在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

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國

立

交

通

大

學

電信工程研究所

碩

士

論

文

在裝置對裝置通訊網路下鄰近搜尋及自我連結建立

之設計與分析

Proximity Discovery and Autonomous Link Setup

in D2D Communication Networks

研究生：林晏陞

指導教授：蘇育德教授

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在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

Proximity Discovery and Autonomous Link Setup in D2D Communication

Networks

研究生：林晏陞 Student：Yen-Sheng Lin

指導教授：蘇育德 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 the Institute of Communications Engineering in Partial Fulfillment of the Requirements

for the Degree of Master of Science

in

Communications Engineering at the

National Chiao Tung University

July 2012

Hsinchu, Taiwan

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在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

學生：

林晏陞

指導教授

：蘇育德博士

國立交通大學電信工程研究所碩士班

摘

要

在傳統的蜂巢式網路底下，連結的建立必須經由基地台和核心網路的幫助。假如裝置對裝置(D2D)具有相對近距離的情況下，蜂巢式網路在多節點跳躍、路由、網路負載或延遲及功率的效能上可能會比D2D連結不具效率。對於在蜂巢式網路底下自動的D2D通訊可以減輕基地台和核心網路的負載並且藉由好的直接連結，可以增強頻譜使用效率和網路吞吐量。

對有效率的 D2D 通訊來說，裝置必須可以追蹤它的周遭環境和尋找適合可以做連結的裝置，在論文中，我們提出了一個裝置對裝置連結建立的流程可以促使裝置建立可靠 D2D 的連結並且在傳送訊號時不能對蜂巢式網路造成過大的干擾。基於提出的流程及相關的訊號品質要求，假設裝置分別由泊松點過程 (PPPs)模型下產生，我們分析成功的 D2D 連結建立(SDLS) 機率。一個精確的干擾表示式是非常複雜的，因此我們分別利用近似和上限的情況，用 PPP 去描述對蜂巢式使用者所造成的干擾源位置並計算相對應蜂巢式使用者的訊號與干擾加雜訊比，在這兩種情況下，SDLS 機率對於傳送功率是一擬凹 (quasiconcave)函數，同時也提出二分法搜尋的上下界，這可以使我們加快演算法的收斂速度並證明在我們所搜尋的區間存在著唯一的最佳探詢訊號的功率。

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Proximity Discovery and Autonomous Link Setup in

D2D Communication Networks

Student : Yen-Sheng Lin Advisor : Yu T. Su

Department of Communications Engineering National Chiao Tung University

Abstract

Conventional cellular networks require that a link be setup through the aids of base stations and the associated core network. It is very ineﬃcient either in terms of required multi-hop link setup, routing and other network overheads or from the viewpoint of delay and power performance if the associated physical device-to-device (D2D) link is in relatively good condition. Autonomous D2D communication as an underlay to an existing cellular network reduces the base stations (eNBs) and core network’s loadings while enhancing the spectral eﬃciency and network throughput by taking the advantage of good direct link qualities.

For eﬃcient D2D communications, a device must be able to track its local environ-ment and discover suitable connecting devices within a short time span. In this thesis, we propose a D2D link setup protocol that enables a device to establish a reliable D2D link using proper radio resources while causing only tolerable interference to the under-laid cellular network. We analyze the success D2D link setup (SDLS) probability based on the proposed protocol and related signal quality requirements, assuming devices are distributed according to some two dimensional Poisson point processes (PPPs). As the exact expression for the sum interference is very complicated, we use an approximation model and an upper bound to describe the active devices’ location distribution in evalu-ating the signal-to-noise-plus-interference ratio of a macrocellular terminal. Using either

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one in computing the SDLS probability, we show that it is a quasiconcave function of the device’ transmit power. We apply a bisection search with the help of the derived upper and lower search bounds to accelerate the search and prove that the existence of the optimal solution.

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誌

謝

一開始我要感謝指導教授蘇育德博士在短短的碩士兩年生活中，不僅是在研究方面的指導，使得碩士論文能夠更加順利的完成，還教導我許多讓我生活中受用的知識，使我在路途中不會迷失了自己的方向。感謝口試委員蘇賜麟教授、呂忠津教授以及林茂昭教授在口試中給予相當多寶貴的意見，以補足在我研究中的不足之處。我也要感謝實驗室的學長姐、同學及學弟妹的幫助與鼓勵，其中要特別感謝的是指導我的博士班研究生劉人仰學長的細心教導，還有張致遠及劉彥成博士學長給予的鼓勵，讓我在研究過程中學習到做研究的態度以及做研究需要注意的地方。最後我要感謝在身邊關心我的家人、朋友以及女朋友，沒有他們在背後的支持，沒有他們在我做研究後的時間陪我聊天，我無法這麼順利的完成碩士生活，也因為有了他們的笑臉與鼓勵，給予了我前進的動力，僅獻上此論文來表達我最深的敬意。林晏陞謹致于新竹國立交通大學

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List of Figures

1.1 D2D communications are an underlay to a cellular network. . . 2

2.1 BPP with bounded set S = [0, 1]× [0, 1], n = 100. . . 10

2.2 PPP with set S = [0, 1]×[0, 1]; left side: homogeneous, λ=100; right side: inhomogeneous, λ(x, y) = 200y. . . . 11

2.3 The connection setup procedure of Bluetooth devices. . . 15

2.4 Device roles in the ZigBee standard. . . 17

3.1 System model of D2D communications underlays a cellular network. . . . 19

3.2 The ﬂow chart of SDLS procedure. . . 22

4.1 BPP model of D2D communications underlays cellular network. . . 25

4.2 Reliable and interference ranges of the active device. . . 27

4.3 The illustration of the intersection area between two circles. . . 28

4.4 Probability-based reliable and interference ranges of an active device. . . 32

4.5 SDLS probability as a function of radius of coverage range rd. . . 36

4.6 SDLS probability as a function of received device number Nd. . . 37

4.7 SDLS probability as a function of distance d_tx (between the active device and eNB). . . 38

4.8 SDLS probability as a function of ζ (ratio between θd and I_min(CU) N₀ ). . . 38

5.1 A two-dimensional network in which multiple active devices share the spectrum with CUs whence result in aggregated interference to the latter. 40

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5.2 pLS is not a concave function. . . 48

5.3 The intersection between z axis and f(z) (one solution). . . 50 5.4 SDLS probability (pLS) performance as a function of the active device

transmit power PD in the upper bound scenario. . . 54

5.5 SDLS probability (pLS) performance as a function of busy probability β

of received device in approximate scenario. . . 55 5.6 SDLS probability (pLS) performance as a function of received device

in-tensity λd in approximate scenario. . . 55

5.7 SDLS probability (pLS) performance as a function of noise power N0 in

approximate scenario. . . 56 5.8 SDLS probability (pLS) performance as a function of the number of RB

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List of Tables

1.1 Summary of Notations . . . 7 4.1 Simulation Parameters under BPP . . . 35 5.1 Simulation Parameters under PPP . . . 52

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Chapter 1 Introduction

The ever increasing demands for multimedia services have made the shortage of the radio resources a very challenge problem in the cellular network (CN) design and deployments. Device-to-device (D2D) communications as an underlay coexistence with CN has been proposed to overcome the resource shortage problem and improve the network throughput. It is a proximity-based technology enabling the cellular devices to communicate with each other directly. Because D2D devices share the same resources with CN, the resulting devices-to-CUs interference is of paramount concern. Therefore, the devices need to limit the interference causing to CN.

