Modern applications involve green communication technologies motivating well optimisation in the power–limited regime. In comparison to most of existing related work that assumes perfect channel state information (CSI) is always available, which is unfortunately not true in reality, this work focuses on an optimal energy efficient solution for resource allocation in multiuser orthogonal frequency division multiple access (OFDMA) networks in the presence of imperfect CSI and data outage conditions. Particularly, in view that wireless channel conditions, circuit power consumptions and users’ quality–of–service (QoS) requirements are heterogeneous in nature, we enable attractive tuning options by letting energy efficiency optimisation objective to assign weights to each allocation link. Also, we interpret effects of data outage due to imperfect CSI using a profound insight on the monotonicity of noncentral chi-squared inverse distribution function, which reveals that our design complies with expected physics and mechanics of conventional energy efficiency approach and that it can be successfully degenerated to the energy efficiency model with perfect CSI. Furthermore, we formulate a mixed combinatorial problem towards maximising the energy efficiency subject to a minimum QoS requirement, channel interference and transmitting power constraints. The problem is transformed into an equivalent quasiconcave problem with respect to power, and concave problem with respect to the subcarrier indexing coefficients using the concept of subcarrier time–sharing. We optimise through a simple and versatile methodology, which uses standard–Lagrangian optimisation technique to obtain joint dynamic subcarrier and adaptive power allocations by means of final formulas. We also examine key properties of the introduced optimal solution in terms of implementation convergence and complexity, level of optimality, and impact of imperfect CSI coefficients and circuit power on network performance. The simulation results demonstrate the effectiveness of our allocation scheme for achieving higher energy efficiency performance with the guaranteed QoS support and lower complexity than existing approaches especially when perfect CSI is not available.