毫微微細胞覆蓋式正交分頻多工網路之分散式資源分配

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國立交通大學

電信工程研究所

碩士論文

毫微微細胞覆蓋式正交分頻多工網路之分

散式資源分配

Distributed Resource Allocation in an

OFDMA-based Femtocell Overlay Network

研究生：

黃泓錫

指導教授：

蘇育德博士

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毫微微細胞覆蓋式

正交分頻多工

網路之

分散式資源分配

Distributed Resource Allocation in an

OFDMA-based Femtocell Overlay Network

研究生：黃泓錫 Student：Hung-Hsi Huang

指導教授：蘇育德博士 Advisor：Dr. Yu T. Su

國立交通大學

電信工程研究所

碩士論文

A Thesis

Submitted to Institute Communications Engineering College of Electrical and Computer Engineering

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

in

Communications Engineering

November 2011

Hsinchu, Taiwan, Republic of China

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毫微微細胞覆蓋式

正交分頻多工網路之

分

散式資源分配

研究生

研究生:

::

:黃泓錫

黃泓錫

指導教授

:

: 蘇育德

:

蘇育德

博士

國立交通大學電信工程學系碩士班

中文

中文摘要

摘要

毫微微蜂巢式網路(femtocell)具有延伸網路涵蓋範圍、提昇網路傳輸容

量、增加服務品質等優勢，此外也可以補強大型基地台（macrocell）無

法涵蓋的區域和死角，並減輕其頻寬負荷。即使毫微微蜂巢式網路有上述

好處，

為了保持大型網路使用者的傳輸品質，這些

毫微微蜂巢式網路皆

會

有最大功率下載限制。

在此篇文章中使用閉路存取之正交分頻多工存取(OFDMA)蜂巢網路，並深

入探討如何提升通道傳輸容量以及干擾控制。我們使用中斷機制來量測大

型網路使用者的訊號品質，除此之外我們也採用有干擾限制下之分散式迭

代法來處理資源分配。中斷機率的運算可以讓毫微微蜂巢式網路基地台不

需要知道大型網路使用者的確切位置、通道上的訊號以及受到的干擾。但

每個

毫微微蜂巢式網路基地台使用

分散式方法計算通道傳輸容量時，則

需

要知其覆蓋範圍底下使用者通道狀況或是訊號干擾雜訊比。

毫微微蜂巢式網路基地台

在分散式資源分配演算法裡的每一回合，會

根據網路內使用者在頻帶上的通道狀態以及訊號干擾雜訊比，將頻帶適當

的分配給其下之使用者，再使用注水演算法來分配所有頻帶上的功率。透

過平均中斷機率的要求，每個頻帶上皆會有最大的功率限制。我們因此提

出修正式注水演算法程序來最大化每個毫微微蜂巢式網路傳輸容量。當我

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們觀察到所提出的方法不一定都會收斂，因此我們再提出多個修正措施來

增加收斂的機率。分散式資源分配也可以視為某種非合作式賽局，透過已

知奈許平衡點之充分條件，試著將其與我們所提出的演算法和修正措施之

收斂性做一個結合。

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Distributed Resource Allocation in an

OFDMA-based Femtocell Overlay Network

Student : Hung-Hsi Huang Advisor : Yu T. Su

Communications Engineering National Chiao Tung University

Abstract

The deployment of femtocells is an attractive solution to cope with the capacity and coverage limitation of the existing macrocellular networks. For femtocells to overlay an existing macrocellular network, it is important that the signal qualities of macrocell users (mMSs) be maintained, i.e., the femto-users induced interference be limited to a tolerable level.

In this thesis, we discuss the capacity enhancement and interference control issues in a closed access two-tier orthogonal frequency division multiple access (OFDMA) based cellular network. We use the average outage probability as the measure of mMS signal quality and employ an iterative distributed resource allocation (RA) based interference control approach. The former measure avoids the need for a femto base station (fBS) to know the exact locations of mMSs and the related signal and interference link gains while the distributed approach assumes that each fBS has access to the link gains or signal to noise-plus-interference ratio (SINR) associated with all downlinks within its coverage only.

At each iteration of the distributed RA algorithm, each fBS selects a femto mobile station (fMS) for every subcarrier according to the link gain and SINR and uses a

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however, impose a peak power constraint on each subcarrier. We thus suggest a modified water-filling procedure to maximize the sum capacity of a femtocell. As we observe that the proposed method does not necessarily converge, we propose several remedies to improve the convergence probability. Regarding the distributed RA as a noncooperative game and use a known sufficient condition for the existence of a Nash equilibrium point, we try to interpret the convergence behavior of our algorithm and its remedies.

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誌

謝

首先要感謝指導教授蘇育德博士，老師除了在研究上諄諄教誨，做人

處事態度也令我受益匪淺。另外也感謝口試委員吳文榕教授、楊谷章教授

以及魏存毅教授給予寶貴意見，彌補此篇論文不足及缺失之處。實驗室方

面，特別感謝劉彥成學長在論文方面大力指導，林坤昌學長及劉人仰學長

指點迷津，以及張致遠學長在精神方面支持。也由衷感謝實驗室其他學長

姐、同學以及學弟妹，在生活上的幫忙以及鼓勵。

最後，感謝我最深愛的家人，能在這一路上不斷支持我，他們的關心

與鼓勵帶給了我無形的動力，僅獻上此論文，以代表我最深的敬意。

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List of Figures

1.1 Typical femtocell deployment scenario. . . 2

2.1 A two-tier OFDMA cellular network that consists of a mBS, multiple femto-blockS, mMSs, fBSs, and fMSs. . . 7

2.2 A femtocell block. . . 7

2.3 Interference between diﬀerent femtocells. . . 8

3.1 Outage probability under diﬀerent power upper bound. . . 15

3.2 Outage probability under diﬀerent power upper bound with distance be-tween mBS and femtoblock=50. . . 16

5.1 Oscillation. . . 27

5.2 Randomization. . . 31

5.3 Illustration of water-ﬁlling interpretation with power upper bound. . . 32

5.4 Illustration of water-ﬁlling interpretation with power upper bound. . . 33

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6.2 Nonconvergence Case of Noncooperative Game. . . 36

6.3 Convergence result by using Variance Reduction . . . 36

6.4 Iteration number with diﬀerent power upper bound. . . 37

6.5 Iteration numbers versus probability of using randomization 1. . . 38

6.6 Iteration numbers versus probability of using randomization 2. . . 38

6.7 Comparison of Femtocell Capacity. . . 39

6.8 Femtocell capacity versus SIR constraints of mMS with diﬀerent power constraints. . . 40

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List of Tables

6.1 Simulation parameters. . . 34

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Chapter 1 Introduction

In recent years, the demand for higher data rates in wireless networks is dramati-cally increased. Besides, extending coverage into residential areas is one of the biggest challenges for current mobile communication networks. Since it is extremely expensive to serve the indoor users with large service demands, a significant interest within the telecommunications industry has recently focused on how to provide service for indoor users in a cost-efficient way and femtocell is introduced to solve the cost and efficiency issues.

The femtocells use the same spectrum with macrocell and it enhances the indoor coverage of macrocell by deploying a low-power, low-cost, and short-range base station in indoor environment. Due to short distance between femtocell base station (fBS) and femtocell mobile users (fMSs), femtocell can achieve high throughput with low transmission power of femtocell. The fBSs can be installed by consumers themselves inside oﬃces or houses. It connects to macrocell system via internet, such as Digital Subscriber Line (DSL), cable modern or ﬁber; the whole femtocell network scenario is illustrated in Fig. 1.1 [1]. Since femtocell is installed in indoor environment, it can provide high data rate for indoor users. Meanwhile, because macrocells only need to allocate resources to outdoor mobile users, the reliability of macrocell mobile users is enhanced.

