Free-Space Optical (FSO) communication through the terrestrial atmospheric channel offers many benefits in the wireless communications arena, like power efficiency; suitability for secure communications; absence of electromagnetic interference; and potentially very high bandwidth. An optical beam propagating through the atmosphere is subject to optical turbulence. Optical turbulence is a random process that distorts the intensity and phase structure of a propagating optical beam and induces a varying signal at the receiver of an FSO communication link. This phenomenon (usually referred to as scintillation) degrades the performance of the FSO link by increasing the probability of error. In this dissertation we seek to characterize the effects of the scintillation-induced power fluctuations by determining the channel capacity of the optical link using numerical methods. We find that capacity decreases monotonically with increasing turbulence strength in weak turbulence conditions, but it is non-monotonic in strong turbulence conditions. We show that low-density parity-check (LDPC) codes provide strong error control capabilities in this channel if a perfect interleaver is used. Multiple transmit optical beams can be used to reduce scintillation. We characterize the spatial correlation of the atmospheric optical channel and determine a scintillation model for the multiple-beam scheme. With this model we can predict the effective reduction in scintillation as a function of the system design parameters. A Multi-channel FSO communications system based on orbital angular momentum (OAM)-carrying beams is studied. We analyze the effects of turbulence on the system and find that turbulence induces attenuation and crosstalk among OAM channels. Based on a model in which the constituent channels are binary symmetric and crosstalk is a Gaussian noise source, we find optimal sets of OAM states at each turbulence condition studied, and determine the aggregate capacity of the multi-channel system at those conditions. At very high data rates the FSO channel shows inter-symbol interference (ISI). We address the problem of joint sequence detection in ISI channels and decoding of LDPC codes. We derive the belief propagation equations that allow the simultaneous detection and decoding of a LDPC codeword in a ISI channel.

This thesis deals with the Shannon-theoretic fundamental limits of channel coding for single-user channels with memory and feedback and for multi-user channels with side information. We first consider the feedback capacity of a class of symmetric channels with memory modelled as nite-state Markov channels. The symmetry yields the existence of a hidden Markov noise process that facilitates the channel description as a function of input and noise, where the function satisfies a desirable invertibility property. We show that feedback does not increase capacity for such class of finite-state channels and that both their non-feedback and feedback capacities are achieved by an independent and uniformly distributed input. As a result, the capacity is given as a difference of output and noise entropy rates, where the output is also a hidden Markov process; hence, capacity can be approximated via well known algorithms. We then consider the memoryless state-dependent multiple-access channel (MAC) where the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information (CSI). For the case where the encoders observe causal, asymmetric noisy CSI and the decoder observes complete CSI, inner and outer bounds to the capacity region, which are tight for the sum-rate capacity, are provided. Next, single-letter characterizations for the channel capacity regions under each of the following settings are established: (a) the CSI at the encoders are non-causal and asymmetric deterministic functions of the CSI at the decoder (b) the encoders observe asymmetric noisy CSI with asymmetric delays and the decoder observes complete CSI; (c) a degraded message set scenario with asymmetric noisy CSI at the encoders and complete and/or noisy CSI at the decoder. Finally, we consider the above state-dependent MAC model and identify what is required to be provided to the receiver in order to get a tight converse for the sum-rate capacity. Inspired by the coding schemes of the lossless CEO problem as well as of a recently proposed achievable region, we provide an inner bound which demonstrates the rate required to transmit this information to the receiver. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-07-12 13:48:59.849

In this thesis we will brush through fundamental multivariate statistical theory and then present MIMO-systems briefly in order to later calculate the channel capacity of a MIMO system. After theory has been presented we will then look at different properties of the channel capacity and then investigate a supposed MIMO system dataset and use standardized methods to verify it’s model. The properties of the limiting channel capacity uses the Marčenko-Pastur law. Therefore we will present some fundamental theorems and definitions of limiting spectral distribution of Wishart and Wigner matrices, and some fundamental properties they hold.