1.1 Concept of D2D Communications

In early 2006, Qualcomm began a project that wanted to exploit D2D communica-tions. The idea was that devices would communicate directly with each other without the need for intermediary infrastructure. The motivation of this idea was quite simple. It is evidently resource ineﬃcient for two proximate devices to communicate via evolved NodeB (eNB). One obvious way to serve some of this demand is to enable direct commu-nications between proximate devices. There is an ongoing discussion on proximity-based services (ProSe) in Long term Evolution-Advanced (LTE-A).

The concept of D2D communications as an underlay to a CN is illustrated in Fig. 1.1. It operates on the same radio resources with CN. Besides cellular operation, where user

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Figure 1.1: D2D communications are an underlay to a cellular network.

is served by eNB in the LTE architecture, device may want to communicate with each other over D2D link. The device in D2D link remains controlled by eNB and cellular operation user. The eNB can control the resources used for D2D link and cellular operation. The eNB also can set up the constraints on the maximum transmit power of D2D transmitters to limit the interference experienced at the cellular user (CU). In the case of a high loading LTE-A network, resources may also be assigned to D2D links. However, cognitive radio (CR) with a CN as the primary service would not have ability to detect locally unused spectrum perfectly.

D2D communications have three types of gains.

1. Proximity of device: provide for relatively high transmission rates, low propagation delays and low transmit power consumption [1].

2. Reuse gain: because the radio resources may be simultaneously used by CN and D2D links, tightening the reuse factor even in a reuse-1 system [2].

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the cellular mode, the both an uplink and a downlink resource are used when communicating via eNB.

But D2D communications still have some disadvantages, it would cause munch overhead and interference to CN when the number of devices is very large. It would decrease the CUs’ performance.

The applications of D2D communications lie mainly in three categories: commer-cial/social use, network oﬄoading, and public safety. Some details can be seen in [3].

1.2 Other Communication Standards

In this section, we describe some existing local (short distance) communication stan-dards which have some features and encounter problems similar to what D2D communi-cations might have. Wireless local area network (WLAN) and Bluetooth both operate in the licenfree industrial, scientiﬁc and medical (ISM) bands, so they maybe meet se-vere interference and no hard quality of service (QoS) guarantees. D2D communication operates in the licensed bands, so it can support interference-controllable and reliable communication. Nevertheless, when users utilize D2D communication service, they need be charged.

A wireless ad-hoc network is a self-conﬁguring wireless network. Namely it does not rely on a preexisting infrastructure. But D2D communication can be controlled by eNB. CR technology is seen as the solution to the problem of low usage of the licensed spectrum. It has been proposed to exploit the spectrum holes–the frequency bands which are not used at some time or space–for license-exempt usages [4]. It has the same goal with D2D communication: to increase spectral eﬃciency. D2D device transmits data signals directly to each other by reusing the cellular network resources, similar to the secondary user (SU) scenario introduced in CR systems. However, with D2D communication can be controlled in cooperation with CNs, whereas the SU in CR systems is not controlled by the primary user (PU) networks [5, 6].

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Machine-to-Machine (M2M) and D2D communication are two important technology trends. M2M is the communication that devices communicate without direct human interaction. D2D communication is the direct link communication between devices which use the cellular spectrum.

Wi-Fi Direct is an application of D2D communications. It allows Wi-Fi devices that can connect to each other without the help of a wireless access point (AP).

1.3 Overhead

Before the two devices can communicate over D2D link, they need to discovery each other which is close. In this section, we study why we consider an autonomous D2D link setup scheme. Supporting a massive number of D2D communications is an unavoidable trend. When establishing an air interface, a device needs to execute random access at random access channel (RACH). But there are few RACHs, supporting a massive random access requests will cause many collisions. Access class barring (ACB) is one of the solutions to combat this problem of RACH [7]. According to the idea of ACB, eNB control u (u is the probability that the device can execute random access at RACH) to let average simultaneous accesses at a common channel to be one. When the number of device is very large, u is relatively small. There will be an unacceptable waiting time for devices. If the device is located at cell edge, the aid of eNB is seen impossible in this case. There may exist a blind vision between eNB and device. Even if the two device are close to each other, they can not communicate with each other directly due to the limitation of eNB. In order to reduce the overhead of eNB and avoid problems as mentioned above, we discuss the autonomous D2D link setup scheme. The eNB will broadcast the message to devices if some RBs are interfered. The devices need to stop transmission. But how to charge the device which uses the D2D communication is a important commercial problem. Here, we don’t discuss this issue. There is also an example to motivate us to consider D2D link setup automatically. FlashLinQ [8] is a proximity-aware technology

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which has been proposed by Qualcomm. The device discovery protocol is a synchronous OFDM-based physical layer. It allows the device to discover other FlashLinQ enabled devices automatically. More details about FlashLinQ are described in the next chapter.

1.4 Literatures Review and Motivation

There exists a problem in D2D communication. Before the two devices can directly communicate with each other, they must discovery that they are close to each other. Most of works on D2D communication have mainly focus on the resource allocation, power control, and mode selection schemes [9-17]. However these works have an unrea-sonable assumption, D2D link has been already set up and most of them only consider a single D2D pair which coexists with CN. Only few works focus on link discovery [18-20]. Therefore, we need to consider multiple D2D pairs, focus on D2D link setup procedure, and how to ﬁnd the usable radio resources such that the interference cause to CN is acceptable.

There are three common technologies that have proximity discovery. There are Blue-tooth, FlashLinQ and Wi-Fi Direct. Because the proximity discovery in Bluetooth is a low-level radio channel to discovery, we apply the concept of proximity discovery in Bluetooth. The environment that we consider is a multi-devices system. The traditional proximity discovery in Bluetooth seems to be very week. Therefore, we need to consider a adequate proximity discovery scheme to make multi-devices communications possible. In our thesis, we consider that there is a single probing channel to support proximity discovery. There will be a very high collision probability. In order to achieve high D2D link setup performance, a multiple probing channels scheme is necessary in future work.

