Resource Allocation with Partitioning Criterion for Macro-Femto Overlay Cellular Networks with Fractional Frequency Reuse

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1 Wireless Pers Commun (3) 68:47 43 DOI.7/s Resource Allocation with Partitioning Criterion for Macro-Femto Overlay Cellular Networks with Fractional Frequency Reuse Chang-Yeong Oh Min Young Chung Hyunseung Choo Tae-Jin Lee Published online: 4 November Springer Science+Business Media, LLC. Abstract The interference mitigation technique based on fractional frequency reuse (FFR) provides improved cell-edge performance with similar overall cell capacity as that of systems with the frequency reuse factor of one. Furthermore, frequency sub-band allocation by FFR has the benefit of allowing flexibility foe deployment of femto-cells through frequency partitioning. Determination of a proper frequency partitioning criterion between the cell-center and the cell-edge, and between the cells with femto-cells is an important issue. In addition, time resource partitioning introduces another degree of freedom to the design of time-frequency resource allocation. In this paper, we propose a novel time-frequency resource allocation mechanism using FFR for a macro-femto overlay cellular network. Feasible frequency sub-band and time resource is allocated to the cell-center and the cell-edge region in a cell by the proposed partitioning criterion and the time partitioning ratio. We provide a guideline for how to determine the partitioning criterion foe regions and how to design the amount of time resource. We derive the average capacity of macro-cells and femto-cells, and introduce a new harmonic mean metric to maximize the average capacity of the regions while achieving the fairness among users in a cell. Keywords Capacity Femto-cell Frequency planning Fractional frequency reuse (FFR) Orthogonal frequency division multiplexing (OFDM) Resource allocation Introduction Orthogonal frequency division multiplexing (OFDM) has been drawing much interest to meet growing demands of mobile users on higher data rate as an air-interface technology A preliminary version of this work was presented at ICCSA [8]. C.-Y. Oh M. Y. Chung H. Choo T.-J. Lee (B) School of Information and Communication Engineering, Sungkyunkwan University, Suwon , Republic of Korea tjlee@ece.skku.ac.kr

2 48 C.-Y. Oh et al. for cellular systems including worldwide interoperability for microwave access (WiMAX) [], 3GPP long term evolution (LTE) [] and LTE-Advanced [3] as well as next generation wireless local area networks (WLANs) [4]. Support for high data rate in OFDM systems can be achieved by employing spectrum reuse and utilizing high spectral efficiency. In an OFDM system with multi-cells, co-channel interference (CCI), i.e., interference from transmitters located in neighbor cells with the same frequency bands as the reference cell of interest, may arise owing to the frequency reuse, leading to performance deterioration. Interference management taking the characteristics of OFDM into consideration has been highlighted recently and the interference mitigation technique by controlling the degree of frequency reuse is one of the most important techniques for interference management [5]. Traditionally, inter-cell CCI has been handled by the cell-clustering technique [6], i.e., a frequency reuse mechanism to allocate frequency resources in a multi-cell environment to reduce CCI. One is the shared frequency allocation mechanism with the frequency reuse factor (RF) of one, in which the base stations (BSs) in clustered cells share all feasible timefrequency resource blocks (RBs) with one another. The other is the orthogonal frequency allocation mechanism which allocates frequency channels to multi-cells with the frequency RF greatean by the pre-determined frequency allocation policy. The former may be viewed as more efficient because all resources are fully utilized in each cell. However, it can suffer from performance degradation since the performance of the users located at the edge of a cell is decreased due to CCI from neighboring cells. So the frequency RF of three or more has been generally employed to mitigate CCI. Typically, the reduction of CCI is gained at the cost of efficiency in the frequency resource utilization. Fractional frequency reuse (FFR), which is the mixture of different frequency reuse schemes, becomes one of the solutions to address the inter-cell CCI problem in OFDMAbased cellular systems [7]. The FFR technology partitions the usable spectrum into some sub-bands and assigns different sub-bands to different regions of a cell. In most FFR schemes [8 ], each cell is partitioned into two regions: cell-center region andcell-edge region. The mobile stations (MSs) in the cell-center region, i.e., around a BS, can use the frequency RF of one because of low CCI from adjacent cells. The MSs in the cell-edge region, i.e., far from a BS, should use different frequency bands from those in adjacent cells, e.g., the frequency RF of three to reduce CCI. Note that FFR can be implemented easily in OFDMA systems because the spectrum of a cell is divided into many sub-channels and the unit of sub-channel is a group of orthogonal sub-carriers []. Related works on FFR mainly focus on frequency sub-band partitioning foe regions. Han et al. [8] propose an FFR scheme to enhance the flexibility of frequency assignment and cell performance, in which the MSs in the cell-center region are allowed to use the subchannels assigned to the center and the edge of a cell according to the proposed frequency partitioning mechanism. Another FFR scheme is introduced by noting that the cell-center regions and the cell-edge regions can be served in a different way not only by frequency sub-bands but also by time slots [9], which is extended further by employing the concept of sectorization []. In [], an approach to adapt radio frequency parameters to an environment taking the user and channel conditions into account is proposed. Femto-cells [3], indoor cellular networks using home BSs with low transmission power, typically connected to high speed backhauls, are one of the emerging cost-effective solutions for both operators and users to enhance coverage and to support higher data rate by bridging mobile handsets with broadband wired networks. In order to deploy femto-cells in a pre-existing cellular network, intelligent frequency band allocation considering the effect of CCI for femto-cells and traditional macro-cells is required if they operate harmoniously in the same network [4]. Frequency sub-band partitioning can also play a useful role for

