A Novel Extension to Craig’s Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis

A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig's Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig's Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami-m fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami-m fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations.