Physical layer security (PLS) is a new paradigm aiming at securing communications between legitimate parties at the physical layer. Conventionally, achieving confidentiality in communication networks relies on cryptographic techniques such as public-key cryptography, secret-key distribution and symmetric encryption. Such techniques are deemed secure based on the assumption of limited computational abilities of a wiretapper. Given the relentless progress in computational capacities and the dynamic topology and proliferation of modern wireless networks, the relevance of the previous techniques in securing communications is more and more questionable and less and less reliable. In contrast to this paradigm, PLS does not assume a specific computational power at any eavesdropper, its premise to guarantee provable security via employing channel coding techniques at the physical layer exploiting the inherent randomness in most communication systems. In this dissertation, we investigate a particular aspect of PLS, which is secret-key agreement, also known as secret-sharing. In this setup, two legitimate parties try to distill a secret-key via the observation of correlated signals through a noisy wireless channel, in the presence of an eavesdropper who must be kept ignorant of the secret-key. Additionally, a noiseless public channel is made available to the legitimate parties to exchange public messages that are also accessible to the eavesdropper. Recall that key agreement is an important aspect toward realizing secure communications in the sense that the key can be used in a one-time pad scheme to send the confidential message. In the first part, our focus is on secret-sharing over Rayleigh fading quasi-static channels. We study the fundamental relationship relating the probability of error and a given target secret-key rate in the high power regime. This is characterized through the diversity multiplexing tradeoff (DMT) concept, that we define for our model and then characterize it. We show that the impact of the secrecy constraint is to reduce the effective number of transmit antennas by the number of antennas at the eavesdropper. Toward this characterization, we provide several schemes achieving the DMT and we highlight disparities between coding for the wiretap channel and coding for secret-key agreement. In the second part of the present work, we consider a fast-fading setting in which the wireless channels change during each channel use. We consider a correlated environment where transmit, legitimate receiver and eavesdropper antennas are correlated. We characterize the optimal strategy achieving the highest secret-key rate. We also identify the impact of correlation matrices and illustrate our analysis with various numerical results. Finally, we study the system from an energy-efficiency point of view and evaluate relevant metrics as the minimum energy required for sharing a secret-key bit and the wideband slope.

This thesis studies some fundamental aspects of wireless systems with partial channel state information at the transmitter (CSIT), with a special emphasis on the high signal-to-noise ratio (SNR) regime. The first contribution is a study on multi-layer variable-rate communication systems with quantized feedback, where the expected rate is chosen as the performance measure. Iterative algorithms exploiting results in the literature of parallel broadcast channels are developed to design the system parameters. Necessary and sufficient conditions for single-layer coding to be optimal are derived. In contrast to the ergodic case, it is shown that a few bits of feedback information can improve the expected rate dramatically. The next part of the thesis is devoted to characterizing the tradeoff between diversity and multiplexing gains (D-M tradeoff) over slow fading channels with partial CSIT. In the multiple-input multiple-output (MIMO) case, we introduce the concept of minimum guaranteed multiplexing gain in the forward link and show that it influences the D-M tradeoff significantly. It is demonstrated that power control based on the feedback is instrumental in achieving the D-M tradeoff, and that rate adaptation is important in obtaining a high diversity gain even at high rates. Extending the D-M tradeoff analysis to decode-and-forward relay channels with quantized channel state feedback, we consider several different scenarios. In the relay-to-source feedback case, it is found that using just one bit of feedback to control the source transmit power is sufficient to achieve the multiantenna upper bound in a range of multiplexing gains. In the destination-to-source-and-relay feedback scenario, if the source-relay channel gain is unknown to the feedback quantizer at the destination, the diversity gain only grows linearly in the number of feedback levels, in sharp contrast to an exponential growth for MIMO channels. We also consider the achievable D-M tradeoff of a relay network with the compress-and-forward protocol when the relay is constrained to make use of standard source coding. Under a short-term power constraint at the relay, using source coding without side information results in a significant loss in terms of the D-M tradeoff. For a range of multiplexing gains, this loss can be fully compensated for by using power control at the relay. The final part of the thesis deals with the transmission of an analog Gaussian source over quasi-static fading channels with limited CSIT, taking the SNR exponent of the end-to-end average distortion as performance measure. Building upon results from the D-M tradeoff analysis, we develop novel upper bounds on the distortion exponents achieved with partial CSIT. We show that in order to achieve the optimal scaling, the CSIT feedback resolution must grow logarithmically with the bandwidth ratio for MIMO channels. The achievable distortion exponent of some hybrid schemes with heavily quantized feedback is also derived. As for the half-duplex fading relay channel, combining a simple feedback scheme with separate source and channel coding outperforms the best known no-feedback strategies even with only a few bits of feedback information. / QC 20100817