3 Resource Allocation for Macro-Femto Overlay Cellular Networks 49 the effective deployment of femto-cells. The authors in [5] propose that the femto-cells in the center region of a cell use different sub-channels from those foe macro-cell users to minimize the interference, and the femto-cells in the outer region of a cell use the same sub-channels as those foe macro-cell if the frequency RF of one or more is supposed. The authors in [6] propose a frequency planning mechanism, in which femto-cells choose the frequency sub-bands not used in the sub-region of a macro-cell using FFR in a macro-femto overlay cellular network. In this paper, we propose a novel resource allocation with the concept of FFR, i.e., co-channel use in low CCI and orthogonal channel use in high CCI as a useful policy to handle the interference for a macro-femto overlay cellular network. In our mechanism, the connections in femto-cells are allowed to transmit their data through the unused sub-bands by macro MSs without affecting much interference to near macro MSs, according to the proposed sub-band partitioning. Moreover, macro-femto interference is controlled by time slot partitioning as well as frequency sub-band partitioning. For efficient resource utilization, we have provided design guidelines foe partitioning of the time resource and foe partitioning of the regions of a cell. In general, the performances of users are expected to be alike regardless of their geographical locations in a given cell from the users perspective. However, the amount of frequency resource for each region in a cell is asymmetric in FFR, i.e., the feasible frequency band foe cell-edge region is smallean that foe cell-center region to enhance the performance of the cell-edge region by mitigating CCI. So we aim to control the time resource foe cell-center and the cell-edge region during the time transmission interval (TTI) so that asymmetric amount of frequency resources by frequency planning can be balanced by an appropriate design of time resources, leading to flexible and desired resource allocation. An important issue foe design of a resource allocation mechanism is to provide a fairness-aware partitioning criterion between the cell-center region and the cell-edge region since the average signal-to-interference-plus-noise-ratio (SINR) of users in each region varies, and the user capacity per TTI is influenced by the region it belongs to. A partitioning criterion between the cell-center region and the cell-edge region has an effect on the number of users sharing the feasible resource, i.e., user population of each region. Although a partitioning criterion is presented to determine the boundary of sub-cell areas in [9] and a time resource allocation scheme with FFR is considered to schedule sub-carriers in [], both are considered in a macro-cell network, and time resource and partitioning of regions are dealt with separately. Our contribution is to propose a unified resource allocation mechanism to balance the fair capacity per TTI among users in a given cell undee influence of femto-macro cells while boosting the cell capacity The remainder of this paper is organized as follows. Section describes the system model and resource allocation in FFR systems. In addition, an appropriate determination mechanism of the time resource ratio and a partitioning criterion between the cell-center region and the cell-edge region is described to enhance the cell-area capacity undee fairness constraint. Section 3 analyzes and evaluates the performance of the proposed resource allocation mechanism, followed by the conclusion in Sect. 4. Proposed Resource Allocation and Partitioning Criterion We focus on down-link (DL) resource allocation for a network with femto-cells and macrocells employing FFR. We define the time resource ratio (β) and the partitioning criterion ( ) between the cell-center region and the cell-edge region as illustrated in Fig.. If we consider

