  This paper studies the coordinated beamforming (CoBF) design for the
multiple-input single-output interference channel, provided that only channel
distribution information is known to the transmitters. The problem under
consideration is a probabilistically constrained optimization problem which
maximizes a predefined system utility subject to constraints on rate outage
probability and power budget of each transmitter. Our recent analysis has shown
that the outage-constrained CoBF problem is intricately difficult, e.g.,
NP-hard. Therefore, the focus of this paper is on suboptimal but
computationally efficient algorithms. Specifically, by leveraging on the block
successive upper bound minimization (BSUM) method in optimization, we propose a
Gauss-Seidel type algorithm, called distributed BSUM algorithm, which can
handle differentiable, monotone and concave system utilities. By exploiting a
weighted minimum mean-square error (WMMSE) reformulation, we further propose a
Jocobi-type algorithm, called distributed WMMSE algorithm, which can optimize
the weighted sum rate utility in a fully parallel manner. To provide a
performance benchmark, a relaxed approximation method based on polyblock outer
approximation is also proposed. Simulation results show that the proposed
algorithms are significantly superior to the existing successive convex
approximation method in both performance and computational efficiency, and can
yield promising approximation performance.
