Today Energy efficiency (EE) is taking a more significant role in the design of modern communication systems. One of the most crucial trade offs in the green communication frame work is the trade off between EE and Spectral Efficiency (SE). In traditional literature, the EE was defined as “information bits per unit of transmit energy”, however, practical concerns result in taking circuit energy consumption into account for the energy consumption model (ECM). The EE metric has been redefined as “information bits per unit of consumed energy (not just transmit energy)”, where an additional circuit power factor needs to be considered. Also, SE is defined as system throughput per unit of bandwidth, is a widely accepted performance indicator of wireless networks. The trade-off between maximizing SE and EE in communication systems prompts desiners to balance the two metrics in future communication networks. It is shown that by the increase of radio access points (RAPs) in a network (relays are good examples of RAPs in wireless networks) the energy consumption of the network (without consideration of the circuitry power) will be improved. However, a tangible proof or graph is not provided to conclude how relay cooperative communication can be helpful in improving EE. In this thesis, the basic concepts of green communication, EE and relay based systems are reviewed. The energy efficiency (EE) of a decode and forward (DF) relay system is studied, where two sources communicate through a half-duplex relay node in one-way and two-way relaying strategies.Two-way relaying is proposed as a cooperative scheme to improve the SE of one-way relaying. One-way relaying leads to the loss of SE due to the pre-log factor one-half in the corresponding capacity expression, however, two-way relaying avoids the pre-log factor one-half still uses half duplex equipment. Both the circuitry power and the transmission power of all nodes are taken into consideration. In addition, three different coding schemes for two-way DF relaying strategy are considered. The aim is to maximize the EE of the system for a constant spectral efficiency (SE). For this purpose, the transmission time and the transmission power of each node are optimized. Simulations are used to compare the EE-SE curve of different DF strategies with one-way and two-way amplify and forward (AF) strategies and direct transmission (DT), to find the best energy efficient strategy in different SE conditions. Analytical and simulation results demonstrate that in low SE conditions, DF relaying strategies are more energy efficient compared to AF strategies and DT. However, in high SE conditions, the EE of two-way AF relaying and DT strategy outperform some of the DF relaying strategies. Also, the impact of different circuitry power and different channel conditions on the EE-SE curves are investigated. Keywords: Green communication, Energy efficiency, Relay based systems, Resource allocation