Generalized solution to symbol error probability integral containingQ (a√γ) Q (b√γ) over different fading models

This paper presents a generalized solution to the symbol error probability (SEP) integral containing the product of two Gaussian Q-functions Q (a root gamma)Q (b root gamma). Numerical integration technique is first used to approximate the polar form of Q (a root gamma) Q (b root gamma)as a sum of exponentials. This approximation is then used to derive a closed-form solution to the related SEP integral. Due to the exponential nature of the approximation, solution to the integral is expressed in terms of moment generating function (MGF) of a fading distribution. Therefore, the solution to integral exists for all fading distributions which have well-defined MGF. The mathematical complexity of the proposed solution is directly proportional to the complexity of MGF expression. For most of the fading models, the corresponding MGF involves power or exponential functions, which guarantees algebraic simplicity of the proposed solution. Further, this generalized solution is used to evaluate the SEP of various modulation schemes over different fading channels. Various computer simulations run in MATLAB for wide range of scenarios confirm the accuracy of the proposed approximation and solution.

Automated summary

This paper presents a generalized solution to calculate the symbol error probability integral containing the product of two Gaussian Q-functions, first using numerical integration technique to approximate the product and derive a closed-form solution, where the complexity of the solution is proportional to the complexity of the fading distribution's moment generating function.