## 1 Introduction  
Green Radio communication has received a lot of attention in the past few years with an aim to decrease the carbon foot print of wireless networks. It has been estimated that nearly 70% of the energy being used by cellular operators is on the radio part [1] and around 9% of the global CO\({}_{2}\) emission is from the communication systems [2]. In addition, one of the main concerns is the User Equipment (UE) battery, which has not shown progression at par with the Radio Access Technology (RAT). This phenomena is highly visible for the cell edge users that despite spending higher energy (due to high pathloss shadow fading and adjacent cell interference) are unable to achieve fair share of the radio resources. In this context, Green communications employing cooperative and fair resource allocation techniques can help in reducing the carbon footprint and increasing Energy Efficiency (EE). Most of the existing wireless systems use Orthogonal Frequency Division Multiple Access (OFDMA) to distribute radio resources among UEs. One of the existing RAT to use OFDMA is Long Term Evolution-Advanced (LTE-A), which has a similar structure to its predecessor LTE. In LTE, each Resource Block (RB) is a time frequency grid element. The basic RB structure contains 15 subcarriers of 12 KHz each and a 10 ms frame. Each frame is subdivided into 10 subframes of 1 ms and each subframe is further divided into 2 slots of 0.5 ms each. Each slot may contain 6 or 7 OFDM symbols depending on a normal or an extended cyclic prefix. The RB allocation can be changed after every Transmission Time Interval (TTI) based upon channel conditions or RB allocation algorithm. OFDMA offers flexibility of RBs Allocation to tailor user and network requirement, such as throughput, fairness, Energy EfficiencyEE, and Spectral Efficiency (SE). For example, in order to support higher peak data rates Carrier Aggregation (CA) is introduced to obtain wider bandwidth. Compared to LTE, CA in LTE-A can support maximum 5 adjacent/non-adjacent component carriers of maximum 20 MHz to achieve 100 MHz bandwidth. In addition, LTE-A allows Layer 3 (L3) relays to be incorporated in the network that can decode and forward the data to a UE [3]. This cooperative communication addresses EE and throughput of the cell edge users by providing channel diversity. As the network can only accommodate finite relays, their placement is, therefore, crucial to manage the overall throughput. The RB allocation between direct link that is Base Station (BS)-UE and two hop link that is (BS)-Relay Node (RN)-UE can be done independently or in a shared manner. In [4], the authors have presented a thorough comparison of basic RB allocation schemes, which are Round Robin (RR), Proportional Fairness (PF), Maximum Throughput (MT), and Maximum Minimum (MM); they presented an alternating MT and PF based resource allocation scheme SAMM (abbreviated with Authors' names) without considering any relay. The paper considered LTE system with a basic RB structure [5], 5 MHz bandwidth with fixed 10 users that are uniformly placed from the BS. These schemes have been compared in terms of sum throughput, individual user throughput and fairness based on JFI (Jains fairness index). The SAMM scheme provides a better tradeoff between throughput and fairness. Cell edge users show some throughput gains due to proportional fairness, however, this scheme fails to address EE. Authors in [6] considered EE for generic OFDMA based downlink system. They presented Bisection based Optimal Power Allocation (BOPA) algorithm for a given RB assignment. The BOPA works as an iterative approach based on water filling principle. This work uses equal power allocation among users for initial users' rate calculation, whereas, a modified algorithm in [7] uses equal power per resource block. In [8], the authors proposed a quality of service (QoS) aware optimization problem for relay-based multi-user cooperative OFDMA uplink system.