The Multi-way Relay Channel

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multi-way relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal in this model is the enabler of communication. In particular, restricted encoders, which ignore the received channel output and use only the corresponding messages for generating the channel input, are considered. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of exchange rates in a symmetric Gaussian network scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the exchange capacity independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward (AF) protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding based achievable schemes, a nested lattice coding based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information Theor

Energy Performance of LDPC Scheme in Multi-Hop Wireless Sensor Network with Two base Stations Model

Conservation of the energy is one of the main design issues in wireless sensor networks. The limited battery power of each sensor node is a challenging task in deploying this type of network. The challenge is crucial in reliable wireless network when implementing efficient error correcting scheme with energy consuming routing protocol. In this work, we investigated the energy performance of LDPC code in multi-hop wireless sensor network. We proposed a model of two base stations to prolong the lifetime and build a reliable and energy-efficient network. Through performed MATLAB simulations, we examine the energy effectiveness of multiple base stations model on reliable wireless sensor network performance in different network dimensions

Design of low-density parity-check codes in relay channels

Recent breakthroughs in forward error correction, in the form of low-density parity-check (LDPC) and turbo codes, have seen near Shannon limit performances especially for pointto- point channels. The construction of capacity-achieving codes in relay channels, for LDPC codes in particular, is currently the subject of intense interest in the research and development community. This thesis adds to this field, developing methods and supporting theory in designing capacity-achieving LDPC codes for decode-and-forward (DF) schemes in relay channels. In the first part of the thesis, new theoretical results toward optimizing the achievable rate of DF scheme in half-duplex relay channels under simplified and pragmatic conditions (equal power or equal time allocation) are developed. We derive the closed-form solutions for the optimum parameters (time or power) that maximize the achievable rates of the DF scheme in the half-duplex relay channel. We also derive the closed-form expression for the DF achievable rates under these simplified and pragmatic conditions. The second part of the thesis is dedicated to study the problem of designing several classes of capacity-achieving LDPC codes in relay channels. First, a new ensemble of LDPC codes, termed multi-edge-type bilayer-expurgated LDPC (MET-BE-LDPC) codes, is introduced to closely approach the theoretical limit of the DF scheme in the relay channel. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach and the bilayer approach with intermediate rates. Second, we address the issue of constructing capacity-achieving distributed LDPC codes in the multiple-access and two-way relay channels, with broadcast transmissions and time-division multiple accesses. We propose a new methodology to asymptotically optimize the code’s degree distribution when different segments within the distributed codeword have been transmitted through separate channels and experienced distinct signal-to-noise ratio in the relay system. Third, we investigate the use of LDPC codes under the soft-decode-and forward (SDF) scheme in the half-duplex relay channel. We introduce the concept of a K-layer doping matrix that enables one to design the rate-compatible (RC) LDPC code with a lower triangular parity-check matrix, subsequently allowing the additional parity bits to be linearly and systematically encoded at the relay. We then present the soft-decoding and soft-re-encoding algorithms for the designed RC-LDPC code so that the relay can forward soft messages to the destination when the relay fails to decode the source’s messages. Special attention is given to the detection problem of the SDF scheme. We propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio of the received signal at the destination for the SDF scheme

