無通道資訊下多輸入多輸出無線傳輸系統之實體層保密技術

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研究生：	劉大源 Liu, Ta Yuan
論文名稱：	無通道資訊下多輸入多輸出無線傳輸系統之實體層保密技術 Physical Layer Secrecy in Multiple-Input Multiple-Output Wireless Systems with No A Priori Channel State Information
指導教授：	洪樂文 Hong, Yao Win
口試委員:	蘇炫榮蔡尚澕翁詠祿林士駿陸曉峯
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2016
畢業學年度：	104
語文別：	英文
論文頁數：	115
中文關鍵詞：	實體層保密技術、竊聽者通道、通道估計、基於訓練訊號之通訊策略、人工雜訊、功率分配、非同調、保密自由度、多天線系統、多跳躍式網路、網路編碼、中繼點
外文關鍵詞：	Physical layer secrecy, wiretap channel, channel estimation, training-based transmission, artificial noise, power allocation, noncoherent, secure degrees of freedom, multiantenna systems, multihop networks, network coding, relay
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這篇論文探討在所有節點都沒有通道資訊(channel state information, CSI) 下之實體層保密通訊技術(physical layer
secrecy)的研究。論文內容可以分成兩個部份，在第一個部份，我們
研究當系統使用基於訓練訊號之傳輸策略(training-based
transmission scheme)時，該如何最佳化訓練階段(training phase)
和資料傳輸階段(data transmission phase)的資源分配以達到最大的保密傳輸速率(achievable secrecy rate)。接著在第二部分，我們更進一步研究當所有傳輸策略都可能被使用的情況下，系統的理論傳輸上限並推導出系統的最大保密自由度(secure degrees of freedom)。
在第一部分，我們考慮多輸入單輸出(multiple-input single-output, MISO)的瑞利區塊衰減竊聽通道(Rayleigh block fading wiretap channel)系統，並將通訊分成兩個階段，訓練階段以及資料傳輸階段，訓練階段所獲得到通道資訊將被用來協助保密資料的傳輸。在訓練階段我們考慮兩種不同的訓練策略，一種是傳統不考慮有竊聽者存在的訓練策略，另一種則是考量竊聽者存在的差異性通道估計(discriminatory channel estimate, DCE)策略，在此訓練策略中傳送端會透過傳送人工雜訊(artificial noise, AN)來干擾竊聽者的通道估計。在資料傳輸階段系統則透過保密波束成型(secrecy
beamforming)技術和人工雜訊的幫助來傳輸保密訊息。為了最佳化兩階段的資源分配，我們首先推導了在非完美通道資訊下的保密傳輸速率的上下界，並進一步證明當系統處於高訊雜比(signal to noise ratio, SNR)時，此上下界是很接近的。接著透過最大化此一保密傳輸速率，我們提出了在訓練訊號、人工雜訊以及資料訊號之間的最佳化功率分配，同時也檢視了該如何有效率地在訓練和資料傳輸階段使用人工雜訊，我們發現當通道變化的很緩慢時，我們應該投入更多的資源在訓練階段使用人工雜訊。然而在系統處於低訊雜比時，使用人工雜訊並沒有辦法帶來太多效益，更甚者我們發現此時基於訓練訊號之傳輸策略並不是最有效率的傳輸方式。
因此在論文的第二部分，我們將不侷限於只考慮基於訓練訊號之傳輸策略，更根本的探討系統的最大保密傳輸速率。在此我們考慮多輸入多輸出(multiple-input multiple-output, MIMO)瑞利區塊衰減竊聽通道，通道在時間T之內將會維持不變，每次經過T時間都會隨機且獨立地變化，傳送端、接收端和竊聽者分別擁有nt、nr及ne根天線，並且考慮通訊系統所有節點都沒有通道資訊的初始狀態。當T>2min(nt,nr)時，我們推導出系統在高訊雜比時的保密傳輸速率隨功率上昇的速率上界(即最大保密自由度) ，會是(min(nt,nr)-ne)(T-min(nt,nr))/T，其中前項可以被看作是合法使用會因為竊聽者的存在而損失了的自由度，而後項則可視為缺乏通道資訊所造成的影響。我們並證明此一最大保密自由度可以透過使用常範數輸入訊號(constant norm input)來達成。在系統沒有通道資訊的情況下，如果想要達到高於0 的保密自由度，則使用者必須要同時擁有複數的空間自由度以及時間自由度。
我們也將第二部分的研究延伸到非同調多跳躍式網路(noncoherent multihop networks)系統，並探討當系統部分中繼點(relay)有被竊聽的風險時，該如何選擇是否雇傭中繼點。我們首先推導此一網路的保密通道容量(secrecy capacity)，並藉由檢視保密通道容量決定是否雇傭有風險的中繼點。當系統所有有風險的中繼點都有一定機率被竊聽，並且有風險的中繼點個數十分眾多時，我們發現只要被竊聽的機率小於一定的閾值，則系統就應該選擇雇傭所有有風險的中繼點。我們同時也提供模擬結果來驗證和說明論文中的各個理論論述。

