Ergodic Channel Capacity Analysis of Downlink in the Hybrid Satellite-Terrestrial Cooperative System

In this paper, the ergodic channel capacity of the downlink is analyzed for a hybrid satellite-terrestrial cooperative system, which consists of a satellite (the source), a mobile terminal (the destination), and several gap fillers (the relays) located at the ground. The links between the satellite and the relays and the link between the satellite and the destination experience independent shadowed Rician fading, and the links between the relays and the destination experience Rayleigh fading. The maximal ratio combining technique is used at the destination to combine the direct signal received from the satellite and the relayed signals from relays with different cooperative protocols, namely amplify-and-forward (AF) and decode-and-forward (DF). The moment generating function (MGF)-based approach is adopted to derive the closed-form expressions of the ergodic downlink channel capacity of the hybrid satellite-terrestrial cooperative system. The numerical results are compared with Monte Carlo simulations and numerical results calculated with the existing analytical expressions. Comparison results show that the analytical expression derived with the MGF-based approach can achieve a higher accuracy in the low signal-to-noise ratio (SNR) regime for the single relay scenario, and significantly reduce the computational complexity with a little loss of accuracy for multiple relays scenario. On the other hand, the ergodic downlink channel capacity of the hybrid satellite-terrestrial DF cooperative system is generally higher than that of the AF cooperative system. Moreover, the ergodic channel capacity of the hybrid satellite-terrestrial cooperative system decreases as the number of participating relays increases, which can be overcome using the best relay selection strategy. In addition, the ergodic downlink channel capacity of the hybrid satellite-terrestrial cooperative system increases when the channel condition of the link between the satellite and the relay goes better, and is larger than that of the no relay land mobile satellite system when the transmitted SNR is below a certain value.