The exponential increase of the intelligent connected devices and the dramatic growth of the wireless data traffic have motivated the development of the green wireless networks as well as the Internet of Things. In this paper, we study the minimization problem of the total power to satisfy the required rate constraints in Internet of Things, where the users simultaneously communicate through multiple independent channels. This problem is complicated due to the non-linear data rate function based on the Shannon capacity formula. To this end, we first transfer the initial problem in power domain to an equivalent problem in rate domain instead of direct approximation for the high data rate. Then, we approximate it to a convex problem with the spectral radius constraints by the use of the Neumann expansion and nonlinear Perron-Frobenius theorem. By doing so, we achieve the close upper bound for this total power minimization problem. Moreover, we obtain the lower bound by making use of the convex relaxation technique, and finally get the global optimal solution by leveraging the branch-and-bound method. Simulation results verify that our proposed algorithms have a good approximation to the global optimal value for the power and rate allocations.

INTRODUCTION

IN recent years, various successful demonstrations of the mobile technologies for the wireless communications have been witnessed. Since its first generation in the last 1970s, the mobile services have come across from the analog system, digital system, internet system to the current worldwide constructed integration system, which is adept at providing high quality mobile broadband services to guarantee the high data rates [1]. Over the last couple of years, the Internet has been in a constant state of evolution and the next generation mobile communication is envisioned to be available after 2020. As a part of this development, 5G and the Internet of Things (IoT) with some emerging technologies are regarded as a new round of industrial and technological revolution after the steam, electric, computer and Internet [2], [3]. IoT is expected to possess important home and business meanings based on the evolution of the sensor networks, to achieve more intelligent applications for the contributions to the quality of life and the global economy [4], [5]. Nowadays, the wireless communications become more efficient in the aspects of the practice and appearance, as the dual standby mode technique enable that the users automatically search networks and switch between them within a tiny moment. Multi-access is useful for the practical applications [6]. However, the utilization and conservation of resources turn into the major issue when the mobile users take the rapid authentication and fast switch between different independent channels [7], with the fact that the mobile users can only use a single channel at a time.