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adopted or considered as a candidate of multiple access scheme for future wide area broadband wireless networks with its robustness against frequency selective fading and its ﬂexibility in radio resource allocation for satisfying various QoS requirements. OFDMA exploits multi-user diversity in time-varying and frequency-selective fading channels by assigning a subcarrier to the user with the best channel gain and by scheduling the transmission of user data opportunistically.

Figure 1.1: Typical femtocell deployment scenario.

However, some technical challenges must be discussed concerning femtocell net-work. For instance, timing and synchronization, cross-tier interference avoidance, access method of femtocell, and handover between macrocell and femtocell, those issues are critical aspects of femtocell technology which still need be studied further. In addition, for the coexistence scheme, the overall capacity may be reduced signiﬁcantly due to the co-channel interference. Therefore, how to deal with the interference management is also an important issue concerning femtocell networks and it is studied in this thesis.

A hybrid spectrum sharing scheme is also proposed to reduce interference in [2]. In [3], spectrum sensing and subchannel assignment are joint considered to reduce intercell

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interference and to increase system capacity in the meanwhile. [4] considered a opti-mization problem maximizing femtocell network capacity with constraints restricting femtocell power such that the communication between macro BS and outdoor users is not interrupted. Chandrasekhar develops interference avoidance strategy in a two-tier Code Division Multiple Access (CDMA) network in [5] and Spatial Poisson Point Process (SPPP) [6] is utilized to model distribution of femtocell base stations.

Nevertheless, assuming the perfect information about the channel and/or location of may not be true in practice. To deal with this issue, we propose average outage probability constraint to restrict interference caused by femtocell without the perfect assumption. We deﬁne that outage event occurs when received SIR of macrocell users below a predeﬁned threshold, and we control femtocell such that the outage probability is lower than the predetermined tolerance threshold. As we known, the outage probability is widely utilized to represent the coverage of a broadcast network. The coverage is based on the outage probability that the carrier-to-noise ratio (CNR) of a received signal at any location within its coverage area is greater than a predetermined threshold [7]. Based on the average outage probability constraint, we transform the average outage probability constrain into the maximum transmission power constraint easily.

After ﬁnding the maximum tolerant transmission power of femtocell according av-erage outage probability constrint, we want to solve the resource allocation problem of femtocell system. In this thesis, the femtocells are secondary users that coexist with pri-mary users that are macro users. The macro users are licensed to operate over certain frequency bands. They do not cooperate with or even provide feedback to the fBSs. One of the main challenges in femtocells is how to design an eﬃcient and adaptive channel access scheme that supports dynamic subcarrier selection and power/rate allocation in a distributed femtocell environment. Here, we want to use game theory to formulate the resource allocation game of our system.

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problem. In [8], the noncooperative game is used to deal with the resource allocation problems. However, the proof of the noncooperative game does not consider the subcar-rier allocation and the standard function seems inappropriate to prove the convergence of the game. Besides, the authors do not discuss the power upper bound for the system to protect the primary users’ rights. In [9], though the authors claim that their nonco-operative game can converge if the subcarrier allocation is stable, they do not prove the game can converge to a unique NE point. In [10], the suﬃcient condition of unique NE point is provided and the algorithm can converge to a NE point under some conditions. However, the authors do not discuss the user selection and only focus on the power allocation.

In [11], the authors use noncooperative pricing game and also claim their game can converge to a Pareto-optimum solution. However, this game needs to use MAC layer to communicate the signals between different users that takes too much time and overhead to communicate each other. A centralized spectrum management scheme was proposed in [12], which greatly improves the system performance over the IWF scheme by utilizing a centralized spectrum management center (SMC). However, such an approach cannot be implemented in an ad hoc opportunistic cognitive radio network (CRN), where none of the cognitive radios has global knowledge of the entire CRN to function as the SMC. Given the above, we are motivated to design a channel/power/rate allocation scheme that can solve the resource allocation problem and can be implemented in a distributed fashion. We provide a noncooperative game that consider not only power allocation but also user selection. Besides, we discuss the sufficient condition of converging to a unique NE point in our noncooperative game. On the other hand, our distributed algorithm can also reduce the non-convergence probability of resource allocation. We also compare the bandwidth efficiency of distributed algorithm with centralized approach. Finally, the simulation of bandwidth efficiency for femtocell system with power upper bound in a practical system is illustrated.

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The rest of this thesis is organized as follows. In following chapter, we present the scenario and assumption of our system model. The outage probability is provided to satisfy the rights of macrocell in chapter 3. In chapter 4, we proposed a noncooperative game and algorithm to solve the resource allocation problem. We investigate the non-convergence cases and prove that our algorithm deﬁnitely reduces the probability of non-convergence in chapter 5. Finally, chapter 6 represents some simulation results and this thesis ends up with some conclusions in chapter 7.

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Chapter 2 Scenario and Assumption

The network layout under investigation is illustrated in Fig. 2.1. An overlay system consists of a macro base station (mBS) at the center of the macrocell and J macro users randomly located in the macrocell is depicted. Without loss of generality, we only need to consider one third sector of a macrocell. We assume a femtoblock, containing K

femtocells, is randomly located in the macrocell. There are Lk (k = 1, 2, ..., K) femtocell

users (fMSs) randomly distributed in the femtocell k. The total bandwidth of the system is equally divided into N OFDM subcarriers.

In Fig. 2.2, a dense-urban femtocell model, each block represents two stripes of

apartments and each stripe has 2N apartments. Each apartment is of size 10m×10m.

There is a street between the two stripes of apartments, with width of 10m. Each

fem-tocell block is of size 10(N+2)m×70m. In each macrocell sector, one or several femtocell

blocks may exist while it is assumed that the femtocell blocks are not overlapping with each other.

While a centralized algorithm can solve our problem eﬀectively, its requirement that the centralized controller needs to know all information about all subcarriers and of high computational complexity to optimize jointly makes it diﬃcult to implement in a practical system. Thus, we consider a more pragmatic system where each fBS only

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͗DĂĐƌŽĐĞůůĂƐĞƐƚĂƚŝŽŶ͗DĂĐƌŽĐĞůůƵƐĞƌ ͗&ĞŵƚŽĐĞůůďůŽĐŬ

Figure 2.1: A two-tier OFDMA cellular network that consists of a mBS, multiple femto-blockS, mMSs, fBSs, and fMSs.

...

STREET 10m 10m 10m 10m 10m apartment femto cell femto BS femto MS

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1.

3.

2.

Figure 2.3: Interference between diﬀerent femtocells.

from other fBSs and mBS to their fMSs. However, if each fBS aims to maximize its own achievable rate with its fMSs selﬁshly without cooperating with other fBSs, it may causes severe interference to the nearby femtocells. Thus, every fBS needs to not only maximize its sum rates but also adapts to other fBSs’ interference. A simpliﬁed example is illustrated in Fig 2.3.

