  We address the problem of downlink beamforming for mitigating the co-channel
interference in multi-cell OFDMA networks. Based on the network utility
maximization framework, we formulate the problem as a non-convex optimization
problem subject to the per-cell power constraints, in which a general utility
function of SINR is used to characterize the network performance. Some
classical utility functions, such as the proportional fairness utility, the
weighted sum-rate utility and the {$\alpha$}-fairness utility, are subsumed as
special cases of our formulation. To solve the problem in a distributed
fashion, we devise an algorithm based on the non-cooperative game with pricing
mechanism. We give a sufficient condition for the convergence of the algorithm
to the Nash equilibrium (NE), and analyze the information exchange overhead
among the base stations. Moreover, to speed up the optimization of the
beam-vectors at each cell, we derive an efficient algorithm to solve for the
KKT conditions at each cell. We provide extensive simulation results to
demonstrate that the proposed distributed multi-cell beamforming algorithm
converges to an NE point in just a few iterations with low information exchange
overhead. Moreover, it provides significant performance gains, especially under
the strong interference scenario, in comparison with several existing
multi-cell interference mitigation schemes, such as the distributed
interference alignment method.
