擴散式分子通訊下之調變設計

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國立臺灣大學電機資訊學院電信工程研究所碩士論文

Graduate Institute of Computer Science and Information Engineering College of Electrical Engineering and Computer Science

National Taiwan University Master Thesis

擴散式分子通訊下之調變設計

Modulation Design in Diffusion-based Molecular Communication System

林維安 Wei-An Lin

指導教授：葉丙成博士 Advisor: Ping-Cheng Yeh, Ph.D.

中華民國 103 年 7 月

July, 2014

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誌謝

在電信所碩士的生活即將畫下句點。這兩年中我學到很多，許多想法也與當初大學畢業的我不同了。首先要感謝指導教授葉丙成老師。感謝老師從大學部專題以來的照顧，不僅是研究上給予我們意見，對我們成長、學習也相當關心。其中印象最深刻的是老師開的簡報課，讓我對上台口頭報告不再那麼害怕，即使是到國外參加 conference，我都有足夠信心向聽眾表達我的想法。另外，老師推薦我們修 Stanford 線上學術寫作課程，實在令我收穫良多。從這門課，我學到即使沒有寫曠世奇作的才華，只要抓住寫作的幾個小技巧，也能讓日常寫作甚至論文寫作相當生動且有條理。修過這門課後，我變得對寫文章更有自信，在碩二考 GRE 寫作時拿到高分。這都得歸功於老師對我們學習上的關心！另外我要謝謝彥奇學長引導我接觸數學的領域。仍記得大學時期一直排斥接觸分析數學，直到彥奇學長的「推坑」，我在研究所一年級上學期，一邊惡補高微一邊修實分析，

改變了我對數學的看法。之後更開啟我對數學的興趣，甚至讓我能以不同的角度理解不同領域的研究，令我獲益良多。謝謝實驗室的同學們，這一屆的博理 515 實在是超棒的！大家一起到處玩、一起討論研究、一起聊天，令我度過相當精彩且快樂的碩士生活。偉軒、圈圈、穴宇、李俊，很高興能與你們在同一個實驗室相處兩年！當然也要感謝分子通訊小組的學弟們。駿挺的見解與研究給我更多的想法，使我能將現有的題材延伸。昀鋒常常和我討論數學的分析，幫我突破許多難關，真的非常感謝。博凱常對我的研究內容提出不同觀點，使我能檢討以前做過的題目。還記得碩一時和博凱一起研究 synchronization ，結果我因為做其他題目而放博凱鳥，實在不好意思…不過後來博凱還是靠自己做出相當棒的成果！

(好加在 XD) 最後要感謝我的爸媽，沒有他們我絕對無法進碩士念書，他們的支持給我很大的幫助，希望你們永遠身體健康、快快樂樂。

差點忘了，我還要感謝上帝，thank God！因為要感謝的人太多，只好謝天了。

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摘要

在奈米尺度的通訊環境下，擴散式分子通訊被視為最可行也最具潛力的方法。

近期對於擴散式分子通訊調變的研究包含利用分子種類、分子數量以及分子濃度

來承載訊息。本篇碩士論文依照承載訊息、偵測方法的差異，將擴散式分子通訊

分為兩大類：同調分子通訊以及非同調分子通訊，藉此研究並設計分子通訊系統。

對於同調分子通訊，我們研究利用分子數量以及分子種類承載訊息。由於擴散通

道的隨機性，錯位效應 (cross over effect) 以及符際干擾 (inter-symbol

interference) 嚴重影響系統效能。本篇論文提出符際干擾消除 (ISI

cancellation) 以及閾值偵測法 (threshold-based detection) 來消除上述對

於系統的負面效應。經由數學分析以及電腦模擬證實，本篇論文針對通道負面效

應所提出的數量-種類調變 (quantity-type modulation) 能有效提升系統效能。

對於非同調分子通訊，本論文建構了統計模型，以數學描述接收端偵測到的濃度

變化。由於此模型適用於傳送端發出任意連續波型，能設計出的調變方法會更加

豐富，同時也利於設計更好的偵測演算法。另外，本論文提出基底展開偵測法

(expansion-based detection) 和廣泛被使用的取樣偵測法 (sample-based

detection) 做比較，電腦模擬結果顯示基底展開偵測法在振幅調變以及脈衝位

置調變下能比取樣偵測法達到更佳的系統效能。

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ABSTRACT

Diffusion-based molecular communication has become a promising scheme for communication between nanoscale devices, and various modulation schemes have recently been proposed, including type, quantity, and concentration modulation.

In this thesis, we investigate molecular communication by separating it into two categories: coherent molecular communication and non-coherent molecular communication, which are based on the adopted signaling and detection methods.

For coherent molecular communication, we study modulations that convey information in molecular quantity or molecular type. Due to the randomness of each molecule in the diffusion channel, problems such as the crossover effect and the inter-symbol interference arise which undermine the system performance. This thesis provides algorithms such as ISI cancellation and threshold-based detection algorithm to deal with the problems. Moreover, it is shown by mathematical derivations and computer simulations that the proposed quantity-type modulation, which is designed against the bad channel effects, has reliable performance.

For non-coherent molecular communication, we construct a stochastic model to describe the concentration magnitude sensed by the receiver. The model enables more modulation designs since it is generalized to the case that the transmitter send any continuous wave to the the receiver. It also allows better design for detection algorithm. Amplitude modulation and pulse-position modulation in non-coherent molecular communication are studied and compared by using the proposed expansion-based detection as well as the widely-used sampling-based detection. Through simulation, it is proved that the expansion-based detection outperforms the sampling-based detection.

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LIST OF FIGURES

1 Diffusion-based molecular communication. . . 2 2 Coherent molecular communication. . . 3 3 Transmission from TN to RN through a fluid medium. . . 7 4 Illustration of quantity-based modulation scheme with L₀ = 2, L₁ =

4, L₂ = 6, L₃ = 8. . . 9 5 Demonstration of the process of finding η in a binary QM system,

where f is the conditional PDF of N given H_m is true. . . 12 6 Theoretical result versus numerical result for one-shot binary quantity-

based modulation. . . 13 7 Binary quantity-based modulation with ISI cancellation. . . 16 8 Quaternary quantity-based modulation with ISI cancellation. . . 16 9 Binary quantity-based modulation with ISI cancellation under dif-

ferent T_s. . . 17 10 A demonstrative example for the majority-vote detection algorithm

and the threshold-based detection algorithm with λ = 1 and λ = 2.