4 4 C.-Y. Oh et al. t β t Fig. Definitions of and β DL performance, t + t is DL TTI, which is the total amount of time resource for DL. So we can find β = t t +t for t and t. The partitioning criterion,, determines the user population of each region, that is, the number of users sharing the feasible region resource. First, we give an overall resource allocation mechanism for macro-cells and femto-cells with an efficient interference mitigation technique by resource reusing and partitioning in both frequency and time domains. Next, we propose a method for fair resource allocation among users in each region per TTI, which is achieved by appropriately controlling the main parameters, β and.. Model and Proposed Resource Allocation We consider a two-tier OFDM-based cellular network consisting of M macro-cells. The macro BSs with omni-directional antenna are located at the center of each macro-cell and serve the macro MSs within their coverage. F i Femto BSs with omni-directional antenna are deployed within macro-cell i and serve the femto MSs within their coverage, i.e., femto-cells. We assume that there exist N macro MSs in a macro-cell and J femto MSs are served in a femto-cell. All macro and femto MSs are assumed to be uniformly distributed in their cell area with radii of R and r, respectively. We assume that there exist K data sub-carriers to be allocated in system bandwidth. In our scheme, three factors, i.e., frequency, time, and space are considered to reduce CCI among femto-cells and macro-cells. A macro-cell is grouped into two parts: cell-center region and cell-edge region as shown in Fig.. The MSs in the cell-center region use the RF of one and those in the cell-edge region use the RF of three. Figure a illustrates the feasible frequency bands for a macro MS according to the region that the macro MS belongs to. Whole sub-channels can be allocated to the macro MSs in the cell-center region while the macro MSs in the cell-edge region use only a third of all sub-channels in a cell. Furthermore, the service times of the cell-center and the cell-edge region are separated by time slots, i.e., t and t. The macro MSs in the cell-center region of macro-cells can be served simultaneously during their service time (t ) because CCI from neighbor macro BSs is limited. The macro MSs in the cell-edge region of macro-cells can also be served simultaneously during their

5 Resource Allocation for Macro-Femto Overlay Cellular Networks 4 3 (a) Frequency band allocation for macro-cells (b) Frequency band allocation for center femto-cells β = t t + t t t (c) Frequency band allocation for edge femto-cells Fig. Proposed resource (frequency bands/time slots) allocation for macro-femto overlay cellular networks using FFR service time (t ) but they must use the orthogonal sub-channels in order to avoid high CCI from neighbor macro BSs. From the femto-cells viewpoint within a given macro-cell, femto BSs should be deployed harmoniously in order not to give much harmful impacts on the macro MSs but to maximize their performance. In Fig. b, the femto-cells within the cell-center region, i.e., center femtocells, can operate during t. So the service time of the macro MSs in the cell-edge region, and the sub-channels unused by macro MSs, e.g., F + F3 at Macro-cell, are used in the center femto-cells to avoid intra CCI from the macro BS within the cell-area that they belong to. For the femto-cells within the cell-edge region, i.e., edge femto-cells, they use small transmission power and the CCI to the macro MSs in the cell-center region and that between the edge femto BSs is small. So they can reuse the whole frequency bands during t but only two thirds of the total band during t, which is similar to the center femto-cells. We assume that the CCI between the femto BSs and the macro MSs in the neighboring macro-cells is limited due to low transmission power of femto BSs and relatively large path-loss, e.g., highly attenuated path-loss by long distance and wall-loss in buildings.. Proposed Resource Allocation with and β We emphasize the importance of the partitioning criterion,, and time resource ratio, β, and they should be considered for efficient resource allocation. The number of users of each region, i.e., domain in which feasible resource should be shared, is decided by only,and β has an effect on the amount of sharing of feasible resources. While the feasible frequency band is predetermined and fixed by considering CCI among multi-cells, the time resource is more flexible and it is utilized to compensate the scarcity of the frequency resource in the

