## 1 Introduction  
The advancement in wireless communications and electronics has enabled the development of low-cost wireless sensor networks (WSNs), which have been widely used in various areas, such as monitoring, disaster relief and target tracking [1]. Since the sensing information must be transmitted to the remote monitoring hosts, the fundamental communication problems are important to WSNs [2]. However, the related researches have mainly focused on the terrestrial WSNs, which may be challenged by the operating environment, such as forest, wilderness and military environments [3; 4]. With the obvious superiority in providing large coverage areas at low cost and supporting fixed and mobile services with various connecting modes, satellite systems have been widely utilized for wireless communications services to worldwide users, especially in the remote and underpopulated areas where terrestrial networks are economically and/or operationally infeasible [5; 6]. Therefore, satellite-based sensor networks have drawn considerable attention and been investigated for various application scenarios [7; 8; 9]. Meanwhile, spectrum scarcity of the satellite communications is an urgent issue due to the increasing demand for the broadband applications and multimedia services. To alleviate pressure on limited spectral resources, cognitive radio (CR) as a promising technology to improve the spectrum efficiency (SE), has been introduced for satellite communications. In such a network, cognitive techniques can be applied in two satellite networks, or in satellite and terrestrials within the same frequency band [10; 11; 12]. Due to the easy implementation and high SE, the underlay technique is widely employed in CR networks, where the secondary user (SU) could simultaneously coexist with the primary user (PU) in the same band [13]. The premise is that the interference generated by the SU would not degrade the PU's communication quality. Therefore, when the terrestrial system operates as the primary network and the satellite system serves as the secondary network [14], it is of crucial importance to design the efficient power allocation schemes for the satellite user in the uplink case. In this regard, the power allocation scheme is proposed for the fixed satellite services system in [15], where the primary system is fixed-service terrestrial microwave system. However, this scheme cannot be adopted into the fading channels. Considering the fading channel scenarios, optimal power control schemes are presented for non-real-time and real-time applications in [16; 17], respectively, where the terrestrial cellular system operates as the primary system. The ergodic capacity of the satellite user is maximized in [16], which is an appropriate performance metric for non-real-time applications. In [17], delay-limited capacity and outage capacity are optimized for the real-time applications from the long-term and short-term perspectives, respectively. However, all the above-mentioned works aim to maximize the capacity of the satellite user and not consider the energy efficiency of the satellite user, which is the main objective in green cognitive radio networks. According to the reports in [18; 19], 2% to 10% of global energy consumption and 2% of the greenhouse gas are generated by information and communication technologies. Thus, in the cognitive radio networks, it is crucial to design the energy efficient transmission. The improved energy efficiency is a basic premise for secondary users to achieve high utilization of the limited transmit power which is consumed not only to improve spectrum efficiency but also implement some additionally important functionalities, e.g., spectrum sensing and reduce operational expenditure and the greenhouse effect. With the emerging environmental and energy cost concerns in communication systems, energy efficiency (EE) has become vital and inevitable in future satellite networks from both financial and ecological viewpoints [20; 21].