The boxed numbers represent the value stored in the counter that reaches the threshold λ. . . 20 11 Block diagram of the threshold-based detection algorithm. . . 21 12 A demonstrative example for the detection result under background

noise using the threshold-based detection algorithm. λ = 3. In the example, the crossover effect is not taken into account. . . 24 13 Example of the events bE₀₀₁^MVD, bE₁₀₀^MVD, and bE₀₀₀^MVD given that the

information sequence ‘0, 1, 0’ is transmitted. . . 29 14 Performance comparison between the majority-vote detection and

the proposed threshold-based detection for the n = 3 quantity- type-modulated system without background noise. The theoretical analysis and the simulation results are also compared. . . 38 15 Performance comparison between the majority-vote detection and

the proposed threshold-based detection for the n = 5 quantity- type-modulated system without background noise. The theoretical analysis and the simulation results are also compared. . . 39 16 Performance comparison of quantity-type-modulated systems with-

out background noise with different n (the number of molecules released at a time) and different detection algorithms. The case of n = 1 corresponds to the type-modulated system. λ = 1 for the threshold-based detection algorithm. . . 40

v

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LIST OF FIGURES vi

17 Performance comparison between the majority-vote detection and the proposed threshold-based detection for the n = 3 quantity-type- modulated system with background noise. The theoretical analysis and the simulation results are also compared. . . 41 18 Performance comparison between the majority-vote detection and

the proposed threshold-based detection for the n = 5 quantity-type- modulated system with background noise. The theoretical analysis and the simulation results are also compared. . . 41 19 Performance comparison between the majority-vote detection and

the proposed threshold-based detection for the n = 3 quantity- type-modulated system with background noise under different block sizes. The theoretical analysis and the simulation results are also compared. λ = 3. . . 42 20 Performance comparison between the majority-vote detection and

the proposed threshold-based detection for the n = 5 quantity- type-modulated system with background noise under different block sizes. The theoretical analysis and the simulation results are also compared. λ = 5. . . 42 21 Performance comparison of quantity-type-modulated systems with

different n using different detection algorithms in the presence of background noise. The case of n = 1 corresponds to the type- modulated system. λ = 3 for the n = 3 quantity-type-modulated system and λ = 5 for the n = 5 quantity-type-modulated system.

L = 40 bits. . . 43 22 Proposed diffusion model for molecular communication in a fluid

medium. . . 46 23 Channel response results from an infinitesimal duration of trans-

mitted signal s(t). . . 46 24 Patterns of the waveform c₀(t) under different distance d and diffu-

sion coefficient D. The time t is normalized with respect to Ts. . . . 56 25 Patterns of the waveform c0(t) under different symbol duration Ts.

The time t is normalized with respect to T_s. . . 56 26 Comparison between the sample-based detection and the expansion-

based detection for the amplitude modulation under different values of diffusion coefficient D. . . 57 27 Comparison between the sample-based detection and the expamsion-

based detection for amplitude modulation under different number of observations K. . . 58 28 Comparison between the sample-based detection and the expansion-

based detection for pulse-position modulation under different values of diffusion coefficient D. . . 59

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LIST OF FIGURES vii

29 Comparison between the sample-based detection and the expansion- based detection for pulse-position modulation under different numbers of observations K. . . 60 30 Comparison between the sample-based detection and the expansion-

based detection for pulse-position modulation under different values of pulse width w. . . 60

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CHAPTER 1 INTRODUCTION

1.1 Overview

Nano-technology has become an important research area and is expected to have great impact on many fields, including medicine, biology, military, and elec- tronics. The advance in nano-technology has enabled the development of nanomachines, which are devices in nanoscale that can perform sensing, computation, and actuation. The computational capability of a single nanomachine, however, is often quite limited due to the ultra-small size and the ultra-low power capacity.

As a result, an efficient information exchange mechanism between nanomachines is required in order to coordinate the nanomachines to accomplish complicated tasks [1].

Unlike modern wireless communication systems in which signals are carried by electromagnetic (EM) waves, communication in nanoscale through EM waves may not be practical due to issues such as antenna size, power consumption, computational complexity, and signal attenuation in fluid environments [2]. Diffusion-based molecular communication is believed to be one of the most promising solutions for communication in nanoscale [3–7], which is composed of a transmission nano- machine (TN), a reception nano-machine (RN), and a diffusion channel between TN and RN. To convey information, TN releases information molecules into sur- rounding environment. Those molecules arrive at RN through diffusion process, RN then captures those arriving molecules and attains information. Fig. 1 shows a picture for diffusion-based molecular communication. This thesis focuses on designing modulation and detection schemes for TN to embed information and RN to attain information by molecules. To discuss modulation techniques thor- oughly, we categorize diffusion-based molecular communication into two types –

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1.2. COHERENT MOLECULAR COMMUNICATION 2

Transmission Nano-machine

(TN)

Reception Nano-machine

(RN) Diffusion

Process

Figure 1: Diffusion-based molecular communication.

coherent or non-coherent molecular communication – according to the signaling and detection method used by TN and RN.

1.2 Coherent Molecular Communication

In communication based on EM wave, “coherent modulation” means receivers can fully recover phase of received signal. Borrowing the idea, we use the term coherent in molecular communication to mention RN can recover timing information of each molecule. In this thesis, coherent molecular communication means that the signaling and detection are done by counting the number of information molecules. Both TN and RN are able to count each molecule at a single position and time instant. Moreover, once an information molecule is captured by RN, it is removed from the diffusion channel. Diffusion model and channel capacity related to coherent molecular communication is first proposed in [8]. In coherent molecular communication, the behavior of each molecule can be investigated sep- arately, in microscopic view. More precisely, for each molecule released by TN, we

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1.2. COHERENT MOLECULAR COMMUNICATION 3

TN releases molecules

time

RN captures molecules

TN

RN

First-hitting time of a molecule

Figure 2: Coherent molecular communication.

can describe the behavior of this molecule by using the time it requires to reach RN, which we call the first-hitting time of a molecule. Fig. 2 shows an example for coherent molecular communication. One major issue in coherent molecular communication is that earlier released molecules may arrive late and later released molecules may arrive early, causing crossovers. When molecules are used to transmit symbols, crossovers between molecules will introduce interference. In this thesis, we investigate the problem known as inter-symbol interference (ISI) in coherent molecular communication, and propose two approaches to mitigate the effect. From simulation, we show that the proposed ISI cancellation algorithm can improve the performance significantly. Moreover, both the modulation and the detection methods have low complexity which are suitable for communication between nanomachines.