6 4 C.-Y. Oh et al. cell-edge region. In addition it is desirable to have the average user capacity of each region to be fair, since we consider a network with FFR, and it is affected by both dominating the average user carrier-to-interference-plus-noise-ratio (CINR) of each region and β determining the radio resource occupancy time. We propose a relationship between and β so that the partitioning criterion is determined efficiently according to the time resource ratio of each region. First, we intend fair resource assignment among all macro MSs undee assumption of uniform user distribution. Then we require the following relationship: π( ) : π(r) π( ) = β : ( β). () 3 In this policy (Policy-), β is to be adaptively decided for varying so that the amount of region resource is proportional to the number of macro MSs. So a macro MS can expect an equal share of resource regardless of its location in a cell if a distributor, i.e., macro BS, is unbiased. In another approach, our concern is that the same amount of resource may not guarantee the same capacity since the spectral efficiency of each MS is different. In this case our policy foe fair user capacity (Policy-), i.e., average user capacity of the cell-center region and that of the cell-edge region is equal, can be conceived as: βc center ( /R) = ( β)c edge ( ( /R) ). () In this policy, β is also adaptively decided by the variation of so that the average user capacity is the same. The numerator denotes the actual mean capacity of cell-center / cell-edge region by considering the channel occupancy time. Additionally, the denominator denotes the ratio between the number of users in the cell-center / cell-edge region and the total number of users in a cell. Policy- intends that a macro MS expects the same average user capacity regardless of the region it belongs to by a proper resource scheduling of a macro BS. We then consider maximizing the sum of each region capacity, i.e., C center + C edge.the capacity of each region is equal to the sum of the average capacity of macro MSs in each region. So we can expect to increase total capacity of macro MSs in a macro-cell. In this case, the gap between C center and C edge can be larger since maximizing C center + C edge can be obtained by maximizing the average capacity of macro MSs in the cell-center region. This naturally raises the fairness problem among users by the regions they belong to. Moreover, the relationships between and β, i.e., Policy- and Policy-, are proposed to considee user fairness by controlling the feasible resources of the regions and the number of macro MSs in each region. We thus propose to maximize the harmonic mean between the actual average capacity of two regions. Now, our main objective is not only to maximize the cellarea capacity but also to support the fairness of average capacity among the macro MSs in the cell-area. Let s define the harmonic mean H as: H(βC center,( β)c edge ) = βc center( β)c edge. (3) βc center + ( β)c edge Our objective is to find β and rth such that: β = argmax β H or r th = argmax H (4) subject to Eqs. () or(), which not only enhances the sum of actual average region capacity but reduces the gap of the actual average region capacity. In this approach, H is the metric to

7 Resource Allocation for Macro-Femto Overlay Cellular Networks 43 show how close two actual average region capacities are and it can be utilized to determine the proper and β to maximize the cell-area capacity of macro MSs undee fairness constraint. 3 Performance Evaluation 3. Analysis In this section, we present an analysis foe capacity of macro MSs and femto-cells in a given cell-area undee proposed resource allocation mechanism. The down-link CINR of user u in macro-cell i {,...,M} on sub-carrier k {,...,K } is: Z(i, u, k) = M P(i, u, k) c l(k) I l (k) +, (5) F i c j (k) I j (k) + N (k) l=, l =i j= where P(i, u, k), I l (k), I j (k), andn (k) are the received power of macro MS u on subcarrier k in macro-cell i, CCI from macro-cell l {,...,M}, CCI from femto-cell j {,...,F i } in macro-cell i, and the power of additive white gaussian noise (AWGN) on sub-carrier k, respectively. In addition, c l (k) {, } is defined as the interference indicator having the value of one if sub-carrier k is allocated to cell l. It then generates CCI to a reference cell, i.e., macro-cell i. When the transmission power of sub-carrier k of the macro BS is P(k), the received power of macro MS u in cell i is given by P(i, u, k) = h(i, u, k) P(k), whereh(i, u, k) is the outdoor channel gain. The channel gain reflects the effect of various physical characteristics such as scattering and absorption of radio waves, shadowing by terrestrial obstacles, and multi-path propagation [7]. The channel gain between the macro BS in cell i and macro MS u on sub-carrier k can be written as: h(i, u, k) = Gd(i, u) α s(u)μ(k) (6) where G is a constant incorporating the transmission and receiving antenna gains, d(i, u) is the distance from the macro BS of macro-cell i to macro MS u, αis the outdoor path-loss exponent (estimated to be about 4. in typical urban environments), s(u) is a random variable foe outdoor shadowingeffect, andμ(k) represents the phasor sum of the multi-path components of sub-carrier k. For simplicity, we consider path-loss only and use the approximated distance of d(i, u) in the worst interference scenario, i.e., all radio resources in the feasible bandwidth of each adjacent cell are fully used, so c l (k) is always one. Then after some manipulations, Eq. (5) can be approximated to: Z(i, u, k) = (d(i,u)) α P(k) (6(D) α +6( 3D) α +6(D) α )P(k)+N (k) Z c (i, u, k), (u U center ) (d(i,u)) α P(k) 6( 3D) α P(k)+N (k) Z e(i, u, k), (u U edge ) where D is the constant approximated distance illustrated in Fig. 3, U center and U edge are the set of users in the cell-center region and the set of users in the cell-edge region, respectively. We note that the intra-cell interference from femto-cells is mitigated and is relatively less than that of the inter-cell interference from adjacent macro-cells in our frequency planning. So the amount of intra-cell interference from femto-cells is not included in the approximation. (7)