We denote by p_k = [p1

k, p2k, ...pNk] the transmission power vector of fBS k, where

pn

k is the transmission power on subcarrier n of fBS k. In addition, we denote by

p = [p₁, p₂, ...p_K] the network power vector. We restrict the total transmission power (i.e., ∑N_n=1pn_k) of each fBS k to be no more than Pf em. We deﬁne Ak = [anl,k]lkxN

as the assignment matrix, where an_l,k is 1 if the subcarrier n is assigned to user l

and 0 otherwise and each subcarrier can be assigned to no more than one fMS in each femtocell.

We let the channel gain containing path loss and independent fading from fBS i to

fMs l in femtocell k on subcarrier n be represented by hn

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from fBS i to fMs l in femtocell k on subcarrier n by pn

il,k. Their mBS counterparts are

denoted by hn_ml,k and pn_ml,k by substituting subscript i by m.

The total interference received by fMs l in femtocell k on subcarrier n is denoted by

In

l,kwhich consists of the interference from mBS pnml,khnml,k and the aggregated interference

from other fBSs except fBS k ∑K_i=1,i_̸=kpn

il,khnil,k. Without loss of generality, the noise

power σ2 _{on all subcarriers are assumed to be the same. We deﬁne the}

gain-to-noise-plus-interference ratio (GINR) of fMS l in femtocell k on subcarrier n as

g_l,kn = h n kl,k In l,k + σ2 = h n kl,k pn ml,khnml,k + ∑K

i=1,i̸=kpnil,khnil,k+ σ2

(2.1)

The sum rate of fMS l in femtocell k is thus N

∑ n=1

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Chapter 3 Outage Probability Constraint

The motivation of using fetmtocell system is to enhance the spectrum utilization by allowing femtocell base stations (fBSs) to share the same spectrum with the macrocell system. While in our overlay downlink system, because fBSs only serve their femtocell users (fMSs) in its severing area, the signal of a fBS is interference to nearby users as mMSs and fMSs in other femtocells.

Since in our overlay system the mMSs are the primary users, fBSs cannot cause too large interference and damage the QoS of their nearby mMSs. Due to the randomness of the mMS locations, it is impractical to assume perfect knowledge of mMS location at a fBS. Besides, the fBSs are installed by consumers; the fBSs do not have the information about the macrocell network, such as the channel state information (CSI) between the mBS and mMSs and the information about the frequency assingments of macrocell network. Therefore, the exact calculation of the interference caused by fBSs to mMSs is diﬃcult. We will illustrate how those fBSs allocate their resource to avoid causing too much interference to their nearby mMSs as well as maintain the mMSs’ QoS.

In this Chapter, the average outage probability constraint for protecting the mMSs’ QoS is discussed. An outage event occurs when the received signal-to-interference-ratio

(SIR) of a mMS on a subcarrier n γnis smaller than or equal to a the predeﬁned threshold

ηn. Then, the corresponding outage probability Po can be expressed as

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The setting of SIR threshold ηndepends on the application and priority of the mMS.

If the received SIR is higher than ηn, the mMS can decode the data correctly. Otherwise,

the mMS cannot have reliable data. The notion of outage probability constraint means

that the outage probability is restricted not to exceed a speciﬁed threshold Pout.

If we limit the outage probability to be less than or equal to the predeﬁned threshold

Pout, the interference will also be restricted; therefore, the QoS of macrocell can be

guaranteed. The determination of outage probability threshold Pout also depends on

the application of the communication link and the priority of the mMS. In general, the higher the QoS is required, the lower the threshold should be.

As a result, the outage probability constraint provides another dimension to adjust

the behavior of fBS. Speciﬁcally, as the threshold Pout may vary across diﬀerent

sub-carriers, a fBS can adjust its power allocation and/or subcarrier assignment based on these diﬀerent outage probability constraints. Therefore, by limiting the possibility of the outage probabilities, we also limit the among of interference such that QoS of mMSs is satisﬁed.

Since the fBS does not have the exact instantaneous information of macrocell (e.g., CSI between mBS and mMSs and the exact locations of mMSs), we need to average out all unknown information of mMSs. Given the fixed locations of mMSs and all fBSs, we average out the channel gain between all fBSs and mMSs and that between a mBS and its mMSs. The closed form of the outage probability conditioned on the fixed locations is first derived. Then we average over different locations of fBSs and mMSs to derive the average outage probability of mMS. With the outage probability, we can find the power upper bound of all fBSs to satisfy the mMSs’ QoS.

While the distance between fBSs and mMSs are determined once the consumer in-stalled them, the mMSs and fBSs are assumed uniformly located in the coverage region

of a mBS. The distance between the mBS and the kth fBS is denoted by rk,m and the

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for-mulate the pdf of the distance rj,m and rk,m in polar coordinate system, which can be represented as frj,m(r) = 2r R2 max− Rmin,j2 (3.2) frk,m(r) = 2r R2 max− Rmin,k2 (3.3)

where r is the distance measured from mBS. The parameters Rmax is the maximum

ra-dius of macrocell, and Rmin,j (Rmin,k) is the minimum distance between the jth mBS and

the kth mMS (fBS). For convenience, we assume that Rmin,m=Rmin,k=Rmin. Moreover,

we can express the distance between the jth mMS and the kth fBS by law of cosines:

rj,k = √

r2

j,m+ r2k,m− 2rj,mrk,mcos θj,k (3.4)

where θj,k is the angle between the line connecting mBS and jth mMS and that

con-necting mBS and the kth fBS.

Recall that the marcocell is a 3-sector system. Since the mMSs and fBSs are

uni-formly random located in the sectorized region, the random variable θj,k is assumed to

conform a uniform random variable with domain [0, 2π₃ ].

The distribution of rj,k thus depends on three independent random variables rj,m,

rk,m, and θj,k. However, direct deriving the exact pdf of rj,k is rather diﬃcult, we will

approximate the outage probability Po via Monte Carlo method. While Po is obtained

by 106 _{realizations of r}

j,m rk,m and θj,k, in the next section we will keep the expression

of frj,k, the pdf of rj,k.

We first derive the closed form of the outage probability conditioned on fixed locations of fBSs and mMSs. Then, we average over possible locations of all mMSs and fBSs to find the average outage probability. We examine two different scenarios: one where each fBS is independent randomly distributed in the macrocell; the other all fBSs gather together in a femto-block which is randomly distributed in the macrocell.

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3.1 Distributed Locations of fBSs

We first fix the locations of mMSs and fBSs and find the outage probability Po,f ix

conditioned on these locations.

Po,f ix = Pr { pn mj,mhnmj,m ∑K k=1pnkl,khnkj,m ≤ ηn|rj,m, rj,1, rj,2...rj,K } (3.5) = Pr { pn mj,m|Hmj,mn |2P L(rj,m) ∑K k=1pnkl,k|Hkj,mn |2P L(rj,k) ≤ ηn|rj,m, rj,1, rj,2...rj,K } (3.6) = Pr {∑K k=1p n kl,k|H n kj,m| 2_{P L(r} j,k) pn mj,m|Hmj,mn |2P L(rj,m) ≥ 1 ηn |rj,m, rj,1, rj,2...rj,K } = Pr { _K ∑ k=1 pn_kl,k|H_kj,mn |2P L(rj,k)≥ γpnmj,m|H n mj,m| 2_{P L(r} j,m)|rj,m, rj,1, rj,2...rj,K } = Pr { _K ∑ k=1 Wk|Hkj,mn |2 ≥ γWm|Hmj,mn |2|rj,m, rj,1, rj,2...rj,K } (3.7) = Pr { z ≥ γWm|Hmj,mn | 2_|r j,m, rj,1, rj,2...rj,K } (3.8) = ∫ _∞ 0 ∫ _∞ γWm|Hmj,mn |2 K ∑ k=1 Ck Wk exp(− z Wk )dz exp(−|H_mj,mn |2)d|H_mj,mn |2 = K ∑ k=1 ∫ _∞ 0 ∫ _∞ γWm|H_mj,mn |2 Ck Wk exp(− z Wk )dz exp(−|H_mj,mn |2)d|H_mj,mn |2 = K ∑ k=1 ∫ _∞ 0 Ckexp(− γWm|Hmj,mn |2 Wk ) exp(−|H_mj,mn |2)d|H_mj,mn |2 = K ∑ k=1 CkWk γWm+ Wk (3.9) Where hn