This dissertation examines the transmission of confidential messages over a wireless wiretap system with no a priori channel state information (CSI) at any terminal. The studies can be divided into two parts. The first part focuses on conventional training-based transmissions schemes and examines the tradeoff between training and data transmission in wiretap channels; the second part makes no assumption on the transmission scheme and evaluates the asymptotic performance of such a system at high SNR.
More specifically, in the first part, training-based transmission schemes are considered for multi-input single-output (MISO) Rayleigh block fading wiretap channels, where each block consists of a training phase followed by a data transmission phase. By taking the cost of obtaining CSI into account, this work considers the joint design of training and data transmission in physical-layer secret communication systems, and examines the role of artificial noise (AN), a key component in many physical layer secret communication techniques, in both of these phases. In particular, AN in the training phase is used to prevent the eavesdropper from obtaining accurate CSI whereas AN in the data transmission phase can be used to mask the transmission of the confidential message. By considering AN-assisted training and secrecy beamforming schemes, upper and lower bounds on the achievable secrecy rate is derived in a closed-form approximation that is asymptotically tight at high signal-to-noise ratio (SNR). Then, by maximizing the approximate achievable secrecy rate, the optimal power allocation between signal and AN in both training and data transmission phases is obtained for both conventional and AN-assisted training based schemes. We show that the use of AN is necessary to achieve a high secrecy rate at high SNR, and its use in the training phase can be more efficient than that in the data transmission phase when the coherence time is large. However, at low SNR, the use of AN provides no advantage since CSI is difficult to obtain in this case. In fact, allocating channel resources for training is inefficient and one can actually do better without it in this case. Numerical results are presented to verify our theoretical claims.
Even though training-based transmission schemes have been widely adopted in practice, the optimality of such an approach is unknown and is in fact disproved in conjunction with the secrecy beamforming scheme mentioned in the first part. Therefore, a more general and fundamental study of the wiretap channel with no CSI anywhere is considered in the second part of this dissertation. In particular, we consider a multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel where the source, the destination, and the eavesdropper have nt, nr and ne antennas, respectively. The length of the coherence interval, where the channel coefficients remain constant within each interval, but vary independently from block to block, is denoted by T. The performance at high SNR is evaluated in terms of the secure degrees of freedom (s.d.o.f.), when T ≥ 2 min(nt, nr). We show that, in this case, the s.d.o.f. is exactly equal to (min(nt, nr)−ne)(T−min(nt, nr))/T . The first multiplicative term in this expression can be interpreted as the loss of ne spatial degrees of freedom at both the transmitter and the legitimate receiver due to the ne receive antennas at the eavesdropper. The second term can be viewed as the ratio of s.d.o.f. remaining after expending resources to acquire CSI at the legitimate receiver. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions. We also show that multiple dimensions in both space and time are needed to achieve a non-zero s.d.o.f. for systems without CSI. That is, one cannot achieve a positive s.d.o.f. with either a long coherence time in a single antenna system or with multiple antennas in a very short (T = 1) coherence time channel.
The techniques developed in the second part is also used to examine the performance of a noncoherent network coding system with multiple hops of intermediate relays. A relay recruitment problem is considered for the case where some of the relays are untrustworthy and may be subject to eavesdropping. The source wishes to enlist their help while keeping the message secret against the eavesdropper. By employing random linear network coding at the relays, the problem can be modeled as a noncoherent finite-field wiretap channel. The secrecy capacity is examined and the input distribution is optimized using an efficient projection-based gradient decent algorithm. The untrusted relay recruitment problem is discussed based on the derived secrecy capacity. An interesting scenario is analyzed where each potentially insecure relay may be randomly eavesdropped with a certain probability. Our asymptotic analysis reveals that, with enough untrusted relays, there exists a threshold on the eavesdropping probability below which all untrusted relays should be recruited. Numerical results are presented to illustrate and verify our theoretical claims.

