## 1 Introduction
Furthermore, [29; 30] investigated the applications of near-space and high altitude platform (HAP)/satellite for the WSNs. The work in [29; 30] proposed a novel integrated HAP/satellite and designed a link-state advertisement to estimate the link state information; ultimately, an innovative adaptive algorithm was addressed to obtain the energy-efficient transmission; whilst introducing several near-space vehicle-based radar configurations, which seems to offer a lower cost, such as near-space passive bistatic radar and high-resolution wide-swath synthetic aperture radar. However, the transmission research of integrated wireless sensor and satellite networks [23; 24; 25; 26; 27; 28; 29] did not consider the interference from the other terrestrial networks. As has been stated, the beam radius of the multibeam satellite covers hundreds of kilometers, tens of times larger than the cell radius of terrestrial wireless communication networks. Some sensor nodes may be outside of the terrestrial communication networks (TCNs) and can transmit through the multibeam satellite, while some other TCNs inside the satellite beam will bring interference to the satellite. Thus, there is potential interference from TCNs in the return link of the IWMSNNs. The work in [31] investigated the spectrum and power efficiency of an extremely high-frequency (EHF) satellite system, being integrated with terrestrial systems, and showed that the terrestrial systems caused interference for the satellite communication system. The work in [32] analyzed the Shannon-theoretic approximation to the Gaussian cellular channel. Using the framework of Wyner's Gaussian cellular channel, [33] studied the performance of the return link for the multibeam satellite systems under Rician fading, but did not consider the terrestrial interference. The work in [34; 35; 36] analyzed the Ka band of cognitive satellite communications with incumbent terrestrial networks, which mainly considered the interference from satellite terminals to the terrestrial networks in the return link of the satellite, as the Ka band is predominantly a kine of sight (LOS) channel. Yet, [37; 38; 39; 40; 41] have performed research mainly concerning the forward link of the hybrid satellite terrestrial communication systems. Hence, this paper first investigates the performance of the integrated wireless sensor and multibeam satellite networks experiencing the Rician fading channel under the terrestrial interference. The main contributions of this paper are summarized as follows. * The performance of integrated wireless sensor and multibeam satellite networks experiencing the Rician fading under the terrestrial interference is firstly analyzed. The hybrid beam models are constructed by introducing the inter-beam interference factor \(\alpha\) and intra-beam interference factor \(\beta\). The relationships between the substitution \(\alpha\) and the beam isolation parameter \(\rho\), the substitution \(\beta\) and the terrestrial interference elevation angle \(\varphi\) are also analyzed. * The optimal joint decoding capacity and linear minimum mean square error capacity approximations are derived by using the Haar approximation for the return link of IWMSNNs. The simulations show that the interference factor \(\alpha\) and \(\beta\) contribute different effects to the capacity of different beam models, and the number of sinks also affects the performance of the optimal capacity and MMSE capacity differently. The capacity is decreased obviously by the Rician fading and is increased to the limit as the Rician factor increases to infinity, which will be turned to the Gauss channel. Meanwhile, the optimal capacity can be considered as the upper bound of the IWMSNNs. The rest of the paper is organized as follows.