Optimization of Femtocell Network Configuration under ... - MWNL

Optimization of Femtocell Network Configuration under Interference Constraints Kwanghun Han,∗ Youngkyu Choi,† Dongmyoung Kim,∗ Minsoo Na,‡ Sunghyun Choi,∗ and Kiyoung Han§ ∗ School

of Electrical Engineering and INMC, Seoul National University, Korea † WiMAX System Lab, Samsung Electronics, Suwon, Korea ‡ Institute of Network Technoloy, SK Telecom, Sungnam, Korea § Communication Lab, Samsung Electronics, Suwon, Korea Email: {khhan, ykchoi, dmkim}@mwnl.snu.ac.kr, [email protected], [email protected], [email protected]

Abstract—Femto BS (Base Station) is emerging as a key technology to secure the coverage and capacity in indoor environments. However, since the existing macrocell network is overlaid on femtocell networks utilizing the same set of frequency channels, femtocell networks can originate severe co-channel interference to the macrocell network unless the femtocell network is carefully configured. Therefore, according to a desired network-wide objective, we optimize the femtocell network with constraints such that the service connectivity with a femto BS is secured in the target indoor area while the signal emitted out of the building, playing as interference to the outdoor users, should be controlled with an appropriate strength in order not to interrupt the communication between macro BS and outdoor users. Each optimization problem is formulated as a mixed integer programming, and as the results, we obtain not only the transmit power and operational frequency channel of each femto BS, but also the optimal femto BS-to-user association pair at each geographical position.

I. I NTRODUCTION Femto BS (Base Station) is a small low-cost BS with a short service range (i.e., 10 to 15 m), referred to as femtocell. It is typically designed to serve under 10 users in indoor environments such as small office and home. A femto BS is typically connected with a macrocell network via a broadband wired connection, e.g., an IP (Internet Protocol) network over xDSL (x Digital Subscriber Line), or a dedicated backhaul network. Today, it is strongly considered a practical candidate solution to secure both the seamless indoor coverage and the high network capacity. The emerging IMT-advanced candidate systems including 3GPP LTE-advanced and IEEE 802.16m also feature this femtocell technology [1]–[3]. Conventional outdoor BSs are referred to as macro BSs in this paper. The functionality of femto BS is almost the same as that of typical macro BS, while the price of femto BS can be significantly lower because (1) a femto BS is expected to serve a small number of users and (2) a relatively low transmit power is enough to cover the service area. Such low cost of the hardware is expected to make the femtocell technology 0 This work is in part supported by Saumsung Electronics and the Ministry of Knowledge Economy, Korea, under the Information Technology Research Center support program supervised by the Institute of Information Technology Advancement (grant number IITA-2009-C1090-0902-0006).

widely accepted since femto BSs can be bought in the market by users and easily installed in a plug-and-play manner. However, as more and more femto BSs are deployed in a given area, unless the femtocell network is properly optimized, the overall network capacity might be significantly compromised due to the co-channel interference. Besides, since the existing macrocell network is assumed to be overlaid on femtocell networks utilizing the same set of operating frequency channels, femtocell networks can originate severe co-channel interference to the macrocell network if the configuration of a femtocell network is not carefully managed. In the meantime, a seamless coverage inside the target indoor area should be also ensured. However, considering the expected huge number of femto BSs, it is almost impossible to keep the network optimized via the manual setting by a human engineer as done in conventional cellular networks. Therefore, the femtocell network is desired to be self-organizing such that the network configuration automatically keeps updated by being aware of the network environmental changes, e.g., addition/deletion of neighboring femto BSs. Consequently, it is very important to address the problem how to optimize the femtocell network (specifically, configuring the transmit power and frequency channel of femto BS) in a systematic manner. In the literature, there has been some related work, especially, in the context of WLAN AP deployments [4]–[6]. However, the considered problem is quite different from the WLAN AP deployment problems due mainly to the cochannel interference to/from macrocells. Moreover, none of the existing schemes deals with BS location determination, power control, frequency channel allocation, and user association altogether , and with Shannon’s capacity directly as an optimization objective. We formulate joint optimization problems, which yield the transmit power, frequency channel, and deployment location for each femto BS along with the desired femto BS-to-user association pair at each geographical position. The rest of the paper is organized as follows: In Section II, we describe the system model. Section III formulates the optimization problems, and then the performance results are discussed in Section IV. We conclude the paper in Section V along with the remark on our ongoing work.

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Fig. 2. Fig. 1.

Three simulation scenarios.

II. S YSTEM M ODEL A. Macrocell and Femtocell Networks We assume WiBro, i.e., a Korean version of Mobile WiMAX, for our system modeling and evaluation [7]. The macrocell network is modeled by a conventional multi-cell honeycomb structure. Each single macrocell is divided into three sectors denoted by S0, S1, and S2 as shown in Fig. 1, and a sector labeled by Sx (x = 0, 1, 2) uses the (x + 1)th frequency channel out of three available channels. Assuming that both macrocell and femtocell networks are perfectly synchronized, the macro BS plays as a downlink interferer to the users in a femtocell network. The architecture of the femtocell-based enterprise network in consideration is illustrated in Fig. 2. A femtocell network is composed of a number of femto BSs and a WSM (Wireless System Management) server, which is a network entity in charge of the optimization of femto BSs’ configuration. The WSM server jointly optimizes the radio parameters of the femto BSs, e.g., transmit power and frequency channel, according to a given network-wide objective. Here, we assume that the WSM server has no authority for configuring the radio parameters of macro BS, and hence, the interference from macrocell network is an uncontrollable factor in the optimization of the femtocell network. Throughout this paper, we assume that the WSM server has the knowledge of all the required information, e.g., the channel gains between each BS and users, required for the network optimization. How to acquire such information should be a separate research topic. We assume that the building, within which the femtocell network is deployed, is a rectangular parallelepiped with a side length of Wbuilding as its first floor plan is illustrated in Fig. 3, and has three floors as shown in Fig. 2. We assume that all the indoor users are associated with one of femto BSs, and all the outdoor users are served by macro BSs. Based on these assumptions, we consider the outdoor region surrounding the building with the width of Wstreet /2 to assess the impact of the interference from the femtocell network on the signal quality, e.g., SINR (Signal to Interference plus Noise Ratio), experienced by outdoor users. We assume that the nine equidistant candidate locations, where femto BSs can be

Femtocell network architecture.

installed, exist on each floor of the building as shown in Fig. 3, and the indices of candidate locations at the same horizontal position on each floor are labeled as x/y/z, where x, y, and z are the index of the 1st, 2nd, and 3rd floor’s candidate location, respectively. B. TPs (Testing Points) In order to evaluate the performance of the target area, i.e., the indoor and outdoor regions, in a mathematically efficient manner, we consider the notion of TP (Testing Point), which is used to measure a continuous object via quantization. The target area can be divided into many square grids and a TP is located at the center of each grid. A particular metric value corresponding to a TP represents the metric at all the other points within the square grid, which the TP belongs to. For instance, the channel gain between a femto BS and a user is represented by the channel gain between the TPs of two grids, which the femto BS and the user belong to, respectively. Specifically, we use the term of internal TP (ITP) and external TP (ETP) to differentiate the indoor users from the outdoor users since different constraints need to be considered depending on the location of a user. Throughout the rest of the paper, we consider that the SINR at every ITP should be at least −3 dB to meet the requirement for the indoor coverage, and the degradation of SINR due to the overall interference from the femtocell network observed at every ETP should not be larger than 1 dB. C. Antenna and Channel Models Macro BSs are assumed to use directional antennas for sectorization. The antenna gain, A (in dBi), is given as a function of the angle θ between a given location of interest and the predefined reference direction. " µ # ¶2 θ A (θ) = − min 12 , Am , −180 ≤ θ ≤ 180, θ3dB where Am is 20 dBi and θ3dB is 70 degrees. On the other hand, both femto BSs and users are assumed to use an omnidirectional antenna, whose gain amounts to 2 and −1 dBi, respectively. Different channel models are considered depending on the point-to-point link of particular interest since the indoor channel characteristic is quite different from that of outdoor channel. More specifically, we consider four different

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TABLE I D EFINITION OF NOTATIONS Notation Ji Je A E F gjaf g 0 jef zaf paf xjaf Fig. 3. Candidate locations for femto BS deployment and TPs covering both indoor and outdoor regions.

