On the integral and derivative identities of bivariate Fox H-function and applications in performance analysis of wireless communications under generalized Gaussian noise

Abstract

In conjunction with an algebraic, exponential, complementary error function, and a generalized Q-function, this paper provides analytical solutions for the integral of the bivariate Fox H-function (BFHF). The paper also includes derivative identities related to function arguments. The proposed formulations are then applied for analyzing the performance of point-to-point wireless communication subjected to fading, the characterization of which involves the bivariate Fox H-function, and additive white generalized Gaussian noise. Novel expressions are presented for evaluating the average symbol error probability performance considering different noise distributions, such as Gamma, Gaussian, and Laplacian. An asymptotic analysis is also conducted to determine the system’s potential diversity order. Finally, the accuracy of the analytical findings is confirmed via comparisons of numerical results with Monte-Carlo simulations.