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1.3. NON-COHERENT MOLECULAR COMMUNICATION 4

1.3 Non-coherent Molecular Communication

By non-coherent molecular communication, we mean the signaling and detection are done by sensing the magnitude of the molecular concentration, i.e. the number of molecules within a small volume around them, at a time instant. Noise model considering diffusion process and counting errors from ligand-binding im- perfection is first proposed in [9]. In [10], information is modulated by pulses of molecules at transmission nano-machine (TN), and RN samples the received concentration waveform to make detection. [11, 12] study possible modulation techniques in molecular communication via different messenger molecules. Most of the existing studies take advantage of Robert’s equation to model the macroscopic behavior of molecules, that is, the concentration distribution, in space and time as:

U (d, t) = N (4πDt)⁻³² exp

− d² 4Dt

, (1.1)

where D is the diffusion coefficient. However, this form simply describes the expec- tation of the molecule behavior. The fluctuation or randomness of concentration level should be taken into account. This thesis is the first study that provides stochastic model for diffusion channel when continuous waveform is applied at TN. Based on the model, we also propose methods for solving a set of basis functions in order to achieve orthogonal expansion for detection.

1.4 Thesis Organization

The rest of the thesis is organized as follows. In Chapter 2, we provide a one-dimensional modulation and detection scheme, under which we design an ISI cancellation algorithm that dramatically improves the system performance. In Chapter 3, we consider a more complicated modulation which embeds information on both quantity and type of molecules. This modulation combats both ISI effect and background noise simultaneously. We also provide principles to choose system parameters to achieve good performance. In Chapter 4 of this thesis, we construct a stochastic model for the diffusion channel starting from Brownian motion of each

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1.4. THESIS ORGANIZATION 5

molecule. Different from the results in [10,12], this model applies to any continuous wave transmitted by TN. We also solve a set of basis functions that can expand the received signals into observation vectors, which enables us to design detection criterion for different modulations. Finally, conclusions and future works are given in Chapter 5.

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CHAPTER 2 QUANTITY MODULATION

2.1 Introduction

In this chapter, we study the communication between two nano-machines with information embedded in different molecular quantity [13]. In the rest of this chapter, we call this kind of modulation as quantity modulation (QM). It is known that in diffusion-based molecular communications, molecules are emitted by the transmitter and move towards the receiver following the laws of molecule diffusion. Recent studies on diffusion-based molecular communications often model the statistical behavior of molecule diffusion as a Brownian motion [8]. Due to the random nature of Brownian motions, molecules that released earlier by TN may arrive late. Therefore, messages carried in current molecules may be interfered by those delayed molecules that were transmitted earlier. This phenomenon is known as the ISI effect in diffusion-based molecular communications. Studies about this effect can be found in [14] and [15].

There are lots of ways to design filters to eliminate the effect of ISI in conventional communication such as linear equalizer, adaptive equalizer and decision- feedback equalizer [16]. However, both linear equalizer and adaptive equalizer do not work well in molecular communication due to time-varying channel response.

In this chapter, we utilize the concept of decision feedback and introduce a method to mitigate the effect of ISI.

The rest of this chapter is organized as follows: In Sec. 2.2, we introduce the settings of a binary QM molecular communication system in details. We also describe the characteristics and the mathematical model of a Brownian motion channel. Sec. 2.3 focuses on deriving the decision rule for one-shot transmission of the binary QM system and extending it to the M-ary transmission case. In

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2.2. SYSTEM MODEL 7

Sec. 2.4, we consider serial transmission and take ISI effect into account. ISI cancellation method is also described in this section. Numerical results are shown in Sec. 2.5.

2.2 System Model

In this section, we first give a general model for transmitter, receiver, and channel in molecular communication. We then describe a QM system of M quantity levels (M -ary modulation) bearing log₂M information bits, which will be used later to apply our ISI cancellation method.

2.2.1 Transmission Nano-machine

Fig. 3 illustrates a transmitter nano-machine TN transmitting molecules to a receiver nano-machine RN. When TN obtains information (e.g. bit pattern) to be transmitted, it starts storing certain number of molecules in a vesicle (container that stores molecules) and releases these molecules simultaneously into the environment. The number of released molecules differs according to the transmitting information. In practical situations, molecules leaves the vesicle with random timing which is discussed in [17]. In this thesis, we simply assume that molecules exit the vesicle simultaneously.

Figure 3: Transmission from TN to RN through a fluid medium.

2.2.2 Reception Nano-machine

RN is located at a position d > 0 apart from TN. There are several receptors capturing molecules on RN. RN counts the number of molecules it captures and perform detection according to the number. We assume the molecules can

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2.2. SYSTEM MODEL 8

be perfectly captured by the receptors and RN does not have counting errors.

Furthermore, once a molecule arrives at RN, it will be removed from the communication medium.

2.2.3 Channel

Consider a fluid medium between TN and RN with positive drift velocity v.

The molecules are all constrained to move in a one-dimensional space. We assume that the trajectory of emitted molecules can be modeled with independent Brow- nian motions [8]. Let X denote the random variable representing the first hitting time of a molecule. If v > 0, it can be shown that the probability density function (PDF) of X is given by the inverse Gaussian (IG) distribution [18]

f_X(x) =











r λ

2πx³ exp

−λ(x − µ)² 2µ²x

, x > 0,

0, x ≤ 0,

(2.1)

µ = d

v and λ = d² 2D,

where D denotes the diffusion coefficient which is given by

D = k_BT 6πτ r,

where k_B is the Boltzmann constant, T_a is the absolute temperature, τ is the viscosity of the fluid medium, and r is the radius of molecules. For simplicity, we assume that the radii for all molecules are the same so that the diffusion coefficients are the same.

