Wireless communications have seen remarkable progress over the past two decades and perceived tremendous success due to their agile nature and capability to provide fast and ubiquitous internet access. Maturation of 3G wireless network services, development of smart-phones and other broadband mobile computing devices however have motivated researchers to design wireless networks with increased capacity and coverage, therefore un-leaching the wireless broadband capabilities. In this thesis, we address two very important design aspects of wireless networks, namely, interference management and control through optimal cross-layer design and channel fading mitigation through relay-assisted cooperative communications. For the former, we address, in the context of wireless network design, the problem of optimally partitioning the spectrum into a set of non-overlapping channels with non uniform spectrumudwidths and we model the combinatorially complex problem of joint routing, link scheduling, and spectrum allocation as an optimization problem. We use column generation decomposition technique (which decomposes the original problem into a master and a pricing subproblem) for solving the problem optimally. We also propose several sub-optimal methods for efficiently solving the pricing subproblems. For the latter problem, we study the joint problem of relay selection and power allocation in both wireless unicast and multicast cooperative cellular networks. We employ convexudoptimization technique to model this complex optimization problem and use branch and bound technique to solve it optimally. We also present sub-optimal methods to reduce the problem complexity and solve it more efficiently.
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