Definition Set of all the internal testing points (ITPs) Set of all the external testing points (ETPs) Set of candidate locations for installing femto BSs Set of macro BSs Set of frequency channels Channel gain between TP j and candidate location a for frequency channel f Channel gain between TP j and Macro BS e for frequency channel f 1 if the femto BS is deployed at location a with frequency channel f , zero otherwise Normalized transmit power of femto BS a with frequency channel f , 0 ≤ paf ≤ 1 1 if ITP j is associated with femto BS a with frequency channel f , zero otherwise

III. P ROBLEM F ORMULATION channel models for the channel link 1) between macro BS and outdoor user; 2) between macro BS and indoor user (including femto BS); 3) between femto BS and indoor user; 4) between femto BS and outdoor user. Basically, all the channel models are based on the ITU-R M.1225 model [8]. First, the path loss P L between a macro BS and an outdoor user is expressed as follows: P L = 40 log10 (d/1000) + 30 log10 (f ) + 49, where d is the distance from the macro BS (in meters) and f is the center frequency of the channel adopted by the macro BS (in MHz). In the case of a WiBro network, three frequency channels are available at the 2.3 GHz band. Second, the path loss between a macro BS and an indoor user (including femto BS) is given as follows: P L = 40 log10 (d/1000) + 30 log10 (f ) + 49 + σ, where σ is the penetration loss arising when the signal comes into (goes out of) the building. We assume σ = 12 dB while it actually varies depending on whether the signal traverses the concrete wall or the glass window. Third, the path loss between a femto BS and an indoor user is represented as follows: P L = 37 + 30 log10 (d) + 18.3n((n+2)/(n+1)−0.46) , where n is the number of floors placed between the transmitter and the receiver. On the same floor, n is zero. Last, the path loss between an femto BS and an outdoor user is represented as follows: P L = 37 + 30 log10 (d) + 18.3n((n+2)/(n+1)−0.46) + σ, where n and σ are also the number of floors and the penetration loss, and we determine the value n as if all the outdoor users are located on the first floor. Using these equations, we generate the channel gains without considering the shadowing and fast fading.

We consider two optimization problems specified by different objectives: 1) maximizing the sum of femto BS transmit powers, referred to as ‘MaxPwr Problem’ and 2) maximizing the sum of Shannon capacity at each ITP, referred to as ‘MaxCap Problem.’ Since we are dealing with the non-linear equations for objectives and constraints, it is quite challenging to formulate each optimization problem with MIP (Mixed Integer Programming). We in this section present the detailed procedure of the problem formulation. A set of notations for the optimization variables used during the problem formulation is presented in Table I. Finally, the solution of each optimization problem yields 1) where to deploy femto BSs, 2) transmit power of each femto BS, 3) frequency channel of each femto BS, and 4) desired association at each ITP, simultaneously. A. MaxPwr Problem Intuitively, the inbuilding coverage can be assured by letting the femto BSs use high transmit powers. For example, if we consider the case that the greedy BSs, which want to maximize their own signal quality, compete each other, they will try to increase their transmit powers. This motivates us to consider the objective of maximizing the total sum of femto BSs’ transmit powers: XX max paf . a∈A f ∈F

In case of conventional cell-planning problems, this objective is trivial because every BS simply uses its maximum transmit power Pmax . In our case, however, the transmit power of femto BS is constrained due to the requirement that the SINR degradation observed at each ETP after the deployment of a femtocell network, should be limited. Since the transmission power of a certain femto BS plays as an interference to users associated with other femto BSs, the MaxPwr problem does not necessarily optimize the performance with respect to the SINR. In spite of the inherent limitation of the MaxPwr problem, it is meaningful to look at

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this objective as an initial step thanks to the linear formulation easiness. Now we express the constraints mathematically one after another. First, we assume that at most M (≤ |A|) femto BSs can be deployed and each femto BS uses only one frequency channel due to the assumption of no sectorization: XX zaf ≤ M, (C1)

(a) Incorrect region: Intersection of affine functions.

a∈A f ∈F

X

zaf ≤ 1,

∀a ∈ A.