2.2.4 QM System

Consider a time-slotted M -ary communication with signaling interval T_B, TN can release M different quantities of molecules into the channel. Denote those M quantities by L_m, where m ∈ {0, 1, 2, · · · , (M −1)}. Assume the a priori probability for releasing L_m molecules to be q_m. At the starting time of each transmission

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2.3. DETECTION IN ONE-SHOT TRANSMISSION 9

time slot, L_m molecules are emitted simultaneously from the transmitter to indi- cate the transmission of a symbol. We assume perfect synchronization between the transmitter and the receiver. During each time slot, RN counts the total number of arriving molecules. An appropriate decision rule, proposed in Sec. 2.3, is then applied to determine the transmitted data bit at the end of each time slot.

The molecules which fail to arrive within the corresponding time slot become a source of interference, which will cause performance degradation to the detections of later coming symbols. Fig. 4 is an example of QM system with M = 4 and uniform quantity levels.

Perfect synchronization between TN and RN is assumed in this chapter, a possible realization which is based on sending training molecular impulses are introduced in [BoKai].

Figure 4: Illustration of quantity-based modulation scheme with L₀ = 2, L₁ = 4, L₂ = 6, L₃ = 8.

2.3 Detection in One-shot Transmission

In this section, we discuss the detection rule of the system for one-shot transmission. The main contribution of our work is that we separate the ISI cancellation problem from the detection to achieve a more flexible and modularized design, which is different from previous works [19].

2.3.1 Binary Detection

We define two hypotheses H₀ and H₁. H₀ is the hypothesis that L₀ molecules are transmitted (indicating bit 0), and H₁ is the hypothesis that L₁ molecules are transmitted (indicating bit 1). Denote the conditional PDF of the number of

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received molecules in a particular time slot, given that hypothesis H_m is true, by Pr{N = n|H_m}, m ∈ {0, 1}. Using the inverse Gaussian PDF given in (2.1), we define the probabilities p_j as:

p_j =

Z (j+1)Ts

jTs

f_X(x)dx (2.2)

for j ∈ {0, 1, · · · }, which is the probability that the traveling time of a molecule falls in the interval [jT_s, (j + 1)T_s], where j is the index of the time slots. Define Y_k to be the indicator random variable showing whether the k-th molecule emitted in a one-shot transmission arrives within T_s given that H_m is true. That is,

Y_k =











1, if the k-th molecule arrives within T_s,

0, otherwise.

(2.3)

Let N be the random variable denoting the total number of molecules arriving at the receiver within a particular time slot. We have the following relation:

Pr{N = n|H_m} = Pr{Y₁+ Y₂+ ... + Y_L_m = n|H_m}. (2.4)

Given the number of the transmitted molecules, N thus follows Binomial(L_m, p₀).

For large L_m, we approximate the binomial distribution by a Gaussian distribution with the knowledge of the mean and variance of N . Namely, we have

Pr{N = n|H_m} ≈ exp

− (n − L_mp₀)² 2L_mp₀(1 − p₀)

p2πLmp₀(1 − p₀) . (2.5) As a special case when M = 2, the distributions of N under two hypotheses can thus be obtained as

Pr{N = n|H₀} ≈ exp

− (n − L₀p₀)² 2L₀p₀(1 − p₀)

p2πL₀p₀(1 − p₀) , (2.6)

Pr{N = n|H₁} ≈ exp

− (n − L₁p₀)² 2L₁p₀(1 − p₀)

p2πL₁p₀(1 − p₀) . (2.7)

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According to the conventional hypothesis testing theory [20, 21], the decision rule can be expressed using the likelihood ratio test Λ(N ) as

Λ(N ) = P (N |H1) P (N |H₀)

H1

H≷0

q0

q₁. (2.8)

If we assume equal a priori probabilities q₀ = q₁ = 1/2, due to the characteristic of Gaussian distribution shown in Fig. 5, the decision rule can be further reduced to

N

H1

H≷0

η (2.9)

for some threshold η, where η is the solution of the following equation:

Pr{N = η|H₀} = Pr{N = η|H₁}. (2.10) By (2.6) and (2.7), we have

r L₁ L0

= exp (L₁− L₀)(η²− p²₀L₀L₁) 2L0L1p0(1 − p0)

. (2.11)

Taking logarithms to both sides, the equation becomes

η = s

L₁L₀ln(L₁/L₀) L1− L0

p₀(1 − p₀) + p²₀L₀L₁. (2.12) In other words, if the received number of molecules is greater than the threshold η, the receiver will determine H₁ as the hypothesis testing result; otherwise H₀ will be decided.

2.3.2 M-ary Detection

The detection rule can be extended to M -ary detection with only a few adjust- ments. Suppose we have multiple hypotheses H_m where m ∈ {0, 1, 2, · · · , (M −1)}

which represent the transmission of L_m molecules. The goal is to decide which ˆm we should choose. The maximum a priori (MAP) detection rule is:

ˆ

m(N ) = argmax

m

P (N |H_m). (2.13)

Due to the properties of Gaussian distribution, the above MAP detection rule can be simplified to pairwise comparisons between the “neighboring” conditional probability distributions.

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Figure 5: Demonstration of the process of finding η in a binary QM system, where f is the conditional PDF of N given H_m is true.

To write down the expressions explicitly, we define a set of thresholds E = {η_j ∈ [−∞, ∞] : j = 0, 1, 2, · · · , M }, and let η₀ = −∞ and η_M = ∞. For j = 1, 2, · · · , (M − 1), η_j can be obtained by solving the equations

Pr{N = η_j|H_j−1} = Pr{N = η_j|H_j}. (2.14)

With the thresholds determined, the detection rule for M -ary transmission can be expressed as

ˆ

m(N ) =

M −1

X

k=0

k · u [−(N − η_k)(N − η_k+1)] . (2.15) where u(·) denotes the unit step function.