8 44 C.-Y. Oh et al. D D D D D D Fig. 3 Approximation of distance between a macro MS in a given cell and macro BSs in neighboring cells to inter-cell distance D In addition, we emphasize that Z(i, u, k) is calculated differently according to the region macro MS u belongs to by FFR. The average capacity of the center / edge macro-cell, C center and C edge, can then be obtained as: C center = π r th W log s c n ( + Z c (i, u, k))rdrdθ n c, (8) c C edge = s e π R W/3 n e log ( + Z e (i, u, k))rdrdθ n e, (9) where s c, s e, W, n c and n e are the area of the cell-center/cell-edge region, the system bandwidth, and the number of macro MSs in the cell-center/cell-edge region, respectively. We assume that macro MSs are uniformly distributed in the cell-area and the frequency resource, i.e., the sub-carriers in the feasible bandwidth of each region, are fairly allocated to each macro MS. Finally, we can find the total macro-cell capacity: C macro = βc center + ( β)c edge. () Femto-cell capacity can be defined similarly. First, the down-link CINR of femto MS m on sub-carrier k in femto-cell j within macro-cell i can be found as: Z (i, j, m, k) = M P (i, j, m, k) c l(k)i l (k) +, () F i c ν(k)i ν (k) + N (k) l= ν=, ν = j where P (i, j, m, k) and I ν (k) are the received power of femto MS m on sub-carrier k in femto-cell j of macro-cell i and CCI from femto-cell ν {,...,F i } in macro-cell i, respectively. When the transmission power of sub-carrier k of the femto BS is P (k), the received poweroffemtomsm is given by P (i, j, m, k) = h (i, j, m, k) P (k). The indoor channel gain:

9 Resource Allocation for Macro-Femto Overlay Cellular Networks 45 h (i, j, m, k) = G d(i, j, m) α s (m)μ (k), () where G is a constant incorporating the transmission and receiving antenna gains, d (i, j, m) is the distance from femto BS j of macro-cell i to femto MS m, α is the indoor path-loss exponent (estimated to be about 6.), s (m) is a random variable foe indoor shadowing effect, and μ (k) represents the phasor sum of the multi-path components of sub-carrier k. Eq. () can be approximated as: Z (i, j, m, k) = Z e (i, j, m, k), j F i,edge (d(i, j,m)) α P (k) 8.5(D) α P(k)+N (k) Z c (i, j, m, k), j F i,center (d(i, j,m)) α P (k) (6( 3D) α P(k)+6(D) α P(k))/+N (k) where F i,center and F i,edge are the set of femto-cells in the cell-center region of macro-cell i and the set of users in the cell-edge region of macro-cell i, respectively.the intra-cell interference from neighboring femto-cells is not included in the approximated form, since it is relatively less than that of the inter-cell interference from adjacent macro-cells in our frequency planning. Then we can find the average capacity of edge femto-cells during t, C fem,andthe average capacity of center/edge femto-cells during t, C fem. C fem = π r f W log n ( + Z c (i, j, m, k))rdrdθ n f, (4) f C fem = s f π r f s f W/3 n f (3) log ( + Z e (i, j, m, k))rdrdθ n f, (5) where s f, r f,andn f are the area of a femto-cell, the radius of a femto-cell, and the number of the femto MSs in a femto-cell, respectively. We assume that femto MSs are uniformly distributed in the femto-cell area and the frequency resource, i.e., sub-channels in the feasible bandwidth of each time, are fairly allocated to each femto MS. Finally, we can find the total femto-cells capacity, i.e., the average total capacity of F i femto-cells in a given macro-cell area during the down-link transmission time interval, by: C femtos,i = β [ C fem ( ( /R) ] )F i + ( β)c fem F i. (6) 3. Numerical Results: Part We present the average total macro-cell capacity according to and β in Fig. 4, whichis a3dplotofeq.(). The maximum macro-cell capacity is achieved when is very small and β is near one. This scenario denotes that the particular MSs being in the proximity of a macro BS and holding highly efficient frequency utilization grab most of the feasible resource because full frequency band is assigned to the macro MSs during only t in the cell-center region. In this case, the cell-center region can be extremely narrow. When is very large andβ is near one, the frequency planning mechanism is similar to the frequency reuse factor of one because there is a very wide area foe cell-center region and full frequency band is assigned during only t. That is, FFR is not adopted in the cell. In this case, there are no orthogonal frequency bands for femto-cells if the proposed frequency planning mechanism is applied.

