Error performance of generalized M-ary QAM over the Beaulieu-Xie fading

In this paper, an accurate framework is proposed for deriving the closed-form expression for the average symbol error probability (ASEP) of generalized M-ary quadrature amplitude modulation (M-QAM) over the Beaulieu-Xie fading channel. This fading channel is extremely useful for characterizing heterogeneous networks, femtocells, and also for modeling of fading channel for high speed trains due to its ability to combine the properties of both Nakagami-m and Rician fading models. Due to efficient bandwidth and high data rate, the M-QAM modulation scheme is utilized for the 4G LTE, 5G network, etc. The closed-form expression for the ASEP of generalized M-QAM in terms of Gauss hypergeometric function is derived in this work. The advantage of this expression is that along with M-QAM, we can evaluate ASEP of many other modulation schemes such as binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), etc. The numerical results are presented for the exact closed-form solution, which are a close match with Monte-Carlo simulations. To achieve ASEP of 10⁻³, 64-QAM requires 4.79 dB more average SNR as compared to 16-QAM for the case of m = 2, K = 1.