Capacity of multi-antenna ad hoc networks via stochastic geometry
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This thesis takes as its objective quantifying, comparing, and optimizing multiple-antenna (MIMO) physical layer techniques in dense ad hoc wireless networks. A framework is developed from the spatial shot noise interference model for packet radio network analysis. The framework captures the behavior of a wide variety of signal and interference distributions, which permit inspection of a number of signal processing methods including representatives from most of the major MIMO techniques. Multi-antenna systems for point-to-point are becoming mature and being developed and deployed in many wireless communication systems due to their potential to combat fading, increase spectral efficiency, and overcome interference. The framework permits an algorithm or system designer to view the network from the perspective of a typical user, to optimize performance in the midst of a given environment, or to view the network as a whole, to determine behavior that maximizes network performance. In particular, it enables questions to be answered quantitatively, such as which MIMO techniques perform best in a given environment? Or what rate and power settings should be used across the available spatial modes? Or what is the maximum benefit of channel state information? Or what gain should an individual device, or the network as a whole expect to see given a particular physical layer strategy? The dissertation begins by developing the framework for a generic set of assumptions on network behavior and signal and interference distributions. It then presents a progression of applications to representative MIMO techniques. Broad and intuitive scaling laws are developed as well as detailed exact results for careful comparison. Capacity scaling with the number of antennas is given for systems employing beamforming, selection combining, space-time block coding, and spatial multiplexing. These applications are used as the basis for developing simple distributed algorithms for optimizing MIMO settings with QoS constraints and in heterogeneous networks. Lastly, the framework is expanded to permit comparison and optimization of MIMO performance under alternative medium access strategies. In general it is found that significant performance gains can be reaped with multi-antenna physical layers, provided the proper techniques are employed. It is also shown that the availability of multiple spatial channels impacts the inherent tradeoff between per-link throughput and spatial reuse.