# Multi-Objective Optimization for EE-SE Tradeoff in Space-Air-Ground Internet of Things Networks
## 1 Introduction  
### Problem Statement  
In recent years, the Internet of Things (IoT) has received widespread attention because of its ability to enhance communication between people and things, and between things and things, which can help improve the quality of life and promote economic development [1]. At present, the Internet of Things has been applied in many fields such as industry, medical care, agriculture, and transportation, and the density of the physical objects connected to the IoT network increases significantly [2]. According to research by [PERSON] and [PERSON], IoT devices will continue to soar, with the total number of devices expected to reach 83 billion by 2024, more than doubling from 35 billion in 2020 [3]. With the significant rise in the number of access devices and growing demand for communication capabilities, traditional ground-based communication methods are becoming insufficient, necessitating the expansion of communication infrastructure to include space-based communication. The space-air-ground integrated network (SAGIN), which builds upon the existing ground-based network and is supplemented and extended by the air-based network and thespace-based network, has received extensive attention. SAGIN boasts wide coverage, high throughput, and flexible deployment, making it an ideal solution for meeting the demands of smart connections across large areas and providing global seamless access. Its ultimate aim is to provide uninterrupted and consistent information services to people all over the world. At present, many organizations have started research on SAGIN, such as SpaceX [4]. The SAGIN network offers extensive coverage and high communication capacity through its use of satellites, enabling it to provide services to remote areas such as deserts and rural regions. The air segment network complements satellite communications, enhancing the overall quality of communication services. Meanwhile, the densely deployed ground segment system can support high data rate access [5]. Therefore, relying on SAGIN, the connectivity, capacity, and energy efficiency of IoT networks can be significantly improved.  
With the rapid development of unmanned aerial vehicle (UAV) technology, UAVs are playing an increasingly important role in communication. Due to their high mobility, high line-of-sight (LoS) probability, flexible deployment, and low cost, UAVs have become the main information carrier of the SAGIN air segment network and have been extensively studied [6; 7]. Since UAVs have limited energy, their duration has been a key constraint on communication performance [8]. Therefore, we consider improving the throughput of the system at the same energy consumption, that is, the energy efficiency (EE). However, while considering the energy efficiency of the system, we should also focus on the spectral efficiency (SE) of the system. Due to the large distance between the UAV and the satellite, the communication link requires a substantial allocation of bandwidth for data transmission, which occupies a considerable amount of limited spectrum resources. Thus, it is essential to comprehensively consider both SE and EE of the system for a compromise optimization approach.  
This paper focuses on the SAG-IoT network, and solves the problem of balancing the EE and SE of the system by optimizing the transmission power of UAVs and IoT devices, sub-channel selection, and UAV position deployment.