# Energy and Spectral Efficiency Balancing Algorithm for Energy Saving in LTE Downlinks
## 2 Related Work  
Several algorithms proposed for LTE downlinks are reviewed in this section. The review focuses on how these algorithms use SE, EE, SET and sleep-mode operations to save energy, where the advantages and limitations of each algorithm are highlighted. Recently, several studies have been conducted to investigate the relationship between SE and EE. In [4], a new paradigm was presented for SET by considering different bandwidth requirements. The scheme analyzed resource efficiency for Orthogonal Frequency-Division Multiple Access (OFDMA) and proved that it utilizes the trade-off between EE and SE by balancing the power consumption and the occupied bandwidth. However, this scheme did not provide an appropriate weight factor to utilize the available bandwidth and power. Later, the trade-off between EE and SE in a delay-constrained wireless system was proposed in [5]. The approach used a generic closed-form approximation to investigate the impact of Quality of Service (QoS) and circuit power consumption on EE and SE, respectively, by applying a curve-fitting mechanism. This approach proved that EE function is a quasi-convex problem that can be solved using a two-step binary search algorithm. However, the scheme lacked a closed-form power allocation approach and a mathematical formulation for the trade-off between EE and Effective Capacity (EC). SET trade-off behavior has been widely considered using various interference-level scenarios. SET with filter optimization in multiple access was analyzed in [6] using two conflicting metrics: throughput maximization and power consumption minimization. An energy-efficient design for an OFDMA network was proposed in [7] based on [PERSON]'s effective capacity approach to maximize system throughput, which is subject to delay QoS requirements. Furthermore, effective EE and EC trade-off were utilized through fractional programming, which converted quasi-concave optimization to a subtractive optimization problem by adopting [PERSON]'s technique. However, this algorithm was not optimal for maximizing EC-based statistical delay provisioning. In [8], a general problem was formulated to minimize total consumption cost while satisfying area SE requirements. The problem was further decomposed into a deployment problem at peak time and an operational problem at off-peak time. However, network performance was jeopardized due to the high energy consumption of the scheme. In [9], a MOP was adopted to examine SET in downlink OFDMA systems with fairness constraints. The scheme uses a weighted sum method to obtain Pareto sets that provides a quantitative insight into SET with various fairness levels. However, the scheme did not achieve trade-off between EE and fairness because the backhaul energy consumption was completely disregarded. Reference [10] proposed a scheme that jointly maximizes overall system EE and SE towards green heterogeneous networks under QoS constraints. The MOP was modeled to dynamically adjust the trade-off parameters of network providers. To obtain a Pareto optimal solution, the problem was transformed into an SOP using a weighted sum method. However, this scheme disregarded the total signaling power of the transmitters, transmission time and power constraints of the antennas. In [11], SET was investigated for a downlink OFDMA single-cell network. The scheme simultaneously optimized EE and SE, which were then formulated as a MOP. It used a weighted linear sum technique to convert the MOP to an SOP where Pareto optimal sets were analyzed. The converted SOP illustrated that the scheme is neither quasi-concave nor quasi-convex. Thereafter, the scheme was solved using particle swarm optimization, which decreased the total transmission power and improved the EE. However, this scheme is neither convex nor concave, thus, finding its optimal solution is difficult and also requires extra processing that consumes more power.