mj,mand hnkj,mcontains the fading gain and path loss, γ =

1

ηn, Wk=p

n

kl,kP L(rj,k)

and Wm=pnmj,mP L(rj,m). In (3.8), we have let z=

∑K

k=1Wk|Hkj,mn |2, a weighted sum of

exponentially distributed random variables, with pdf being ∑K_k=1 Ck

Wkexp(− z Wk), where Ck= ∏K i=1,i̸=k 1 1−Wi Wk [13].

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outage probability Po is derived by average: Po = Pr{γn ≤ ηn} (3.10) = Erj,m,rj,1,...,rj,K [ _K ∑ k=1 CkWk γWm+ Wk ] (3.11) = ∫ ... ∫ ∫ ∑K k=1 CkWk γWm+ Wk frj,m(ro)frj,1(r1), ..., frj,K(rK)dr0dr1, ..., drK (3.12)

3.2 fBSs Fixed in Femtoblock

Here, we discuss the case where K fBSs gather together in a femtoblock. In this accumulative scenario, all femtocells are located as illustrated in Fig. 2.2. Similarly,

Po,f ix = Pr{ pn_mj,mhn_mj,m ∑K k=1p n kl,khnkj,m ≤ ηn} (3.13) = Pr{ pn_mj,m|H_mj,mn |2P L(rmj,m)⋆ ∑K k=1p n kl,k|H n kj,m|2P L(rkj,m)⋆ ≤ ηn} (3.14) = K ∑ k=1 C⋆ kWk⋆ γW⋆ m+ Wk⋆ (3.15) Note that the signal of all fBSs may penetrate more than one wall to reach mMSs. Here we use super script ⋆ to represent the path loss containing the penetration reﬂecting this eﬀect.

Because K fBSs gather in a femtoblock, we may assume the distance between each fBS and mMSs are the same when K is not too large. However, the numbers of walls

between each fBS and mMSs may diﬀer according to their locations thus aﬀecting W⋆

k’s. Therefore, in this scenario, the outage probability can be approximated as

Po = Pr{γn≤ ηn} (3.16) ≈ ∫ ∫ ∑K k=1 C⋆ kWk⋆ γW⋆ m+ Wk⋆ frj,m(r0)frj,k(rk)dr0drk (3.17)

We have formulated two closed forms of outage probability with ﬁxed locations of mMSs and fBSs. Thus the power upper bound of each fBS with diﬀerent scenarios can

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0 0.5 1 1.5 2 2.5 3 3.5 x 10−3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Power upper bound of fBS per subcarrier (W)

Outage Probability of mMS

Outage probability versus different power upper bound

Threshold of mMS = 0 dB Threshold of mMS = 5 dB Threshold of mMS = 10 dB Threshold of mMS = 15 dB Threshold of mMS = 20 dB Threshold of mMS = 25 dB

Figure 3.1: Outage probability under diﬀerent power upper bound.

be obtained by averaging all possible locations produced by Monte Carlo method. The simulation results with two diﬀerent scenarios shown in the next section.

3.3 Simulated Outage Probabilities

The outage probability we can tolerate in our system is 5% that means we only let 5% mMSs suﬀer severe interference and need to protect 95% mMSs’ QoS. The BER

we can accept in our fading channel system with channel coding is assumed 10−2 that

means the SIR threshold of mMSs needs more than 10 dB. The outage probability of distributed locations of fBSs is shown in Fig. 3.1, we can find that as the QoS of mMSs increases, the mMSs restrict the maximum power fBSs can transmit. Thus the outage probability increases as the transmit power of fBSs increases. Besides, different SIR thresholds of mMSs also result in different outage probability.

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0 0.5 1 1.5 2 2.5 3 3.5 x 10−3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Outage probability versus different power upper bound with femtoblock distance=50 Threshold of mMS = 0 dB Threshold of mMS = 5 dB Threshold of mMS = 10 dB Threshold of mMS = 15 dB Threshold of mMS = 20 dB Threshold of mMS = 25 dB

Figure 3.2: Outage probability under diﬀerent power upper bound with distance between mBS and femtoblock=50. 0 0.5 1 1.5 2 2.5 3 3.5 x 10−3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3.3: Outage probability under diﬀerent power upper bound with distance between mBS and femtoblock=300.

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0 0.5 1 1.5 2 2.5 3 3.5 x 10−3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figure 3.4: Outage probability under diﬀerent power upper bound with distance between mBS and femtoblock=700. 0 0.5 1 1.5 2 2.5 3 3.5 x 10−3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3.5: Outage probability under diﬀerent power upper bound with distance between mBS and femtoblock=1500.

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and mBS from Fig. 3.2–3.5. We can ﬁnd as the requirements of mMSs’ SIR threshold increase, the outage probability of mMSs also increases. The more power fBSs can transmit, the higher outage probability mMSs achieve.

These four simulations also imply a fact that the outage probability has relation with the ratio of the distance between mBS and mMS to the distance between fBS and mMS

that should be limited within a threshold rth mainly dominated by the transmit power of

mBS and fBSs, numbers of fBS, penetration loss and SIR requirement of mMSs. Thus, when the distance between fBS and mMS is 50m in Fig 3.2, the ratio of the distance between mBS and mMS to the distance between fBS and mMS is usually smaller than

rth, so the outage probability is low.

However, the distance between femtoblock and mBS is 700m in Fig. 3.4, the

prob-ability of the ratio of the distance that cannot satisfy the rth increases, so the outage

probability increases obviously. When fBSs are moved to location where the distance between mBS and fBSs is 1500 in Fig. 3.5, the outage probability with SIR threshold above 20dB is smaller than that in Fig. 3.4. The reason is that the outer part of the 1500m is limited by the convergence of mBS and the outer part of location at 700m from mBS is more than that of location at 1500m.

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Chapter 4 Noncooperative Game

In this chapter, “game theory” is introduced to solve our resource allocation problem distributedly. Game theory is a tool to observe the interactions of players in decision-making processes, and provides some characteristics to be analyzed. The greedy behavior inherited in our sum-rate maximization problem and the interactions of femtocells in decision-making processes of resource allocation can be modeled and analyzed using game theory.

4.1 Noncooperative Game

We model the self-organized resource allocation as a non-cooperative game. In general, the noncooperative game consists of three components: players, strategies, and

utilities, which can be mathematically deﬁned as G = {K, {Sk}k∈K,{uk}k∈K}. The set

of players and the set of strategies associated with player k are denotes as K and Sk,

respectively. The utility function of player k, uk:S → R, maps each possible combination

of the strategies of all players S = S1× S2× · · · × Sk, k ∈ K, to a real value. The utility function represents the degree of satisfaction of player k as a function of the strategy it chooses, sk, and the strategy of the other players, s−k = (s1, ..., sk−1, sk+1, ..., sK). The objective of each player is to choose the best strategy among the available strategies in order to maximize its own utility.