(C2)

f ∈F

In addition, there exist both minimum and maximum bound for transmit power: C 0 zaf ≤ paf ≤ zaf ,

∀a ∈ A, f ∈ F ,

(C3)

where C 0 , Pmin /Pmax . Pmin and Pmax are the minimum and maximum transmit powers of a femto BS, respectively. A normalized power paf is 0 if zaf is 0, and paf ranges from C 0 to 1, otherwise. Accordingly, if a femto BS should not be deployed at the location a, zaf for all f ∈ F are set to zero. After the optimization problem is solved, the actual transmit power Paf of femto BS a is determined by paf Pmax . Assuming that each ITP corresponds to a user, any user is allowed to associate with only one femto BS in one frequency channel: XX xjaf = 1, ∀j ∈ J i , (C4)

Fig. 4.

xjaf ≤ 1,

i

∀j ∈ J , a ∈ A,

(C5)

∀j ∈ J i , a ∈ A, f ∈ F.

(C6)

f ∈F

xjaf ≤ zaf ,

In order to guarantee the coverage, we need to maintain both SNR and SINR of ITPs over the predefined threshold. First, the SNR constraint with a threshold µ is formulated as follows: Inf (1 − xjaf ) + gjaf Pmax paf P 0 ≥ µ, ∀j ∈ J i , a ∈ A, f ∈ F N0 + gjef PMacro e∈E

(C7) where Inf is a virtually P 0 infinite value; N0 is the background gjef PMacro is the total interference power noise power; and e∈E

Linear approximation of − log(x).

While the SNR constraint looks unnecessary if the SINR constraint is also considered, we deliberately add this constraint to reduce the solving time by shrinking the solution set. Next, we consider the SINR constraint of ITP. Compared with the above SNR constraint, it additionally considers the cochannel interference from other femto BSs as follows: Inf (1 − xjaf ) + gjaf Pmax paf P P 0 ≥ γ, gjef PMacro + gjbf Pmax pbf N0 + e∈E

a∈A f ∈F

X

(b) Correct region: Union of affine functions by selection technique.

b∈A\a

∀j ∈ J i , a ∈ A, f ∈ F,

(C8)

where γ is the SINR threshold for the coverage guarantee. Another major concern is minimizing the impact of the interference from femtocell network on the outdoor users, who are connected to macro BSs. To meet this requirement, we restrict the SINR degradation at each ETP j under 1 dB: ³ ´ 0 max gjef PMacro + Inf (1 − yjf ) e∈E P P 0 ≥ κj , gjaf Pmax paf gjef PMacro + N0 + a∈A e∈E 0 ¡ 0 ¢ 0 E , E\ arg max gjef PMacro , ∀j ∈ J e , f ∈ F, (C9) e∈E

where κj is the minimum bound of the SINR at ETP j experienced after the deployment of femtocell network. Since the original SINR at ETP j can be precomputed, κj can be also predetermined such that κj (dB) is equal to the original SINR (dB) minus 1 dB. Note ³that ETP j ´is assumed to be 0 PMacro . Since the SINR attached to macro BS arg max gjef

from macro BSs. The SNR constraint is valid only for ITP j, which is associated with femto BS a using frequency channel f , namely, xjaf = 1. Note that if xjaf = 1, it also holds that zaf = 1 by (C7). For this purpose, Inf (1 − xjaf ) is e∈E introduced because (C8) can be safely ignored unless xjaf is constraint is valid only for the single frequency channel used 1. This technique is frequently used during our formulation. by the sector, which is associated by ETP j, Inf (1 − yjf ) is Definitely, it can be transformed to the linear inequality introduced to safely ignore the SINR constraint if yjf = 0. constraint1 for MIP: To ensure that yjf = 1 for a certain frequency channel, an à ! additional constraint for auxiliary variable y is considered jf X 0 Inf · xjaf − gjaf Pmax paf ≤ Inf − µ N0 + gjef PMacro .as follows: X e∈E yjf = 1, ∀j ∈ J e . (C10) 1 Other

fractional constraints can be transformed to a linear form, similarly.

f ∈F

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Finally, the MaxPwr problem is formulated as follows: XX max paf a∈A f ∈F

s.t. C1, C2, C3, C4, C5, C6, C7, C8, C9, C10. As addressed previously, the MaxPwr problem does not necessarily maximize the inbuilding capacity since the impact of cochannel interference from other femto BSs is not reflected to the objective. For this reason, we consider the MaxCap problem in the next section.

(a) Before the deployment of femtocell network.

