In this study, we present an innovative approach to modelling the propagation channels of land mobile satellite (LMS) systems by employing the \(\eta -\mu \) distribution for a comprehensive narrowband channel model, which is crucial for the foundation of wideband models. This model is pivotal for accurately representing the complexities of satellite-to-mobile user channels, especially under non-line-of-sight (NLOS) conditions. By adopting the \(\eta -\mu \) distribution, our model transcends the limitations of conventional lognormal-based models by offering a more accessible statistical analysis through expressions for the envelope probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF) and the average channel capacity. The model facilitates easy performance evaluation for various modulation schemes. Numerical results demonstrate its effectiveness in calculating the average bit error rate (ABER) for binary differential phase shift keying (BDPSK), non-coherent binary frequency shifting keying (BFSK), and binary phase shift keying (BPSK) modulation schemes. With computational efficiency and adaptability, this model serves as a valuable tool for practitioners and system designers to analyze and decide on LMS communication systems.
