Part of the book: Fourier Transform
The heterogeneous cellular network (HCN) is most significant as a key technology for future fifth-generation (5G) wireless networks. The heterogeneous network consists of randomly macrocell base stations (MBSs) overlaid with femtocell base stations (FBSs). Stochastic geometry has been shown to be a very powerful tool to model, analyze, and design networks with random topologies such as wireless ad hoc, sensor networks, and multi-tier cellular networks. HCNs can be energy-efficiently designed by deploying various BSs belonging to different networks, which has drawn significant attention to one of the technologies for future 5G wireless networks. In this chapter, we propose switching off/on systems enabling the BSs in the cellular networks to efficiently consume the power by introducing active/sleep modes, which is able to reduce the interference and power consumption in the MBSs and FBSs on an individual basis as well as improve the energy efficiency of the cellular networks. We formulate the minimization of the power consumption for the MBSs and FBSs as well as an optimization problem to maximize the energy efficiency subject to throughput outage constraints, which can be solved by the Karush-Kuhn-Tucker (KKT) conditions according to the femto tier BS density. We also formulate and compare the coverage probability and the energy efficiency in HCN scenarios with and without coordinated multi-point (CoMP) to avoid coverage holes.
Part of the book: Towards 5G Wireless Networks
We present a COVID-19 DNA-RNA genetic code where A=T=U=31% and C=G=19%, which has been developed from a base matrix CUAG where C, U, A, and G are RNA bases while C, U, A, and T are DNA bases that E. Chargaff found them complementary like A=T=U=30%, and C=G=20% from his experimental results, which implied the structure of DNA double helix and its complementary combination. Unfortunately, they have not been solved mathematically yet. Therefore, in this paper, we present a simple solution by the information theory of a doubly stochastic matrix over the Shannon symmetric channel as well as prove it mathematically. Furthermore, we show that DNA-RNA genetic code is one kind of block circulant Jacket matrix. Moreover, general patterns by block circulant, upper-lower, and left-right scheme are presented, which are applied to the correct communication as well as means the healthy condition because it perfectly consists of 4 bases. Henceforth, we also provide abnormal patterns by block circulant, upper-lower, and left-right scheme, which cover the distorted signal as well as COVID-19.
Part of the book: Matrix Theory