# Energy and Spectrally Efficient Modulation Scheme for IoT Applications
## 1 Introduction  
Recently, the dawn of the Internet of Things (IoT) has intensified the research efforts to fulfill the escalating demand for low-power budget wireless transceiver systems. Overnight, the communication industry experienced an explosion in the number of sensors and terminals that connect mobile users to the internet [1, 2]. However, low-cost, low-power, and low-bitrate sensors and terminals are mandatedfor the IoT technology in order to fulfill the vast IoT applications [3]. Therefore, the mobile service operators are motivated to seek novel low-cost architectures in order to design the physical (PHY) layer associated with the IoT devices [4; 5]. The IoT technology is protruded today as one of the main use cases in the upcoming generations of the wireless communication networks such as the fifth generation (5G) and beyond [6]. As such, it is expected that the IoT devices will form the main center stages that represent the major elements of the 5G networks [6]. Whereupon, serving such an enormous number of devices mandates the 5G networks to deploy a growing number of antennas i.e., hundreds or even thousands, in the base station (BS) to simultaneously serve multiple terminals over the same frequency resource. Using enormous numbers of antennas is one of the most widespread communication technologies, which is commonly termed today as massive multiple-input multiple-output (MIMO) [7; 8]. In the massive MIMO, equipping the BSs with an enormous number of antennas provides a worthwhile enhancement in the system capacity, however, it results in a considerable increase in both the power consumption and the hardware complexity, since, each antenna unit requires a dedicated radio frequency (RF) chain circuit [9]. Therefore, using power-consuming elements such as RF chains hinders the massive MIMO systems being beneficially used in designing the PHY layer of the IoT devices [10]. Hence, more research efforts have been relentlessly poured into finding low-cost and low-power hardware elements, which can be efficiently used to relax both the power consumption and the hardware complexity of the massive MIMO systems. At the forefront of these efforts is the use of massive MIMO with the low-resolution one-bit analog to digital converter (ADC) at the receiver (RX) side, which comes as one of the potential solutions that can countervail the consequences of using multiple RF chains [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. However, harsh quantization errors resulted as a consequence of removing most of the amplitude information of the received signal due to the use of low resolution one-bit ADC with the massive MIMO at the RX side. Hence, the channel estimation process of the massive MIMO systems with the one-bit ADC should be carefully handled for more practicality. Referring to the existing literature, the concept of using a one-bit ADC along with the massive MIMO systems was touched upon in [11], where a least squares (LS) channel estimator based upon a maximal ratio combining (MRC) and zero-forcing (ZF) detectors was introduced to overwhelm the severe quantization noise of the one-bit ADC. [PERSON] et al. [12] extended this LS estimator to higher-order constellations in order to fulfill a higher achievable data rate than that attained in [11]. The channel is estimated based upon the near maximum likelihood (nML) detector in [13] in order to support higher-order constellations, as in [12]. A linear minimum mean square error (LMMSE) channel estimation algorithm using the Bussgang decomposition was suggested in [13]. Such an estimator was applied to both flat and frequency selective fading channels, and it offered a superior enhancement over the estimator presented in [14]. Furthermore, a pilot-based channel estimator with the Bussgang decomposition and with MRC or ZF detectors was introduced in [15]. Here, the performance of the infinite resolution case could be reached using ADCs with few bits of resolution. A joint channel-and-data (JCD) estimation algorithm based upon Bayes-optimal inference was presented in [16].