# Energy and Spectral Efficiency Balancing Algorithm for Energy Saving in LTE Downlinks
## 3 The Proposed SET Algorithm
### Energy-Efficient Battery Lifetime Algorithm  
Reference [3] analytically investigated the efficiency of the DRX mechanism and the effect of RRC state transmission on saving battery life. The performance of this scheme has been evaluated by considering only idle-state RRC. However, this scenario causes an increase in packet delay that might result in high energy consumption. The major difference between the proposed scheme and the DRX power-saving algorithm is the manner in which the sleep-mode of RRC is adjusted: the initial state (\(initial_{state}\)) and final state (\(final_{state}\)). Furthermore, the performance of the proposed algorithm is evaluated analytically and through experimental simulation. Moreover, packet arrival interval and transmission time in DRX are adjusted on the basis of exponential and general distributions, respectively. In contrast with DRX, the proposed SET algorithm dynamically adjusts three parameters on the basis of the packet arrival pattern. The basic concept behind the sleep operation is to improve power consumption by minimizing energy. In general, eNodeB goes into sleep-mode when UE has no request for packet processing. The communication between UE and eNodeB with their corresponding sleep operation has been illustrated in Figure 1, where the eNodeB remains in the idle state unless it receives a message from UE that a packet has to be transmitted. Consequently, the eNodeB transits from a listening state to an aware mode by sensing and then responding to the UE that is ready to receive an incoming packet for transmission. The time that the incoming packet arrived at the eNodeB scheduler and the time spent before it is being transmitted are recorded. When the current time (spent-time-arrival-time) is longer than 1 ms, the packet is in the transmission state. During the transmission state, the Initial Energy Consumption (IEC) and the Final Energy Consumption (FEC) are computed using Equations (1) and (2), respectively. After all the packets are transmitted, eNodeB returns to sleep-mode while waiting for a request from the UE to transmit another incoming packet. This process is repeated continuously until an optimal value is obtained for IEC and FEC. Given that the remaining energy at eNodeB is consumed, the act of eventually saving energy is crucial. IEC has an impact on energy consumption and packet response delay, which should be adjusted by considering the remaining energy in eNodeB as indicated in Equation (1):  
\[IEC=max(\frac{E_{total}-E_{remained}}{E_{total}})\times E_{max} \tag{1}\]  
where \(E_{total}\) denotes the total energy of eNodeB, \(E_{remained}\) represents the remaining energy, and \(E_{max}\) is the maximum energy. Similarly, FEC is calculated using Equation (2):  
\[FEC=a\ \times E_{max}+b\times E_{min} \tag{2}\]  
where \(E_{min}\) is the minimum energy, and \(a+b=1\), which represents the weight of each value and bases the estimates of the current IAT on the past IAT. The primary modification and improvement of the proposed SET algorithm have been illustrated in Figure 2, in which the packet processing time is set to \(\geq\)1 ms as described in 3 GPP Release 9 [22], and the initial and final energy states are introduced. Figure 1: SET algorithm operation with awake and sleep-modes. The corresponding algorithm is presented in Algorithm 1, which illustrates how the two parameters are dynamically adjusted based on the downlink stochastic packet arrival pattern. Firstly, the idle, initial, and final states initialized at the UE, which begins in normal sleep-mode operation and waits for a short period; if no packet is received, then it sends a request message to the eNodeB to enter into sleep-mode. The eNodeB computes the initial and final sleep windows for the UE using Equations (1) and (2), and then sends the results back to the UE for it to proceed to sleep-mode.