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This article presents a new method of fast symbolic computations of very complex calculations, which are necessary for the analysis, simulation, and design of wireless communication systems using CAS (Computer Algebra System). CAS is applied to formulate hypotheses and define joint probability density functions of certain modulation technique. This is used to prepare for the semi-symbolic calculation to complete specify wireless system by using CAS. We have developed an iteration-based simulation method that aids to solve semisymbolic expressions and gives closed form solutions (with some parameters specified as numbers and some as symbols). So far, they are solved by numerical methods. Students can perform performance analysis and understand the processes in the data transfer. Engineers and researchers may have a better insight into the impact of the important parameters necessary to properly transmit and detect information unlike traditional numerical methods. The main contribution is to obtain solutions for the probability density function, and outage probability where no solution can be obtained using numerical methods. A strong emphasis is placed on very fast calculations that significantly save the time of analysis, simulation, and design.

Fast computation of the iteration-based simulation method - case study of non-coherent ask with shadowing