Abstract—In this paper, the authors propose a novel, precise, and approximate expression for the generalized fading model using the Moment-Generating Function (MGF). We have evaluateda closed-form mathematical solution for the Average Bit Error Rate (ABER) of Binary Phase Shift Keying (BPSK), the Symbol Error Rate (SER)or symbol error probability (SEP) of Quadrature Phase Shift Keying (QPSK), andTriangular Quadrature Amplitude Modulation (TQAM) overα–η–μ fading channel. Notably, this fading model represents a small-scale variation of the fading signal and encompasses important fading models like Rayleigh, Nakagami-m, Hoyt, one-sided Gaussian, Weibull, and η-μ as special cases. Additionally, it accurately captures the nonlinearity and non-homogeneous nature of the fading channel without a Line-of-Sight (LOS) component. To simplify the evaluation of ABER and SER, we utilize exponential-based approximations of the Gaussian Q-function, providing an accurate and mathematically straightforward solution to the SER integral. This approach simplifies the complicated integrals, resulting in an analytically tractable SER expression. The SER results of QPSK, obtained through the exact, proposed analytical expression, Monte Carlo simulation methods, and, result obtained using the Q-function approximation proposed by M. Bilim and D. Karaboga for the combination of fading parameters (ɑ = 0.5, η = 1.2, μ = 1.5) are 0.0163445278046601, 0.0163403059168915, 0.0162660000000000, and 0.0186945839664040, respectively, at 28 dB. These findings affirm the superiority of the proposed scheme. We have validated the analytical findings through Monte-Carlo simulations. Moreover, the analytical and simulated SER curves presented in this paper for various modulation formats and fading parameter values further confirm the effectiveness of the proposed SER expression.