무선 중계 네트워크에서 신호대잡음비의 누적분포함수 기반 중계기 선택 기법의 성능 분석

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 이재홍.무선 중계 기술은 차세대 무선통신 시스템에서 요구되는 높은 서비스 품질 및 데이터 전송률 달성을 위해 고려되고 있는 대표적인 기술 중 하나이다. 무선 중계 기술이 갖고 있는 다양한 장점으로 인해 현재까지 IEEE 802.16j 및 3GPP LTE-Advanced 등의 무선통신 시스템 표준에 반영되기도 하였다. 실질적으로 두 노드 사이 채널의 통계적 특성은 그들의 위치에 따라 달라지기 때문에 각 채널들의 통계적 특성은 서로 동일하지 않다. 각 채널들의 통계적 특성이 동일하지 않을 때, 무선 중계 기술에서 가장 유용한 기법 중 하나인 중계기 선택 기법은 특정 중계기들이 더 자주 선택되는 등의 공정성 문제를 유발시킬 수 있다. 특히, 이 문제는 제한된 배터리를 가진 중계기들로 구성된 네트워크에서 네트워크의 수명을 줄이게 하는 요인이 될 수 있다. 따라서 이러한 네트워크에서는 사용자들의 통신 신뢰도 뿐만 아니라, 중계기에서의 선택 공정성도 함께 고려할 필요가 있다. 본 논문에서는 무선 중계 네트워크에서 사용자들의 통신 신뢰도와 중계기 간의 선택 공정성을 함께 고려하기 위해 수신 신호대잡음비의 누적분포함수를 기반으로 하는 새로운 중계기 선택 기법을 제안한다. 주요한 연구 결과는 다음과 같다. 먼저, 나카가미-m 페이딩 채널 환경을 가진 일방향 중계 네트워크를 위한 프로액티브(proactive) 및 리액티브(reactive) 방식의 수신 신호대잡음비 누적분포함수 기반 중계기 선택 기법을 제안한다. 각각의 중계기 선택 기법을 위해 중계기 선택 확률을 유도하여 제안된 각 중계기 선택 기법들의 평균 중계기 공정성을 분석한다. 또한 각 선택 기법에 대한 불능 확률을 수식으로 유도하고, 유도한 불능 확률을 점근적 표현으로 나타내어 각 기법들이 얻을 수 있는 다이버시티 차수를 분석한다. 모의실험을 통해 얻어진 평균 중계기 공정성과 불능 확률이 유도한 평균 중계기 공정성 및 불능 확률 값과 일치함을 확인한다. 그리고 제안된 기법이 중계기들 사이에 공정성을 완벽하게 보장하고 네트워크 수명을 증가시키며, 다이버시티 차수가 중계기의 수와 페이딩 파라미터 m 값에 따라 달라짐을 확인한다. 둘째, 나카가미-m 페이딩 채널 환경을 가진 양방향 중계 네트워크를 위한 프로액티브 및 리액티브 방식의 수신 신호대잡음비 누적분포함수 기반 중계기 선택 기법을 제안한다. 제안된 프로액티브 방식의 중계기 선택 기법에 대해서는 정확한 중계기 선택 확률의 유도를 통해 평균 중계기 공정성을 분석한다. 제안된 리액티브 방식의 중계기 선택 기법에 대해서는 중계기 선택 확률의 적분 및 근사 표현을 유도하여 평균 중계기 공정성을 분석한다. 또한 각 선택 기법에 대한 불능 확률을 수식으로 유도하고, 유도한 불능 확률을 점근적 표현으로 나타내어 각 기법들이 얻을 수 있는 다이버시티 차수를 분석한다. 모의실험을 통해 얻어진 평균 중계기 공정성과 불능 확률이 유도한 평균 중계기 공정성 및 불능 확률 값과 일치함을 확인한다. 그리고 제안된 기법이 중계기들 사이에 공정성을 완벽하게 보장하고 네트워크 수명을 증가시키며, 다이버시티 차수가 중계기의 수와 페이딩 파라미터 m 값에 따라 달라짐을 확인한다.Wireless relay technology is one of the most promising technologies for the future communication systems which provide coverage extension and better quality of service (QoS) such as higher data rate and lower outage probability with few excessive network loads. Due to its advantages, it has been adopted in wireless standards such as IEEE 802.16j and 3GPP LTE-Advanced. In practice, since statistics of the channel between any two nodes vary depending on their locations, they are not identical which means that channels can experience different fading. When statistics of the channel are not identical, relay selection, which is one of the most useful techniques for wireless relay technology, can cause fairness problem that particular relays are selected more frequently than other relays. Especially, this problem can cause reduction of lifetime in the network with multiple relays having limited battery power. In this network, it is needed to focus on selection fairness for relays as well as reliability at end-users. In this dissertation, to focus on both selection fairness for relays and reliability at end-users, we propose novel relay selection schemes based on cumulative distribution functions (CDFs) of signal-to-noise ratios (SNRs) in wireless relay networks. The dissertation consists of two main results. First, we propose the proactive and the reactive relay selection schemes based on CDFs of SNRs for one-way relay networks over Nakagami-m fading channels. If a relay is selected before the source transmission, it is called as proactive relay selection. Otherwise, if a relay is selected after the source transmission, it is called as reactive relay selection. For both the proactive and the reactive relay selection schemes, we analyze average relay fairness by deriving relay selection probability. For the proactive relay selection scheme, we obtain diversity order by deriving the integral and asymptotic expressions for outage probability. Also, for the reactive relay selection scheme, we obtain diversity order by deriving the exact closed-form and asymptotic expressions for outage probability. Numerical results show that the analytical results of the