1.5 Contributions

We analyze the success D2D link setup (SDLS) probability under two diﬀerent point processes describing the locations of communication terminals, namely, the Binomial

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point process (BPP) and the Poisson point process (PPP). The point process is used to model the locations of CU and devices. We propose a D2D link setup scheme. Based on this scheme, we analyze the SDLS probability with the help by some mathematical functions and stochastic geometry. Under BPP model, we consider a quite simple case here. The deterministic and stochastic also covered in our analysis. We obtained the close-form of SDLS probability without channel fading eﬀect. But in stochastic scenario, the performance is evaluated by numerical method. Under PPP model, we respectively use an approximate scenario and a upper bound scenario to model the interference sources which are generated by PPP and let the SDLS probability as an optimization problem in upper bound scenario. The goal is to ﬁnd the optimal transmit power PD of

active device to maximize the SDLS probability. We prove that the objective function is quasiconcave and use the bisection method to ﬁnd the only optimal solution. We also ﬁnd a scheme to set up the upper limit of this method. However, the optimal transmit power P_D∗ is based the parameters of wireless environment. Therefore, the power control is needed in active devices to make the SDLS probability larger.

1.6 Thesis Structure

The rest of this thesis is organized as follows. In chapter 2, we review the point process, some mathematical tools, and connection setup procedure for some existing wireless communication standards. The following chapter 3 introduces system model and the procedures to set up a D2D communication link. SDLS analysis and analytical results under Binomial point process and Poisson point process models are described respectively in chapter 4 and chapter 5. Finally, we draw our conclusion and future work in chapter 6. In the table 1.1, we give some symbol descriptions of our thesis.

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Table 1.1: Summary of Notations

Symbol Description

Rd _{d-dimensional space}

R+ _{positive real numbers}

A∩ B the intersection of set A and set B

P(A) probability of event A

E(X) expectation of random variable X

α path loss exponent

d number of dimensions of the network

|A| Lebesgue measure of set A. For d = 1, 2, or 3, it consists with the standard measure of length, area, or volume.

· Euclidean norm

cd volume of the d-dim. unit ball

LX(s) = E(e−sX) Laplace transform of random variable X

Φ ={Xi} ⊂ Rd point process

FX(x) =P(X ≤ x) cumulative distribution function of random variable X

PD common transmit power of active devices

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Chapter 2 Preliminaries

The signal-to-interference-plus-noise-ratio (SINR) is the primary signal quality met-ric that must be satisﬁed by a communication link. The interference is an important term in wireless network. However, it is a function of network topology, path loss, and channel fading eﬀect. There are two main tools to help us analyze the interference: stochastic geometry [21] and random geometric graphs [23]. Because the nodes appear-ing in the wireless network may follow some spatial distribution, stochastic geometry is useful in modeling the network topology, and analyzing the average behavior over many spatial realizations of a network. Then, we will introduce some concepts about stochastic geometry. They called it point process (PP). Later, there will be some math-ematical tools and functions to help us compute some properties that we are interested in of wireless communication systems. Finally, the connection procedure of some wire-less communication standards such as FlashLinQ, Bluetooth, WLAN, and ZigBee are introduced.

2.1 Point Process

In the stochastic geometry, the basic objects are point processes. A PP can be described as a stochastic collection of points in the space. For a detailed concept and analysis of PP, readers can refer to [21-22, 24]. Why do we consider the PP? When we describe the locations of nodes, a PP can be used to model these nodes on the space

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that we are interested in. It can help us do some mathematical analysis of the wireless network.

φ(B) denotes the number of points of φ in B ⊂ Rd. N denotes the smallest sigma algebra such that the mappings φ→ φ(B) are measurable for all Borel sets B ⊂ Rd. Deﬁnition 1 (Point process, [24]) It is a measurable mapping function Φ onRd_from

the probability space (Ω,A, P) to (N, N ).

Φ : Ω→ N (2.1)

A point process is a stochastic variable which takes the values in the set of the sequences N. There are some terminologies about PP Φ in the following.

1. If a PP is said to be simple ⇒ no two points with the same location (at most one point at a location).

lim

|A|→0

P(Φ(A) ≥ 1)

P(Φ(A) = 1) = 1 (2.2)

where Φ(A) is the number of points in set A.

2. If a PP is said to be stationary ⇒ the regulation of the PP is invariant by trans-lation.

Φ + s ={u + s|u ∈ Φ} ∼ Φ, s ∈ Rd (2.3)

3. If a PP is said to be isotropic ⇒ the regulation of the PP is invariant by rotation. RΦ ={Ru|u ∈ Φ} ∼ Φ ∀R ∈ Md×d ={d × d Orthogonal Matrix} (2.4)

where R denotes the rotation around the origin.

If the PP is both stationary and isotropic, it is also called a motion-invariant PP. Deﬁnition 2 (Intensity Measure, [24]) The intensity measure of the PP Φ is equal to the average number of points in the set B ⊂ Rd_.

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0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 2.1: BPP with bounded set S = [0, 1]× [0, 1], n = 100.

If Φ is a stationary PP, then Λ(B) = λ|B| where λ is called the intensity of Φ.

Deﬁnition 3 (Probability Generating Functional, [24]) Let ψ(x) : Rd → [0, ∞)

be measurable. The probability generating functional (PGFL) of the PP can be defined.

G(ψ) =E x∈Φ ψ(x) (2.6)

The subsequent subsections will introduce two types of PP, namely Binomial point process (BPP) and Poisson point process (PPP).

2.1.1 Binomial Point Process

In a bounded domain, the BPP is generally used to construct the location of wireless nodes with a ﬁxed number n. It is a quite simple point process. The n points are inde-pendently and uniformly distributed in a bounded and closed set B ⊂ Rd_{(d-dimensional}

space). The BPP can be illustrated in Fig. 2.1. The probability that there are k points in A⊂ B is given by P(Φ(A) = k) = n k |A| |B| k 1− |A| |B| n−k (2.7) where Φ(A) is deﬁned as the number of points in set A and |A| stands for the Lebesgue measure of the set A.

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0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 2.2: PPP with set S = [0, 1]× [0, 1]; left side: homogeneous, λ=100; right side: inhomogeneous, λ(x, y) = 200y.

Note that the Φ(A) and Φ(B) are not independent even if A∩B = ∅. This property makes the analysis of the received interference in the wireless network more diﬃcult.

The PGFL of BPP Φ is equal to G(ψ) = 1 |A| A ψ(x)dx n (2.8)

2.1.2 Poisson Point Process

The PPP is a most well-studied point process. Its importance comes from its ease to analyze. Therefore, the PPP provides a handy computational framework for diﬀerent performance metric of interest.

1. If a PP is said to be a homogeneous PPP ⇒ the value of intensity keeps the same across space. It is isotropic and stationary process. It may be the simplest point process. It can be illustrated on the left side in Fig. 2.2.