2.3.3 Error Rate Analysis

After the construction of the transmission and decision rules, we then analyze how it performs in terms of symbol or bit error rate. Consider a specific case for M = 2 and q₀ = q₁ = 1/2. Denote the false alarm probability as P_F and the missing probability as P_M. The error rate can be written as

P_e = q₀P_F+ q₁P_M= 1

2(P_F+ P_M). (2.16)

From Fig. 5 and the decision rule derived in Sec. 2.3.1, it can be shown that

P_F = Pr{N > η|H₀} = Q η − L₀p₀ pL₀p₀(1 − p₀)

!

, (2.17)

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2.4. SERIAL TRANSMISION AND ISI CANCELLATION 13

P_M = Pr{N < η|H₁} = Q L₁p₀ − η pL₁p₀(1 − p₀)

!

, (2.18)

where Q(·) denotes the Q-function. By substituting (2.12) into equation (2.17) and (2.18), we can evaluate the error rate P_ein (2.16). Fig. 6 shows the comparison between our analysis and numerical results.

10 20 30 40 50 60 70

10

⁻⁸

10

⁻⁶

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⁻⁴

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⁻²

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⁰

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1

(Maximum number of molecules transmitted per symbol)

SER

Numerical curve Theoretical curve

Figure 6: Theoretical result versus numerical result for one-shot binary quantity- based modulation.

2.4 Serial Transmision and ISI Cancellation

The above described QM molecular communication system seems to work already. However, in practical situations, we need to perform serial transmissions rather than one-shot transmission. Thus the ISI effect must be taken into account.

Our results show that if we do not modify our one-shot detection rule, the system performance will fall dramatically under serial transmission environments due to the severe ISI effect. To solve this problem, we propose a method to mitigate the ISI effect.

In order to mitigate the ISI effect, we first need an estimation of the number of

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2.4. SERIAL TRANSMISION AND ISI CANCELLATION 14

the delayed molecules that come from former time slots. If we know the conditional probability distribution of the number of ISI molecules conditioned on the current received number, then we can estimate the ISI effect as the conditional mean.

However, the conditional distribution does not have a closed-form solution for inverse Gaussian random variables. Here, we proposed another intuitive way to do this estimation.

First, we define “memory-Γ cancellation” to mean that the ISI effect during the past Γ time slots are taken into account when making decision. We first use memory-1 cancellation as a demonstrative example. If the number of molecules received during the (i−1)-th time slot is n_i−1and the decided transmission quantity level is ˆl_i−1, where ˆl_i−1 ∈ {L₀, L₁, · · · , L_{M −1}}, we then subtract ˆl_i−1· [F_X(2T_s) − F_X(T_s)] (the a priori expected received number in the i-th time slot from the (i − 1)-th time slot) from n_i before making the i-th decision, where F_X(·) is the cumulative distribution function (CDF) of the first-hitting time of molecules. In other words, the actual number ˜n_i used in making decision is

˜

n_i = n_i− ˆl_i−1· [F_X(2T_s) − F_X(T_s)]. (2.19) Likewise, we can perform memory-Γ cancellation if we have enough buffer at the receiver end to memorize temporarily the recently received numbers of molecules.

More explicitly, denote the probabilities that a single transmitted molecule arrives during the time interval [jTs, (j + 1)Ts] by pj for j ∈ N ∪ {0} as before.

If the decided transmission quantity level of the current time slot is ˆl, where ˆl ∈ {L₀, L₁, · · · , L_{M −1}}, then the received number of molecules j time slots later should be subtracted by ˆl · p_j+1 before making decision. In other words, if the number of molecules received in i-th time slot is n_i, the actual number ˜n_i used in making decision is

˜

n_i = n_i−

Γ

X

j=1

ˆl_i−jp_j+1. (2.20)

For binary QM systems, the decision rule can be written as

˜

n_i = n_i−

Γ

X

j=1

ˆl_i−jp_j+1^H≷¹

H0

η. (2.21)

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2.5. NUMERICAL RESULTS 15

The extension to M-ary QM systems is straightforward.

2.5 Numerical Results

In this section, we first discuss the binary and M -ary QM modulation systems with and without performing ISI cancellation. After that, we make comparisons of the system performance under different time slot durations.

The number of molecules is one of the main resources utilized in molecular communications. Analogous to the “power” concept in conventional communications, we need to take this number into account when comparing the system performances. In the following subsections, we present the results under different maximum number of molecules allowed per symbol, and the quantity levels are uniformly spaced. The simulation parameters are d = 0.2 cm, drift velocity v = 0.01 cm/sec, diffusion coefficient D = 0.05 cm²/sec , and time slot duration T_s = 5 sec.

2.5.1 SER Comparison with and without ISI Cancellation

In Fig. 7, a binary transmission system with memory-1 and memory-2 cancellation is considered. The SER drops from 0.04 to 0.01 when L₁ = 30, and drops from 10⁻² to 10⁻⁴ when L₁ = 90. The improvement grows as L₁ increases, which means that by choosing L₁ properly, a reliable end-to-end transmission can be achieved. We also observe that even without ISI cancellation, the error rate will drop as L₁ increases. The reason is that the spacing between symbols is increased.

However, as shown in Fig. 8, it is not the case for the quaternary transmission system. It can be seen that even though L₃ becomes large, the error rate is still high without ISI cancellation, which means we cannot rely solely on increasing the maximum number of molecules without ISI cancellation.

It is worth mentioning that the ISI cancellation method can be performed not only in such quantity-based modulation systems, but it can also be used in other systems like on-off keying¹ with slight modifications.

1Transmitting zero or a single molecule.

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No ISI cancellation

Memory−1 ISI cancellation Memory−2 ISI cancellation

Figure 7: Binary quantity-based modulation with ISI cancellation.

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No ISI cancellation Memory−1 cancellation Memory−2 cancellation

Figure 8: Quaternary quantity-based modulation with ISI cancellation.

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2.5.2 Performance Under Different Duration of Time Slot

In this subsection, we consider a binary transmission system with and without ISI cancellation for different time slot durations. From Fig. 9, we can observe that the SER decreases as the duration T_s increases. In other words, to improve performance, one can increase the duration of the time slot as shown in Fig. 9.

