The application of optimization techniques for resource management in wireless communication networksis considered in this thesis. It is understood that a wide variety of resource management problems of recentinterest, including power/rate control, link scheduling, cross-layer control, network utility maximization,beamformer design of multiple-input multiple-output networks, and many others are directly or indirectlyreliant on the general weighted sum-rate maximization (WSRMax) problem. Thus, in this dissertation agreater emphasis is placed on the WSRMax problem, which is known to be NP-hard.
A general method, based on the branch and bound technique, is developed, which solves globally thenonconvex WSRMax problem with an optimality certificate. Efficient analytic bounding techniques arederived as well. More broadly, the proposed method is not restricted to WSRMax. It can also be used tomaximize any system performance metric, which is Lipschitz continuous and increasing on signal-to-interference-plus-noise ratio. The method can be used to find the optimum performance of any networkdesign method, which relies on WSRMax, and therefore it is also useful for evaluating the performance lossencountered by any heuristic algorithm. The considered link-interference model is general enough toaccommodate a wide range of network topologies with various node capabilities, such as singlepackettransmission, multipacket transmission, simultaneous transmission and reception, and many others.
Since global methods become slow in large-scale problems, fast local optimization methods for theWSRMax problem are also developed. First, a general multicommodity, multichannel wireless multihopnetwork where all receivers perform singleuser detection is considered. Algorithms based on homotopymethods and complementary geometric programming are developed for WSRMax. They are able to exploitefficiently the available multichannel diversity. The proposed algorithm, based on homotopy methods,handles efficiently the self interference problem that arises when a node transmits and receivessimultaneously in the same frequency band. This is very important, since the use of supplementarycombinatorial constraints to prevent simultaneous transmissions and receptions of any node iscircumvented. In addition, the algorithm together with the considered interference model, provide amechanism for evaluating the gains when the network nodes employ self interference cancelationtechniques with different degrees of accuracy. Next, a similar multicommodity wireless multihop networkis considered, but all receivers perform multiuser detection. Solutions for the WSRMax problem areobtained by imposing additional constraints, such as that only one node can transmit to others at a time orthat only one node can receive from others at a time. The WSRMax problem of downlink OFDMA systemsis also considered. A fast algorithm based on primal decomposition techniques is developed to jointlyoptimize the multiuser subcarrier assignment and power allocation to maximize the weighted sum-rate(WSR). Numerical results show that the proposed algorithm converges faster than Lagrange relaxationbased methods.
Finally, a distributed algorithm for WSRMax is derived in multiple-input single-output multicelldownlink systems. The proposed method is based on classical primal decomposition methods andsubgradient methods. It does not rely on zero forcing beamforming or high signal-to-interference-plus-noiseratio approximation like many other distributed variants. The algorithm essentially involves coordinatingmany local subproblems (one for each base station) to resolve the inter-cell interference such that the WSRis maximized. The numerical results show that significant gains can be achieved by only a small amount ofmessage passing between the coordinating base stations, though the global optimality of the solution cannotbe guaranteed.