10 46 C.-Y. Oh et al. C macrocell [bps] x β.6.8 Fig. 4 Average total macro-cell capacity according to and β x 8 3 β=. β=.3 β=.5 β=.7 β=.9 C macrocell [bps] Fig. 5 Average total macro-cell capacity according to and β We can observe the trend of C macro according to the variation of and β in Fig. 5 more intuitively. As becomes larger, C macro becomes smaller, which results from the increase of macro MSs far from a macro BS and they are served during t.asβ becomes larger, i.e., large t, C macro also increases. It is natural that as macro MSs in the cell-center region utilize more resources than those in the cell-edge region C macro grows, and it is maximized at the largest and the smallest β. We also present the average total femto-cells capacity according to and β in Fig. 6, which is a 3Dplotof Eq. (6). Basically, the amount of feasible bandwidth for femto-cells is asymmetric. So C femtos can be adjusted by controlling and β. In the case of large and β close to, C femtos is drastically decreased because of the lack of resources for femto-cells.

11 Resource Allocation for Macro-Femto Overlay Cellular Networks 47 C femtocell [bps] x β Fig. 6 Average total femto-cells capacity according to and β 9 x C femtocell [bps] β=. β=.3 β=.5 β=.7 β= Fig. 7 Average total femto-cells capacity according to and β As decreases, the number of edge femto-cells increases. In this case, large β guarantees the sufficient resource for edge femto-cells, so C femtos is improved as β increases. In contrast, at large, i.e., when the number of center femto-cells is greatean that of edge femto-cells, C femtos decreases as β increases since there are few resources for center femto-cells during t in the proposed frequency planning mechanism. The trends are shown clearly in Fig. 7. Foe wide range of, C femtos is insensitive to the change of when β is small. We have observed C macro and C femto for varying. The decrease of improves the capacity from the macro-cell s viewpoint, but the outage rate of macro MSs in the cell-edge region can be worse. The decrease of also improves the capacity from the femto-cell s viewpoint. However large β is favorable for large capacity of macro MSs. Small β guaran-

12 48 C.-Y. Oh et al..8.7 Fair resource assignment(policy ) Fair user capacity(policy ).6.5 β Fig. 8 Change of for varying tees rather constant capacity regardless of to femto-cells. By these preliminary results, we emphasize that proper, i.e., partitioning criterion, and β, i.e., a factor to determine the amount of resource assigned, for both macro-cells and femto-cells are required. 3.3 Numerical Results: Part In this section, we evaluate the capacity performance of a macro-cell and femto-cells in a given cell-area under Policy- and Policy- according to the variation of and β. Furthermore, we intend to determine appropriate and β based on our proposed harmonic mean metric H, and observe if femto-cells performance is also reasonable at that point. Figure 8 shows the variation of β according to.as increases, β also increases and there exists little difference in the slope of each policy. In fact, C center and C edge are differentiated by sub-carrier scheduling in Policy-. In Fig. 8, we select a fair scheduling algorithm as derived in Sect. 3.. The slope of Policy- can be varied by sub-carrier scheduling and that of Policy- is affected by user distribution. It is natural that demands for time resource grow as the cell-center region enlarges. Figure 9 shows total/center/edge macro-cell capacity and H of macro-cell according to under Policy-. We can observe that large is preferred from the perspective of capacity maximization, which means most resources for DL are allocated to the large cell-center region. This situation is undesirable since the large gap between the average capacity of the cell-center region and that of the cell-edge region does not meet our objective in terms of user fairness among regions. Moreover, performance enhancement of femto-cells by sub-band partitioning is hardly expected since there is no orthogonally feasible resource for femto-cells. Instead, we choose the point maximizing H, i.e., 4 and β., although the average capacity of the cell-center region and the cell-edge region are not the same. So we can confirm that H considers an increase/decrease in the rate of the average capacity of the cell-center region and the cell-edge region by the variation of or β. Figure shows total/center/edge femto-cells capacity and H of femto-cells according to under Policy-. We can observe that the selected point for macro MSs is also appropriate for femto-cells.