proposed schemes match the simulation results well. It is shown that the proposed schemes guarantee strict fairness among relays and extend network lifetime. Also, it is shown that diversity order depends on the number of relays and fading severity parameters. Second, we propose the proactive and the reactive relay selection schemes based on CDFs of SNRs for two-way relay networks over Nakagami-m fading channels. For the proactive relay selection scheme, we analyze average relay fairness by deriving relay selection probability. Also, we analyze diversity order by deriving the integral and asymptotic expressions for outage probability. For the reactive relay selection scheme, we analyze average relay fairness by deriving the integral and asymptotic expressions for relay selection probability. Also, we obtain diversity order by deriving the asymptotic expression for outage probability. Numerical results show that the analytical results of the proposed schemes match the simulation results well. It is shown that the proposed schemes guarantee strict fairness among relays and extend network lifetime. Also, it is shown that diversity order depends on the number of relays and fading severity parameters.Contents Abstract i 1 Introduction 1 1.1 Background and Related Work . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Wireless Relay Technology . . . . . . . . . . . . . . . . . . . . 3 1.2 Outline of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Relay Selection Based on CDFs of SNRs for One-Way Relay Networks 14 2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Proactive CDF-Based Relay Selection . . . . . . . . . . . . . 19 2.1.2 Reactive CDF-Based Relay Selection . . . . . . . . . . . . . . 20 2.2 Performance Analysis of Proactive CDF-Based Relay Selection . . . . 22 2.2.1 Average Relay Fairness Analysis . . . . . . . . . . . . . . . . . 22 2.2.2 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . 27 2.3 Performance Analysis of Reactive CDF-Based Relay Selection . . . . 34 2.3.1 Average Relay Fairness Analysis . . . . . . . . . . . . . . . . . 34 2.3.2 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . 36 2.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.4.1 Average Relay Fairness . . . . . . . . . . . . . . . . . . . . . . 39 2.4.2 Network Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4.3 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . . 53 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3 Relay Selection Based on CDFs of SNRs for Two-Way Relay Networks 66 3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.1.1 Proactive CDF-based Relay Selection . . . . . . . . . . . . . . 68 3.1.2 Reactive CDF-based Relay Selection . . . . . . . . . . . . . . 72 3.2 Performance Analysis of Proactive CDF-Based Relay Selection . . . . 73 3.2.1 Average Relay Fairness Analysis . . . . . . . . . . . . . . . . . 73 3.2.2 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . 74 3.3 Performance Analysis of Reactive CDF-Based Relay Selection . . . . 82 3.3.1 Average Relay Fairness Anlaysis . . . . . . . . . . . . . . . . . 82 3.3.2 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . 86 3.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.4.1 Average Relay Fairness . . . . . . . . . . . . . . . . . . . . . . 89 3.4.2 Network Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.3 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . . 105 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4 Conclusion 116 4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.2 Possible Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2.1 Device-to-Device (D2D) Communications . . . . . . . . . . . 118 4.2.2 Low Power Body Sensor Networks . . . . . . . . . . . . . . . 120 4.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Bibliography 122 Korean Abstract 139Docto