The theory of lattices --- a mathematical approach for representing infinite discrete points in Euclidean space, has become a powerful tool to analyze many point-to-point digital and wireless communication systems, particularly, communication systems that can be well-described by the linear Gaussian vector channel model. This is mainly due to the three facts about channel codes constructed using lattices: they have simple structure, their ability to achieve the fundamental limits (the capacity) of the channel, and most importantly, they can be decoded using efficient decoders called lattice decoders. Since its introduction to multiple-input multiple-output (MIMO) wireless communication systems, sphere decoders has become an attractive efficient implementation of lattice decoders, especially for small signal dimensions and/or moderate to large signal-to-noise ratios (SNRs). In the first part of this dissertation, we consider sphere decoding algorithms that describe lattice decoding. The exact complexity analysis of the basic sphere decoder for general space-time codes applied to MIMO wireless channel is known to be difficult. Characterizing and understanding the complexity distribution is important, especially when the sphere decoder is used under practically relevant runtime constraints. In this work, we shed the light on the (average) computational complexity of sphere decoding for the quasi-static, LAttice Space-Time (LAST) coded MIMO channel. Sphere decoders are only efficient in the high SNR regime and low signal dimensions, and exhibits exponential (average) complexity for low-to-moderate SNR and large signal dimensions. On the other extreme, linear and non-linear receivers such as minimum mean-square error (MMSE), and MMSE decision-feedback equalization (DFE) are considered attractive alternatives to sphere decoders in MIMO channels. Unfortunately, the very low decoding complexity advantage that these decoders can provide comes at the expense of poor performance, especially for large signal dimensions. The problem of designing low complexity receivers for the MIMO channel that achieve near-optimal performance is considered a challenging problem and has driven much research in the past years. The problem can solved through the use of lattice sequential decoding that is capable of bridging the gap between sphere decoders and low complexity linear decoders (e.g., MMSE-DFE decoder). In the second part of this thesis, the asymptotic performance of the lattice sequential decoder for LAST coded MIMO channel is analyzed. We determine the rates achievable by lattice coding and sequential decoding applied to such a channel. The diversity-multiplexing tradeoff under such a decoder is derived as a function of its parameter--- the bias term. In this work, we analyze both the computational complexity distribution and the average complexity of such a decoder in the high SNR regime. We show that there exists a cut-off multiplexing gain for which the average computational complexity of the decoder remains bounded. Our analysis reveals that there exists a finite probability that the number of computations performed by the decoder may become excessive, even at high SNR, during high channel noise. This probability is usually referred to as the probability of a decoding failure. Such probability limits the performance of the lattice sequential decoder, especially for a one-way communication system. For a two-way communication system, such as in MIMO Automatic Repeat reQuest (ARQ) system, the feedback channel can be used to eliminate the decoding failure probability. In this work, we modify the lattice sequential decoder for the MIMO ARQ channel, to predict in advance the occurrence of decoding failure to avoid wasting the time trying to decode the message. This would result in a huge saving in decoding complexity. In particular, we will study the throughput-performance-complexity tradeoffs in sequential decoding algorithms and the effect of preprocessing and termination strategies. We show, analytically and via simulation, that using the lattice sequential decoder that implements a simple yet efficient time-out algorithm for joint error detection and correction, the optimal tradeoff of the MIMO ARQ channel can be achieved with significant reduction in decoding complexity.