B. MaxCap Problem The achievable capacity at an ITP is given by Shannon capacity, i.e., log2 (1 + SIN R), and hence we need to incorporate this equation to the objective function to address the inbuilding capacity optimization. However, since log function is nonlinear, it is impossible to directly deal with it via MIP. Alternatively, we take the approach to approximate the nonlinear Shannon capacity equation into piecewise linear functions, which can be managed by MIP. To do so, we first look at the characteristic of Shannon capacity assuming that ITP j is associated with femto BS a: log2 (1 + SIN R) Ã ! X X 0 = log N0 + gjef PMacro + gjbf Pmax Pbf 

e∈E

− log N0 +

X e∈E

b∈A 0 gjef PMacro +

X

 gjbf Pmax Pbf  .

b∈A\a

As seen above, Shannon capacity is decomposed into log and − log function, which takes the sum of linear variables as the input. Therefore, if we can approximate the log and − log into linear functions, Shannon capacity is also approximated into linear functions. Fortunately, log is a concave function, which can be easily approximated as the sum of piecewise affine functions: an x + bn ≤ log(x) ≤ an x + bn + ∆, where n is an index variable and ∆ is a positive value. Specifically, the parameters of each line and the number of lines can be adjusted according to the required precision. By using this approximation technique, we can represent log part of Shannon capacity at ITP j as follows: Ã ! X X 0 Sj ≤ cn N0 + gjef PMacro + gjbf Pmax Pbf e∈E

b∈A

+ dn + Inf (1 − xjaf ) + W, ∀j ∈ J i , a ∈ A, f ∈ F, n, (C11) where Sj is a real variable which delegates the intersection region of the affine functions; cn and dn are approximation parameters; and W is the offset value to make Sj positive. Inf (1 − xjaf ) term is for a selection technique.

(b) After the deployment of femtocell network. Fig. 5. Spatial distribution of SINR illustrated by using colormap at 1st/2nd/3rd floors. Each rectangle corresponds to a floor, and the boundary region of the left-most rectangle represents the street region right next to the building.

While log(x) can be directly approximated through simple intersection, − log(x) cannot be done as shown in Fig. 4(a), but can be approximated by getting the union region as shown in Fig. 4(b). To do so, we need to select a proper affine function depending on domain x. More specifically, we will add the virtual infinite value to the other affine functions except the proper affine function to safely ignore them. Accordingly, we take the selection technique again, and hence, an indicator variable vjn is introduced to choose the proper affine function, which gives the biggest value for a given input. Finally, we obtain the inequality conditions given as follows:   X X 0 Qj ≤ −cn N0 + gjbf Pmax Pbf  gjef PMacro + e∈E

b∈A\a

− dn + Inf (2 − vjn − xjaf ) + W, ∀j ∈ J i , a ∈ A, f ∈ F, n, (C12) where W is the offset used to make Qj positive. A constraint for vjn is also required: X vjn = 1, ∀j ∈ J i . (C13) n∈N

Finally, we can define the MaxCap problem as follows: X (Sj + Qj ) max j∈J i

s.t. C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13. The MaxCap problem directly addresses the improvement of inbuilding SINR, and hence, it effectively optimizes the femtocell network from the viewpoint of the site performance.

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Fig. 6.

The CDF of SINR, when the building is located at L#1.

TABLE II S OLUTIONS OF M AX P WR AND M AX C AP OPTIMIZATION PROBLEMS , WHEN THE BUILDING IS LOCATED AT L#1 BS index 2 4 6 8 11 13 15 17 20 22 24 26

MaxPwr Freq. Ch. Power (mW) 3 0.01 1 0.01 2 0.01 2 0.01 3 0.01 1 0.02 2 0.03 2 0.01 3 0.13 1 0.18 3 0.05 2 0.13

MaxCap Freq. Ch. Power (mW) 3 0.08 1 0.06 2 0.01 2 0.05 1 0.01 1 0.08 2 0.02 2 0.01 3 0.05 1 0.64 2 0.01 2 0.04