2. If a PP is said to be an inhomogeneous PPP ⇒ the value of intensity doesn’t keep the same across space, and it can be used to model the distribution with non-uniform type across space. Like in a city, the intensity is not the constant everywhere. It can be illustrated on the right side in Fig. 2.2.

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The homogeneous PPP Φ with intensity (or density) λ is characterized by the below properties:

1. For all the disjoint sets A1, . . . , Ak, the random variables Φ(Ai) are independent.

2. All the random variables Φ(Ai) are Poisson random variables with mean λ|Ai|.

P(Φ(A) = k) = e−λ|A|(λ|A|)k

k! (2.9)

Conditioned on the fact that there are n points in set A, the n points are independently and uniformly distributed in set A, namely BPP. There are some important properties of the PPP as the following.

1. The superposition of two or more independent PPPs with intensities λ₁, . . . , λk is

also a PPP with intensity Σk i=1λi

2. The independent thinning of the PPP with intensity λ results in independent PPPs with intensity κiλ such that

K

i=1κi = 1.

3. If Φ is a homogeneous PPP with unit intensity (λ=1), then λ−1/dΦ is a homoge-neous PPP with intensity λ.

4. The PGFL of PPP Φ is equal to G(ψ) = exp − Rd (1− ψ(x))Λ(dx) (2.10)

2.2 Mathematical Tools

2.2.1 Gamma Function

The deﬁnition of Gamma function is given by

Γ(a) _∞

0

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Corollary 1 (Convex, [24]) When X is a exponential random variable with unit mean, then the m-th moment of X is given by

E[Xm ] = Γ(1 + m) (2.12) Proof: E[Xm_{] =} _∞ 0 xme−xdx = _∞ 0 x(m+1)−1e−xdx = Γ(1 + m)

There is an important functional equation: Euler’s reﬂection formula. Γ(1− a)Γ(a) = π

sin(πa) (2.13)

2.2.2 Other Function

Deﬁnition 4 (Convex, [25]) A function f is convex if and only if _{dom f is convex} and for any x, y ∈ dom f and 0 ≤ θ ≤ 1,

f (θx + (1− θ)y) ≤ θf(x) + (1 − θ)f(y) (2.14)

If f is convex, −f is concave.

Deﬁnition 5 (Quasiconvex, [25]) A function f is quasiconvex if and only if _{dom f} is convex and for any x, y ∈ dom f and 0 ≤ θ ≤ 1,

f (θx + (1− θ)y) ≤ max{f(x), f(y)} (2.15)

If f is quasiconvex, −f is quasiconcave.

Consider a d-dimensional homogeneous PPP with intensity λ. Let’s determine the distance D between the device k and its nearest neighbor. The cumulative distribution function (CDF) of random variable D:

FD(x) = P(D ≤ x) = 1 − P(D > x)

= 1− P(there exist no other devices in ball centered at the device k with volume cdxd)

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where cd is the volume of the d-dimensional unit ball and deﬁned in the following. cd ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ πm2 (m 2)! , for even d πd−12 2d₍d−1 2 )! d! , for odd d (2.17)

Therefore, the probability density function (PDF) of D: fD(x) =

d

dxFD(x) = λcddx

d−1

exp(−λcdxd) (2.18)

For example, by letting d=2, then fD(x) = 2λπx exp(−λπx2) and FD(x) = 1−exp(−λπx2).

2.3 Connection Setup Procedure

In this section, we describe how these local wireless communication standards (Flash-LinQ, Bluetooth, WLAN, and ZigBee) perform connection setup respectively.

2.3.1 FlashLinQ

It is a synchronized device device discovery operation [26, 27]. All devices are synchronized to an external time resource. The device uses a small fraction of time-slots to discover the existence of other nodes in the neighborhood. Every device sends its own discovery signal and listens to other discovery signals from other devices to detect the device of interest in the proximity periodically. All devices are required to play a part in device discovery even if they are not active.

There are 5600 logical channels for device discovery and repeats every 8 seconds. The question is how to pick the logical channel in a distributed way. Carrier sensing is a way to pick the logical channel.

2.3.2 Bluetooth

Bluetooth is a short-range technology which operates in the 2.4 GHz ISM band. The transmission range of Bluetooth is about 10 meters, and its signals do not require line-of-sight (LOS) which can pass through most physical barriers. The procedures of

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Figure 2.3: The connection setup procedure of Bluetooth devices.

Bluetooth connection setup can be divided into two steps: Bluetooth device discovery and connection setup. In Fig. 2.3, the procedures of connecting with other Bluetooth device is illustrated. When a Bluetooth device wants to setup a connection with other Bluetooth devices, it enters the inquiry state to discover other devices. During inquiry state, the device generates an inquiry hopping sequence and broadcasts inquiry messages so that it sequentially changes to each channel according to the hopping sequence.

Discoverable devices periodically enter the inquiry scan state. If the device executes the inquiry scan and receives an inquiry message, it will enter the inquiry response state and feedback an inquiry response message. This response contains the remote (slave) device’s address and clock. All the discoverable devices that are within the range of the broadcaster will reply to the inquiry device. A list of all discovered devices will be shown in the broadcaster. The user needs to manually choose the desired Bluetooth device.

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paging state to setup a connection with remote device. In this state, the local device generates a hopping sequence. A device periodically enters the page scan state if it allows other devices to connect. When the remote device receives the page packet, it will reply a page response packet to the local device. Upon receiving the response, the local device sends a Frequency Hopping Synchronization (FHS) packet to the remote device. Once the remote device receives the FHS packet, it sends an acknowledgement (ACK) to the local device. If the paging procedure is complete, the devices enter the connection state. The local device will send a poll packet to the remote device to conﬁrm that the transition of hopping sequence is successful. Then, they will communicate with each other. Some technical details can refer to [28].

2.3.3 WLAN

IEEE 802.11 is the set of standards for executing wireless local area network (WLAN). It is a local area network which doesn’t depend on wired connections. It provides short-range wireless connections between mobile devices and nearby APs. Because the wireless signal is broadcast in the wireless environment, every device which is nearby to the broadcaster can share it. Therefore, several security protections are necessary. The range of WLAN can cover from a small oﬃce to a large campus. The procedures of establishing a connection with WLAN can be classiﬁed into two scanning modes. [29].

1. Passive scanning mode: a device listens to the WLAN traﬃc for detecting APs and measures the noise level and signal strength.

2. Active scanning mode: a device transmits a request frame which contains the broadcast address and waits for responses from APs.

2.3.4 ZigBee

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Figure 2.4: Device roles in the ZigBee standard.

standard can be classiﬁed into three roles as shown in Fig. 2.4. Note that a ZigBee end device is neither a router nor a coordinator.