Capacity Approaching Coding Strategies for Machine-to-Machine Communication in IoT Networks

Radio access technologies for mobile communications are characterized by multiple access (MA) strategies. Orthogonal MA techniques were a reasonable choice for achieving good performance with single user detection. With the tremendous growth in the number of mobile users and the new internet of things (IoT) shifting paradigm, it is expected that the monthly mobile data traffic worldwide will exceed 24.3 exabytes by 2019, over 100 billion IoT connections by 2025, and the financial impact of IoT on the global economy varies in the range of 3.9 to 11.1 trillion dollars by 2025. In light of the envisaged exponential growth and new trends, one promising solution to further enhance data rates without increasing the bandwidth is by increasing the spectral efficiency of the channel. Non-orthogonal MA techniques are potential candidates for future wireless communications. The two corner points on the boundary region of the MA channel are known to be achievable by single user decoding followed by successive decoding (SD). Other points can also be achieved using time sharing or rate splitting. On the other hand, machine-to-machine (M2M) communication which is an enabling technology for the IoT, enables massive multipurpose networked devices to exchange information among themselves with minor or no human intervention. This thesis consists of three main parts. In the first part, we propose new practical encoding and joint belief propagation (BP) decoding techniques for 2-user MA erasure channel (MAEC) that achieve any rate pair close to the boundary of the capacity region without using time sharing nor rate splitting. While at the encoders, the corresponding parity check matrices are randomly built from a half-rate LDPC matrix, the joint BP decoder employs the associated Tanner graphs of the parity check matrices to iteratively recover the erasures in the received combined codewords. Specifically, the joint decoder performs two steps in each decoding iteration: 1) simultaneously and independently runs the BP decoding process at each constituent sub-graph to recover some of the common erasures, 2) update the other sub-graph with newly recovered erasures and vice versa. When the number of erasures in the received combined codewords is less than or equal to the number of parity check constraints, the decoder may successfully decode both codewords, otherwise the decoder declares decoding failure. Furthermore, we calculate the probability of decoding failure and the outage capacity. Additionally, we show how the erasure probability evolves with the number of decoding iterations and the maximum tolerable loss. Simulations show that any rate pair close to the capacity boundary is achievable without using time sharing. In the second part, we propose a new cooperative joint network and rateless coding strategy for machine-type communication (MTC) devices in the multicast settings where three or more MTC devices dynamically form a cluster to disseminate messages between themselves. Specifically, in the basic cluster, three MTC devices transmit their respective messages simultaneously to the relay in the first phase. The relay broadcasts back the combined messages to all MTC devices within the basic cluster in the second phase. Given the fact that each MTC device can remove its own message, the received signal in the second phase is reduced to the combined messages coming from the other two MTC devices. Hence, this results in exploiting the interference caused by one message on the other and therefore improving the bandwidth efficiency. Furthermore, each group of three MTC devices in vicinity can form a basic cluster for exchanging messages, and the basic scheme extends to N MTC devices. Furthermore, we propose an efficient algorithm to disseminate messages among a large number of MTC devices. Moreover, we implement the proposed scheme employing practical Raptor codes with the use of two relaying schemes, namely amplify and forward (AF) and de-noise and forward (DNF). We show that with very little processing at the relay using DNF relaying scheme, performance can be further enhanced. We also show that the proposed scheme achieves a near optimal sum rate performance. In the third part, we present a comparative study of joint channel estimation and decoding of factor graph-based codes over flat fading channels and propose a simple channel approximation scheme that performs close to the optimal technique. Specifically, when channel state information (CSI) is not available at the receiver, a simpler approach is to estimate the channel state of a group of received symbols, then use the approximated value of the channel with the received signal to compute the log likelihood ratio. Simulation results show that the proposed scheme exhibits about 0.4 dB loss compared to the optimal solution when perfect CSI is available at the receiver

Multi-way relay networks: characterization, performance analysis and transmission scheme design

Multi-way relay networks (MWRNs) are a growing research area in the field of relay based wireless networks. Such networks provide a pathway for solving the ever in- creasing demand for higher data rate and spectral efficiency in a general multi-user scenario. MWRNs have potential applications in video conferencing, file sharing in a social network, as well as satellite networks and sensor networks. Recent research on MWRNs focuses on efficient transmission protocol design by harnessing different network coding schemes, higher dimensional structured codes and advanced relaying protocols. However, the existing research misses out the characterization and analysis of practical issues that influence the performance of MWRNs. Moreover, the existing transmission schemes suffer some significant limitations, that need to be solved for maximizing the benefits of MWRNs. In this thesis, we investigate the practical issues that critically influence the perfor- mance of a MWRN and propose solutions that can outperform existing schemes. To be specific, we characterize error propagation phenomenon for additive white Gaus- sian noise (AWGN) and fading channels with functional decode and forward (FDF) and amplify and forward (AF) relaying protocols, propose a new pairing scheme that out- performs the existing schemes for lattice coded FDF MWRNs in terms of the achievable rate and error performance and finally, analyze the impact of imperfect channel state information (CSI) and optimum power allocation on MWRNs. At first, we analyze the error performance of FDF and AF MWRNs with pair- wise transmission using binary phase shift keying (BPSK) modulation in AWGN and Rayleigh fading channels. We quantify the possible error events in an L-user FDF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) other users. We show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a FDF MWRN. We derive the average BER of a user in a FDF or AF MWRN under high SNR conditions and provide simulation results to verify them. Next, we propose a novel user pairing scheme for lattice coded FDF MWRNs. Lattice codes can achieve the capacity of AWGN channels and are used in digital communica- tions as high-rate signal constellations. Our proposed pairing scheme selects a common user with the best average channel gain and thus, allows it to positively contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. In addition, considering M-ary QAM with square constellation as a special case of lattice codes, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates and error performance, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. Finally, we investigate lattice coded FDF and AF MWRNs with imperfect CSI. Con- sidering lattice codes of sufficiently large dimension, we obtain the bounds on the com- mon rate and sum rate. In addition, considering M-ary quadrature amplitude mod- ulation (QAM) with square constellations, we obtain expressions for the average SER in FDF MWRNs. For AF MWRNs, considering BPSK modulation as the simplest case of lattice codes, we obtain the average BER. Moreover, we obtain the optimum power allocation coefficients to maximize the sum rate in AF MWRN. For both FDF and AF relaying protocols, the average common rate and sum rate are decreasing functions of the estimation error. The analysis shows that the error performance of a FDF MWRN is an increasing function of both the channel estimation error and the number of users, whereas, for AF MWRN, the error performance is an increasing function of only the channel estimation error. Also, we show that to achieve the same sum rate in AF MWRN, optimum power allocation requires 7 − 9 dB less power compared to equal power allocation depending upon users’ channel conditions

