Energy Efficiency and Spectral Efficiency Trade-off for OFDM Systems with Imperfect Channel Estimation

In this paper, the power loading problem for orthogonal frequency division multiplexing (OFDM) with imperfect channel estimation is investigated considering the trade-off between energy efficiency (EE) and spectral efficiency (SE). Unlike traditional research that uses the EE as an objective function and imposes constraints either on the SE or the achievable rate, we propound a multiobjective optimization approach that can flexibly switch between the EE and the SE functions or change the priority level of each function using a trade-off parameter. Our dynamic approach is more tractable than conventional approaches and more convenient to realistic communication applications and scenarios. The system model considers the path loss and shadowing effect in modeling the EE and SE metrics, in addition to taking the channel estimation error into account. We first solve the marginal problems of maximizing the EE and the SE individuality, and then prove that the multiobjective optimization of the EE and the SE is equivalent to a simple problem that maximizes the capacity and minimizes the total power consumption. Finally, we use numerical results to discuss the choice of the trade-off parameter and study the effect of the estimation error, transmission power budget and channel-to-noise ratio on the multiobjective optimization.