# Energy Efficient Constellation for Wireless Connectivity of IoT Devices
## 1 Introduction
### Literature Review  
In the literature, there are various methods to exploit the discontinuity of the information sources to save energy. The LTE architecture exploits the idea of Discontinuous Reception (DRX) andDiscontinuous Transmission (DTX) to provide a concrete solution to the power saving. LTE provides methods for the user equipment (UE) to micro-sleep even in the active state to reduce power consumption while providing high QoS and connectivity [9; 10]. If no transmissions are detected for a specific period, the UE is allowed not to monitor the downlink control channel in the given subframe and to go to power saving mode for a short period (short DRX cycle). This is a simple method to keep the UE alive, especially useful for bursty traffic, as opposed to regular. If for several DRX Short Cycles there are no transmissions, a long DRX Cycle is activated. The long DRX cycle is used during UE's inactivity periods, when it only has to check the control channels and no resources are assigned. During both short and long DRX Cycles, the radio-frequency (RF) modem is turned on periodically for several consecutive subframes to listen to the control channels. When data activity is detected both in downlink or uplink, the short DRX cycle for UE is triggered, increasing the responsiveness and connectivity of UE. Basically, the LTE standard, and others similarly, exploit the silence of the source using two power save periods with different granularity to adapt to different discontinuous sources. During these power saving periods, the RF module is activated regularly to control if transmissions are planned, thus consuming energy as well. Moreover, only two cycles (short and long) seem to be less adaptive to the traffic generated by discontinuous sources.  
More recently, several papers have been published on this topic (see [11; 12; 13] and references therein). In particular, in [14] a joint optimization of constellation size, energy allocation per bit and relay location assuming fixed end-to-end distance is proposed. In [15], an energy-efficient collaborative space-time block code (STBC) is proposed. In [16], a multi-dimensional compact constellations that minimize the average symbol energy is given, while in [17] the energy-saving gained from optimizing the constellation size is investigated. In [18], a multidimensional secure constellation (MSC) design to improve the energy efficiency, security, and bit error rate (BER) performance is described. In [19], an energy-based pulse amplitude modulation (PAM) constellation design framework for noncoherent detection in massive single-input multiple-output (SIMO) systems is proposed, while in [20] an energy-efficient multi-layer modulation constellation to manage the multiuser interference for broadcast system over Poisson channel is given. In [21], a symbol-level precoding for multiuser multiple-input single-output (MISO) to minimize the peak transmission energy over symbol time slots in downlink scenario is described. In [22], performance of a device-to-device (D2D) multiple-input and multiple-output (MIMO) communications using an amplify-and-forward relaying for various energy-efficient modulation schemes is investigated. In [23], a quadrature space-frequency index modulation (QSF-IM) scheme for 5G system energy-efficiency is proposed, while in [24] implementation scenarios of spatial modulation (SM) techniques for spectral and energy efficiency of 5G wireless networks are discussed. In [25], an energy-efficient framework for adaptively controlling the transmit power and data rate of the IoT device in order to minimize the energy-consumption in 5G networks is discussed, while in [26] and [27] index modulation is proposed as a key technique to provide spectral and energy efficiency in 5G networks. In [28], an orbital angular momentum (OAM) based, energy-efficient multidimensional coded modulation is proposed. In [29], an energy model for a cooperative amplify-and-forward (AF) relay system is proposed.