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Multiple antennas at each side of the communication channel seem to be vital for future wireless communication systems. Multi-antenna communication provides throughput gains roughly proportional to the smallest number of antennas at the communicating terminals. On the other hand, multiple antennas at a terminal inevitably increase the hardware complexity of the latter. For efficient design of such systems relevant mathematical tools, capable of capturing the most significant features of the wireless multi-antenna channel - such as fading, spatial correlation, interference - are essential. This thesis, based on the asymptotic methods from statistical physics and random matrix theory, develops a series of asymptotic approximations for various metrics characterizing the performance of multi-antenna systems in different settings. The approximations become increasingly precise as the number of antennas at each terminal grows large and are shown to significantly simplify the performance analysis. This, in turn, enables efficient performance optimization, which would otherwise be intractable. After a general introduction, provided in Chapter 2, this thesis provides four different applications of large-system analysis. Thus, Chapter 3 analyzes multi-antenna multiple-access channel in the presence of non-Gaussian interference. The obtained large-system approximation of the sum rate is further used to carry out the precoder optimization routine for both Gaussian and finite-alphabet types of inputs. Meanwhile, Chapter 4 carries out the large-system analysis for a multi-hop relay channel with an arbitrary number of hops. Suboptimality of some conventional detectors has been captured through the concept of generalized posterior mean estimate. The obtained decoupling principle allows performance evaluation for a number of conventional detection schemes in terms of achievable rates and bit error rate. Chapter 5, in turn, studies achievable secrecy rates of multi-antenna wiretap channels in three different scenarios. In the quasi-static scenario, an alternating-optimization algorithm for the non-convex precoder optimization problem is proposed. The algorithm is shown to outperform the existing solutions, and it is conjectured to provide a secrecy capacity-achieving precoder. In the uncorrelated ergodic scenario, a large-system analysis is carried out for the ergodic secrecy capacity yielding a closed-form expression. In the correlated ergodic scenario, the obtained large-system approximation is used to address the corresponding problem of precoder optimization. Finally, Chapter6 addresses a practical case of random network topology for two scenarios: i) cellular mobile networks with randomly placed mobile users and ii) wiretap channel with randomly located eavesdroppers. Large-system approximations for the achievable sum rates are derived for each scenario, yielding simplified precoder optimization procedures for various system parameters. / <p>QC 20140901</p>

The effect of large size ratios of solute to solvent on the critical properties and phase behaviour of binary mixtures of spherical particles is investigated using an "augmented van der Waals" equation of state. The equation used is essentially a van der Waals equation with an improved hard sphere repulsive term. Molecular dynamics and constant-pressure Monte Carlo simulations of binary mixtures of hard spheres with different diameter ratios and mole fractions are undertaken to check the adequacy of the hard sphere equation. Good agreement is found, even for systems with large differences in size. Furthermore, many of the hard sphere mixtures exhibited a transition from a fluid to a solid phase at high densities. Phase boundaries are calculated for model mixtures comprising spheres of different sizes between which there are long-ranged attractive forces. Particular attention is paid to the case in which the ratio of sizes is infinite. The systems show a wide variety of behaviour that includes liquid-liquid and gas-gas immiscibility, and the formation of negative azeotropes. Calculations investigating the effect of different attractive interactions between the small and large spheres show that as the magnitude of this interaction is increased, liquid-liquid immiscibility becomes the dominant feature of the phase diagram at moderate temperatures. The extent of liquid-liquid coexistence is greatest at large size differences. These model systems are shown to reproduce some of the behaviour of aqueous solutions of surfactants if it is assumed that the large spheres are models of the micelles and the small spheres models of the solvent molecules. The properties of binary lattice mixtures of bifunctional molecules whose ends are chosen to mimic surfactant and solvent molecules are also briefly investigated, to determine the effect of the asymmetric surfactant molecule on the phase separation. Closed-loops emerge in the phase diagrams as the surfactant character of one of the species is increased.

Solid-state amorphization of a crystalline solid to an amorphous phase is extensively studied as a first order phase transition at low temperature for almost thirty years. In this dissertation, we report the recent progress on phenomenological models employed for thermodynamic description of macroscopic systems and fluctuations and nucleation of mesoscopic inhomogeneous systems in binary solid solutions under polymorphic constraints with no long-range diffusion involved. Based on our understanding on atomic picture of solid-state amorphization in binary solid solutions, we propose a Landau free energy to describe amorphization as the first order phase transition. The order parameter is defined which represents the loss of long-range translational order. The elastic strain field induced by composition disorder plays the important role through the bilinear coupling with the order parameter. Elastic softening and amorphization happen simultaneously. From the similarity between the melting and amorphization, we use the temperature and composition as two external variables and treat solid-state amorphization as low temperature melting under polymorphic constraints. For homogeneous system, the phase diagrams for endothermic melting and exothermic melting are built separately and the corresponding thermodynamic quantities are presented. A microscopic homogeneous nucleation mechanism is proposed conceptually in binary solid solutions under polymorphic constraints. The formation of an amorphous embryo is initiated from the composition modulation in the crystal state and a subsequent polymorphous nucleation within the as-formed heterophase fluctuation. This homogeneous nucleation path is thought to be associated with the nonlinear energy localization mechanism connected with the localized large-amplitude excitations of atoms, which are induced by nonlinear and disorder. A Landau-Ginzburg free energy is constructed to describe the critical nucleus and the growth of the new phase in one-dimensional systems. Analytical and numerical methods contribute to the understanding the fluctuations and nucleation processes. Size-dependent melting and amorphization in nanosolids are investigated. Two models are proposed for nanocrystalline solid solutions to glass transformations. Based on the thin film model with finite thickness, we build one-dimensional Landau-Ginzburg approach, which includes surface contribution and size dependence, and numerical results do show similarity with experimentsâ results qualitatively.

Thesis (Ph.D.)--McMaster University, 2004. / Supervisor: R.K. Bhaduri. Includes bibliographical references (p. 127-133). Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: J. S. Preston. Includes bibliographical references (leaves 111-117).

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: J. S. Preston. Includes bibliographical references (leaves 111-117).

Thesis (Ph. D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 52-10, Section: B, page: 5290. Supervisor: M.F. Collins.

Thesis (M.S.)--Ohio University, March, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 61-62).

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008. / Committee Chair: Uzer, Turgay; Committee Member: Aral, Mustafa; Committee Member: Flannery, Raymond; Committee Member: Raman, Chandra; Committee Member: Schatz, Michael.