Analysis and design of physical-layer network coding for relay networks

Physical-layer network coding (PNC) is a technique to make use of interference in wireless transmissions to boost the system throughput. In a PNC employed relay network, the relay node directly recovers and transmits a linear combination of its received messages in the physical layer. It has been shown that PNC can achieve near information-capacity rates. PNC is a new information exchange scheme introduced in wireless transmission. In practice, transmitters and receivers need to be designed and optimized, to achieve fast and reliable information exchange. Thus, we would like to ask: How to design the PNC schemes to achieve fast and reliable information exchange? In this thesis, we address this question from the following works: Firstly, we studied channel-uncoded PNC in two-way relay fading channels with QPSK modulation. The computation error probability for computing network coded messages at the relay is derived. We then optimized the network coding functions at the relay to improve the error rate performance. We then worked on channel coded PNC. The codes we studied include classical binary code, modern codes, and lattice codes. We analyzed the distance spectra of channel-coded PNC schemes with classical binary codes, to derive upper bounds for error rates of computing network coded messages at the relay. We designed and optimized irregular repeat-accumulate coded PNC. We modified the conventional extrinsic information transfer chart in the optimization process to suit the superimposed signal received at the relay. We analyzed and designed Eisenstein integer based lattice coded PNC in multi-way relay fading channels, to derive error rate performance bounds of computing network coded messages. Finally we extended our work to multi-way relay channels. We proposed a opportunistic transmission scheme for a pair-wise transmission PNC in a single-input single-output multi-way relay channel, to improve the sum-rate at the relay. The error performance of computing network coded messages at the relay is also improved. We optimized the uplink/downlink channel usage for multi-input multi-output multi-way relay channels with PNC to maximize the degrees of freedom capacity. We also showed that the system sum-rate can be further improved by a proposed iterative optimization algorithm

Compute-and-Forward in Multi-User Relay Networks: Optimization, Implementation, and Secrecy

