Mobile communication industries are increasingly contributing to the worldwide energy consumption and CO2 emission. This study addresses a number of key radio resource management (RRM) strategies across PHY and MAC layers for reducing base station energy consumption, as measured by a `Joules per bit` metric. These strategies including power efficient link adaptation, exploitation of multi-user diversity and trading bandwidth for energy efficiency. By collectively taking advantage of those RRM strategies, a multi-user adaptive power and resource allocation algorithm is proposed to ease the power requirements of a base station, while maintaining the same levels of service to the user. The scheduling algorithm is applied to an LTE downlink simulator and its performance is evaluated for various traffic load conditions. The results show that the proposed algorithm achieves a significant energy saving (up to 86`) over a conventional non-energy aware resource allocation scheme. Furthermore, the energy efficiency performance of various multiple antenna techniques is evaluated along with the impact of control signalling overhead. These multiple antenna schemes are then incorporated into the proposed scheduling algorithm and the additional achievable energy savings are quantified.