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action including power and subcarrier allocation and the union set of all other play-ers’ action p_−k , where p_−k=[p₁, p₂, ...p_k₋₁, ...p_k+1, ...p_K]. Because our fBSs want to maximize their own sum capacity, the utility function of fBS k here is deﬁned by

uk(p, Ak)= ∑Lk l=1 ∑N n=1a n l,klog2(1 + pnl,kgl,kn ).

Let G = {K, {Pk × Ak}, {uk}} denotes a noncooperative resource allocation

game (NRAG), where k ∈ K = {1, 2, ..., K} is the index set of the fBS. {Pk × Ak}

is the strategy space of each fBS k with Pk = {pk| 0 ≤

∑N n=1pnk ≤ Pf em} and Ak = {Ak| anl,k ∈ {0, 1}, ∑ l∈Lka n l,k = 1∀l, k}.

4.2 Non-cooperative Resource Allocation Game

For a speciﬁc femtocell k, it wants to maximize its utility function.

(p.1) max uk(p, Ak) = Lk ∑ l=1 N ∑ n=1 an_l,klog₂(1 + pn_kl,kgn_l,k) (4.1) subject to Lk ∑ l=1 N ∑ n=1 an_l,kpn_kl,k ≤ Pf em (4.2) pn_kl,k ≥ 0 ∀l, n; (4.3) an_l,k ∈ {0, 1} ∀l, n (4.4) Lk ∑ l=1 an_l,k ≤ 1 ∀n (4.5) pn_kl,k ≤ ¯P_macn ∀l; (4.6)

Equation (4.2) is the total power constraint of fBS k while the power constraints on

each subcarrier are given in (4.3) and (4.6), where ¯Pn

macobtained by outage probability in

Chapter 3 represents the power upper bound on subcarrier n to satisfy the requirement of mMs’ QoS. The indicator constraints (4.4) and (4.5) are imposed to ensure that each subcarrier can be assigned to no more than one user.

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The utility function of our noncooperative game is a non-convex problem and hard to solve, so we separate our problem into two parts: one is subcarrier allocation; the other power allocation. In the following sections, we will discuss the algorithm and the outcome of our game.

4.2.1 Nash Equilibrium

As the deﬁnition in the context of game theory, Nash equilibrium (NE) is a state where given other players’ strategy, no player can improve its utility level by changing its own strategy unilaterally. If our noncooperative game can converge to a NE point, it means at this point no fBS wants to change its strategy of subcarrier and power allocation given other fBSs’ strategies.

4.2.2 Algorithm of Noncooperative Game

Step 0: Initialize t=0 and Tout; Step 1: t=t+1;

Step 2: Each fMS measures the channel (GINR) for all the sub-channels and feeds back the measured values to the fBS.

Step 3: The fBS performs sub-channel assignment to the fMSs according to the algo-rithm of subcarrier assignment.

Step 4: The fBS performs power allocation according to the proposed power allocation method.

Step 5: (Oscillation monitoring) If the fBS observes there is oscillation on its subcarriers or power allocation compared to the previous stage, then it performs variation reduction.

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Step 6: If the sum rate of each femtocell cannot achieve stable state, then go to step

1. If t> Tout or sum rate of all fBSs become is stabilized, terminate.

Remark: (i) This algorithm is performed within each fBS. (ii) The convergence condi-tion is that this fBS’s capacity variacondi-tion is less than 1%.

4.2.3 Algorithm of Subcarrier Assignment

Step 1: Initialize an l,k = 0,∀k ∈ {1, 2, .., K}, ∀l ∈ {1, 2..., Lk} and ∀n ∈ {1, 2..., N} and S ={1, 2...N} In l,k(0) = 0 Step 2: for k=1 to K while (|S| ≥ 1)

l⋆(n⋆) = arg maxl,ngnl,k(t) = arg maxl,n hn l,k/σ2 In l,k(t−1)+1, an⋆ l⋆_,k = 1, S = S\{n} end end

Remark: At the subcarrier allocation of the ﬁrst stage, we do not need to consider the interference of other fBS because no fBS decides their power allocation.

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4.2.4 Noncooperative Power Allocation Game

As the subcarrier assignment for all femtocells can be decided by previous section, the noncooperative resource allocation problem turns into a noncooperative power allocation game deﬁned as (p.2) max u(p_k, p_−k) = N ∑ n=1 an_l⋆⋆_,klog₂(1 + pn ⋆ kl⋆_,k(t)gn ⋆ l⋆_,k(t)) (4.7) subject to pn_kl⋆⋆_,k(t) ≥ 0 ∀l, n; (4.8) N ∑ n=1 pn_kl⋆⋆_,k(t) ≤ Pf em (4.9) pn_kl⋆⋆_,k(t) ≤ ¯P_man ∀l; (4.10)

The diﬀerence between (p.1) and (p.2) is that in (p.2), we use time index to distinguish the current parameters that fBS needs to solve with last iteration parameters. For example, the GINR of fMS l in femtocell k is deﬁned as

g_l,kn (t) = h n kl,k In l,k(t− 1) + σ2 = h n kl,k pn ml,k(t− 1)hnml,k+ ∑K

i=1,i̸=kpnil,k(t− 1)hnil,k+ σ2

(4.11)

where the interference from mBS and other fBSs is decided at the previous stage.

The solution of (p.2) can be derived easily via water ﬁlling, i.e., p_k = W Fk(p_−k),

∀k ∈ K, where the water-ﬁlling operator W Fk(·) on subcarrier n is deﬁned as [W Fk(p_−k)]n = pnl⋆_,k ={ 1 λk − σ 2₊∑K i=1,i̸=kp n il⋆_,khn_il⋆_,k hn kl⋆_,k }P¯n mac 0 ,∀n (4.12)

where (x)b_a, max{a, b} and λk is such that

N ∑ n=1

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4.2.5 Randomization

Due to the occurrences of oscillation, a procedure called randomization is called for to achieve convergence. We will discuss on what condition the oscillation happens and why randomization can reduce the probability of oscillation in the next chapter. Here, we propose two randomization schemes.

I Scheme 1

Step 0: Initialize a biased coin with head probability Pc by fBSs. If this randomization

is used again then skip this step.

Step 1: The fBSs start to toss coin if they meet oscillation. When tail occurs, those fBSs choose the fMS whose GINR is the second largest in the same femtocell; or remain using the same fMS with the largest GINR.

I Scheme 2

Step 0: Initialize a biased coin with head probability Pc by fBSs. If this randomization

is used again then skip this step.

Step 1: The fBSs start to toss coin if they meet oscillation. When tail occurs, those fBSs do not change strategy determined in the previous iteration; or remain using the strategy decided in this iteration.

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Chapter 5 Convergence and Unique NE point

We have discussed the noncooperative resource allocation game and algorithm in the previous chapter and we want to make sure whether our game can converge to a unique point. In [14][15], the authors prove that under some (sufficient) conditions on transmit powers, channels and network topology, the NE for game is unique. Since there is no reason to expect our system to be initially at the equilibrium, the concept of equilibrium has a useful meaning in practice only if one is able to find a procedure that reaches such an equilibrium from non-equilibrium states. Since we are interested in a decentralized implementation, where no signaling among different femtocells is allowed, we consider only totally distributed iterative algorithms, where each fBS acts independently of the others to optimize its own resource allocation while perceiving the other fBSs as interfer-ence. If we can meet the sufficient condition mentioned below, the NRAG can converge to the unique NE point.