The theory of lattices --- a mathematical approach for representing infinite discrete points in Euclidean space, has become a powerful tool to analyze many point-to-point digital and wireless communication systems, particularly, communication systems that can be well-described by the linear Gaussian vector channel model. This is mainly due to the three facts about channel codes constructed using lattices: they have simple structure, their ability to achieve the fundamental limits (the capacity) of the channel, and most importantly, they can be decoded using efficient decoders called lattice decoders. Since its introduction to multiple-input multiple-output (MIMO) wireless communication systems, sphere decoders has become an attractive efficient implementation of lattice decoders, especially for small signal dimensions and/or moderate to large signal-to-noise ratios (SNRs). In the first part of this dissertation, we consider sphere decoding algorithms that describe lattice decoding. The exact complexity analysis of the basic sphere decoder for general space-time codes applied to MIMO wireless channel is known to be difficult. Characterizing and understanding the complexity distribution is important, especially when the sphere decoder is used under practically relevant runtime constraints. In this work, we shed the light on the (average) computational complexity of sphere decoding for the quasi-static, LAttice Space-Time (LAST) coded MIMO channel. Sphere decoders are only efficient in the high SNR regime and low signal dimensions, and exhibits exponential (average) complexity for low-to-moderate SNR and large signal dimensions. On the other extreme, linear and non-linear receivers such as minimum mean-square error (MMSE), and MMSE decision-feedback equalization (DFE) are considered attractive alternatives to sphere decoders in MIMO channels. Unfortunately, the very low decoding complexity advantage that these decoders can provide comes at the expense of poor performance, especially for large signal dimensions. The problem of designing low complexity receivers for the MIMO channel that achieve near-optimal performance is considered a challenging problem and has driven much research in the past years. The problem can solved through the use of lattice sequential decoding that is capable of bridging the gap between sphere decoders and low complexity linear decoders (e.g., MMSE-DFE decoder). In the second part of this thesis, the asymptotic performance of the lattice sequential decoder for LAST coded MIMO channel is analyzed. We determine the rates achievable by lattice coding and sequential decoding applied to such a channel. The diversity-multiplexing tradeoff under such a decoder is derived as a function of its parameter--- the bias term. In this work, we analyze both the computational complexity distribution and the average complexity of such a decoder in the high SNR regime. We show that there exists a cut-off multiplexing gain for which the average computational complexity of the decoder remains bounded. Our analysis reveals that there exists a finite probability that the number of computations performed by the decoder may become excessive, even at high SNR, during high channel noise. This probability is usually referred to as the probability of a decoding failure. Such probability limits the performance of the lattice sequential decoder, especially for a one-way communication system. For a two-way communication system, such as in MIMO Automatic Repeat reQuest (ARQ) system, the feedback channel can be used to eliminate the decoding failure probability. In this work, we modify the lattice sequential decoder for the MIMO ARQ channel, to predict in advance the occurrence of decoding failure to avoid wasting the time trying to decode the message. This would result in a huge saving in decoding complexity. In particular, we will study the throughput-performance-complexity tradeoffs in sequential decoding algorithms and the effect of preprocessing and termination strategies. We show, analytically and via simulation, that using the lattice sequential decoder that implements a simple yet efficient time-out algorithm for joint error detection and correction, the optimal tradeoff of the MIMO ARQ channel can be achieved with significant reduction in decoding complexity.

This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks. KPP networks can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable. Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.

