Energy-efficient power allocation for pilots in training-based downlink OFDMA systems

In this paper, power allocation between pilots and data symbols is investigated to maximize energy efficiency (EE) for downlink orthogonal frequency division multiple access (OFDMA) networks. We first derive an EE function considering channel estimation error, which depends on large-scale channel gains of multiple users, allocated power to pilots and data symbols, and circuit power consumption. Then an optimization problem is formulated to maximize the EE under overall transmit power constraint. Exploiting the quasiconcavity property of the EE function, we propose an alternating optimization method in the low transmit power region and reformulate a joint quasiconcave problem in the high transmit power region. Analysis and simulation results show that the power ratio for pilots decreases with the circuit power. When the circuit power is small, the optimal overall transmit power increases with the circuit power. Otherwise, the optimal transmit power does not depend on it. Transmitting more data symbols to the users with higher channel gains improves the EE but at a cost of sacrificing the fairness among multiple users. Simulation results also demonstrate that compared with spectral efficiency (SE)-oriented design, the EE-oriented design can improve the EE performance significantly with a relatively small SE loss.