In this thesis we investigate the effects of the physical constraints such as antenna aperture size, antenna geometry and non-isotropic scattering distribution parameters (angle of arrival/departure and angular spread) on the performance of coherent and non-coherent space-time coded wireless communication systems. First, we derive analytical expressions for the exact pairwise error probability (PEP) and PEP upper-bound of coherent and non-coherent space-time coded systems operating over spatially correlated fading channels using a moment-generating function-based approach. These analytical expressions account for antenna spacing, antenna geometries and scattering distribution models. Using these new PEP expressions, the degree of the effect of antenna spacing, antenna geometry and angular spread is quantified on the diversity advantage (robustness) given by a space-time code. It is shown that the number of antennas that can be employed in a fixed antenna aperture without diminishing the diversity advantage of a space-time code is determined by the size of the antenna aperture, antenna geometry and the richness of the scattering environment. ¶ In realistic channel environments the performance of space-time coded multiple-input multiple output (MIMO) systems is significantly reduced due to non-ideal antenna placement and non-isotropic scattering. In this thesis, by exploiting the spatial dimension of a MIMO channel we introduce the novel use of linear spatial precoding (or power-loading) based on fixed and known parameters of MIMO channels to ameliorate the effects of non-ideal antenna placement on the performance of coherent and non-coherent space-time codes. The spatial precoder virtually arranges the antennas into an optimal configuration so that the spatial correlation between all antenna elements is minimum. With this design, the precoder is fixed for fixed antenna placement and the transmitter does not require any feedback of channel state information (partial or full) from the receiver. We also derive precoding schemes to exploit non-isotropic scattering distribution parameters of the scattering channel to improve the performance of space-time codes applied on MIMO systems in non-isotropic scattering environments. However, these schemes require the receiver to estimate the non-isotropic parameters and feed them back to the transmitter. ¶ The idea of precoding based on fixed parameters of MIMO channels is extended to maximize the capacity of spatially constrained dense antenna arrays. It is shown that the theoretical maximum capacity available from a fixed region of space can be achieved by power loading based on previously unutilized channel state information contained in the antenna locations. We analyzed the correlation between different modal orders generated at the transmitter region due to spatially constrained antenna arrays in non-isotropic scattering environments, and showed that adjacent modes contribute to higher correlation at the transmitter region. Based on this result, a power loading scheme is proposed which reduces the effects of correlation between adjacent modes at the transmitter region by nulling power onto adjacent transmit modes. ¶ Furthermore, in this thesis a general space-time channel model for down-link transmission in a mobile multiple antenna communication system is developed. The model incorporates deterministic quantities such as physical antenna positions and the motion of the mobile unit (velocity and the direction), and random quantities to capture random scattering environment modeled using a bi-angular power distribution and, in the simplest case, the covariance between transmit and receive angles which captures statistical interdependency. The Kronecker model is shown to be a special case when the power distribution is separable and is shown to overestimate MIMO system performance whenever there is more than one scattering cluster. Expressions for space-time cross correlations and space-frequency cross spectra are given for a number of scattering distributions using Gaussian and Morgenstern's family of multivariate distributions. These new expressions extend the classical Jake's and Clarke's correlation models to general non-isotropic scattering environments.

