The design of feedback channels for wireless networks : an optimization-theoretic view
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The fundamentally fluctuating nature of the strength of a wireless link poses a significant challenge when seeking to achieve reliable communication at high data rates. Common sense, supported by information theory, tells us that one can move closer towards achieving higher data rates if the transmitter is provided with a priori knowledge of the channel. Such channel knowledge is typically provided to the transmitter by a feedback channel that is present between the receiver and the transmitter. The quality of information provided to the transmitter is proportional to the bandwidth of this feedback channel. Thus, the design of feedback channels is a key aspect in enabling high data rates. In the past, these feedback channels have been designed locally, on a link-by-link basis. While such an approach can be globally optimal in some cases, in many other cases, this is not true. In this thesis, we identify various settings in wireless networks, some already a part of existing standards, others under discussion in future standards, where the design of feedback channels is a problem that requires global, network-wide optimization. In general, we propose the treatment of feedback bandwidth as a network-wide resource, as the next step en route to achieving Gigabit wireless. Not surprisingly, such a global optimization initiative naturally leads us to the important issue of computational efficiency. Computational efficiency is critical from the point-of-view of a network provider. A variety of optimization techniques are employed in this thesis to solve the large combinatorial problems that arise in the context of feedback allocation. These include dynamic programming, sub-modular function maximization, convex relaxations and compressed sensing. A naive algorithm to solve these large combinatorial problems would typically involve searching over a exponential number of possibilities to find the optimal feedback allocation. As a general theme, we identify and exploit special application-specific structure to solve these problems optimally with reduced complexity. Continuing this endeavour, we search for more intricate structure that enables us to propose approximate solutions with significantly-reduced complexity. The accompanying analysis of these algorithms studies the inherent trade-offs between accuracy, efficiency and the required structure of the problem.