Although the error rate is already quite acceptable, it can be further improved by the ISI cancellation approach. The improvements is about 10 times better when T_s = 10 sec and L₁ = 70. Note that when T_s is small, say T_s = 1 sec, compared to the expected first-hitting time d/v, the error rate increases even if we increase L₁ when no cancellation is performed. This is because when T_s is small, molecules tend not to arrive in one symbol time but stay in the background, and that a larger L₁ will cause a larger amount of molecules to be in the background and hence larger interference.

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SER

Without ISI cancellation With memory−1 cancellation

T

s

= 10 sec

T

s

= 5 sec T

s

= 1 sec

Figure 9: Binary quantity-based modulation with ISI cancellation under different T_s.

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CHAPTER 3 QUANTITY-TYPE MODULATION

3.1 Introduction

To communicate between two nano-machines, several modulation techniques have been proposed to bear information [10, 12, 22–25]. Among various kinds of modulation, quantity [22] and type [23, 24] modulation is of our interests. Based on the design paradigms of both works, that the type of molecules could yield ad- ditional embedded information, and that the increase in the quantity of molecules per transmission could result in higher performance, we propose a new modulation scheme called quantity-type modulation. Consider a type-based modulated system, the transmitter releases different types of molecules representing different information bits or symbols. When the molecules arrive at the receiver, the receiver captures those molecules and attains information based on their types.

Nevertheless, the arrival times of the molecules at the receiver are random due to the diffusion process. This results in the phenomenon that the molecules released earlier may arrive late, leading to wrong information detection. A way to remedy this is to release a group of molecules of the same type at a time to improve the system reliability.

An intuitive method to detect the quantity-type modulated molecular communication system is using majority vote—information bits are detected according to the type of molecules that outnumber another. However, as it is shown in this paper, the performance of the majority vote detection algorithm is disappointing.

Hence, in this chapter, we introduce a novel detection algorithm called threshold- based detection by exploiting the characteristics of the diffusion channel. Theo- retical approximations of the bit error rate (BER) performance of the proposed threshold-based detection algorithm for the quantity-type-modulated molecular

18

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3.2. SYSTEM MODEL 19

communication system are derived. Both the simulation and theoretical results confirm the significant performance improvement over the majority vote detection, either without or with background noise.

3.2 System Model

In this section, based on the diffusion channel modeled by Brownian motion as in 2.2, we introduce the communication scheme adopted in this chapter.

3.2.1 Quantity-type Modulation

We assume that two types of information molecules , ‘A’ and ‘B’, have the same radius r and are distinguishable for both transmitter and receiver. This can be achieved by using isomers as described in [26]. The transmission is assumed to be time-slotted with interval T_s and the transmitter releases n molecules of one type at the beginning of each time slot to represent an information bit, where n is an odd number. That is, n type-A molecules represent bit ‘1’ and n type-B molecules represent bit ‘0’. In addition, the information bits are firstly partitioned into blocks with L bits. When nL molecules are released, the transmitter should wait for a period of time T before the next transmission. The receiver always gathers molecules on arrival, that is, there is no fixed time slots at the receiver and the asynchronous detection, i.e., majority-vote detection or threshold-based detection, is performed. Moreover, whenever nL molecules are captured, the receiver should also wait for a period of time T before the next detection. The waiting time between blocks is set to avoid detection errors caused by background noise (which will be mentioned in the next subsection) affecting the next block.

3.2.2 ISI and Noise Effect on Quantity-type Modulation

Due to the randomness of the first hitting times of transmitted molecules, a molecule may arrive at the receiver in advance of the molecule(s) released earlier . We use the term crossover to describe this phenomenon. Crossovers result in intersymbol interference (ISI) and may lead to detection errors.

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3.3. DETECTION ALGORITHMS 20

Figure 10: A demonstrative example for the majority-vote detection algorithm and the threshold-based detection algorithm with λ = 1 and λ = 2. The boxed numbers represent the value stored in the counter that reaches the threshold λ.

In diffusion-based molecular communications, it is likely for the receiver to capture molecules that are not released by the corresponding transmitter. Those unintended molecules, which we call background noise in the rest of this study, may come from the environment or other transmitters. We model the number of arriving unintended molecules as a Poisson random process {N (t) : t ≥ 0} and N (t + τ ) − N (t) follows Poisson(ατ ) with noise rate α.

3.3 Detection Algorithms

In this section, we first describe the majority-vote detection algorithm and then elaborate the proposed threshold-based detection algorithm.

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Figure 11: Block diagram of the threshold-based detection algorithm.

3.3.1 Majority-vote Detection

An intuitive detection method of the quantity-type-modulated molecular communication system is the majority vote, which counts the majority type of molecules once n molecules are gathered. We use an example to explain the majority-vote detection in Fig. 10. To illustrate that different types of molecules are released by the transmitter at different time slots, we use (U₁, U₂, U₃, · · · ) to represent that the transmitter releases a set of molecules U₁ at t = t₀, molecules U₂ at t = t₀+T_s, and molecules U₃at t = t₀+2T_s, and so on. Let us consider the example in Fig. 10, the transmitter releases (AAA, BBB, AAA, AAA, BBB) to convey the information sequence ‘1, 0, 1, 1, 0’. Due to the diffusion channel, the arriving molecules may be out of order. In this example, the receiver captures the molecules in the order of

‘A, A, B, A, B, A, B, A, A, A, A, B, B, B, A’. (3.1)

Note that in both (3.1) and “Received pattern” in Fig. 10, we do not show the time difference between two adjacently captured molecules, which may not be identical.

The majority-vote algorithm groups the molecules as ‘A, A, B’, ‘A, B, A’, ‘B, A,

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A’, ‘A, A, B’, and ‘B, B, A’, and determines the majority type in each group as

‘A’, ‘A’, ‘A’, ‘A’, and ‘B’. Therefore, the detected bits are ‘1, 1, 1, 1, 0’, which has one bit error. This error results from the effect of ISI as described in Sec. 3.2.2.