In this thesis, we investigate physical-layer network coding in an L × M × K relay network, where L source nodes want to transmit messages to K sink nodes via M relay nodes. We focus on the information processing at the relay nodes and the compute-and-forward framework. Nested lattice codes are used, which have the property that every linear combination of codewords is a valid codeword. This property is essential for physical-layer network coding. Because the actual network coding occurs on the physical layer, the network coding coefficients are determined by the channel realizations. Finding the optimal network coding coefficients for given channel realizations is a non-trivial optimization problem. In this thesis, we provide an algorithm to find network coding coefficients that result in the highest data rate at a chosen relay. The solution of this optimization problem is only locally optimal, i.e., it is optimal for a particular relay. If we consider a multi-hop network, each potential receiver must get enough linear independent combinations to be able to decode the individual messages. If this is not the case, outage occurs, which results in data loss. In this thesis, we propose a new strategy for choosing the network coding coefficients locally at the relays without solving the optimization problem globally. We thereby reduce the solution space for the relays such that linear independence between their decoded linear combinations is guaranteed. Further, we discuss the influence of spatial correlation on the optimization problem. Having solved the optimization problem, we combine physical-layer network coding with physical-layer secrecy. This allows us to propose a coding scheme to exploit untrusted relays in multi-user relay networks. We show that physical-layer network coding, especially compute-and-forward, is a key technology for simultaneous and secure communication of several users over an untrusted relay. First, we derive the achievable secrecy rate for the two-way relay channel. Then, we enhance this scenario to a multi-way relay channel with multiple antennas. We describe our implementation of the compute-and-forward framework with software-defined radio and demonstrate the practical feasibility. We show that it is possible to use the framework in real-life scenarios and demonstrate a transmission from two users to a relay. We gain valuable insights into a real transmission using the compute-and-forward framework. We discuss possible improvements of the current implementation and point out further work.In dieser Arbeit untersuchen wir Netzwerkcodierung auf der Übertragungsschicht in einem Relay-Netzwerk, in dem L Quellen-Knoten Nachrichten zu K Senken-Knoten über M Relay-Knoten senden wollen. Der Fokus dieser Arbeit liegt auf der Informationsverarbeitung an den Relay-Knoten und dem Compute-and-Forward Framework. Es werden Nested Lattice Codes eingesetzt, welche die Eigenschaft besitzen, dass jede Linearkombination zweier Codewörter wieder ein gültiges Codewort ergibt. Dies ist eine Eigenschaft, die für die Netzwerkcodierung von entscheidender Bedeutung ist. Da die eigentliche Netzwerkcodierung auf der Übertragungsschicht stattfindet, werden die Netzwerkcodierungskoeffizienten von den Kanalrealisierungen bestimmt. Das Finden der optimalen Koeffizienten für gegebene Kanalrealisierungen ist ein nicht-triviales Optimierungsproblem. Wir schlagen in dieser Arbeit einen Algorithmus vor, welcher Netzwerkcodierungskoeffizienten findet, die in der höchsten Übertragungsrate an einem gewählten Relay resultieren. Die Lösung dieses Optimierungsproblems ist zunächst nur lokal, d. h. für dieses Relay, optimal. An jedem potentiellen Empfänger müssen ausreichend unabhängige Linearkombinationen vorhanden sein, um die einzelnen Nachrichten decodieren zu können. Ist dies nicht der Fall, kommt es zu Datenverlusten. Um dieses Problem zu umgehen, ohne dabei das Optimierungsproblem global lösen zu müssen, schlagen wir eine neue Strategie vor, welche den Lösungsraum an einem Relay soweit einschränkt, dass lineare Unabhängigkeit zwischen den decodierten Linearkombinationen an den Relays garantiert ist. Außerdem diskutieren wir den Einfluss von räumlicher Korrelation auf das Optimierungsproblem. Wir kombinieren die Netzwerkcodierung mit dem Konzept von Sicherheit auf der Übertragungsschicht, um ein Übertragungsschema zu entwickeln, welches es ermöglicht, mit Hilfe nicht-vertrauenswürdiger Relays zu kommunizieren. Wir zeigen, dass Compute-and-Forward ein wesentlicher Baustein ist, um solch eine sichere und simultane Übertragung mehrerer Nutzer zu gewährleisten. Wir starten mit dem einfachen Fall eines Relay-Kanals mit zwei Nutzern und erweitern dieses Szenario auf einen Relay-Kanal mit mehreren Nutzern und mehreren Antennen. Die Arbeit wird abgerundet, indem wir eine Implementierung des Compute-and-Forward Frameworks mit Software-Defined Radio demonstrieren. Wir zeigen am Beispiel von zwei Nutzern und einem Relay, dass sich das Framework eignet, um in realen Szenarien eingesetzt zu werden. Wir diskutieren mögliche Verbesserungen und zeigen Richtungen für weitere Forschungsarbeit auf

Advanced tensor based signal processing techniques for wireless communication systems and biomedical signal processing

