Abstract: This paper considers the energy efficient precoding design for the multicell multiuser downlinksystems. Different from the conventional sum-power constraint, this letter adopts a more realistic per-antenna power constraint since in practical implementations each antenna is equipped with its own power amplifier and its power is limited individually by the linearity of the amplifier. The optimization objective of interest is formulated as maximizing the energy/spectrum efficiency of the multicell multiuser downlink systems subject to per-user target rate requirements and per-antenna power constraints.To address the problem of interest, the original non-convex optimization problem is first transformed into a convex optimization problem by exploiting convex approximation methods. Then, an effective iterative optimization algorithm is developed to solve the approximated problem. Final, numerical simulation results are given to validate the effectiveness and the performance of the developed algorithm.