A ZigBee network constructs its topology when devices become active. Like in a mesh network, the ﬁrst full-function device (FFD) that begins communicating can setup itself as the ZigBee coordinator. By sending association requests, other devices can join the network. There is no additional regulator required to setup a network, so the ZigBee networks are called as self-forming networks. When a mesh network is setup, there may exist more than one transmission path to relay the message from the source to the destination. There will exist one path to route the message eﬃciently. If the network condition changes, the change of the routing path in the network is necessary. In contrast to other networking technologies, ZigBee networks have no infrastructure. For example, in WLAN, there is a wireless AP. More details of the ZigBee standard can refer to [30].

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Chapter 3 System Model and Link Setup

Procedure

We present in this chapter the system model and related D2D link setup procedure. The system model is the environment that we consider. Some detailed settings are described respectively in chapters 4 and 5. In the next section, we will introduce the procedure to set up a D2D communication link.

3.1 System Model

The structure of system that we consider is a two-dimensional (plane) single cell orthogonal frequency-division multiple access (OFDMA) system. The whole spectrum is divided into equal and consecutive orthogonal sub-channels. We assume that all the radio resources are assigned to CUs. Therefore, D2D transmitter needs to share the same resources with CUs without causing harmful interference (we assume that the D2D device reuses the downlink resources of the CN). There are three types of users in our scenario:

1. Cellular user: the user who uses the orthogonal resource units assigned by the eNB.

2. Active device: the device which wants to communicate with a received device over D2D link. It has a common transmit power PD. It does not need a speciﬁc received

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Figure 3.1: System model of D2D communications underlays a cellular network.

device. Every device which is idle can connect with it.

3. Received device: the device which wants to receive the data from an active device over D2D link.

Fig. 3.1 depicts a scenario which includes active CUs, active devices, received devices, and an eNB. Both CUs and devices are equipped with single antenna. The coverage range of the eNB is deﬁned as R. The radius of cell coverage range is Rc. Without

loss of generality, the location of eNB is deﬁned as origin (0,0). There are M resource blocks (RBs) per (sub)frame. Each active CU is given average amount of all the RBs orthogonally. Namely, if there are Nu active CUs, every CU obtains M/Nu RBs. Due to

the exhaustion of battery, the received device which is power oﬀ or not in discoverable mode, we deﬁne busy probability of received device as β. As there is no cell inter-ference, no inter-CU interference exists. However, as multiple active devices share the same OFDMA RBs with CUs, the resulting devices-to-CUs interference is of paramount concern. The CUs’ locations are modeled by BPP in the bounded domain R. Namely, CUs are uniformly distributed within the coverage range R of the eNB. The active and received devices’ locations follow two point processes, BPP and PPP. In the next two chapters, the D2D link setup analysis based on BPP and PPP models will be shown.

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1. BPP: the numbers of active and received devices are given with two ﬁxed numbers Na and Nd respectively in the bounded domain R. These devices are uniformly

distributed in R.

2. PPP: the locations of active and received devices are modeled by two independent homogeneous PPPs Φa and Φd with intensity λa and λd (over an area much larger

than a cell).

To have a reliable link between the active and received devices, and an acceptable interference to CUs, we deﬁne the following two primary parameters: θd and θu.

1. θd: the minimum signal-to-noise-ratio (SNR) requirement of the received device.

2. θu: the minimum SINR requirement of the CU.

Deﬁnition 6 (Outage Probability, [31]) The outage is the event that capacity is smaller than the information rate R. The outage probability is defined as

ν P(log₂(1 + SIN R) < R) (3.1)

For a given information rate R, θu is obtained.

θu 2R− 1

The goal is that there are active devices which want to communicate with other received device over D2D link which has a reliable link condition and shares the spectral resources with CUs, but they can not cause much interference to make CU outage. Therefore, the distance between two devices needs to be close enough and the interference from devices to CUs needs to be small enough. According to these two requirements, the SDLS condition is deﬁned in the following.

Deﬁnition 7 (Conditions for SDLS) The SDLS includes two conditions. There is at least one idle received device which received the SNR larger than pre-determined threshold

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θd. There are also existing Q usable RBs that the active device can share with CUs and

satisfy the CU’s SINR requirement θu (non-outage).

The transmitted signal suffers from a deterministic path loss in the deterministic channel or channel fading effect (including path loss) in the stochastic channel, i.e., the received signal power is a deterministic or random function of the transmitted power, the transmission distance, or channel fading effect.

3.2 SDLS Procedure

From the existing connection setup procedure of some wireless communication stan-dards introduced in chapter 2, we propose a link setup procedure for D2D communi-cation. The SDLS procedure includes four steps: access the probing channel, device discovery, resource discovery, and D2D link setup. The ﬂowchart will be shown in Fig. 3.2.

1. Access the probing channel: A probing channel (resource block, RB) is reserved for devices’ initial link discovery application. When the active device wants to probe other received devices at a probing channel, it needs to check the probing channel whether it is being used or not. It uses carrier sense multiple access (CSMA)-type MAC scheme. If there are active devices using the probing channel, it re-senses the probing channel after a random nonzero delay.

2. Device discovery: If the active device senses that there are no other active devices using the probing channel, it emits a probing signal with power PD at

the probing channel to check if any idle received devices are within its probing range. An idle received device which received the SNR larger than pre-determined threshold will respond with a consent-to-send message along with a preferred RB list. If there exists more than one received device responses, the active device will choose one amongst all the devices which have responded. If no received devices

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Start

The active device senses the

probing channel

any received device

responded?

random nonzero

back off

The active device selects

one received device and

emits a probing signal with

power P

D

in preferred RB

any CU is

interfered?

Both devices start a hand-shaking process to

determine the RBs, the modulation/coding scheme.

Having reached a consensus, the communication

session then commences.

End

Y

The active device emits a

probing signal with power P

D

in a probing channel

probing channel is idle?

Y Y

random nonzero

back off

probe another

preferred RB

The number of

usable RBs Q

Y N Y N N Y

t

random nonzero

back off

ŏ ŏ

Access the probing channel

Device discovery

Resource discovery

D2D link setup

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respond for a pre-deﬁned period (this period depends on the round-trip time which is based on coverage radius), the active device re-executes step-1 after a random nonzero delay.

3. Resource discovery: Then, the active device emits a probing signal with power PD in the ﬁrst preferred RB to check if any CU is interfered. If there are no CUs

interfered (the device does not receive any negative-acknowledgement (NACK) from CUs), the active device can reuse this RB and check whether the number of usable RBs satisfy the constraint (at least Q usable RBs) or not. If the number of usable RBs≤ Q, the active device probes another preferred RB. On the contrary, if the CU is interfered (the device receives a NACK from the CU), the active device re-broadcasts the probing signal in next preferred RB. It repeats this setup until the number of usable RBs ≥ Q or all the preferred RBs are testing over. If there exists at least Q usable RBs that the active device can share with CUs without causing harmful interference, the active device executes step 4. On the contrary, the active device re-executes step-1 after a random nonzero delay.

