## 1 Introduction
Due to the poor scattering character and limited processing capability on satellites, a multi-antenna with phase controller is usually considered in SATCOM [21; 22; 23]. For the coexistence of service and backhaul links in a satellite-terrestrial integrated network, the authors in [22] designed analog beamforming vectors to mitigate the co-channel interference. To flexibly meet the various requirements of different regions, the authors in [23] proposed a novel amplitude controllable phased array antenna. Precisely, the phase and amplitude can be adjusted separately for each beam. To the best of our knowledge, phased array antennas have not been fully discussed in SATCOM star networks, especially in spectral-resource-limited scenarios. In this paper, we propose a spectrum-saving transmission method in the SATCOM star network, where the satellite and UTs are equipped with multiple antennas. Realizing that the antenna gain at the hub station is much higher than that at UTs, we allocate the UTs within the spectral resource occupied by the HS. To distinguish the required information from the mixed signals, successive interference cancellation (SIC) and parallel filtering is designed at the HS. The ergodic sum rate is further derived for performance evaluation. In addition, the impact of the number of accessed UTs is also analyzed theoretically. Simulation results are shown from the aspects of ergodic sum rate and bit error rate (BER). The main contributions of the paper can be summarized as follows:  
* By fully analyzing the characters of the SATCOM star network, we found the transmit and receive gain differences of the antennas equipped at the HS and UTs, which could be equivalent to the channel gain difference for the receiver. * We proposed a spectrum-saving transmission method where the HS could share the bandwidth with UTs. Thanks to the novel scheme, we do not need to allocate an exclusive frequency band for the UTs, which may spare plenty of spectral resource. * To facilitate performance evaluation, the expression of ergodic sum rates for the proposed and conventional methods were derived. Furthermore, system availability was also defined to analyze the impact of the accessed UTs, which could help to design a more efficient star network. The rest of the paper is organized as follows. Section 2 describes the system model of a SATCOM star network, and presents the conventional spectrum isolation transmission method. In Section 3, the spectrum-saving scheme is proposed, where the HS shares the frequency band with UTs. To evaluate the performance, ergodic sum rate is derived and analyzed theoretically in Section 4. The impact of UTs on the novel transmission method is also studied. Simulation results of the ergodic sum rate and BER are presented and discussed in Section 5, and the paper is concluded in Section 6. Notation: Vectors and matrices are presented by lowercase and uppercase bold letters, respectively. The transpose and Hermitian transpose are denoted by superscripts T and H, respectively. The statistical expectation and the probability are presented by \(\mathbb{E}[\cdot]\) and \(\mathbb{P}(\cdot)\), respectively, while \(\mathcal{CN}(\mathbf{a},\mathbf{R})\) denotes the distribution of circularly symmetric complex Gaussian (CSCG) random vectors with mean vector \(\mathbf{a}\) and covariance matrix \(\mathbf{R}\).