  Weighted-sum energy efficiency (WSEE) is a key performance metric in
heterogeneous networks, where the nodes may have different energy efficiency
(EE) requirements. Nevertheless, WSEE maximization is a challenging problem due
to its nonconvex sum-of-ratios form. Unlike previous work, this paper presents
a systematic approach to WSEE maximization under not only power constraints,
but also data rate constraints, using a general SINR expression. In particular,
the original problem is transformed into an equivalent form, and then a
sequential convex optimization (SCO) algorithm is proposed. This algorithm is
theoretically guaranteed to converge for any initial feasible point, and, under
suitable constraint qualifications, achieves a Karush-Kuhn-Tucker (KKT)
solution. Furthermore, we provide remarkable extensions to the proposed
methodology, including systems with multiple resource blocks as well as a more
general power consumption model which is not necessarily a convex function of
the transmit powers. Finally, numerical analysis reveals that the proposed
algorithm exhibits fast convergence, low complexity, and robustness
(insensitivity to initial points).
