  In this paper we study energy efficient joint power allocation and
beamforming for coordinated multicell multiuser downlink systems. The
considered optimization problem is in a non-convex fractional form and hard to
tackle. We propose to first transform the original problem into an equivalent
optimization problem in a parametric subtractive form, by which we reach its
solution through a two-layer optimization scheme. The outer layer only involves
one-dimension search for the energy efficiency parameter which can be addressed
using the bi-section search, the key issue lies in the inner layer where a
non-fractional sub-problem needs to tackle. By exploiting the relationship
between the user rate and the mean square error, we then develop an iterative
algorithm to solve it. The convergence of this algorithm is proved and the
solution is further derived in closed-form. Our analysis also shows that the
proposed algorithm can be implemented in parallel with reasonable complexity.
Numerical results illustrate that our algorithm has a fast convergence and
achieves near-optimal energy efficiency. It is also observed that at the low
transmit power region, our solution almost achieves the optimal sum rate and
the optimal energy efficiency simultaneously; while at the middle-high transmit
power region, a certain sum rate loss is suffered in order to guarantee the
energy efficiency.