Abstract i
Contents iv
1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Related Works 9
2.1 Training-based Transmission Scheme with/without Secrecy Consideration . . 10
2.2 Secure Degrees of Freedom with Different Levels of Channel State Information 11
2.3 Secure Network Coding and Wiretap Channels with Untrusted Relays . . . . 13
3 Training-Based Transmission Schemes for Fading Wiretap Channels 15
3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Training Phase - AN-Assisted Training . . . . . . . . . . . . . . . . . 17
3.1.2 Data Transmission Phase - AN-Assisted Secrecy Beamforming . . . . 19
3.2 Bounds on the Achievable Secrecy Rate with Channel Estimation Error . . . 21
iv
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3.3 AN-Assisted Secrecy Beamforming with Conventional Training in the High
SNR Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Asymptotic Approximation of the Achievable Secrecy Rate . . . . . . 24
3.3.2 Joint Power Allocation between Training and Data Transmission . . . 27
3.4 AN-Assisted Secrecy Beamforming with DCE (i.e., AN-Assisted) Training in
the High SNR Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Asymptotic Approximation of the Achievable Secrecy Rate . . . . . . 29
3.4.2 Joint Power Allocation between Training and Data Transmission . . . 32
3.4.3 Comparison with the Conventional Training Case . . . . . . . . . . . 34
3.5 Secrecy Rate in the Low SNR Regime . . . . . . . . . . . . . . . . . . . . . . 35
3.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Fundamental Limits of Fading Wiretap Channels with No CSI 44
4.1 System Model and Problem Formulation . . . . . . . . . . . . . . . . . . . . 44
4.2 Summary of the Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 Proof of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.1 Converse Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2 Achievability Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . 57
4.5 Proof of Lemma 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Secure Degrees of Freedom for Short Coherence Time Systems . . . . . . . . 60
5 Extensions to Secure Network Coding Systems with Untrusted Relays 64
v
_
5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 Secrecy Capacity of the Noncoherent Secure Network Coding System . . . . 68
5.4 Untrusted Relay Recruitment Problem . . . . . . . . . . . . . . . . . . . . . 70
5.4.1 Eavesdropping of All Untrusted Relays Near the Destination . . . . . 72
5.4.2 Random Eavesdropping of Untrusted relays . . . . . . . . . . . . . . 74
5.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6 Conclusion 79
Appendices 81
A Proofs in Chapter 3 82
A.1 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
A.1.1 Lower Bound of I(sd; yd|ˆ h) . . . . . . . . . . . . . . . . . . . . . . . . 82
A.1.2 Upper Bound of I(sd; yd|ˆ h) . . . . . . . . . . . . . . . . . . . . . . . 83
A.2 Proof of Theorem 2 and Corollary 2 . . . . . . . . . . . . . . . . . . . . . . . 85
A.2.1 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A.2.2 Proof of Corollary 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
A.3 Proof of (3.24) in Section 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.4 Proof of Theorem 3 and Corollary 3 . . . . . . . . . . . . . . . . . . . . . . . 89
A.4.1 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
A.4.2 Proof of Corollary 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
vi
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A.5 Proof of Corollary 4 in Section 3.4 . . . . . . . . . . . . . . . . . . . . . . . . 92
B Proofs in Chapter 4 95
B.1 Proof of Lemma 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
B.2 Proof of Lemma 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.3 Proof of Lemma 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B.4 Proof of Lemma 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
B.5 Proof of Lemma 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
B.6 Proof of Lemma 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
C Proofs in Chapter 5 109
C.1 Proof of Theorem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

                                

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