# Blind Turbo Equalization of Short CPM Bursts for UAV-Aided Internet of Things
## 1 Introduction  
Driven by the explosive surge of Internet of Things (IoT) services for sixth-generation (6G) mobile communications systems, different new 6G use cases have been proposed and are under intensive research discussion recently, such as IoT industry automation, maritime machine-type communication networks, and other applications [1; 2]. As one of the key technologies to achieve the vision of the Internet of Everything, UAVs have been widely used to perform diversified tasks [3; 4; 5] due to their low cost and flexible deployment. There has been a recent surge of studies on the use of UAVs for IoT communication [6; 7; 8], such as data collection [9; 10] and mobile edge computing [11]. However, with the dramatic increase in the number of connected machines, the number of IoT devices deployed world-wide is expected to grow to 75.4 billion by 2025 [12]. There is a growing demand for low complexity and high power efficiency in UAV-aided IoT communication due to the limited payload of the devices. Continuous phase modulation (CPM) is suitable for power- and bandwidth-limited systems because of its good spectral efficiency and its higher power efficiency relative to linear modulations with comparable spectral efficiency. Moreover, the constant envelope property of CPM allows the nonlinear power amplifier (PA) to be operated at a high efficiency, which further increases the power efficiency of the system [13]. For battery-powered IoT nodes and UAVs, energy efficiency and cost are key factors because these devices are difficult to recharge or recycle once depleted. Therefore, CPM is one of the preferred modulation schemes in UAV-aided IoT communications systems due to its favorable low power consumption, which can greatly increase the life of terminal devices. However, CPM transmission over multipath fading channels is a challenging task due to the high computational complexity in the receiver. If the design of the waveform is poor, it will reduce the overall power of the communications systems, even offsetting the increased power efficiency achieved by the PA. Therefore, we focus our attention on the receiver design at the physical layer for CPM over frequency-selective channels employing low data rates and short bursty transmissions, which is a fundamental tool to implement UAV-aided IoT. In general, the main contributions of this paper include the following:  
* We combed the literature related to CPM and summarized it in the Table 1.
* To meet the demands of low data rates and short-burst transmission scenarios of the UAV-aided IoT system, a short burst structure of CPM is designed in this paper, and a link-level simulation platform of the communications system is established on this basis. * A low complexity approach for soft-input soft-output (SISO) blind equalization is proposed to achieve a fast and accurate blind equalizer in the UAV-aided IoT system. The first step utilizes the soft-output Lazy Viterbi algorithm instead of the Viterbi algorithm to perform the expectation step and obtain a low complexity expectation-maximization Lazy Viterbi algorithm (EMLVA), while the second step applies the BCA method to establish a set of initializers, denoted as the BCA initializers, which achieves a high global convergence probability. * The blind turbo equalization for short-burst CPM is proposed based on the new SISO blind equalization with iterative detection, where the blind equalizer and decoder exchange extrinsic information in the form of log-likelihood ratios (LLRs). To further improve the convergence of iteration and reduce the average iteration number, the decision-aided (HDA) algorithm based on weighted extrinsic information exchange is proposed. * The blind turbo equalization based on EMLVA is proposed and evaluated on a link-level simulation platform. Simulation results show that EMLVA can obtain a good trade-off between complexity and BER performance. When the HDA with weighted extrinsic information is applied, the convergence of iterative detection and real-time performance can be further improved.