On the Integral and Derivative Identities of Bivariate Fox H-Function: Application in Wireless System Performance Analysis

TL;DR

This paper develops analytical integral and derivative identities for bivariate Fox H-functions, applying them to wireless communication performance metrics like outage probability, verified through simulations and asymptotic analysis.

Contribution

It introduces new integral and derivative identities for bivariate Fox H-functions and demonstrates their application in analyzing wireless system performance.

Findings

Derived integral and derivative identities for bivariate Fox H-functions.

Provided asymptotic expressions for outage and error probabilities.

Validated analytical results with numerical and Monte Carlo simulations.

Abstract

The present work proposes analytical solutions for the integral of bivariate Fox H-function in combination with algebraic, exponential, and complementary error functions. In addition, the work also presents the derivative identities with respect to function arguments. Further, the suitability of the proposed mathematical solutions is verified with reference to wireless communication environment, where a fading behaviour of the channel acquired the bivariate Fox H-function structure. Further more, asymptotic results for the outage probability and average symbol error probability are presented utilizing the origin probability density function based approach. The obtained results are free from complex analytical functions. At last, the analytical findings of the paper are compared with the numerical results and also with the Monte-Carlo simulation results to confirm their accuracy.