Pareto Optimality in Multiuser Relay Network

Pareto optimality is a desired property in multiuser communication networks. In this thesis, we study the multiuser amplify-and-forward (AF) relay network and assume each node is equipped with multiple antennas. The objective is to optimize the power and the beamforming vectors at the transmitters, the processing matrices at the relays and the beamforming vectors at the receivers for Pareto optimality in maximizing users' signal-to-interference-plus-noise ratio (SINR) tuple.;We first study Pareto optimality with respect to the power of the transmitters by making use of SINR balancing analysis. For the SINR balancing problem considered, we propose efficient algorithms to obtain the optimal power vector. We give necessary and sufficient conditions for an SINR tuple to be Pareto optimal with respect to the power of the transmitters under various types of power constraints. These conditions lay the foundation for the study of Pareto optimality with respect to the beamforming vectors and the relay processing matrices in later chapters.;In Chapter 3, Pareto optimality is first studied with respect to the transmit and receive beamforming vectors with channel state information (CSI) of all local links, based on the SINR balancing analysis and the Collatz-Wielandt formula. By suitable reformulation, the beamforming vectors can be optimized locally at each transmitter and receiver in a distributed way. We present the algorithm to achieve the necessary and sufficient condition for Pareto optimality. Numerical results show that significant improvement in performance is achieved, compared with the random scheme. With CSI of the desired link only, we give a sufficient condition for the transmit covariance matrix to be Pareto optimal and present a transmission scheme achieving this condition.;In Chapter 4, we unify the study of Pareto optimality with respect to the relay processing matrices under different power constraints into one framework, by formulating different relay power constraints into a common form. Then optimization of the relay processing matrices is studied by two approaches. The first one is to use the rate profile method and the semidefinite relaxation (SDR) method. The second one is based on the SINR balancing analysis. The two optimization approaches are compared via numerical results.