IV. P ERFORMANCE E VALUATION In this section, we compare both the MaxPwr and MaxCap problems. Note that no other algorithms in the literature can satisfy all the constraints in consideration, so they are not compared. We are interested in the overall performance improvement of the target inbuilding area and the overall performance degradation of outdoor region. As a result, we expect to obtain the theoretical performance bound of the femtocell deployment optimization with the proposed objectives. For this purpose, we evaluate the cumulative distribution function (CDF) of the SINR measured at all the grids.2 The SINR at an outdoor grid is defined as the maximum SINR, which can be observed from one of macro BSs, assuming that the user selects the BS to associate with according to the maximum SINR policy. Without femtocell network, the SINR at any inbuilding grid is determined exactly in the same manner as the outdoor SINR. When the femtocell network is employed, the SINR at each inbuilding grid is defined as the maximum SINR, which can be observed from one of femto BSs, assuming that the indoor user also follows the maximum SINR policy for its association. From the CDF of 2 The grid size for SINR measurement is not necessarily equal to that used to build TPs since it has nothing to do with the problem complexity.

SINR, we can obtain various interesting information, e.g., the probability of coverage hole due to SINR outage, the statistics of transmission rate, the performance degradation of outdoor users due to the interference from femtocell network. For the numerical analysis, we use CPLEX as the MIP solver [9]. We consider two-tier cellular environment for the macro network as presented in Section II and the cell radius is assumed 800 m. The transmit power PMacro of macro BS is fixed to 20 W and the maximum transmit power Pmax of femto BS is assumed 100 mW. We consider that the building size Wbuilding =50 m and street size Wstreet = 30 m, respectively. We consider three building location cases, where a building in cell 0 is located at different positions within the same cell, i.e., L#1, L#2, and L#3 indicated in Fig. 1. The reason why we consider these three cases is that each position holds distinctive features of interference originating from macro BSs: in the case of L#1, the signals from sector 1 of cell 0, sector 2 of cell 0 and sector 0 of cell 2 are almost of the same strengths, and hence, it is likely that whatever a frequency channel is chosen, the outdoor users operating at that frequency channel would be found in the vicinity of the building. In the case of L#2, the signal levels both from sectors 1 and 2 of cell 0 are relatively stronger than that from sector 0 of cell 2, and the strengths of two signals are almost the same. Therefore, it is highly probable that there is no outdoor user using frequency channel 1. For L#3, the signal level from sector 0 of cell 0 is the strongest one, and hence, most outdoor users around the building will operate in frequency channel 1. Among these three locations, we present the results obtained only for L#1 and L#2. The major difference between L#2 and L#3 cases is whether the number of frequency channels, which are mainly used by the outdoor users around the building, is 2 or 1. Note that, at building location L#3, the degree of freedom in determining the radio parameters of femto BS will increase, since the constraint, i.e., limiting the interference on the outdoor users, is easily satisfied if a frequency channel dominantly used by the outdoor users is avoided by femto BSs. For our evaluation, we exclude the decision problem of the location of femto BSs, which is less relevant to our major interest, namely, an automatic radio parameter configuration of femto BSs. To do so, we fix M = 12 such that the four locations at each floor are considered including the location indices, i.e., 2, 4, 6, 8, 11, 13, 15, 17, 20, 22, 24, and 26. For other location indices a, zaf is fixed to zero for all f ∈ F. For the evaluation of MaxPwr and MaxCap problems, we place an ITPs on each of 2-by-2 m grids, which cover the whole inbuilding region. Fig. 5 shows the effect of femtocell network configured by MaxCap optimization via illustrating the spatial distribution of SINR when the building is located at L#1. While the entire indoor region of the building experiences SINR under −5 dB before deploying the femtocell network due to the heavy penetration loss of the signal from macro BSs, the femtocell network is observed to boost up the SINR of the whole indoor area to over −3 dB. Looking at the color of the street region

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Fig. 7.

The CDF of SINR, when the building is located at L#2.

TABLE III S OLUTIONS OF M AX P WR AND M AX C AP OPTIMIZATION PROBLEMS , WHEN THE BUILDING IS LOCATED AT L#2 BS index 2 4 6 8 11 13 15 17 20 22 24 26

MaxPwr Freq. Ch. Power (mW) 3 0.01 1 0.01 1 20.11 2 0.22 3 0.03 1 0.01 1 100 3 0.01 1 60.97 1 59.95 1 100 1 60.98

