In this paper, a new approach in solving and analysing the performances of
the digital telecommunication non-coherent FSK/ASK system in the presence of
noise is derived, by using a computer algebra system. So far, most previous
solutions cannot be obtained in closed form, which can be a problem for
detailed analysis of complex communication systems. In this case, there is no
insight into the influence of certain parameters on the performance of the
system. The analysis, modelling and design can be time-consuming. One of the
main reasons is that these solutions are obtained by utilising traditional
numerical tools in the shape of closed-form expressions. Our results were
obtained in closed-form solutions. They are resolved by the introduction of
an iteration-based simulation method. The Wolfram language is used for
describing applied symbolic tools, and SchematicSolver application package
has been used for designing. In a new way, the probability density function
and the impact of the newly introduced parameter of iteration are performed
when errors are calculated. Analyses of the new method are applied to several
scenarios: without fading, in the presence of Rayleigh fading, Rician fading,
and in cases when the signals are correlated and uncorrelated.