Energy efficiency optimization for amplify and forward relay networks with channel estimation errors

Due to the rapidly increasing energy consumption of the wireless communication systems, designing an energy-efficient system has become an important challenge. One can consider cooperative communication as a promising solution to reduce energy consumed by wireless networks. Hence, in this paper, we study the problem of maximizing energy efficiency by optimally allocating power in three cooperative channel scenarios. Unlike the previous works, imperfect channel state information is considered for all channels. Therefore, energy efficiency functions are derived considering channel estimation errors, and the following optimization problems are formulated to maximize the energy efficiency under the maximum transmission power and the minimum spectral efficiency constraints. Regarding the energy efficiency function behavior, an alternating optimization algorithm is used to find pilot and data transmission power at the source node. It also optimizes the power amplification gain of pilot and data at the relay node. Simulation results demonstrate that the imperfect channel state information condition can degrade the energy efficiency performance significantly. However, using the proposed power allocation method can improve the performance and compensate for the negative effect of channel estimation error. Moreover, the effect of circuit power on the optimal energy efficiency is investigated. It is shown that for a lower range of spectral efficiency, the negative effect of circuit power is greater than the channel estimation error’s negative effect, while for the higher values, the estimation error dominates the circuit power. We also observe that the results obtained from the proposed power allocation algorithms are close to the results of the global search method.