4. D2D link setup: Both devices start a hand-shaking process to determine the modulation/coding scheme. Having reached a consensus, the communication ses-sion then commences.

The analysis under BPP and PPP models which are described respectively in chapters 4 and 5 are based on an example case, we assume that the received device responds one preferred RB and Q = 1 which means the active device uses one preferred RB to communicate over D2D link. Note that in the transmission of D2D communication, if some CUs are interfered, the eNB has the right to forbid the active devices’ transmission.

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Chapter 4 Performance Analysis in BPP

Environments

In this chapter, we consider the scenario that an active device wants to setup a D2D link (a reliable link between the active device and received device) using the same spectrum with CUs without causing intolerable interference. Therefore, the link range has to be close enough and the interference from the active device to CUs has to be small enough. According to Definition 7, we analyze the SDLS performance using the BPP model with deterministic and stochastic channels respectively. Closed-form expressions of the SDLS performance are derived and related numerical results are given.

4.1 System Model

To begin with, we consider the special case that there is only a single active device so that there is no need for accessing the probing channel. The system architecture under BPP model is shown in Fig. 4.1. To establish a D2D link this device has to ﬁnd an idle device without causing too much interference to CUs. We assume that a proper power control scheme is in place to ensure that the same average power PCU is received for

every CU and each CU within the coverage region has the same tolerable interference I_min(CU)(PCU

θu − N0).

Given the active device location c=(x,y) and its distance dtx=

x2_{+ y}2 _{in a reference}

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Figure 4.1: BPP model of D2D communications underlays cellular network.

CUs and the potential receiving devices are uniformly distributed within the coverage range R of the eNB and denote by μ(k)_d (rd|dtx), the probability that the active device

ﬁnds k received devices within a radius-rd circle (centered at c).

Because we skip the accessing the probing channel step, SDLS procedure includes three steps:

1. Received device discovery.

2. Resource discovery: ﬁnd the spectral resources to share with CUs without causing harmful interference.

3. D2D link setup.

In the next two sections, we analyze the SDLS performance in the deterministic and stochastic channels respectively.

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4.2 Deterministic Channel

The received signal power P_D(d)_i at the ith received device terminal and the corre-sponding SNR γ_D(d)

i in deterministic channel are given respectively by

P_D(d) i = PD dα tx,Di , i = 1,· · · , Nd (4.1) and γ_D(d) i = P_D(d) i N₀ , i = 1,· · · , Nd (4.2)

where d_tx,D_i is the distance between the active device and the ith received device. The received interference power I_CU(d)

i at the ith CU in deterministic channel is given

by I_CU(d) i = PD dα tx,CUi , i = 1,· · · , Nu (4.3)

where dtx,CUi is the distance between the active device and the ith CU.

4.2.1 SDLS Analysis

In order to have a reliable link to the received device and a tolerable interference to CU, we need to set up the constraints in (4.4) and (4.5).

γ_D(d) i = PD dα tx,DiN0 ≥ θd, i = 1,· · · , Nd (4.4) and I_CU(d) i = PD dα tx,CUi ≤ I(CU) min , i = 1,· · · , Nu (4.5)

From (4.4) and (4.5), we can obtain the radius of the reliable range and interference range by letting the equality satisfy in (4.4) and (4.5).

rd PD N₀θd 1 α (4.6) ru PD I_min(CU) 1 α (4.7)

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Figure 4.2: Reliable and interference ranges of the active device.

rd is a function of PD and θd. When the active device transmit power PD is getting

larger, the reliable range also becomes larger. The reliable range is relative to the SNR requirement of received device. ru is a function of PD and I_min(CU). When active device

transmit power PD is getting larger, the interference to CU also becomes larger. The

interference range is relative to the tolerable received interference power level at the CU. From equations (4.6), (4.7) and deﬁne the ratio between θd and

I_min(CU)

N₀ as ζ where

ζ = N0θd

I_min(CU), the relation between rd and ru can be obtained.

ru = rdζ

1

α (4.8)

From the above assumptions, we summarize the concept of reliable and interference ranges.

1. Reliable range: A received device must lies within a circle of radius rd from the

active device to be able to detect the probing pilot and have a reliable commu-nication link with the broadcaster. It can be illustrated on the left side in Fig. 4.2.

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Figure 4.3: The illustration of the intersection area between two circles.

active device, so the interference to CU is tolerable. It can be illustrated on the right side in Fig. 4.2.

Lemma 1 The intersection area between the coverage range R of the eNB and a radius-r circle centered at c with distance d_tx from eNB is [17]

A_intersect(r|d_tx) = πr2_, _{if 0}_{≤ r ≤ R} c− dtx Ar(r, θ₀)+Ar(Rc, φ0), if Rc− dtx < r≤ Rc (4.9) where Ar(x, y) = x2 y−sin 2y 2 θ0 = cos−1 d2_tx+ r2 − R2_c 2d_txr φ₀ = cos−1 d2 tx+ R2c − r2 2d_txRc

The illustration of the intersection of two ranges can be seen in Fig. 4.3. Device Discovery

The active device emits a probing signal with power PD at the probing channel

to check if any idle received device is within its probing range. An idle received device which is inside the reliable range of the active device will respond with a consent-to-send message along with a preferred RB number. Let pa(r|dtx) denote the probability that

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the received device is within a radius-r circle centered at c with distance d_tx from eNB. pa(r|dtx) = A_intersect(r|d_tx) πR2 c (4.10) Therefore, the probability μ(k)_d (rd|dtx) is obtained.

μ(k)_d (rd|dtx) = Nd k (pa(rd|dtx))k(1− pa(rd|dtx))Nd−k , k = 0, . . . , Nd (4.11)

Next, we deﬁne the probability μ(k)_d (rd|dtx) that there are k received devices inside

the reliable range of the active device and exit at least one idle received device. μ(k)_d (rd|dtx) = Nd k (pa(rd|dtx))k(1− pa(rd|dtx))Nd−k(1− βk), k = 0, . . . , Nd (4.12) For a given active device location, the received device discovery probability p(d)_dd(rd|dtx)

In (4.13), the term βpa(rd|dtx) of (βpa(rd|dtx) + 1− pa(rd|dtx)) stands for the

proba-bility that the received device is inside the reliable range, but it is busy. (1− pa(rd|dtx))

stands for the probability that the received device is outside the reliable range. There-fore, equation (4.13) means that there exists at least one idle received device inside the reliable range of the active device.

Resource Discovery

When at least one received device responded, the active device chooses one amongst all the received devices which have responded and emits a probing signal with power PD

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in the preferred RB to check if any CU is interfered. If the received SINR at CU doesn’t meet his requirement, the active devices can not reuse its spectral resources. Namely, if the CU is inside the interference range of the active device, the CU will be interfered. Similar to the above results, the active device can reuse the CU’s spectral resource with probability p(d)_rd(ru|dtx).

p(d)_rd(ru|dtx) = 1− pa(ru|dtx) (4.14)

In (4.14), it stands for the probability that the active device can share the spectral resources with the CU which received interference power lower than the pre-determined threshold.

