  In this paper, we propose a new beamforming design to maximize energy
efficiency (EE) for multiple input single output interfering broadcast channels
(IFBC). Under this model, the EE problem is non-convex in general due to the
coupled interference and its fractional form, and thus it is difficult to solve
the problem. Conventional algorithms which address this problem have adopted an
iterative method for each channel realization, which requires high
computational complexity. In order to reduce the computational complexity, we
parameterize the beamforming vector by scalar parameters related to beam
direction and power. Then, by employing asymptotic results of random matrix
theory with this parametrization, we identify the optimal parameters to
maximize the EE in the large system limit assuming that the number of transmit
antennas and users are large with a fixed ratio. In the asymptotic regime, our
solutions depend only on the second order channel statistics, which yields
significantly reduced computational complexity and system overhead compared to
the conventional approaches. Hence, the beamforming vector to maximize the EE
performance can be determined with local channel state information and the
optimized parameters. Based on the asymptotic results, the proposed scheme can
provide insights on the average EE performance, and a simple yet efficient
beamforming strategy is introduced for the finite system case. Numerical
results confirm that the proposed scheme shows a negligible performance loss
compared to the best result achieved by the conventional approaches even with
small system dimensions, with much reduced system complexity.
