Achievable rate region for a hub-remote three-terminal satellite network

We study the performance of amplify-forward (AF) protocols in a three-terminal hub-remote satellite exchange channel, which is an extension of the two-way relay channel. We want to answer two questions: 1) Can non-orthogonal signaling and partial interference cancellation bring as much improvement as what have seen in the two-way relay channel? 2) Which decoding method achieves the largest achievable rate region? Theoretical analysis and numerical plots show that for the three-flow case, three-user simultaneous signalling outperforms a time-shared AF protocol, while for the four-flow case, three-user simultaneous signalling only shows advantage when the hub terminal has much higher SNR than remote terminals.