# Energy and Spectral Efficiency Balancing Algorithm for Energy Saving in LTE Downlinks
## 2 Related Work
In [12], the authors proposed an energy-aware power management scheme that dynamically updates sleep parameters in accordance with the remaining energy of Inter-Arrival Time (IAT) to prolong battery life. The scheme achieved minimum response delay under sufficient energy but resulted in high energy consumption under insufficient energy. Reference [13] investigated the EE aspects of the BS deployment mechanism for cellular networks. The mechanism explored the impact of power consumption on the basis of deployment strategies. In addition, the concept of area power consumption was introduced. The scheme achieved an average throughput improvement but resulted in high energy consumption. After that, a scheme for power allocation and antenna port selection in Orthogonal Frequency-Division Multiplexing (OFDM) distributed antenna systems was proposed in [14]. Two schemes were investigated to maximize the downlink received signal. Firstly, the scheme selected the distributed antenna on the basis only of large-scale fading and power allocation. Secondly, the scheme selected the distributed antenna using large- and small-scale fading coupled with optimal power. The scheme achieved low complexity but disregarded delay performance, which resulted in a waste of energy. Energy-efficient link adaptation with transmitter Channel State Information (CSI), which was proposed in [15], aimed to minimize the total energy consumption of a mobile terminal. Flat and frequency-selective fading channels were used to determine the consumed energy. The algorithm achieved a decrease in energy consumption with an increase in bandwidth, however, it could not guarantee the user's QoS. In [16], an energy-efficient subcarrier and bit allocation for multi-user OFDMA systems were proposed. SET was analyzed by considering fairness constraints among users. The algorithm was formulated as an optimization problem for integer fractional programming. Moreover, an iterative programming method was used to solve the optimization problem by minimizing system complexity. However, the algorithm resulted in poor energy efficiency because it assumed that CSI is always perfect. In fact, CSI can be corrupted when the scheduled data rate surpasses the maximum channel size. The authors of [17] investigated SET in a fading communication link. An optimization problem to maximize ergodic SE with a constraint of minimum ergodic EE was introduced. The scheme achieved an improvement in SE while minimizing channel circuit power, but it did not consider the impact of the user's data rate, which resulted in inefficient resource utilization. To alleviate this problem, Reference [18] proposed SET for a heterogeneous network with QoS constraints. This scheme aimed to simultaneously maximize SE and EE while satisfying the data rate requirement of each user. It was designed on the basis of three stages. Firstly, the cell center radius was selected using fractional frequency reuse. Secondly, frequency resources were allocated to satisfy user data requirements. Lastly, the Levenberg-Marquardt approach was used to solve the power allocation subproblem. This scheme achieved higher outage probabilities because of increased inter-cell interference, however, it resulted in high energy consumption. The authors of [19] proposed SET in cellular networks. The algorithm developed a theoretical framework that is applicable to OFDMA networks based on transmission power and optimal resource allocation. Initially, the algorithm focused on using a single-cell scenario but was later extended to a multi-cell scenario using the stochastic geometry approach. It achieved tractable outcomes but using a large number of antennas resulted in high energy consumption. SET in an interference-limited algorithm was proposed in [20], which concurrently optimizes EE and SE. Firstly, the scheme was formulated as a MOP by applying the constraint of the transmission power limit. A weighted linear sum technique was used to convert the MOP to an SOP.