3.3.2 Threshold-based Detection

To develop a detection algorithm that is suitable for operating under the diffusion channel, let us first gain some insights about how the diffusion-based molecular communication system is performed. Consider a case that the transmitter releases (A, B), i.e., the transmitter releases a molecule of type A and then a molecule of type B after a time duration T_s. It is likely that the receiver receives ‘B, A’, which results in bit errors. However, if the transmitter releases (AAA , BBB), i.e., the transmitter releases three molecules of type A and then three molecules of type B after a time duration T_s, the probability that the receiver receives ‘B, B, B, A, A, A’ is small since it requires many crossovers happening to obtain this pattern. It is more likely that at least one type-A molecule arrives earlier than all the type-B molecules. Therefore, a reasonable principle for designing detection algorithm would be: once the receiver captures a type-A molecule before capturing a type-B molecule, the receiver infers that the transmitter releases (AAA) before (BBB). The remaining two type-A molecules that arrive later provide relatively little information, and they may even introduce ISI to other molecules; hence the receiver should ignore those two late-arriving molecules.

Based on the above observation, we propose the threshold-based detection algorithm. As shown in Fig. 11, the detector is composed of a classifier, two counters, and two threshold comparators. The classifier recognizes the type of the arriving molecules. If the arriving molecule belongs to type A, the classifier generates a signal to counter A; if the arriving molecule belongs to type B, the classifier generates a signal to counter B. Counter A and counter B are used to count the number of arriving molecules of type A and B, respectively. Whenever a signal is sensed by the counter, it increases its stored value by one. The values stored in the counters are denoted by V_A and V_B respectively. When the value stored in

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the counter reaches a predetermined threshold λ, bit ‘1’ or ‘0’ is generated. Once the stored value reaches n, the stored value is reset to zero. Note that when V_Aor V_B is in the region (λ, n], no output is generated by the detector. That is, n − λ molecules with the same type are ignored by the receiver.

Fig. 10 shows a simple example that does not consider the noise effect (or the noise rate α is negligibly small). The detection result in this example has no bit error. An example of the threshold-based detection algorithm considering the background noise is shown in Fig. 12. The transmitter releases three molecules at a time and the receiver applies the threshold-based detection with threshold λ = 3. In this example, only the background noise caused by type-A molecules is considered. The unintended molecules are equivalently inserted into the receiving molecule pattern. The inserted molecules cause wrong increment of the value stored in the counter, making the receiver output an erroneously detected bit.

This is termed bit insertion. When this happens, the detected bit sequence is right-shifted compared with the actual bit sequence.

Since n molecules are released in each symbol duration, the total number of arriving molecules at the receiver should be nL for each block. However, due to the background noise, the total number of molecules may be greater than nL. The proposed scheme in Sec. 3.2.1 suggests that after nL molecules are received, the receiver ignores the late-arriving molecules for a period of T . We set T = 2T_s since the probability that a molecule arrives late for more than 2T_s is small.

3.3.3 Trade-offs when Combating ISI and Noise Effect on Quantity- type Modulation

ISI comes from the crossover effect of the released molecules. Intuitively, adopt- ing a larger signaling interval T_s at the transmitter will decrease the probability of crossovers. However, as T_s grows larger, the number of unintended molecules captured by the receiver during each symbol detection will increase. Thus, we expect that there should be an optimal T_s which minimizes the detection error caused by both ISI and background noise. The optimal T_s for threshold-based

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Figure 12: A demonstrative example for the detection result under background noise using the threshold-based detection algorithm. λ = 3. In the example, the crossover effect is not taken into account.

detection will be derived in Sec. 3.4.

It can be observed that detection errors occur when unintended molecules are captured by the receiver, which causes the value stored in the counter to reach the threshold λ too early. Therefore, to combat the background noise, we may increase the value of λ. However, as will be shown later, a small λ is better for combating ISI. Details in determining λ is discussed in Sec. 3.5. Moreover, the value of n also affects the system performance since λ ≤ n, that is, n limits the possible choices of λ.

To deal with the background noise, it is also possible to modify the block size L. The effects of background noise can be mitigated by using a smaller L since the number of unintended molecules in a block can be reduced. Nevertheless, when a smaller block size is used, the total throughput decreases due to the longer duration between blocks.

In the next section, we analyze the system performance in the sense of bit

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3.4. BER ANALYSIS 25

error rate (BER). Based on the BER performance, principles of choosing the above-mentioned system parameters will be discussed in Sec. 3.5.

3.4 BER Analysis

In this section, we mathematically compare the BER performance of the majority- vote detection algorithm and the proposed threshold-based detection algorithm.

In the following, we first derive BER under the case that the background noise is negligible, i.e. α approaches zero. We then analyze the case when α is not negligible such that increasing T_s would introduce more unintended molecules at the receiver.

3.4.1 Preliminaries

For the i-th information bit s_i ∈ {0, 1}, n molecules of type A or B are released.

By assuming that the prior probabilities Pr{s_i = 0} = Pr{s_i = 1} = 1/2, the BER can be written as

Pr{bs_i 6= s_i} = 1

2Pr{bs_i = 1|s_i = 0} +1

2Pr{bs_i = 0|s_i = 1}

= Pr{bs_i = 0|s_i = 1}, (3.2)

where bs_i is the information bit detected by the receiver. Equivalently, we can compute (3.2) by

Pr{bs_i 6= s_i} = 1

4Pr{bs_i = 0|s_i−1= 0, s_i = 1, s_i+1 = 0} +1

4Pr{bs_i = 0|s_i−1= 0, s_i = 1, s_i+1= 1}

+ 1

4Pr{bs_i = 0|s_i−1= 1, s_i = 1, s_i+1 = 0} +1

4Pr{bs_i = 0|s_i−1= 1, s_i = 1, s_i+1= 1}.

(3.3) Each term in (3.3) is affected by the ISI from {s_i−2, s_i−3, · · · } and {s_i+2, s_i+3, · · · }.

Here, we assume that the errors due to crossover of molecules happening to neighboring information bits are dominant compared with the error due to crossover of molecules happening to information bits that are more than two time intervals apart. Therefore, we compute (3.3) by considering the relations of s_i−1, s_i, and s_i+1 only.

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Denote the first hitting time of the n molecules released for representing s_i as independent and identically distributed (i.i.d.) random samples X₁(i), · · · , X_n(i).

