problem. Thereore, we ind a nearoptimal solution by calculating the objective unction over the easible region o x. Because the original problem has been simpliied to a single variable problem and the easible region o x is bounded, we can ind the near-optimal solution x without excessively complex computations.

10 THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIGHT MAY BE TRANSFERRED WITHOUT NOTICE, AFTER WHICH THIS VERSION MAY NO LONGER BE ACCESSIBLE 1 The perormance gain o mms and MS in the hybrid access emtocell networks is achieved at the cost o the average perormance degradation o an oms by using β >. Fig. 5 describes the ratio between the throughputs o omss and mmss in open access emtocells and hybrid access emtocells based on analysis. omss in the open access emtocells enjoy much larger throughput perormance than omss in the hybrid access emtocells thanks to the resource-air intra scheduling o the BS. However, it is unair that the omss achieve such large throughput because the omss and mmss are actually the same type o users who do not pay any cost or the emtocell deployment. On the other hand, the hybrid access BS distinguishes the MS rom the omss and the average throughput o omss are properly controlled so that the similar quality o services are provided to the mmss and omss. Fig. 5 shows that the average throughput o an oms in the hybrid access emtocell networks is exactly K times larger than that o an mms, where K is generally a small value. VII. PERFORMANCE EVALUATION A. Evaluation Environments and Comparing Schemes In this section, we evaluate our proposed schemes based on both numerical analysis and computer simulations. As described in Section III, macrocell users and BSs are randomly deployed according to SPPP, while one constraint that the distance between the BSs should be less than 2D h is additionally given in the simulation settings. The channel model used or the numerical analysis and simulation is described in Section III, and the basic values o the evaluation parameters are provided in Table II 12], 34]. We consider the random mobility o macrocell users in the simulations, and the perormances o users located in the interested area, i.e., a single macrocell area, are considered or the perormance analysis. In our evaluations, the proposed schemes are compared with some comparing schemes. The basic comparing scheme is CoRSSI where the mbss and BSs share the same bandwidth, and a user associates with the cell which provides the best signal strength including both macrocells and emtocells. CoRSSI is excellent in the aspect o sum capacity by ully reusing the bandwidth, but the beneit achieved by mms can be smaller than the dedicated bandwidth based schemes due to the limited oloading gain as will be shown in Section VII-B. In order to show the maximum oloading gain in a cochannel deployment, we also introduce CoLB Cochannel Load Balancing) scheme where the system promotes the users to access emtocell as much as possible while the basic requirement or service coverage o emtocell is satisied. The details o CoLB is described in Section VII-B. DivRSSI is the scheme which assigns the dedicated orthogonal resources to emtocells like the proposed schemes, and each MS associates with the BS which provides the best RSSI value like CoRSSI. In DivRSSI, the bandwidth is divided into the macro and emtocell resources with the optimal ratio, i.e., ρ, while maintaining the constraints T MT m and T KT o. The optimal ρ is chosen based on the simulation results in DivRSSI because no numerical analysis model exists or DivRSSI. Finally, emtocells do not allow any open or hybrid access o omss to access emtocells in CoCA and DivCA, where CA stands or Closed Access. Similarly to DivRSSI, the optimal bandwidth dedicated to emtocell is applied or DivCA based on the simulation results, while the whole resources are shared by macrocell and emtocell users in CoCA. B. Analysis and Simulation Results In this section, we evaluate the perormance o proposed schemes using numerical analysis. The deault evaluation parameters speciied in Table II are used unless mentioned otherwise. First, we show that the numerical analysis is valid in spite o the simpliying assumptions and approximations in the numerical analysis. We obtain the average spectral eiciency and average throughput o an MS, oms, and mms when the service radius d values are given. Ater simulations with 1, distributions, we compare the average simulation results with the analysis result as shown in Fig. 6a). The validation results indicate that the errors between the results o the numerical analysis and computer simulation are negligible, i.e., less than 1 %. Fig. 6b) shows the average throughput o an mms. We ind that the perormance o mmss is enhanced by utilizing the proposed schemes in most regions. When the required beneit rom MSs is small, the more aggressive traic oloading rom macrocell users is easible. Thereore, the perormance gains o OA and OA-Thin are more signiicant when M is small. Among the comparing schemes CoRSSI provides comparable or even better average throughput perormance to mmss than the proposed schemes when the required MS s beneit exceeds a certain value. This result shows that co-channel deployment could be more eicient to guarantee very large perormance beneits to MSs. However, this phenomenon happens when M is very large, e.g., M > 5 in this example, and such large beneits or MSs might not be required in reality. HA-Thin) schemes achieve the better average throughput o an mms than OA-Thin) schemes. Especially, the gain o hybrid access emtocell is still very signiicant even in the environments where M is very large, while the open access emtocell s oloading gain is limited in the environments. In HA-Thin) schemes, the perormance o mmss and MSs are improved by preventing the omss rom achieving the perormance gain much more than necessary. OA-Thin and HA-Thin schemes obtain the urther perormance gain by improving the SINR status and extending the maximum emtocell coverage. As discussed in Section V-C, the partial utilization o emtocell resources, i.e., OA/HA-Thin, is preerred when M is small. The impact o the number o BSs in a macrocell area is shown in Fig. 6c). In the open access emtocell networks, the perormance o mms is enhanced as the number o BSs increases because the chances or the oloading o macrocell s traic increases. As the previous propositions implicate, the intererence thinning in OA/HA-Thin becomes useul when the number o BSs is large where the load balancing eiciency is maximized. Obviously, the perormance o CoCA scheme, i.e., co-channel deployment based on the closed access emtocells, is rapidly degraded as N increases due to the excessive cochannel intererence.