Generalized average BER expression for SC and MRC reciever over Nakagami-m fading channels

This paper presents simple and accurate approximation of the normalized incomplete upper and lower gamma functions that frequently appear in Nakagami-m fading channels. Based on the proposed approximation and in conjunction with the approximation of the Q-function proposed by Chiani, Dardari, and Simon [1], simple and accurate generalized closed-form expressions for the average Bit Error Rate (BER) over Nakagami-m fading channels are derived for Selection Combining (SC) and Maximum Ratio Combining (MRC) receivers for any number of diversity branches. The derived expressions are applicable for any coherent modulation scheme with any constellation order for both Rayleigh and Nakagami-m fading channels. Monte Carlo simulation of the average BER curves for both SC and MRC using different digital modulation schemes with different constellation order over Nakagami-m fading channels are compared with the closed-forms. The closed-forms numerical results coincide with the Monte Carlo simulation for different values of the fading parameter m. These expressions are simple and can be used to analyze the average BER over Nakagami-m fading channels with high accuracy.