A closed-form expression can potentially give you better understanding of how different design variables affect the performance. Does the performance grow linearly with the SNR, or logarithmically, or neither?

Closed-form expressions are also more useful for performance optimization since one can then easily compute the first and second order derivatives, which are often used in numerical optimization methods.

Dear Emil Björnson

Thank you so much for your valuable response.

In the recent works univatiate and bivariate Fox-H function are used to represent the performance parameters of the communication systems in closed-form.

The Fox-H function can not be directly evaluated in the packages like MATLAB/MATHEMATICA. The integration function is used to implement the performance parameters having Fox-H function.

The original representation was in integral form and the closed-form obtained in Fox-H function. Then how this closed-form solution is beneficial for a design engineer.

Thanks and Regards

Closed-form expressions are usually considered useful in characterizing the impact of dfferent input/system parameters on the considered performance metrics. Moreover, there is a high computational cost associated to performing the numerical integrations which necessitates the derivation of closed-form expressions for their applications in runtime algorithms etc; e.g, channel conditions prediction etc.