This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

Abstract This thesis is devoted to studying two wireless relay network models, namely wireless tandem multiple-input-multiple-output (MIMO) relay networks and wireless two-hop multicast relay networks. Regarding wireless tandem MIMO relay networks, we develop a systematic approach to analyze their fundamental diversity-multiplexing tradeoff (DMT) under the assumption that the relays implement a class of practical full-duplex techniques that enable them to opt for either full-duplex or half-duplex mode. Based on the analysis, we make contribution from the following aspects: First of all, we thoroughly compare the performance of full-duplex and half-duplex mode operations in the framework of wireless tandem relay networks. We find that both full-duplex and half-duplex modes have opportunity to outperform each other. Specifically, for many tandem relay networks, in the low multiplexing gain region, the best relay-mode configuration is to let all the relays operate in half-duplex mode since this relay-mode configuration achieves the best diversity gain in the low multiplexing gain region. However, in the high multiplexing gain region, the best diversity gain is usually achieved by switching some relays to full-duplex mode. Furthermore, we study how residual interference at relays working in full-duplex mode affects the DMT of a tandem network. We find that residual interference not only derogates the performance of full-duplex mode, but also affects the optimal power allocation of the network. Specifically, if residual interference is zero or has a sufficiently low power level, a linear power allocation scheme can achieve the optimal DMT of the network. Otherwise, the optimal DMT is achieved by a nonlinear power allocation scheme. Finally, the DMT analysis illustrates an effective principle to deal with general multi-hop wireless networks, which is to break them down into small scale subnetworks with certain key structures. Then, studying the general multi-hop wireless networks essentially becomes studying those small scale subnetworks and the relationship among them. Regarding wireless two-hop multicast relay networks, we focus on a case study where a single source multicasts to two destinations through the assistance of two relays. We propose and analyze the performance of a partial decode-and-forward protocol for the network, which includes the full decode-and-forward protocol as a special case and achieves a better performance in general. Specifically, we prove that the achievable rate of the partial decode-and-forward protocol can either reach arbitrarily close to the cut-set upper bound of the network or reach within 1 bit/s/Hz to that, asymptotically with respect to the transmit power. We also show that the partial decode-and-forward protocol can achieve the optimal DMT of the network. Then, we discuss the perspective of implementing the partial decode-and-forward strategy to more general multicast relay networks. / Tiivistelmä Tämä opinnäytetyö tutkii kahta langatonta välitysverkkomallia, nimittäin langatonta tandem multiple-input-multiple-output (MIMO) välitysverkkoa ja langatonta monilähetysvälitysverkkoa kahdelle hypylle. Kehitämme systemaattisen lähestymistavan diversiteetti-multipleksointi vaihtokaupan (DMT) analysointiin langattomiin tandem MIMO välitysverkkoihin, olettaen välittäjien käyttävän käytännöllisiä full-duplex lähetystekniikoita, jotka mahdollistavat valinnan joko full-duplex tai half-duplex lähetystilan välillä. Analyysin perusteella kontribuoimme seuraavilla tavoilla: Ensinnäkin, vertailemme perusteellisesti full-duplex sekä half-duplex lähetystiloja langattomissa tandem välitysverkoissa. Huomaamme, että molemmat full-duplex ja half-duplex lähetystilat voivat suoriutua toinen toistaan paremmin. Tarkemmin sanoen, monissa tandem välitysverkoissa silloin kun multipleksoinnin hyöty on alhainen, paras välitystapa on antaa kaikkien välittäjien käyttää half-duplex lähetystilaa, koska silloin saavutetaan paras diversiteettilisäys. Toisaalta, kun multipleksointilisäys on suuri, paras diversiteettilisäys saadaan yleensä asettamalla jotkin välittäjät full-duplex lähetystilaan. Lisäksi, tutkimme kuinka full-duplex lähetystilaa käyttävien välittäjien jäljelle jäävä interferenssi vaikuttaa tandemverkon DMT:aan. Huomaamme, että jäljelle jäävä interferenssi vähentää full-duplex mallin tehokkuutta ja lisäksi vaikuttaa optimaaliseen tehonjakamiseen verkossa. Tarkemmin sanoen, jos jäljelle jäävä interferenssin tehotaso on nolla tai tarpeeksi lähellä sitä, lineaarisella tehojaolla voi saavuttaa verkon optimaalisen DMT:n. Muutoin, optimaalinen DMT saavutetaan epälineaarisella tehojaolla. Lopuksi, DMT analyysi havainnollistaa tehokkaan periaatteen yleisluontoisten monihyppyverkkojen käsittelemiseen, eli verkon jakamisen pienempiin osiin erilaiin avainrakenteisiin. Tämän jälkeen yleisluntoisten langattoimen monihyppyverkkojen tutkiminen tapahtuu tutkimalla näitä pieniä osia ja niiden välisiä vuorovaikutussuhteita. Langattomaan kahden hypyn monilähetysvälitysverkkon osalta keskitymme tapaustutkimukseen, jossa yksi lähettäjä monilähettää kahdelle vastaanottajalle kahden välittäjän avulla. Ehdotamme tälle verkolle osittaista decode-and-forward protokollaa, joka sisältää täyden decode-and-forward protokollan erikoistapauksena ja saavuttaa yleisesti tätä protokollaa paremman tehokkuuden. Tarkemmin sanoen, todistamme että tällä protokollalla siirtonopeus lähetystehon suhteen joko lähenee asymptoottisesti verkon cut-set ylärajaa mielivaltaisen lähelle tai saavuttaa sen 1 bit/s/Hz sisään. Osoitamme myös, että osittainen decode-and-forward protokolla voi saavuttaa verkon optimaalisen DMT:n. Tämän jälkeen, käsittelemme osittaisen decode-and-forward strategian impelentointia yleisluontoisille monilähetysvälitysverkoille.

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