Abstract
This paper presents a method for shortening the computation time and reducing the number of math operations required in complex calculations for the analysis, simulation, and design of processes and systems. The method is suitable for education and engineering applications. The efficacy of the method is illustrated with a case study of a complex wireless communication system. The computer algebra system (CAS) was applied to formulate hypotheses and define the joint probability density function of a certain modulation technique. This innovative method was used to prepare microsimulation-semi-symbolic analyses to fully specify the wireless system. The development of an iteration-based simulation method that provides closed form solutions is presented. Previously, expressions were solved using time-consuming numerical methods. Students can apply this method for performance analysis and to understand data transfer processes. Engineers and researchers may use the method to gain insight into the impact of the parameters necessary to properly transmit and detect information, unlike traditional numerical methods. This research contributes to this field by improving the ability to obtain closed form solutions of the probability density function, outage probability, and considerably improves time efficiency with shortened computation time and reducing the number of calculation operations.
Highlights
Theoretical, experimental, and computational approaches are the basis for the study of observed phenomena
This expression cannot be manually obtained by using numerical tools
This paper presents a new method to accelerate the computation and reduce the number of calculation operations in the iteration-based simulation method
Summary
Theoretical, experimental, and computational approaches are the basis for the study of observed phenomena. The common feature among all these issues is how to directly obtain results for further processing or exploitation To address this challenge, complex mathematical tools are used to perform analyses and simulations of the performance of the observed processes and systems. The numerical computation generates a large amount of data, which may sometimes lead to erroneous results [10,11] These incorrect results may be due to the finite word length in the records, or errors occurring during the shortening of numbers in fractions, for example. We present the above methods directly applied to two examples Both examples require complex analysis and use symbolic closed form expressions, and their numerical analysis is time-consuming.
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