Cooperative wireless communication uses relays to enhance the capacity and reliability of data transmission. Adaptive transmission is typically used in conventional non-cooperative communications to exploit the time-varying nature of the wireless channel. In this thesis, we combine these two techniques. We consider decode-and-forward (DF) and amplify-and-forward (AF) relays. The wireless environment is modeled by using the Nakagami-m distribution. The achievable channel capacity with rate adaptive transmission is analytically derived for DF and AF cooperative networks. The performance of a DF cooperative network is analyzed with a constant power rate adaptive scheme consisting of a discrete set of transmission modes. The effect of decoding errors on DF cooperative networks is also analyzed. To this end, a new heuristic approximation of the total received signal-to-noise ratio at the destination is developed. This approximation enables simple yet accurate performance analysis. / Communications

Backpacks are used by more than 90% of schoolchildren worldwide and over 40 million students in the United States on a regular basis. The carriage of loaded backpacks is associated with kinematic and physiological changes, as well as complaints of neck and back pain. Since a history of backpain in childhood is the strongest predictor of having musculoskeletal discomfort and back pain as an adult, development of back pain due to backpack use is of prognostic concern. The purpose of this dissertation was to examine the effects of backpack weights (up to 20% body weight (BW)) on children’s posture, subjective complaints of pain and perceived exertion, and walking endurance. A secondary goal was to examine the data to identify and recommend a weight limit for backpacks carried by elementary school children based on the results. In Chapter 2, we performed a preliminary study designed to examine the effects of loaded backpacks on forward head posture in school children. The results of this study found that forward head posture increased with both backpack weight and condition. The greatest differences were noted at the 15% and 20%BW backpack loads with initial loading, but after 6 minutes of walking the forward head posture was similar for all backpack loads. In Chapter 3, we conducted a study to evaluate multiple postural angles and the subjective complaints of pain and perceived exertion/fatigue in children to determine the effects of both the weight and time spent carrying loaded backpacks up to 20%BW. Subjects showed significant changes in all measures including the Six Minute Walk Test (6MWT), OMNI Walk/Run Scale of perceived exertion/fatigue and subjective complaints of pain, as well as the postural angles of Craniovertebral Angle, Forward Trunk Lean, and Pelvic Tilt. Subjects demonstrated immediate and significant changes in forward head posture, forward trunk lean, and pelvic tilt while wearing backpacks weighing 10%, 15% and 20%BW, but the 10%BW backpack resulted in the least amount of change. This study also found that these postural angles changed additionally after walking 6 minutes while carrying the loaded backpacks. Subjects also demonstrated decreased 6MWT distances and increased reports of perceived exertion and pain after carrying backpacks weighing 10%, 15% and 20%BW. In Chapter 4, we discussed the clinical implications of this research. It was determined that backpack loads weighing 10%, 15% and 20%BW of a child’s body weight result in immediate changes in posture, which continue to increase after walking six minutes with the loaded backpack. The backpack loads significantly impacted the children’s walking endurance as well as their reports of perceived exertion/fatigue and regional pain. This study found that of the loads tested, the 10%BW resulted in the least amount of change in all outcome measures. However, the 10%BW load was not innocuous, as it still created significant changes in posture and subjective complaints. Backpack weight limit guidelines need to be written to protect children from carrying backpacks weighing more than 10% body weight.

In the wireless sensor network environment (WSN), the system transmits signals often need to rely on the stability and reliability of the relay node of each path of cooperation with each other to achieve balance between leisure and stability. In general, relay adopted Amplify-and-Forward (AF) and Decode-and-Forward (DF) to relaying the signal to destination. Unfortunately, in reality, the relay node itself had a problem of limited energy supplies, would make the overall performance degrade before reaching the optimal performance. Therefore, we propose two novel relay selection schemes and through the multi-hop transmission with cooperation. We also derived the optimal power allocation algorithms for all relay nodes. Finally, simulation results show that our proposed scheme obtained the better lifetime and performance where compared with the traditional schemes in a fair environment.

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Today, there is a large amount of assets which are offered to investors, and if we consider the possibility of relocating the investor's funds, we come to a very complicated problem, which this thesis aims to cover. The main objective is to explore the basics of the portfolio theory and its real usage in practice. Emphasis is put on the periodic re-optimizing of the investor's portfolio and getting the answer to the question of whether such conduct is more successful than the standard and investment in equity indices. The theoretical part summarizes the currently used approaches to optimization which are tested in the practical part on real data and evaluated.

Next-generation wireless communication systems will need to contend with many active mobile devices, each of which will require a very high data rate. To cope with this growing demand, network deployments are becoming denser, leading to higher interference between active users. Conventional architectures aim to mitigate this interference through careful design of signaling and scheduling protocols. Unfortunately, these methods become less effective as the device density increases. One promising option is to enable cellular basestations (i.e., cell towers) to jointly process their received signals for decoding users’ data packets as well as to jointly encode their data packets to the users. This joint processing architecture is often enabled by a cloud radio access network that links the basestations to a central processing unit via dedicated connections. One of the main contributions of this thesis is a novel end-to-end communications architecture for cloud radio access networks as well as a detailed comparison to prior approaches, both via theoretical bounds and numerical simulations. Recent work has that the following high-level approach has numerous advantages: each basestation quantizes its observed signal and sends it to the central processing unit for decoding, which in turn generates signals for the basestations to transmit, and sends them quantized versions. This thesis follows an integer-forcing approach that uses the fact that, if codewords are drawn from a linear codebook, then their integer-linear combinations are themselves codewords. Overall, this architecture requires integer-forcing channel coding from the users to the central processing unit and back, which handles interference between the users’ codewords, as well as integer-forcing source coding from the basestations to the central processing unit and back, which handles correlations between the basestations’ analog signals. Prior work on integer-forcing has proposed and analyzed channel coding strategies as well as a source coding strategy for the basestations to the central processing unit, and this thesis proposes a source coding strategy for the other direction. Iterative algorithms are developed to optimize the parameters of the proposed architecture, which involve real-valued beamforming and equalization matrices and integer-valued coefficient matrices in a quadratic objective. Beyond the cloud radio setting, it is argued that the integer-forcing approach is a promising framework for interference alignment between multiple transmitter-receiver pairs. In this scenario, the goal is to align the interfering data streams so that, from the perspective of each receiver, there seems to be only a signal receiver. Integer-forcing interference alignment accomplishes this objective by having each receiver recover two linear combinations that can then be solved for the desired signal and the sum of the interference. Finally, this thesis investigates the impact of channel coherence on the integer-forcing strategy via numerical simulations.

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Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.