Link Setup

If the active device ﬁnishes the device and resource discovery procedures, the active device and the desired received device start a hand-shaking process to determine the modulation/coding scheme. Having reached a consensus, the communication session then commences.

According to the above SDLS procedure, we define the probability p(d)_LS that the active device can finish all the link setup procedures in deterministic channel. Namely it can find a close received device and reuse the same spectral resources with the CU without causing harmful interference.

Therefore, (4.15) implies that there exists a CU that the active device can share its spec-tral resources without causing harmful interference and at least one idle device having a received SNR (with signal from the active device) greater than the pre-determined threshold.

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4.3 Stochastic Channel

The diﬀerence between deterministic and stochastic channel models is the inclusion of the random channel fading eﬀect in the latter.

With the stochastic model, the received signal power P_D(s)

i and the corresponding

SNR, γ_D(s)

i, at the ith received device are given respectively by

P_D(s) i = hiPD dα tx,Di , i = 1,· · · , Nd (4.16) and γ_D(s) i = P_D(s) i N₀ , i = 1,· · · , Nd (4.17)

where hi is independent and identically distributed (i.i.d.) exponential random variable

with unit mean for all i in Rayleigh fading scenario. The received interference power I_CU(s)

i at the ith CU in stochastic channel is given by

I_CU(s) i = giPD dα tx,CUi , i = 1,· · · , Nu (4.18)

where gi is i.i.d. exponential random variable with unit mean for all i in Rayleigh fading

scenario.

4.3.1 SDLS Analysis

As the channel fading eﬀect is taken into account, we are unable to determine the reliability and interference range like those were done before and the cell range can not be divided into two parts anymore. In fact, these two ranges are random variables and a proper parameter would be the outage probability deﬁned in Definition 6. When the distance between the active device and a received device (the CU) is rd (ru), the outage

probability is e−1.

The requirements of having a reliable link to a device with a tolerable interference to a CU are given by γ(s)_D i = P_D(s) i N ≥ θd, i = 1,· · · , Nd (4.19)

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Figure 4.4: Probability-based reliable and interference ranges of an active device. I_CU(s) i = giPD dα tx,CUi ≤ I(CU) min , i = 1,· · · , Nu (4.20)

Using the above equations, we can obtain the probability-based reliable and in-terference ranges by normalizing channel fading eﬀect as shown in Fig. 4.4. Let p(s)_D,reliable(d_tx,D, rd|dtx) be the probability that active device has a reliable link to

re-ceived device with distance d_tx,D between the active device and the received device, and p(s)_{CU,interfered}(d_tx,CU, ru|dtx) be the probability that active device has an interfered link to

CU with distance dtx,CU between the active device and the CU.

p(s)_D,reliable(d_tx,D, rd|dtx) = P hPD dα tx,DN0 ≥ θd = P h≥ θdd α tx,DN0 PD = P h≥ d_tx,D rd α = _∞ _dtx,D rd αe −x_dx = e− _dtx,D rd α (4.21)

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Similarly, from (4.21), p(s)_{CU,interfered}(d_tx,CU, ru|dtx) can be also derived as p(s)_{CU,interfered}(d_tx,CU, ru|dtx) = e− _dtx,CU ru α (4.22)

where the deﬁnitions of rd and ru are described in the previous section.

Because devices and CUs are uniformly distributed in the cell range and conditioned on ﬁxed active device position, the term d_tx,D in (4.21) and d_tx,CU in (4.22) will be normalized by the below equation.

p(x|d_tx) = ⎧ ⎨ ⎩ 2x R2_c, if 0≤ x ≤ Rc− dtx 2x cos−1 d2_tx+x2−R2_c 2dtxx πR2_c , if Rc − dtx≤ x ≤ Rc+ dtx

Based on above equation, we obtain

p(s)_D,reliable(rd|dtx) = Rc+dtx 0 p(s)_D,reliable(x, rd|dtx)p(x|dtx)dx = Rc−dtx 0 e− x rd α 2x R2 c dx + Rc+dtx Rc−dtx e− x rd α2x cos−1 d2_tx+x2−R2c 2dtxx πR2 c dx (4.23)

Similarly, p(s)_{CU,interfered}(ru|dtx) can be calculated as

p(s)_{CU,interfered}(ru|dtx) = Rc−dtx 0 e−(rux) α_2x R2 c dx + Rc+dtx Rc−dtx e−(rux) α2x cos−1 d2_tx+x2−R2c 2dtxx πR2 c dx (4.24)

p(s)_D,reliable(rd|dtx) and p(s)CU,interfered(ru|dtx) can be computed by numerical methods.

Similarly in (4.13) and (4.14), we can obtain device discovery probability p(s)_dd(rd|dtx)

and resource discovery probability p(s)_rd(ru|dtx) in stochastic channel.

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Therefore, the probability p(s)_LS that the active device can ﬁnish all the link setup proce-dures in stochastic channel can be deﬁned.

p(s)_LS = p(s)_dd(rd|dtx)p(s)rd(ru|dtx) = 1− βp(s)_D,reliable(rd|dtx) + 1− p(s)D,reliable(rd|dtx) N_d 1− p(s)_{CU,interfered}(ru|dtx) (4.27)

In (4.27), the term βp(s)_D,reliable(rd|dtx) of

βp(s)_D,reliable(rd|dtx) + 1− p(s)D,reliable(rd|dtx)

is the probability that although a received device may yield a SNR larger than the threshold, it is not idle.

1− p(s)_D,reliable(rd|dtx)

is the probability that the received SNR of a device is lower than the threshold. The term

1− p(s)_{CU,interfered}(ru|dtx)

stands for the probability that the active device can share the spectral resources with a CU which suﬀers from interference power less than the threshold in a stochastic channel. Therefore, (4.27) means that there exists a CU that the active device can reuse its spectral resources without causing harmful interference and at least one idle received device which received the SNR from the transmission of active device larger than the threshold in stochastic channel.

4.4 Numerical Results

In this section we examine the analytical results of SDLS performance under the BPP assumption. The parameters of our simulation are shown in Table 4.1. We already check the analytical results which are matched to simulation results under BPP model.

