Confidence interval based model predictive control of transmit power with reliability constraint Wei Sun 1 • Hao Yu 1 • Yangzhao Yang 2 • Qiyue Li 1 • Daoming Mu 1 • Xiaobing Xu 1 Ó Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract Because the wireless signal, such as 5G, is propagated in the medium of air, it is easily been interfered by other devices or environmental factors. Adjusting the transmit power of wireless transceiver could control the signal-to-noise ratio (SNR) and accordingly improves the reliability of communication. However, the control of stochastic SNR with deterministic requirements is still a challenging problem. Hence we study the control of transmit power to satisfy the reliability requirements and, in the meanwhile, save battery energy. To deal with the stochastic character of the wireless link, we introduce the confidence interval bound and then propose confidence interval based model predictive control (CI-MPC), in which we creatively separated the SNR as the feedback signal and the confidence interval based compensating signal. To verify the performance of our CI-MPC, we compared it with the state-of-the-art methods by simulation. Besides, we also tested the proposed CI-MPC method in the real-world industrial environment on the test-bed to show its effectiveness. Keywords Transmit power control  Confidence interval  Model predictive control  Wireless communication reliability  Internet of things 1 Introduction With the fast development of wireless communication technologies, the 5G digital cellular networks with higher bandwidth and less communication delay is expected to be widely deployed in the near future. Although the coverage of 5G is limited, the device-to-device communicating in 5G helps to build ubiquitous networks in any environment [5, 7]. Consequently, the physic-devices, equipped with 5G radio transceivers, electronic sensors, and actuators, can interact with others to form wireless connections, further extend the range of Internet and constitute the so-called Internet of Things (IoT) [10, 22]. When physical objects getting connected, monitored and controlled via IoT, demand for automatically controlling those machines without or with quite a few human interventions is motivated to build huge smart autonomous systems, such as smart grid system [11], smart transport system, etc. [12]. Since the performance of control systems via a network is very sensitive to the communicating delay and reliability, in those autonomous systems, there are very strict requirements to the communication performances [8]. The transmit power of wireless communication affects those performances. On the one hand, reducing the transmit power of radio transceiver could save battery energy. However, this will decrease the signal-to-noise ratio (SNR) and therefore affect the reliability of wireless communi- cation. Although the re-transmission mechanism can improve the overall reliability when a failure occurred, the transmit attempts lead to more channel resources occupa- tions. In this way, communication delay and battery energy consumption will be multiplied. On the other hand, increasing transmit power could improve the SNR. How- ever, this will consume more energy and produce a larger range of inference to other D2D devices, which may oppositely affect the overall efficiency of networking sys- tems. So, the higher transmit power may produce degra- dation of network efficiency as well. Therefore, the overall effects on the battery energy consumption and network & Qiyue Li liqiyue@mail.ustc.edu.cn 1 School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China 2 China Academy of Electronics and Information Technology, Beijing 100041, China 123 Wireless Networks https://doi.org/10.1007/s11276-019-02202-4