From the theorem of order statistics, if X₁(i), · · · , X_n(i) are arranged in increasing order as X₍₁₎(i) ≤ · · · ≤ X_(n)(i), the PDF and the cumulative density function (CDF) for the k-th smallest one are, respectively,

fX_(k)(y) = nn − 1 k − 1

FX(y)^k−1[1 − FX(y)]^n−kfX(y), (3.4) and

F_X_(k)(y) =

n

X

j=k

n j

F_X(y)^j[1 − F_X(y)]^n−j, (3.5) where F_X(y) is the CDF of X. Note that both (3.4) and (3.5) are defined on y > 0.

Now we define the switching between two symbols s_i and s_j as the event bsi = sj,bsj = si for si 6= sj. For convenience, we define the events Epqr and bEpqr

respectively as

E_pqr = {s_i−1= p, s_i = q, s_i+1= r},

Eb_pqr = {bs_i−1= p,bs_i = q,bs_i+1= r}. (3.6) We use the superscript to distinguish the majority-vote detection and the threshold- based detection forbs_i and bE_pqr, i.e.,bs^MVD_i and bE_pqr^MVD for the majority-vote detection, and bs^TD_i and bE_pqr^TD(λ) for the threshold-based detection with threshold λ.

3.4.2 Analysis when Background Noise is Negligible

Let us begin by analyzing the majority-vote detection. To calculate the BER of the majority-vote detection, denoted by P_c^MVD, (3.3) is rewritten as

P_c^MVD = Pr{bs^MVD_i 6= s_i}

= 1

4Pr{bs^MVD_i = 0|E₀₁₀} + 1

4Pr{bs^MVD_i = 0|E₀₁₁} +1

4Pr{bs^MVD_i = 0|E₁₁₀} + 1

4Pr{bs^MVD_i = 0|E₁₁₁}. (3.7)

In the first term of (3.7), given E₀₁₀, the event bs_i = 0 happens when either of the following conditions is satisfied:

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1. Molecules representing s_i cross over molecules representing s_i+1and then the event bE₀₀₁^MVD happens.

2. Molecules representing s_i−1cross over molecules representing s_i and then the event bE₁₀₀^MVD happens.

3. Molecules representing s_i−1, s_i, and s_i+1cross over in the way that the type- B molecules outnumber type-A molecules for all three detected symbols, and then the event bE₀₀₀^MVD happens.

Note that the above observation is made with the assumption in Sec. 3.4.1 that detection errors due to ISI is dominated by the crossovers of molecules from neighboring information bits, namely, s_i−1 and s_i+1. Fig. 13 shows example outcomes given the event E₀₁₀ which corresponds to the conditions mentioned above: the first outcome results from two crossovers between s_i and s_i+1, the second outcome results from two crossovers between s_i and s_i−1, and the third outcome results from one crossover between s_i and s_i+1 and one between s_i and s_i−1. The second and third terms in (3.7) follow similar arguments. Given E₀₁₁ or E₁₁₀, the event bs_i = 0 is equivalent to bE₁₀₁^MVD. The final term in (3.7) equals 0 since given event E₁₁₁, bs_i = 0 is impossible. Therefore, by the assumption in Sec. 3.4.1, we have P_c^MVD≈ 1

4Pr{ bE₀₀₁^MVD∪ bE₁₀₀^MVD∪ bE₀₀₀^MVD|E₀₁₀} +1

4Pr{ bE₁₀₁^MVD|E₀₁₁} +1

4Pr{ bE₁₀₁^MVD|E₁₁₀}.

(3.8) To furthur compute (3.8), we need the following lemma.

Lemma. Assume that the switching other than s_i and s_i+1is negligible. Under the quantity-type modulation and majority-vote detection without background noise, two transmitted symbols s_i and s_i+1 switch if and only if s_i 6= s_i+1, and the order statistics X₍ⁿ⁺¹

2 )(i) and X₍ⁿ⁺¹

2 )(i + 1) satisfy X₍ⁿ⁺¹

2 )(i) > X₍ⁿ⁺¹

2 )(i + 1) + T_s. (3.9)

Proof. Without loss of generality, we assume that s_i = 1 and s_i+1 = 0. For the

“if” part, the condition (3.9) is equivalent to having the crossover between the

擴散式分子通訊下之調變設計

國立臺灣大學電機資訊學院電信工程研究所 碩士論文

Graduate Institute of Computer Science and Information Engineering College of Electrical Engineering and Computer Science

National Taiwan University Master Thesis

擴散式分子通訊下之調變設計

Modulation Design in Diffusion-based Molecular Communication System

林維安 Wei-An Lin

指導教授：葉丙成 博士 Advisor: Ping-Cheng Yeh, Ph.D.

中華民國 103 年 7 月

July, 2014

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ABSTRACT

TABLE OF CONTENTS

LIST OF FIGURES

CHAPTER 1

INTRODUCTION

1.1 Overview

Transmission Nano-machine

(TN)

Reception Nano-machine

(RN) Diffusion

Process

1.2 Coherent Molecular Communication

time

time

TN

RN

1.3 Non-coherent Molecular Communication

1.4 Thesis Organization

CHAPTER 2

QUANTITY MODULATION

2.1 Introduction

2.2 System Model

2.3 Detection in One-shot Transmission

10 20 30 40 50 60 70

10

10

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10

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L

(Maximum number of molecules transmitted per symbol)

Numerical curve Theoretical curve

2.4 Serial Transmision and ISI Cancellation

2.5 Numerical Results

10 20 30 40 50 60 70 80 90

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10

10

10

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(Maximum number of molecules transmitted per symbol)

No ISI cancellation

Memory−1 ISI cancellation Memory−2 ISI cancellation

100 150 200 250 300 350 400 450 500

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10

10

10

10

10

L

(Maximum number of molecules transmitted per symbol)

No ISI cancellation Memory−1 cancellation Memory−2 cancellation

10 20 30 40 50 60 70

10

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國立臺灣大學電機資訊學院電信工程研究所碩士論文

指導教授：葉丙成博士 Advisor: Ping-Cheng Yeh, Ph.D.

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