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In wireless communication systems, energy efficiency (EE) and spectral efficiency (SE) tradeoff is a challenging issue as they are inversely proportional to each other. Most previous work has provided the communication between two points that may lead to the inefficient use of network resources. It is crucial to study optimal power allocation (PA) including relay nodes in order to improve power saving and data rate. This paper proposes a PA optimization method for multi-user, based on EE and SE in Long Term Evolution-Advanced (LTE-A). The optimization problem is formulated as multi-objective optimization (MOO), considering both downlink and uplink transmissions. The mathematical expression of optimal power for EE and SE (OPES) is derived for Transparent and Non-Transparent modes with amplify-and-forward (AF) relay. Numerical results confirm the effectiveness of the proposed OPES formula compared …