5.1 Suﬃcient Condition for Unique NE Point

The convergence of our algorithm to a unique NE point is guaranteed under the following suﬃcient conditions.

Theorem: Assume that the following condition is satisﬁed:

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where Smax

KxKis deﬁned in (5.2) and ρ(SKxKmax) denotes the spectral radius of Smax. Then our algorithm can converges to the unique NE point of noncooperative resource allocation game for any set of feasible initial conditions and updating schedule.

S_KxKmax , { maxn∈Dk∩Di hn il⋆,kPi hn kl⋆,kPk , if k ̸= i 0, otherwise. (5.2) =        0 h n 2l⋆,1P2 hn 1l⋆,1P1 ... h n i−1l⋆,1Pi−1 hn 1l⋆,1P1 hn il⋆,1Pi hn 1l⋆,1P1 hn 1l⋆,2P1 hn 2l⋆,2P2 0 ... h n i−1l⋆,1Pi−1 hn 2l⋆,2P2 hn il⋆,2Pi hn 2l⋆,2P2 . . ... . . hn 1l⋆,iP1 hn il⋆,iPi hn 2l⋆,iP2 hn il⋆,iPi ... h n i−1l⋆,iPi−1 hn il⋆,iPi 0        (5.3)

There is still another suﬃcient condition for unique point given by one of the two following set of conditions:

∑ i̸=k max n∈Dk∩Di hn il⋆,kPi hn kl⋆,kPk < 1,∀k ∈ K (5.4) ∑ k̸=i max n∈Dk∩Di hn_il⋆,kPi hn kl⋆,kPk < 1,∀i ∈ K (5.5)

Condition (5.4) imposes a constraint on the maximum amount of interference that each receiver can tolerate. Condition (5.5) introduces an upper bound on the maximum level of interference that each transmitter is allowed to generate.

Proof: If we want to use the contraction mapping with ﬁxed point theory, the exis-tence of a NE for the game is guaranteed by the exisexis-tence of ﬁxed point for mapping T.

Given WF(p)=(W Fk(p_−k))k∈K

||WF(p(1)_)-WF(p(2)₎_{|| = ||T(p}(1)_)-T(p(2)₎_{|| ≤ β||p}(1)_{− p}(2)_{||, ∀p}(1)_{, p}(2) _{∈ P}

where|| || is a proper vector norm and β ∈ [0, 1), where β is deﬁned in the next page.

If the contraction mapping with β ∈ [0, 1) are satisﬁed, then ∥Smax

KxK∥∞ < 1. where β =∥Smax KxK∥∞ S_KxKmax , { maxn∈Dk∩Di hn il⋆,kPi hn kl⋆,kPk , if k ̸= i 0, otherwise. (5.6)

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1/SINR₁ 1/SINR₁ 1/SINR₂ 1/SINR₂ 1/SINR₂ 1/SINR₂ 1/SINR₁ 1/SINR₁

Case1: Subcarrier Oscillation Case2: Power Oscillation

Figure 5.1: Oscillation.

5.2 Non-Convergence of Distributed Approach

5.2.1 Causes and Cases of Oscillation

Why there exists oscillation? Here, we provide two different cases that cause oscil-lation. The first case is that fBSs find the GINR of some subcarriers is good, so the fBSs allocate more power on these subcarriers. In some femtocell the fMS with the best GINR is selected to use the subcarrier. When other fBSs allocate more power on these subcarrier, the fMSs with best GINR may suffer more severe interference than other fMSs in the same femtocell. In the next iteration, the fMS with the best GINR in the previous iteration may become worse because of severe interference and fMS with better GINR is selected to use the subcarrier in this iteration and other femtocells also have the same situation. Those fBSs allocate lower power on this subcarrier that may reduce the interference to nearby fBSs. Thus at next iteration, the GINR of this subcarrier in

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those femtocell also becomes better because the interference from other fBSs is reduced. Thus the user selection may change to the one before the previous iteration with the best GINR. The same condition iterates again and again that results in the oscillation of user selection in this subcarrier.

Another case is that at least two fBSs decide to transmit more power at the same subcarrier. But at next iteration, the GINR of this subcarrier of all fBSs decreases be-cause of increasing interference from other fBSs and power allocated on this subcarrier become less because of worst GINR of selected fMS. But at next iteration, the inter-ference from other fBSs decreases and the GINR of all fMSs become better than that in the previous iteration, so the fBSs allocate more power on this subcarrier with the selected fMS. The same condition repeats again and again so the game cannot converge to a stable state.

Here we show two simple cases. From Case 1 (depicted in Fig. 5.1), we ﬁrst choose fMS 1 to use the subcarrier because of better GINR. But at next iteration, fMS 1 suﬀers severe interference from other fBS than fMS 2 that the GINR of fMS 2 is better than fMS 1 in this iteration so the fBS in this cell chooses fMS 2 to use the subcarrier. However, because other fBSs also have the same condition at this iteration, they allocate less power on this subcarrier because of worse GINR. At next iteration, because the interference from other fBSs is reduced on this subcarrier, the GINR of fMS 1 is better than fMS 2, the fBS reselect the fMS 1 to use this subcarrier. The oscillation of user selection happens again and again.

As with Case 2 (depicted in Fig. 5.1), the oscillation in power allocation process happens within two or more fBSs. At ﬁrst the fMS 1 is selected with better GINR and allocated power. However, the same situation may happen in other femtocells so at next iteration the fMS1 is allocated less power because of worse GINR. At the next iteration, because the interference from other fBS is reduced, the same condition become as origin that the oscillation happens.

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5.2.2 Randomization for Reducing the Probability of

Oscilla-tion

Why randomization can reduce the probability of non-convergence? The reason is that when fBSs meet the oscillation and start to use the ﬁrst scheme of randomization, we use the second largest GINR to use the subcarrier. After water ﬁlling allocation, the allocated power on this subcarrier will decrease so the interference from this fBS or other fBSs may decrease. Thus the probability of Case 1 and Case 2 will be reduced. By second scheme of randomization, when the fBS does not change its strategy this iteration, then the interference from this fBS to other fBSs still remain the same. Thus the Probability of Case1 and Case 2 is also reduced and the illustration shown in Fig. 5.2.

5.2.3 Power Allocation with per Subcarrier Power Constraint

With the power upper bound, the power on all subcarriers of all femtocells are restricted. It is obvious that interference caused by every fBS to nearby femtocells can thus be reduced. In addition, the stricter the power upper bound is, the less occurrences of non-convergence happens. In the following part, we provide some explanations about this phenomenon and also use two possible cases as previous section with fBS1 and fBS2 located in a same femtocell.

Case 1 (depicted in Fig. 5.1)–the user selection oscillation. While the power upper bound employed on all fBSs, the interference level is controlled. So the user selection oscillation in Case 1 of ﬁgure1 will decrease because the interference from other fBSs is reduced and the GINR of fMS 1 is not easily worse than fMS 2. Thus oscillation of the user selection will be reduced obviously. Case 2 (depicted in Fig. 5.1)–the power allocation oscillation. While the interference from all fBS is reduced because of power upper bound, the probability of oscillation is also reduced.

