Abstract
In this dissertation, we study the coordinated beamforming (CoBF) design in the multiple-input single-output (MISO) interference channel (IFC), assuming only channel distribution information (CDI) given a priori at the transmitters. The CoBF design is formulated as an optimization problem that maximizes a predefined system utility subject to constraints on the individual probability of rate outage and power budget. This problem is non-convex and appears difficult to handle due to the intricate outage probability constraints. We first conduct a complexity analysis of the outage constrained CoBF problem, and show that the outage constrained CoBF problem with the weighted sum-rate utility is intrinsically difficult, i.e., NP-hard. Moreover, the outage constrained CoBF problem with the weighted min-rate utility is also NP-hard except the case when all the transmitters are equipped with single antenna. These results confirm that efficient approximation methods are indispensable to the outage constrained CoBF problem, especially for the applications to large-scale networks. Due to the complexity analysis results, we then focus on computationally efficient algorithms for obtaining high-quality approximate solutions, e.g., stationary points, of the outage constrained CoBF problem. Specifically, using the idea of successive convex approximation (SCA), we propose a Gauss-Seidel type distributed algorithm called the distributed SCA (DSCA) algorithm for handling the outage constrained CoBF problem. The DSCA algorithm is the first polynomial-time algorithm in the literature yielding stationary-point solution to the outage constrained CoBF problem. Nevertheless, the DSCA algorithm is not yet a practical solution when the problem size increases, since the computational complexity of the DSCA algorithm grows as a high-order polynomial of the network size and the number of transmit antennas. Based on a judicious problem reformulation, we further propose, by leveraging on the block successive upper bound minimization (BSUM) method in optimization, a more efficient Gauss-Seidel type distributed algorithm, called distributed BSUM (DBSUM) algorithm. In addition, by exploiting a weighted minimum mean square error (WMMSE) reformulation, we also propose a Jocobi-type distributed algorithm, called distributed WMMSE (DWMMSE) algorithm, which can optimize the weighted sum-rate utility in a fully parallel manner. Both algorithms are shown to converge to the stationary points of the original NP-hard problems with much lower computational complexity and less communication overhead compared with the DSCA algorithm. To further provide a performance benchmark, a relaxed approximation method based on polyblock outer approximation is also proposed. Simulation results show that the DBSUM algorithm and the DWMMSE algorithm are significantly superior to the DSCA algorithm in both performance and computational efficiency, and can yield promising approximation performance by comparing with the performance benchmark.