Many observed signals in signal processing applications including wireless communications, biomedical signal processing, image processing, and machine learning are multi-dimensional. Tensors preserve the multi-dimensional structure and provide a natural representation of these signals/data. Moreover, tensors provide often an improved identifiability. Therefore, we benefit from using tensor algebra in the above mentioned applications and many more. In this thesis, we present the benefits of utilizing tensor algebra in two signal processing areas. These include signal processing for MIMO (Multiple-Input Multiple-Output) wireless communication systems and biomedical signal processing. Moreover, we contribute to the theoretical aspects of tensor algebra by deriving new properties and ways of computing tensor decompositions. Often, we only have an element-wise or a slice-wise description of the signal model. This representation of the signal model does not reveal the explicit tensor structure. Therefore, the derivation of all tensor unfoldings is not always obvious. Consequently, exploiting the multi-dimensional structure of these models is not always straightforward. We propose an alternative representation of the element-wise multiplication or the slice-wise multiplication based on the generalized tensor contraction operator. Later in this thesis, we exploit this novel representation and the properties of the contraction operator such that we derive the final tensor models. There exist a number of different tensor decompositions that describe different signal models such as the HOSVD (Higher Order Singular Value Decomposition), the CP/PARAFAC (Canonical Polyadic / PARallel FACtors) decomposition, the BTD (Block Term Decomposition), the PARATUCK2 (PARAfac and TUCker2) decomposition, and the PARAFAC2 (PARAllel FACtors2) decomposition. Among these decompositions, the CP decomposition is most widely spread and used. Therefore, the development of algorithms for the efficient computation of the CP decomposition is important for many applications. The SECSI (Semi-Algebraic framework for approximate CP decomposition via SImultaneaous matrix diagonalization) framework is an efficient and robust tool for the calculation of the approximate low-rank CP decomposition via simultaneous matrix diagonalizations. In this thesis, we present five extensions of the SECSI framework that reduce the computational complexity of the original framework and/or introduce constraints to the factor matrices. Moreover, the PARAFAC2 decomposition and the PARATUCK2 decomposition are usually described using a slice-wise notation that can be expressed in terms of the generalized tensor contraction as proposed in this thesis. We exploit this novel representation to derive explicit tensor models for the PARAFAC2 decomposition and the PARATUCK2 decomposition. Furthermore, we use the PARAFAC2 model to derive an ALS (Alternating Least-Squares) algorithm for the computation of the PARAFAC2 decomposition. Moreover, we exploit the novel contraction properties for element wise and slice-wise multiplications to model MIMO multi-carrier wireless communication systems. We show that this very general model can be used to derive the tensor model of the received signal for MIMO-OFDM (Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao coded MIMO-OFDM, and randomly coded MIMO-OFDM systems. We propose the transmission techniques Khatri-Rao coding and random coding in order to impose an additional tensor structure of the transmit signal tensor that otherwise does not have a particular structure. Moreover, we show that this model can be extended to other multi-carrier techniques such as GFDM (Generalized Frequency Division Multiplexing). Utilizing these models at the receiver side, we design several types for receivers for these systems that outperform the traditional matrix based solutions in terms of the symbol error rate. In the last part of this thesis, we show the benefits of using tensor algebra in biomedical signal processing by jointly decomposing EEG (ElectroEncephaloGraphy) and MEG (MagnetoEncephaloGraphy) signals. EEG and MEG signals are usually acquired simultaneously, and they capture aspects of the same brain activity. Therefore, EEG and MEG signals can be decomposed using coupled tensor decompositions such as the coupled CP decomposition. We exploit the proposed coupled SECSI framework (one of the proposed extensions of the SECSI framework) for the computation of the coupled CP decomposition to first validate and analyze the photic driving effect. Moreover, we validate the effects of scull defects on the measurement EEG and MEG signals by means of a joint EEG-MEG decomposition using the coupled SECSI framework. Both applications show that we benefit from coupled tensor decompositions and the coupled SECSI framework is a very practical tool for the analysis of biomedical data.Zahlreiche messbare Signale in verschiedenen Bereichen der digitalen Signalverarbeitung, z.B. in der drahtlosen Kommunikation, im Mobilfunk, biomedizinischen Anwendungen, der