13 Resource Allocation for Macro-Femto Overlay Cellular Networks 49 Capacity[bps] 3.5 x Total Macrocell Center region Edge region Harmonic Mean x H[bps] Fig. 9 Total/center/edge macro-cell capacity and H of macro-cell according to under Policy- 8 x 8 x 8 4 Capacity[bps] 6 4 Total Femtocells Center Femtocells Edge Femtocells Harmonic Mean 3 H[bps] Fig. Total/center/edge femto-cells capacity and H of femto-cells according to under Policy- 4Conclusion In this paper, we have proposed a resource (frequency band/time slots) allocation mechanism for macro-femto overlay networks using FFR, which takes femto-cells into consideration for an OFDMA-based cellular system. Furthermore, we focus on the determination of a proper partitioning criterion and a time resource ratio between the cell-center region and the celledge region foe proposed resource allocation. We have analyzed the average capacity of macro-cells and femto-cells by varying the partitioning criterion and the time resource ratio, and investigated the properties of the capacity. As an approach to appropriately adjust the partitioning criterion and the time resource ratio, we have derived a relationship between the partitioning criterion and the time resource ratio to assign the amount of feasible resource

14 43 C.-Y. Oh et al. to each region fairly when FFR under asymmetric frequency sub-band allocation is adopted. The harmonic mean between the average capacity of each region to achieve relatively fair performance of users in a cell has been introduced to formally capture the trade-off between the fairness and the capacity maximization. Acknowledgments This work was supported by Priority Research Centers Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (- 8397), and the MKE (The Ministry of Knowledge Economy), Korea, undee ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA--(C9--5)). References. WiMAX Forum. (6). Mobile WiMAX Part I: A technical overview and performance evaluation. White Paper. 3GPP. (8). E-UTRA and E-UTRAN overall description; Stage (Release 8). Technical specification. TS 36.3 V GPP. (8). Requirements for further advancements for E-UTRA (LTE-Advanced) (Release 8). Technical Specification. TR V Hiertz, G. R., Denteneer, D., Stibor, L., Zang, Y., Costa, X. P., & Walke, B. (). The IEEE 8. Universe. IEEE Communications Magazine, 48(), Boudreau, G., Panicker, J., Ning, G., Rui, C., Neng, W., & Vrzic, S. (9). Interference coordination and cancellation for 4G networks. IEEE Communications Magazine, 47(4), Rahman, M., & Yanikomeroglu, H. (). Enhancing cell-edge performance: A downlink dynamic interference avoidance scheme with inter-cell coordination. IEEE Transactions on Wireless Communications, 9(4), Elayoubi, S. -E., Ben Haddada, O., & Fourestie, B. (8). Performance evaluation of frequency planning schemes in OFDMA-based networks. IEEE Transactions on Wireless Communications, 7(5), Han, S. S., Park, J., Lee, T. -J., Ahn, H. G., & Jang, K. (8). A new frequency partitioning and allocation of subcarriers for fractional frequency reuse in mobile communication systems. IEICE Transactions on Communications E, 9-B(8), Giuliano, R., Monti, C., & Loreti, P. (8). WiMAX fractional frequency reuse for rural environments. IEEE Wireless Communications, 5(3), Hamoudal, S., Yeh, C., Kim, J., Wooram, S., & Kwon, D. S. (9). Dynamic hard fractional frequency reuse for mobile WiMAX. In IEEE international conference on pervasive computing and communications (PerCom) 9 (pp. 6).. Lȯpez-Pėrez, D., Juttner, A., & Zhang, J. (9). Dynamic frequency planning versus frequency reuse schemes in OFDMA networks. In Vehicular technology conference fall (VTC 9-Spring) (pp. 5).. Ali, S. H., & Leung, V. C. M. (9). Dynamic frequency allocation in fractional frequency reused OFDMA networks. IEEE Transactions on Wireless Communications, 8(8), Chandrasekhar, V., & Andrews, J. G. (8). Femtocell networks: A survey. IEEE Communications Magazine, 46(9), Lȯpez-Pėrez, D., Valcarce, A., Roche, G., & Zhang, J. (9). OFDMA femtocells: A roadmap on interference avoidance. IEEE Communications Magazine, 47(9), Guvenc, I., Jeong, M. -R., Watanabe, F., & Inamura, H. (8). A hybrid frequency assignment for femtocells and coverage area analysis for co-channel operation. IEEE Communications Letters, (), Lee, P., Lee, T., Jeong, J., & Shin, J. (). Interference management in LTE femtocell systems using fractional frequency reuse. In International conference on advanced communication technology (ICACT ) (pp. 47 5). 7. Choi, J.-G., & Bahk, S. (7). Cell-throughput analysis of the proportional fair scheduler in the single-cell environment. IEEE Transactions on Vehicular Technology, 56(), Oh, C.-Y., Chung, M. Y., Choo, H., & Lee, T.-J. (). A novel frequency planning for femtocells in OFDMA-based cellular networks using fractional frequency reuse. In International conference on computational science and applications (ICCSA ) (pp. 96 6).