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power upper bound. When our system does not consider the power upper bound, the power allocation obviously depends on the GINR of fMSs. However, when we add power upper bound on each subcarrier, as the power on subcarrier with the best GINR reach the power upper bound, then extra power is removed from this subcarrier and reallocated to other subcarriers not satisﬁed the restriction of power upper bound. As the power upper bound becomes more strict, more subcarriers easily satisfy the power upper bound and more extra power is removed to reallocated on the other subcarriers. As our power upper bound become too tight, power on each subcarrier satisﬁes the power upper bound easily and become equal on every subcarrier. Thus the power allocation become equal power without considering the GINR of fMSs. Under this condition, the oscillation of subcarrier and power allocation will gradually disappear because the oscillation is no more dominated by the interference.

The figures with the employment of different power upper bound are shown from Fig. 5.3 to Fig. 5.4, and the power allocation will gradually become without considering GINR no matter the GINR is good or not. In Fig. 5.4, we can find that as the power upper bound is set very tight, the power on each subcarrier becomes equal power so that the power allocation no more depends on the GINR.

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1/SINR₁ 1/SINR₁ 1/SINR₂ 1/SINR₂ 1/SINR₂ 1/SINR₂ 1/SINR₁ 1/SINR₁

Case1: Subcarrier Oscillation Case2: Power Oscillation

Randomization Randomization

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૚ Őϭ ૚ ŐϮ ૚ Őϯ ૚ Őϯ ૚ Őϰ ૚ ŐϮ ૚ Őϭ ૚ Őϰ

E

n

e

rg

y

E

n

e

rg

y

Index of subcarrier, n

૚ Őϭ ૚ ŐϮ ૚ Őϯ ૚ Őϰ

E

n

e

rg

y

Index of subcarrier, n

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૚ Ő_ϭ ૚ Ő_Ϯ ૚ Ő_ϯ ૚ Ő_ϯ ૚ Ő_ϰ ૚ Ő_ϰ ૚ Ő_Ϯ ૚ Ő_ϭ

E

n

e

rg

y

E

n

e

rg

y

Index of subcarrier, n

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Chapter 6 Numerical Results and Discussions

In this chapter we revisit the scenarios discussed in Chapter 2 and examine the nu-merical performance of our distributed algorithm applied to solve the femtocell resource allocation problems. The parameters of our simulation and path loss model are shown in table 6.1 and 6.2.

Parameter Value Parameter Value

Macrocell radius 1732 (m) Femtocell radius 10 (m)

mBS number 1 FBS number ϰ

mMS number 16 FMS number each

femtocell Ϯ Macrocell total power 43 dBm (20 Watt) Femtocell total power 23dBm (200mW) System bandwidth ϭϬD,ǌ Number of subcarriers ϭϮϴ Subcarrier bandwidth ϳϴ͘ϭϮϱ<,ǌ EŽŝƐĞƉŽǁĞƌ ƐƉĞĐƚƌƵŵĚĞŶƐŝƚǇ ͲϭϳϰĚŵͬ,ǌ EŽŝƐĞĨŝŐƵƌĞŽĨ ŵĂĐƌŽĐĞůů ϱĚ EŽŝƐĞĨŝŐƵƌĞŽĨ ĨĞŵƚŽĐĞůů ϴĚ

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WĂƚŚůŽƐƐŵŽĚĞůƐĨŽƌƵƌďĂŶ;ĚĞŶƐĞĂƉĂƌƚŵĞŶƚͿĚĞƉůŽǇŵĞŶƚ

ȋȌ

 ȋȌα͵ͺǤͶ͸ΪʹͲͳͲ  ȋȌαȋͳͷǤ͵Ϊ͵͹Ǥ͸ͳͲǡ͵ͺǤͶ͸Ϊ ʹͲͳͲȌΪȗ  ȋȌαͳͷǤ͵Ϊ͵͹Ǥ͸ͳͲΪȗ  ȋȌαͳͷǤ͵Ϊ͵͹Ǥ͸ͳͲ  ȋȌαͳͷǤ͵Ϊ͵͹Ǥ͸ͳͲΪȗ ǦȋȌ >ŽǁŝƐƚŚĞƉĞŶĞƚƌĂƚŝŽŶůŽƐƐŽĨĂŶŽƵƚĚŽŽƌǁĂůů͕ǁŚŝĐŚŝƐϭϬĚ α α α

Table 6.2: Pathloss model.

1 2 3 4 5 6 7 8 9 10 11 0 2 4 6 8 10 12 14 16 18 20 X: 2 Y: 18.03 Iteration Femtocell Capacity(bit/s/Hz/subcarrier)

Femtocell Capacity versus Iteration Numbers with femtoblock=50m

X: 4 Y: 18.13 X: 3

Y: 18.13

Total Sum Capacity of all fBSs Capacity of fBS 1

Capacity of fBS 2 Capacity of fBS 3 Capacity of fBS 4

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1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 14 16 18 Iterative numbers Femtocell Capacity(bit/s/Hz/subcarrier)

Femtocell Capacity versus Iteration Numbers

Total Sum Capacity of all fBSs Capacity of femtocell 1 Capacity of femtocell 2 Capacity of femtocell 3 Capacity of femtocell 4

Figure 6.2: Nonconvergence Case of Noncooperative Game.

1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16 18 Iterative numbers Femtocell Capacity(bit/s/Hz/subcarrier)

Femtocell Capacity versus Iteration Numbers

Capacity of femtocell 1 Capacity of femtocell 2 Capacity of femtocell 3 Capacity of femtocell 4 Total Sum Capacity of all fBSs

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0 0.5 1 1.5 2 2.5 x 10−3 3 3.2 3.4 3.6 3.8 4 4.2 4.4

Power Upper Bound of fBS per Subcarrier (W)

Iteration Numbers

Iteration Numbers under Different Power Upper Bound

Figure 6.4: Iteration number with diﬀerent power upper bound.

Fig. 6.1 shows the capacity tendency of normal case. But in Fig. 6.2, we ﬁnd some-times the non-convergence case may happen with our distributed algorithm. However, with several variation reduction approaches, the non-convergence case can be reduced obviously and shown in Fig. 6.3.

From Fig. 6.4, while the power upper bound of our system is tight, the allocated power on all subcarrier becomes equal that is discussed in chapter 5. We ﬁnd that as the

power upper bound is under 1.5x10−3, the power allocation on all subcarriers is equal.

At the third iteration, all fBSs do not change the power allocation and the interference from other fBSs remains the same so fBSs ﬁnish the game. As the power upper bound is

above 1.5x10−3, the power allocation varies on diﬀerent subcarriers and the interference

from diﬀerent fBSs may aﬀect the power allocation of all fBSs that leads to increasing iteration numbers of noncooperative game.

If our fBSs ﬁnd oscillation and start to use randomization, the requirement of itera-tion numbers from using randomizaitera-tion to convergence is shown in Fig. 6.5 and Fig. 6.6.

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0.1 0.3 0.5 0.7 0.9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Probability of Using Randomization 1

Iteration Numbers

Iteration Numbers versus Probability of Using Randomization 1

Figure 6.5: Iteration numbers versus probability of using randomization 1.

0.1 0.3 0.5 0.7 0.9 0 0.5 1 1.5 2 2.5 3 3.5 4

Probability of Using Randomization 2

Iteration Numbers

Iteration Numbers versus Probability of Using Randomization 2

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1 2 3 4 5 6 7 8 9 10 11 0 5 10 15 20 25 X: 2 Y: 24.04 Iteration Femtocell Capacity(bit/s/Hz/subcarrier)

Comparison of Femtocell Capacity

X: 2 Y: 17.91 X: 3 Y: 18.02 X: 4 Y: 18.02 Centralized Approach Distributed Approach

Figure 6.7: Comparison of Femtocell Capacity.

