Distributed Power and Beam Optimization for Wireless Interference Networks

This thesis studies resource allocation for wireless interference networks. In particular, we first focus on distributed algorithms for allocating powers and adjusting beams in a peer-to-peer wireless network with multiple antennas at each terminal. The objective is to maximize the total utility (or rate) summed over all users. We start with Multi-Input Single-Output (MISO) channels and propose a distributed algorithm for joint power and beam optimization. Specifically, each receiver announces an interference price, representing the marginal cost of interference to that particular receiver. Each transmitter then updates its power and beamforming vector to maximize its utility minus the interference cost to other users, which is determined from their announced interference prices. We show that when these updates are iterated, the beams converge to a locally optimal solution under certain conditions on the utility functions. For Multi-Input Multi-Output (MIMO) channels, we aim at finding precoders that maximize the total utility. Some iterative approaches are considered based on treating beams separately and updating them using a similar interference pricing technique as for MISO networks. The convergence is guaranteed when the precoding matrix has rank one. We then study interference alignment in multi-carrier networks. When each transmitter transmits a single data stream, we show a necessary condition for zero interference (alignment across sub-channels) and characterize the sum rate at high Signal-to-Noise Ratio (SNR) by bounding the SNR offset (x-intercept) of the asymptote of the sum rate vs SNR curve. Finally, we extend the discussion of beamformer design and power control to the scenario where the channel state information is not initially available at each node. The proposed beam adaptation algorithm uses a period of bi-directional training with a least-squares objective to adapt the receive filters and transmit beamformers iteratively. Power adaptation is done by directly estimating powers to maximize a payoff objective based on interference pricing, where now this objective is also estimated via pilot transmissions. Combining the adaptive beamforming and power control algorithms, a joint algorithm is presented to update both beams and powers iteratively.