In this research radio resource allocation with considering circuit power and the gain of power amplifier as an energy efficient optimization problem is formulated in OFDM, OFDMA and relay systems. The low complexity energy efficient resource allocation is important for the two following reasons: first, reducing the consumed power of computational processors and second, rapid adaptation of the resource allocation algorithm to the rapid changes of channel for improved accuracy and system efficiency. Then a novel scheme is proposed to further reduce the computational complexity of obtaining a near optimal solution for energy efficient radio resource allocation in OFDM and OFDMA systems. This solution consists of subcarrier and power allocation to each user as well as power distribution among subcarriers and optimal power selection to maximize energy efficiency. Finally, an energy efficient resource allocation scheme is proposed in OFDM and amplify-and-forward relay based systems. Considering cooperative relaying in OFDM systems, allocation of optimal transmission power to the source and relay, and making decision about using or not using relays in each subcarrier results in extra complexity. Keywords Circuit power, energy efficiency, OFDM(A) systems, relay, resource allocation