15 Resource Allocation for Macro-Femto Overlay Cellular Networks 43 Author Biographies Chang-Yeong Oh has received the B.S. degree in electronics, electrical and computer engineering from Hanyang University, Seoul, Korea in 8 and the MS degree in mobile systems engineering from Sungkyunkwan University, Suwon, Korea in. He is currently pursuing his PhD degree in department of mobile systems engineering at Sungkyunkwan University since March. His research interests include femtocell networks, resource allocation, wireless cooperative communications, and wireless LAN. Min Young Chung received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from the Korea Advanced Institute of Science and Technology (KAIST), Taejeon, Korea, in 99, 993, and 999, respectively. From January 999 to February, he was a Senior Member of Technical Staff with the Electronics and Telecommunications Research Institute (ETRI), where he was engaged in research on the development of multiprotocol label switching systems. In March, he joined the faculty of Sungkyunkwan University, Suwon, Korea, where he is currently an associate professor with the School of Information and Communication Engineering. His research interests include performance evaluation, resource management, Medium Access Control (MAC), and design of Internet and routing, mobile IP, wireless MAN/LAN/PAN, and next generation wireless communication networks. He worked as an Editor of the Journal of Communications and Networks from January 5 to February, and is a member of ACM, IEEE, IEICE, KICS, KIPS, and KISS. Hyunseung Choo received the B.S. degree in mathematics from Sungkyunkwan University, Korea, in 988, the M.S. degree in computer science from the University of Texas at Dallas, in 99, and the Ph.D. degree in computer science from the University of Texas at Arlington, in 996. From 997 to 998, he was a Patent Examiner at the Korean Industrial Property Office. Since 998, he has been with the School of Information and Communication Engineering, Sungkyunkwan University, and is an Associate Professor and Director of the Convergence Research Institute. Since 5, he has been the Director of the Intelligent HCI Convergence Research Center supported by the Ministry of Knowledge Economy (Korea) undee Information Technology Research Center support program supervised by the Institute of Information Technology Assessment. He is Vice President of the Korean Society for Internet Information (KSII). He has published over 5 papers in international journals and refereed conferences. His research interests include wired/wireless/optical embedded networking, mobile computing, and grid computing. Dr. Choo has been Editor-in-Chief of the Journal of Korean Society for Internet Information foree years and Journal Editor of the Journal of Communications and Networks, the ACM Transactions on Internet Technology, the International Journal of Mobile Communication, Springer-Verlag Transactions on Computational Science Journal, and Editor of the KSII Transactions on Internet and Information Systems since 6. He is a member of the ACM and IEICE.

16 43 C.-Y. Oh et al. Tae-Jin Lee received his B.S. and M.S. in electronics engineering from Yonsei University, Korea in 989 and 99, respectively, and the MSE degree in electrical engineering and computer science from University of Michigan, Ann Arbor, in 995. He received the Ph.D. degree in electrical and computer engineering from the University of Texas, Austin, in May 999. In 999, he joined Corporate R&D Center, Samsung Electronics where he was a senior engineer. Since, he has been an Associate Professor in the School of Information and Communication Engineering at Sungkyunkwan University, Korea. He was a visiting professor in Pennsylvania State University from 7 to 8. His research interests include performance evaluation, resource allocation, Medium Access Control (MAC), and design of communication networks and systems, wireless MAN/LAN/PAN, ad-hoc/sensor/rfid networks, next generation wireless communication systems, and optical networks. He has been a voting member of IEEE 8. WLAN Working Group, and is a member of IEEE and IEICE.