On the analysis and design of wireless communication systems using tools from statistical physics
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The present dissertation is concerned with the analysis and design of wireless communication systems using mathematical tools imported from the field of statistical mechanics. In particular, methods traditionally used to study macroscopic properties of disordered physical systems are used to analyze certain wireless channels as the number of transmitting and receiving elements gets large. The thesis consists of three parts: an introduction, a collection of three papers, and three independent appendices. The introduction starts by presenting the basic theory of statistical mechanics as it pertains to the analysis of disordered systems, where randomness appears not only in the microscopic state of the system, but also in the interactions between its constituent parts; the concept of self-averaging is presented and emphasized. Then a connection is drawn between the randomness in the wireless multiple-input/multiple-output (MIMO) channel and that exhibited by the interactions in systems with quenched disordered. Afterwards, specific mathematical methods dealing with quenched disorder are presented and justified, in particular the so called replica method and also the annealed approximation, which constitute the basic machinery in the analysis presented in the remainder of the thesis. The introduction concludes with a summary of the papers presented in the second part, some suggestions for future research, and a brief overview of the appendices in the third part. The second part of the thesis consists of a collection of three papers. In these papers different schemes are explored which allow for low complexity detection at the receiver end of multiuser vector channels. Specifically we propose and explore different non-linear vector precoding schemes for both single-user and multiuser MIMO channels in high-dimensions; convex spaces are suggested to relax original constellations and the replica method is used to characterize the energy penalty in the transmission process. We shall also explore a single-user vector channel where the input is preselected to conform with a strict complexity constraint at the receiver; in this case the annealed approximation is used to obtain the information capacity of the channel. The three independent appendices at the end of the thesis show some results that, although not part of any published work, are of theoretical interest and potentially useful in future research within vector precoding.