MaxCap Freq. Ch. Power (mW) 1 100 1 0.01 1 0.01 2 0.04 3 0.08 2 0.01 2 0.01 1 0.04 1 0.01 1 0.06 2 0.01 1 14.74

surrounding the 1st floor, we see that there is no significant degradation in the SINR the outdoor users experience due to the deployment of the femtocell network. The solutions given by MaxPwr and MaxCap optimization at L#1 are listed in Table II. The transmit power value (in mW) is rounded off to the second decimal place. Both solutions exploit all the frequency channels because all the frequency channels are used by the outdoor users near the building. That is, if any femto BSs in any frequency channel use large transmission power values, the SINR constraints of some ETPs will not be satisfied. Consequently, all the femto BSs use small transmission power values for both MaxPwr and MaxCap. Fig. 6 shows that the SINR of the indoor region is dramatically improved by both optimizations. Indeed, the SINR degradation at the outdoor region is observed be to less than 1 dB, which was given as the requirement. Interestingly, we can observe that MaxCap improves the region with the low-to-mid SINR (less than 15 dB) more efficiently than MaxPwr optimization. The solutions given by MaxPwr and MaxCap optimization at L#2 are listed in Table III. The CDF of the SINR is also depicted in Fig. 7. For both cases, some femto BSs operating in frequency channel 1 use large transmission power values, since all the outdoor users on the street use either frequency channel 2 or 3 to satisfy their QoS requirements since sectors 1

and 2 use frequency channels 2 and 3, respectively. Compared with the previous case, the most noteworthy observation from Fig. 7 is that the gap of the indoor SINR performance between MaxPwr and MaxCap is quite remarkable. This phenomenon can be explained as follows: from the discussion about the implication according to the building location, we can infer that it plays more strictly at L#1 than at L#2 the constraint that the SINR degradation of the outdoor users should be limited. Therefore, MaxPwr optimization at L#2 can have more chances to increase the transmit power of femto BS without violating the constraints. However, as we discussed the limitation of MaxPwr optimization earlier in its formulation, the higher transmit power of the entire BSs does not necessarily yield the network-wide configuration optimized from the SINR perspective. Indeed, Table III shows that MaxPwr optimization configures relatively high transmit power to the femto BS indices including 20, 22, 24, and 26, which are located at the same floor. V. C ONCLUSION We formulated the femtocell network optimization problems with constraints on the inbuilding coverage and the interference given to the outdoor users for two different objectives. The MaxPwr and MaxCap problems aim to maximize the capacity of the target indoor area by maximizing the sum of femto BSs’ transmit power and by maximizing the sum of approximated cell capacity respectively. Through the numerical results based on a widely used channel model, we verified the benefit of the femtocell network and analyzed the solutions obtained for each optimization objective. Our results show the theoretical performance bound by network optimization in such an environment. As future work, we plan to develop low complexity algorithms and tackle the network-wide throughput optimization problem considering the intracell and networkwide fairness policy. R EFERENCES [1] Draft [Report on] Requirements Related to Technical System Performance for IMT-Advanced Radio Interface(s) [IMT.TECH], ITU-R Std. R07WP5D-080 128-TD-0028, Jan. 2008. [2] The 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA); Medium Access Control (MAC) protocol specification, (Release 8), 3GPP Std. TS 36.321 v8.1.0, Dec. 2007. [3] Draft IEEE 802.16m System Description Document (SDD), IEEE Std. 802.16m-08/003, Apr. 2008. [4] X. Ling and K. L. Yeung, “Joint access point placement and channel assignment for 802.11 wireless LANs,” IEEE Trans. Wireless Commun., vol. 5, no. 10, pp. 2705–2711, Oct. 2006. [5] A. Eisenblatter, H.-F. Geerdes, and I. Siomina, “Integrated access point placement and channel assignment for wireless LANs in an indoor office environment,” in Proc. WoWMoM, Jun. 2007. [6] S. Hurley, “Planning effective cellular mobile radio networks,” IEEE Trans. Veh. Technol., vol. 51, no. 2, pp. 243–253, Mar. 2002. [7] Specifications for 2.3GHz band Portable Internet Service (PHY & MAC Layer), TTAS Std. TTAS.KO-06.0082/R1, Dec. 2005. [8] Guidelines for evaluation of radio transmission technologies for IMT2000, ITU-R Std. Recommendation ITU-R M.1225, Feb. 1997. [9] Ilog, Inc., “Solver cplex.” [Online]. Available: http://www.ilog.com/ products/cplex/.