Enabling cooperation among nodes of a wireless network can significantly reduce the required transmit power as well as the induced intra-network interference. Due to the practical half-duplexity constraint of the cooperating nodes, they are prohibited to simultaneously transmit and receive data at the same time-frequency resource. The purpose of this dissertation is to illustrate the value of cooperation in such an environment. To understand how to cooperate efficiently, information theory is employed as a useful tool, which not only determines the fundamental limits of communication (i.e., capacity) over the considered network, but also provides insights into the design of a proper transmission scheme for that network. In this thesis, two simple but yet important types of wireless networks, namely Relay Channel, and Interference Channel are studied. In fact, these models constitute building blocks for larger networks. The first considered channel is a diamond-shaped relay channel consisting of a source, a destination, and two parallel relays. The second analyzed channel is an interference channel composed of two transmitter-receiver pairs with out-of-band transmitter cooperation, also referred to as conferencing encoders. While characterizing the capacity of these channels are difficult, a simpler and a more common approach is to find an achievable scheme for each channel that ensures a small gap from the capacity for all channel parameters. In chapter 2, the diamond relay channel is investigated in detail. Because of the half-duplex nature of the relays, each relay is either in transmit or receive mode, making four modes possible for the two-relay combination, specifically, 1) broadcast mode (both relays receive) 2,3) routing modes (one relay transmits, another receives) 4) multiple-access mode (both relays transmit). An appropriate scheduling ( i.e., timing over the modes) and transmission scheme based on the decode-and-forward strategy are proposed and shown to be able to achieve either the capacity for certain channel conditions or at most 3.6 bits below the capacity for general channel conditions. Particularly, by assuming each transmitter has a constant power constraint over all modes, a parameter Δ is defined, which captures some important features of the channel. It is proven that for Δ=0 the capacity of the channel can be attained by successive relaying, i.e., using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when Δ≠0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of Δ>0 and Δ<0 should be treated differently. Using new upper bounds based on the dual problem of the linear program associated with the cut-set bounds, it is proven that the successive relaying strategy needs to be enhanced by an additional broadcast mode (mode 1), or multiple access mode (mode 4), for the cases of Δ<0 and Δ>0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel. In chapter 3, a two-user Gaussian Interference Channel (GIC) is considered, in which encoders are connected through noiseless links with finite capacities. The setup can be motivated by downlink cellular systems, where base stations are connected via infrastructure backhaul networks. In this setting, prior to each transmission block the encoders communicate with each other over the cooperative links. The capacity region and the sum-capacity of the channel are characterized within some constant number of bits for some special classes of symmetric and Z interference channels. It is also established that properly sharing the total limited cooperation capacity between the cooperative links may enhance the achievable region, even when compared to the case of unidirectional transmitter cooperation with infinite cooperation capacity. To obtain the results, genie-aided upper bounds on the sum-capacity and cut-set bounds on the individual rates are compared with the achievable rate region. The achievable scheme enjoys a simple type of Han-Kobayashi signaling, together with the zero-forcing, and basic relaying techniques.

A central feature of wireless networks is multiple users sharing a common medium. Cellular systems are among the most common examples of such networks. The main phenomenon resulting from this inter-user interaction is interference, and thus analyzing interference networks is critical to determine the capacity of wireless networks. The capacity region of an interference network is defined as the set of rates that the users can simultaneously achieve while ensuring arbitrarily small probability of decoding error. It is an inherently hard problem to find the capacity region of interference networks. Even the capacity region of a general 2-user interference channel is a prominent open problem in information theory. This work's goal is to derive achievable regions that are improved over known results, and when possible, capacity theorems, for K user interference networks. Another multiuser channel that is commonly found in wireless systems is a broadcast channel. Broadcast channels stand side by side with Interference channels as the two of the most important channels for which capacity results are still not completely known. In this work we develop inner and outer bounds on the capacity region of fading broadcast channels, using which we find a part of the capacity region under some conditions. In summary, this work first presents coding arguments for new achievable rate regions and, where possible, capacity results for K-user interference networks. Second, it provides inner and outer-bounds for a class of fading broadcast channels. / text

The ever-increasing demands for transmission capacity are the cause for the quick evolution of optical communication systems. Channel transmission at 100 Gb/s is already being considered by network operators. The major transmission impairments at these high rates are intra-channel and inter-channel nonlinearities, nonlinear phase noise, and polarization mode dispersion. By implementing LDPC-coded modulation schemes with soft decoding and Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm for equalization we have demonstrated significant improvements in system performance experiencing several impairments simultaneously. The new turbo-equalization scheme is used as a mean to simultaneously mitigate both linear and nonlinear impairments. This approach is general and applicable to both direct and coherent detection.We provide comprehensive study of LDPC codes suitable for implementation in high-speed optical transmission systems. We determine channel capacity based on the forward step of the BCJR algorithm and show that by using LDPC codes we can closely approach the maximum transmission capacity that is possible. We propose the multilevel maximum a posteriori probability (MAP) turbo equalization scheme based on multilevel BCJR algorithm and an LDPC decoder, which considers independent symbols transmitted over both polarizations as two dimensional super-symbols. The use of multilevel modulation schemes provide higher spectral efficiency, while all related signal processing is performed at lower symbol rates, where dealing with PMD compensation and fiber nonlinearities mitigation is more manageable. We show significant improvement in system performance over a system employing an equalizer that considers symbols transmitted in different polarizations as independent.

