It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as a model of a signal reduced to a discrete form. A special case of such a signal model are functions that take values in Galois fields. It is shown that, along with Galois fields, in certain cases, algebraic rings contain zero divisors can be used to construct signal models. This representation is convenient because in this case it becomes possible to independently operate with the digits of the number that enumerates the signal levels. A simple and intuitive method for constructing rings is proposed, based on an analogy with the method of algebraic extensions.
There given to discuss the study results about one of three deployment scenarios performance (in-band deployment mode) of the narrow-band internet of things (NB-IoT) technology. The study is carrying out with help of simulation modeling and experimental testing of the main network parameters, namely: radio coverage, network capacity, user experience, and their dependencies on each other. Comparison of the results of a physical experiment and simulation modeling shows their high convergence and confirms the adequacy of the applied testing methodology. As a case scenario provided an example of NB-IoT implementation on a 4G mobile network in the 800 MHz band, in a suburban area for remote metering applications. The article presents the applying testing methodology of NB-IoT that adapted to the local conditions of radio network planning. Based on the obtained data, adducing the main conclusions about the feasibility of using an in-band scenario for deploying NB-IoT on a 4G network in a suburban environment.
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