Bild- oder akustischen Signalverarbeitung und dem maschinellen Lernen sind mehrdimensional. Tensoren erhalten die mehrdimensionale Struktur und stellen eine natürliche Darstellung dieser Signale/Daten dar. Darüber hinaus bieten Tensoren oft eine verbesserte Trennbarkeit von enthaltenen Signalkomponenten. Daher profitieren wir von der Verwendung der Tensor-Algebra in den oben genannten Anwendungen und vielen mehr. In dieser Arbeit stellen wir die Vorteile der Nutzung der Tensor-Algebra in zwei Bereichen der Signalverarbeitung vor: drahtlose MIMO (Multiple-Input Multiple-Output) Kommunikationssysteme und biomedizinische Signalverarbeitung. Darüber hinaus tragen wir zu theoretischen Aspekten der Tensor-Algebra bei, indem wir neue Eigenschaften und Berechnungsmethoden für die Tensor-Zerlegung ableiten. Oftmals verfügen wir lediglich über eine elementweise oder ebenenweise Beschreibung des Signalmodells, welche nicht die explizite Tensorstruktur zeigt. Daher ist die Ableitung aller Tensor-Unfoldings nicht offensichtlich, wodurch die multidimensionale Struktur dieser Modelle nicht trivial nutzbar ist. Wir schlagen eine alternative Darstellung der elementweisen Multiplikation oder der ebenenweisen Multiplikation auf der Grundlage des generalisierten Tensor-Kontraktionsoperators vor. Weiterhin nutzen wir diese neuartige Darstellung und deren Eigenschaften zur Ableitung der letztendlichen Tensor-Modelle. Es existieren eine Vielzahl von Tensor-Zerlegungen, die verschiedene Signalmodelle beschreiben, wie die HOSVD (Higher Order Singular Value Decomposition), CP/PARAFAC (Canonical Polyadic/ PARallel FACtors) Zerlegung, die BTD (Block Term Decomposition), die PARATUCK2-(PARAfac und TUCker2) und die PARAFAC2-Zerlegung (PARAllel FACtors2). Dabei ist die CP-Zerlegung am weitesten verbreitet und wird findet in zahlreichen Gebieten Anwendung. Daher ist die Entwicklung von Algorithmen zur effizienten Berechnung der CP-Zerlegung von besonderer Bedeutung. Das SECSI (Semi-Algebraic Framework for approximate CP decomposition via Simultaneaous matrix diagonalization) Framework ist ein effizientes und robustes Werkzeug zur Berechnung der approximierten Low-Rank CP-Zerlegung durch simultane Matrixdiagonalisierung. In dieser Arbeit stellen wir fünf Erweiterungen des SECSI-Frameworks vor, welche die Rechenkomplexität des ursprünglichen Frameworks reduzieren bzw. Einschränkungen für die Faktormatrizen einführen. Darüber hinaus werden die PARAFAC2- und die PARATUCK2-Zerlegung in der Regel mit einer ebenenweisen Notation beschrieben, die sich in Form der allgemeinen Tensor-Kontraktion, wie sie in dieser Arbeit vorgeschlagen wird, ausdrücken lässt. Wir nutzen diese neuartige Darstellung, um explizite Tensormodelle für diese beiden Zerlegungen abzuleiten. Darüber hinaus verwenden wir das PARAFAC2-Modell, um einen ALS-Algorithmus (Alternating Least-Squares) für die Berechnung der PARAFAC2-Zerlegungen abzuleiten. Weiterhin nutzen wir die neuartigen Kontraktionseigenschaften für elementweise und ebenenweise Multiplikationen, um MIMO Multi-Carrier-Mobilfunksysteme zu modellieren. Wir zeigen, dass dieses sehr allgemeine Modell verwendet werden kann, um das Tensor-Modell des empfangenen Signals für MIMO-OFDM- (Multiple- Input Multiple-Output - Orthogonal Frequency Division Multiplexing), Khatri-Rao codierte MIMO-OFDM- und zufällig codierte MIMO-OFDM-Systeme abzuleiten. Wir schlagen die Übertragungstechniken der Khatri-Rao-Kodierung und zufällige Kodierung vor, um eine zusätzliche Tensor-Struktur des Sendesignal-Tensors einzuführen, welcher gewöhnlich keine bestimmte Struktur aufweist. Darüber hinaus zeigen wir, dass dieses Modell auf andere Multi-Carrier-Techniken wie GFDM (Generalized Frequency Division Multiplexing) erweitert werden kann. Unter Verwendung dieser Modelle auf der Empfängerseite entwerfen wir verschiedene Typen von Empfängern für diese Systeme, die die traditionellen matrixbasierten Lösungen in Bezug auf die Symbolfehlerrate übertreffen. Im letzten Teil dieser Arbeit zeigen wir die Vorteile der Verwendung von Tensor-Algebra in der biomedizinischen Signalverarbeitung durch die gemeinsame Zerlegung von EEG-(ElectroEncephaloGraphy) und MEG- (MagnetoEncephaloGraphy) Signalen. Diese werden in der Regel gleichzeitig erfasst, wobei sie gemeinsame Aspekte derselben Gehirnaktivität beschreiben. Daher können EEG- und MEG-Signale mit gekoppelten Tensor-Zerlegungen wie der gekoppelten CP Zerlegung analysiert werden. Wir nutzen das vorgeschlagene gekoppelte SECSI-Framework (eine der vorgeschlagenen Erweiterungen des SECSI-Frameworks) für die Berechnung der gekoppelten CP Zerlegung, um zunächst den photic driving effect zu validieren und zu analysieren. Darüber hinaus validieren wir die Auswirkungen von Schädeldefekten auf die Messsignale von EEG und MEG durch eine gemeinsame EEG-MEG-Zerlegung mit dem gekoppelten SECSI-Framework. Beide Anwendungen zeigen, dass wir von gekoppelten Tensor-Zerlegungen profitieren, wobei die Methoden des gekoppelten SECSI-Frameworks erfolgreich zur Analyse biomedizinischer Daten genutzt werden können