From the illustrations we can realize that if the probability of using randomization is few, the oscillation still happens that causes more iteration numbers to converge. In other words, the iteration numbers can be reduced if the fBSs use randomization frequently.

In Fig. 6.7, we want to compare the femtocell capacity with two different approaches: one is centralized algorithm, the other is distributed method. The centralized approach is exhausted research that requires all combinations of user selection with jointly iterative power allocation solved by convex-optimization soft cvx. As shown in the illustration, the centralized approach can gain 25% bandwidth efficiency than distributed method. Though centralized approach can achieve higher bandwidth efficiency, high computa-tional complexity and knowing all information are impractical in the practical system.

Finally, we want to investigate the femtocell capacity with power upper bound im-posed on the fBSs. From Fig. 6.8, we can ﬁnd the femtocell capacity near the mBS is lower than that far from mBS because the fBSs near mBS suﬀer more macrocell in-terference. However, the femtocell capacity at distance 1500 is also lower than that at

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0 5 10 15 20 25 30 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 SIR constraints of mMSs (dB) Femtocell Capacity(bits/sec/Hz/subcarrier)

Femtocell capacity versus SIR constraints of mMS with different total power constraints

Distance of femtoblock=50 Distance of femtoblock=300 Distance of femtoblock=700 Distance of femtoblock=1500

Figure 6.8: Femtocell capacity versus SIR constraints of mMS with diﬀerent power constraints.

distance 300 and 700. The reason is that the fBSs at distance 1500 have been imposed strict power upper bound to protect the QoS of mMSs and are allocated equal power on all subcarriers that cause less capacity than water filling power allocation. As the requirements of mMSs’ QoS increase, all fBSs are imposed more strick power upper bound on all subcarriers. The fBSs at location 50 suffer not only noise power but also severe interference from macrocell, so the femtocell capacity decreases rapidly. The fem-tocell capacity at different distance does not decrease rapidly because the interference is mainly dominated from other fBSs and larger than power noise. Only when the power upper bound is too tight that the noise power also affects the SINR of fBSs, the femtocell capacity decreases as the requirement of mMSs’ SIR achieves 30 dB.

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Chapter 7 Conclusion

Femtocell network can eﬀectively enhances indoor coverage and provides high data rate for indoor users due to the short distance between fBS and fMSs. However, how to manage interference between macrocell and femtocell network is a critical issue. One of our goal in this thesis is to ﬁnd a solution of interference management problem without information about channel conditions and locations of mMSs. Then resolve the downlink resource allocation problem for femtocell by distributed approach in the femtocell and macrocell overlay network.

First, we propose average outage probability constraint for fBS as a criterion to protect the QoS of mMSs. However, without assuming perfect information about channel conditions and locations of mMSs, calculating the average probability constraint is a difficult task for fBSs. Thus, we provide the closed form outage probability with fixed locations of mMSs and fBSs in chapter 3. After finding the outage probability of fixed locations of fBSs and mMSs, we can find the outage probability with two different schemes: one is distributed locations of fBSs, the other is fBSs fixed in femtoblock. At last, we can find the the maximum acceptable power of fBSs from the average outage probability constraint.

The distributed approach is proposed to solve the resource allocation problem in an OFDMA-based femtocell overlay network. Regarding the distributed RA as a

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non-cooperative game, the sufficient condition for existence of a Nash equilibrium point is provided. On the other hand, several variation reduction remedies are provided to re-duce the non-convergence probability of resource allocation. We also try to interpret the convergence of our algorithm and the remedies. Finally, the simulation shows the bandwidth efficiency of femtocell system is influenced by power upper bound and mutual interference of fBSs.

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Bibliography

[1] Femto forum. http://www.femtoforum.org.

[2] Y. Bai, J. Zhou, L. Liu, L. Chen, and H. Otsuka, “Resource coordination and in-terference mitigation between macrocell and femtocell,” in Proc. PIMRC, Tokyo, Japan, pp.1401-1405, Sept. 2009

[3] D. Lopez-Perez, A. Ladanyi, A. Juttner, and J. Zhang, “OFDMA femtocells: a self-organizing approach for frequency assignment,” in Proc. PIMRC, Tokyo, Japan, pp.2202-2207, Sept. 2009

[4] K. Han, Y. Choi, D. Kim, M. Na, S. Choi, and K.Han, “Optimization of femto-cell network conﬁguration under interference constraints,” in Proc. WIOPT, Seoul, Korea, pp.1-7, June 2009

[5] V. Chandrasekhar, and J. G. Andrews, “Uplink capacity and interference avoidance for two-tier femtocell networks,” IEEE Trans. Commun., vol.8, pp.3498-3509, July 2009

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[8] Hojoong Kwon, and Byeong Gi Lee, “Distributed Resource Allocation through Non-cooperative Game Approach in Multi-cell OFDMA Systems,” in Proc. IEEE ICC, June 2006, pp. 4345V4350.

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毫微微細胞覆蓋式正交分頻多工網路之分散式資源分配

國 立 交 通 大 學

電信工程研究所

碩 士 論 文

毫微微細胞覆蓋式正交分頻多工網路之分

散式資源分配

Distributed Resource Allocation in an

OFDMA-based Femtocell Overlay Network

研究生：

黃泓錫

指導教授：

蘇育德 博士

毫微微細胞覆蓋式

正交分頻多工

網路之

分散式資源分配

Distributed Resource Allocation in an

OFDMA-based Femtocell Overlay Network

研 究 生：黃泓錫 Student：Hung-Hsi Huang

指導教授：蘇育德 博士 Advisor：Dr. Yu T. Su

國 立 交 通 大 學

電 信 工 程 研 究 所

碩 士 論 文

毫微微細胞覆蓋式

毫微微細胞覆蓋式

毫微微細胞覆蓋式

毫微微細胞覆蓋式

正交分頻多工網路之

正交分頻多工網路之

正交分頻多工網路之

正交分頻多工網路之

分

分

分

分

散式資源分配

散式資源分配

散式資源分配

散式資源分配

研究生

研究生

研究生

研究生:

::

:黃泓錫

黃泓錫

黃泓錫

黃泓錫

指導教授

指導教授

指導教授

指導教授

:

:

: 蘇育德

:

蘇育德

蘇育德

蘇育德

博士

博士

博士

博士

國立交通大學電信工程學系碩士班

國立交通大學電信工程學系碩士班

國立交通大學電信工程學系碩士班

國立交通大學電信工程學系碩士班

中文

中文

中文

中文摘要

摘要

摘要

摘要

毫微微蜂巢式網路(femtocell)具有延伸網路涵蓋範圍、提昇網路傳輸容

量、增加服務品質等優勢，此外也可以補強大型基地台（macrocell）無

法涵蓋的區域和死角，並減輕其頻寬負荷。即使毫微微蜂巢式網路有上述

好處，

為了保持大型網路使用者的傳輸品質，這些

毫微微蜂巢式網路皆

國立交通大學

碩士論文

蘇育德博士

研究生：黃泓錫 Student：Hung-Hsi Huang

指導教授：蘇育德博士 Advisor：Dr. Yu T. Su

國立交通大學

電信工程研究所

碩士論文

首先要感謝指導教授蘇育德博士，老師除了在研究上諄諄教誨，做人