Fig. 4.5 (a) and (b) show the eﬀect of the coverage radius rd of the active device. If

the coverage range becomes larger, the received device falls into this region with high probability. But it also increases the interference range. Therefore, when rd is large

enough, the SDLS probability decreases. The transmit power of active device needs to be limited. Fig. 4.6 (a) and (b) show the eﬀect of received device number Nd. The D2D

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Table 4.1: Simulation Parameters under BPP

Parameter Value

Cell radius (Rc) 2km

Path loss exponent (α) 2, 4, 6

Number of received device (Nd) 1000

Radius of reliable range (rd) 100

Ratio between θd and I_min(CU) N₀ N₀θ_d I_min(CU) 10 Noise power (N₀) 1

Distance between the active device and eNB (d_tx) 1500 Busy probability of received device (β) 0.3

choices to set up a D2D link with another received device. When there is no channel fading effect, the performance increases when the path loss exponent α becomes larger for fixed rd. The stochastic model leads us to different results. The performance with

high α is not always better than the performance with low α. This phenomenon can also seen in Fig. 4.5.

Fig. 4.7 shows the effect of the distance d_tx between the active device and eNB. We can see when the active device approaches the cell edge, the SDLS performance degraded. This is due to few devices appear in the cell edge, the active device is hard to find another device to communicate over D2D link. Fig. 4.8 shows the effect of ζ. This affects the ratio between the radius of coverage and interference ranges. If ζ becomes larger, the acceptable interference at CU is lower. The SDLS probability decreases when ζ becomes larger. The path loss exponent α also affects the ratio between the radius of coverage and interference ranges. For fixed rd and ζ, ru decreases as α increases.

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80 100 120 140 160 180 200 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 r d = 70 to 200

D2D link setup probabilty

No channel fading

α = 2

α = 4

α = 6

(a) Without channel fading eﬀect.

80 100 120 140 160 180 200 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 r d = 70 to 200

channel fading

α = 2

α = 4

α = 6

(b) With channel fading eﬀect.

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500 1000 1500 2000 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 N d = 500 to 2000

No channel fading

α = 2

α = 4

α = 6

(a) Without channel fading eﬀect.

500 1000 1500 2000 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 N d = 500 to 2000

channel fading

α = 2

α = 4

α = 6

(b) With channel fading eﬀect.

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1800 1850 1900 1950 2000 0.55 0.6 0.65 0.7 0.75 0.8 0.85 d tx = 1800 to 2000

No channel fading

α = 2

α = 4

α = 6

Figure 4.7: SDLS probability as a function of distance d_tx (between the active device and eNB). 1 2 3 4 5 6 7 8 9 10 0.805 0.81 0.815 0.82 0.825 0.83 ζ = 1 to 10

No channel fading

α = 2

α = 4

α = 6

Figure 4.8: SDLS probability as a function of ζ (ratio between θd and I_min(CU)

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Chapter 5 Performance Analysis in PPP

Environments

We have analyzed the SDLS probability using the BPP model in the previous chapter. In this chapter, we consider another point process model, namely the PPP model. We consider there are multiple active devices that want to establish D2D links using the same CU band simultaneously. To maintain the existing CU links’ qualities, the transmit device has to be constrained. We shall analyze the corresponding SDLS performance according to Definition 7. We use an approximate scenario and a upper bound scenario to model the interference sources which are generated by PPP model. For the latter scenario, we convert the problem of computing the SDLS probability into an optimization problem. We then propose a solution and obtain some analytical results for the SDLS performance.

5.1 System Model

The PPP model is a more realistic scenario where both the numbers and locations of devices are random variables. The diﬀerence between BPP and PPP models is that the active and received devices are modeled by two independent homogeneous PPPs Φaand

Φd with intensity λa and λd respectively (over an area much larger than the coverage

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Figure 5.1: A two-dimensional network in which multiple active devices share the spec-trum with CUs whence result in aggregated interference to the latter.

system architecture under PPP model is shown in Fig. 5.1. Denote the given position of CU by y, the eNB transmit power by PT, and the distance between eNB and CU

by d_eNB,CU. We further deﬁne a parameter which is the ratio between the number of dimensions of the network and path loss exponent.

δ d

α (5.1)

Because we consider a two-dimensional system, δ is equal to _α2 in our scenario.

5.2 SDLS Analysis

According to chapter 3, SDLS procedure includes four steps: 1. Access the probing channel for active devices.

2. Idle device discovery.

3. Resource discovery: ﬁnd proper resources to share with CUs without causing harm-ful interference.

(53)

4. D2D link setup.

5.2.1 Access Probing Channel

The active devices use CSMA-type MAC scheme to sense the probing channel. The received interference power Ir at the active device A from the transmission of another

active device terminal in deterministic channel is given by Ir =

PD

dα tx,Da

(5.2) where dtx,Da is the distance between the active device A and another active device.

If the two active devices can use the probing channel simultaneously, the distance between these two active devices needs to satisfy the constraint in (5.3).

Ir =

PD

dα tx,Da

≤ θa (5.3)

where θa is the tolerable interference for accessing.

From (5.3), we can obtain the minimum acceptable distance ra that the two active

devices can communicate through the probing channel simultaneously by letting the equality satisfy in (5.3). ra PD θa 1 α (5.4) Let pa be the probability for accessing the probing channel successfully. According to

equation (2.16), the pa is obtained.

pa = exp(−λaπra2) = exp −λaπ PD θa δ (5.5)

In (5.5), it means that there are no other active devices within a radius-racircle centered

at the active device A, so the active device A can access the probing channel successfully.

5.2.2 Device Discovery

If the active device A senses that there are no other active devices using the probing channel around it, it emits a probing signal with power PD at the probing channel to

在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

國

立

交

通

大

學

電信工程研究所

碩

士

論

文

在裝置對裝置通訊網路下鄰近搜尋及自我連結建立

之設計與分析

Proximity Discovery and Autonomous Link Setup

in D2D Communication Networks

研 究 生：林晏陞

指導教授：蘇育德 教授

在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

Proximity Discovery and Autonomous Link Setup in D2D Communication

Networks

研 究 生：林晏陞 Student：Yen-Sheng Lin

指導教授：蘇育德 Advisor：Dr. Yu T. Su

國 立 交 通 大 學

電信工程研究所

碩 士 論 文

在裝置對裝置通訊網路下鄰近搜尋及自我連結建立之設計與分析

學生：

指導教授

國立交通大學電信工程研究所碩士班

摘

要

Proximity Discovery and Autonomous Link Setup in

D2D Communication Networks

誌

謝

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1

Concept of D2D Communications

1.2

Other Communication Standards

1.3

Overhead

1.4

Literatures Review and Motivation

1.5

Contributions

1.6

Thesis Structure

Chapter 2

Preliminaries

2.1

Point Process

2.1.1

Binomial Point Process

2.1.2

Poisson Point Process

2.2

Mathematical Tools

2.2.1

Gamma Function

2.2.2

Other Function

2.3

Connection Setup Procedure

2.3.1

FlashLinQ

2.3.2

Bluetooth

2.3.3

WLAN

2.3.4

ZigBee

Chapter 3

System Model and Link Setup

Procedure

研究生：林晏陞

指導教授：蘇育德教授

研究生：林晏陞 Student：Yen-Sheng Lin

國立交通大學

碩士論文