Enabling cooperation among nodes of a wireless network can significantly reduce the required transmit power as well as the induced intra-network interference. Due to the practical half-duplexity constraint of the cooperating nodes, they are prohibited to simultaneously transmit and receive data at the same time-frequency resource. The purpose of this dissertation is to illustrate the value of cooperation in such an environment. To understand how to cooperate efficiently, information theory is employed as a useful tool, which not only determines the fundamental limits of communication (i.e., capacity) over the considered network, but also provides insights into the design of a proper transmission scheme for that network. In this thesis, two simple but yet important types of wireless networks, namely Relay Channel, and Interference Channel are studied. In fact, these models constitute building blocks for larger networks. The first considered channel is a diamond-shaped relay channel consisting of a source, a destination, and two parallel relays. The second analyzed channel is an interference channel composed of two transmitter-receiver pairs with out-of-band transmitter cooperation, also referred to as conferencing encoders. While characterizing the capacity of these channels are difficult, a simpler and a more common approach is to find an achievable scheme for each channel that ensures a small gap from the capacity for all channel parameters. In chapter 2, the diamond relay channel is investigated in detail. Because of the half-duplex nature of the relays, each relay is either in transmit or receive mode, making four modes possible for the two-relay combination, specifically, 1) broadcast mode (both relays receive) 2,3) routing modes (one relay transmits, another receives) 4) multiple-access mode (both relays transmit). An appropriate scheduling ( i.e., timing over the modes) and transmission scheme based on the decode-and-forward strategy are proposed and shown to be able to achieve either the capacity for certain channel conditions or at most 3.6 bits below the capacity for general channel conditions. Particularly, by assuming each transmitter has a constant power constraint over all modes, a parameter Δ is defined, which captures some important features of the channel. It is proven that for Δ=0 the capacity of the channel can be attained by successive relaying, i.e., using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when Δ≠0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of Δ>0 and Δ<0 should be treated differently. Using new upper bounds based on the dual problem of the linear program associated with the cut-set bounds, it is proven that the successive relaying strategy needs to be enhanced by an additional broadcast mode (mode 1), or multiple access mode (mode 4), for the cases of Δ<0 and Δ>0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel. In chapter 3, a two-user Gaussian Interference Channel (GIC) is considered, in which encoders are connected through noiseless links with finite capacities. The setup can be motivated by downlink cellular systems, where base stations are connected via infrastructure backhaul networks. In this setting, prior to each transmission block the encoders communicate with each other over the cooperative links. The capacity region and the sum-capacity of the channel are characterized within some constant number of bits for some special classes of symmetric and Z interference channels. It is also established that properly sharing the total limited cooperation capacity between the cooperative links may enhance the achievable region, even when compared to the case of unidirectional transmitter cooperation with infinite cooperation capacity. To obtain the results, genie-aided upper bounds on the sum-capacity and cut-set bounds on the individual rates are compared with the achievable rate region. The achievable scheme enjoys a simple type of Han-Kobayashi signaling, together with the zero-forcing, and basic relaying techniques.

With the fast adoption of LTE and IEEE 802.11N, more devices are employing multiple antennas to boost the data rate and reliability of the communication link. Traditionally, fixed antennas are used in such devices. In recent years, reconfigurable antennas have been sought out to further boost the performance, which can adaptor to the changing wireless channel by altering their radiation characteristics, and maintain or exceed the performance of fixed antennas. This thesis studies the possibility of performance increase using pattern reconfigurable antennas as receivers. Their performance potential was first estimated using simulations, and then demonstrated using two electrically steerable passive array radiator (ESPAR) antennas against a pair of monopole antennas on a hardware bit error rate (BER) testbed. The former produces equal performance in BER with certain pattern combinations and excels in theoretical capacity with substantial lead making pattern reconfigurable antenna a potent option as receiver in MIMO-related applications.

With the fast adoption of LTE and IEEE 802.11N, more devices are employing multiple antennas to boost the data rate and reliability of the communication link. Traditionally, fixed antennas are used in such devices. In recent years, reconfigurable antennas have been sought out to further boost the performance, which can adaptor to the changing wireless channel by altering their radiation characteristics, and maintain or exceed the performance of fixed antennas. This thesis studies the possibility of performance increase using pattern reconfigurable antennas as receivers. Their performance potential was first estimated using simulations, and then demonstrated using two electrically steerable passive array radiator (ESPAR) antennas against a pair of monopole antennas on a hardware bit error rate (BER) testbed. The former produces equal performance in BER with certain pattern combinations and excels in theoretical capacity with substantial lead making pattern reconfigurable antenna a potent option as receiver in MIMO-related applications.