## 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]. Thus, the maximization of the EE instead of the capacity of the satellite is the novelty in this paper. The issue of optimal energy allocation and admission control is addressed for communications satellites in earth orbit in [

22]. The authors in [

21] make an overview of EE and satellite networking from a holistic perspective as well as the prospective greener architectures. The energy efficient power allocation problems in multibeam downlink satellite network is analyzed in [

23]. Besides, the authors in [

24] investigate the relationship between SE and EE for hybrid satellite terrestrial network, where overhead costs, transmission and circuit power, backhaul of gateway (GW), and density of small cells are taken into consideration. The energy efficiency of a multibeam downlink system is investigated in [

25], which maximizes the ratio of system throughput over consumed power. However, to the best knowledge of the authors, energy-efficient power allocation problem in cognitive satellite terrestrial networks has not yet been solved in existing literature.

In this paper, a novel integrated wireless sensor and cognitive satellite terrestrial network architecture is first presented, where the cognitive satellite user plays the role of the sink for the terrestrial sensor network and the sensing data is transmitted through the satellite communication networks. Then, energy-efficient optimal power allocation schemes are proposed for non-real-time and real-time applications in cognitive satellite terrestrial networks, which aim to maximize the EE of the cognitive satellite user while guaranteeing the interference at the primary terrestrial user below an acceptable level. To guarantee the quality of the primary terrestrial user, average interference power (AIP) constraint is considered in the proposed schemes. To solve the nonlinear concave fractional programming problem, we combine Dinkelbach’s method [

26] with Lagrange duality method [

27] and decouple the problem into multiple parallel subproblems. Then, an iterative algorithm is presented to search the optimal transmit power of the satellite user. Extensive numerical results evaluate the performance of the proposed energy efficient power allocation schemes and show that the fading of the terrestrial interference link is favorable to the satellite user who can achieve EE gain under the ATP constraint comparing to the PTP constraints.

The remainder of this paper is structured as follows:

Section 2 presents the system model and link budget. The energy-efficient optimal power allocation problem is formulated for both non-real-time and real-time applications and the solutions are derived in

Section 3.

Section 4 presents simulation results. We conclude this paper in

Section 5.

## 2. System Model

Figure 1 shows the architecture of the integrated wireless sensor and cognitive satellite terrestrial networks, where the mobile satellite terminal plays the role of the sink for the terrestrial sensor network. In this system, an uplink cognitive satellite terrestrial network consisting of one primary terrestrial network and one secondary satellite network is considered, where the satellite system shares the spectral resource with terrestrial system to improve the spectral efficiency. In the considered architecture, the satellite network (e.g., DVB-SH) acts as the secondary system, whereas the terrestrial cellular network (e.g., UMTS or LTE) corresponds to the primary system [

16,

17]. Herein, we focus on the underlay scenario as mentioned above. In addition, the weak interference from primary terrestrial user to the satellite can be negligible due to the large distance [

28].

In traditional WSNs, sensor nodes are distributed in the sensing field whereupon detecting some events of interest, nodes report the sensed event back to some static sink(s) through multi-hop or single hop communication. One major drawback of such communication infrastructures is that the sensor nodes close to the sink will consume more energy, and thus their energy supply will be rapidly depleted [

29]. To deal with this issue, the concept of mobile sink was introduced in [

30,

31], that not only results in balanced energy consumption among the nodes but can also be exploited to connect isolated segments of the network [

32]. Moreover, some applications explicitly require sink mobility in the sensor field. For instance, a rescuer equipped with a PDA moves around in a disaster area to search any survivors [

33], and a farmer while walking around a field would be interested in knowing which segment of the field requires watering, fertilizers, etc. Thus, the sink in this paper i.e., the satellite user is selected as a mobile terminal.

The operating power refers to the power needed for running the network equipment, e.g., the satellite terminal. In the considered system model, the satellite terminal is a vehicle equipment, which is commonly powered by on-board batteries, that is to say, the satellite terminal is limited in energy storage capacity. In this regard, energy efficiency is a fundamental constraint in the operation and design of communication networks consisting of battery-operated terminals. In addition, DVB-SH transmissions are subject to long-fading durations which degrade the quality of experience if not tackled efficiently. The long propagation delay in satellite networks (especially in GEO-based networks) and fast changing link conditions impose challenges on the energy efficiency optimizations [

21]. Therefore, it is of importance to optimize the power allocation mechanism from the energy efficiency perspective of the satellite vehicle terminal.

When the transmit power of the satellite user is

${P}_{t}$, the receive power

${P}_{r}$ at the satellite can be calculated as

where

${G}_{t}\left(\theta \right)$ is the transmit antenna gain of the satellite user,

${G}_{r}\left(\phi \right)$ denotes the receive antenna gain at the satellite, which can be obtained as

where

$\theta $ is the elevation angle,

${G}_{r,max}$ is the maximum beam gain at the onboard antenna boresight and

$J\left(\xb7\right)$ is the Bessel function. Moreover,

$u=2.07123\frac{sin\phi}{sin{\phi}_{3\mathrm{dB}}}$, where

$\phi $ is the angle between the location of the satellite user and the beam center with respect to the satellite, and

${\phi}_{3\mathrm{dB}}$ is the 3-dB angle.

${L}_{S}$ is the free space loss of the secondary link. Besides,

${h}_{S}$ is the fading channel power gain of the secondary link. Herein, we employ the widely-adopted Shadowed-Rician fading model with closed formula, which can be used for mobile/fixed terminals operating in various propagation environment. According to [

34], the probability density function (PDF) of

${h}_{S}$ is shown as

where

${}_{1}{F}_{1}\left(\xb7,\xb7,\xb7\right)$ denotes the confluent hypergeometric function [

35] and

$\alpha $,

$\beta $ and

$\delta $ can be calculated as

where

$2{b}_{S}$ is the average power of the scatter component,

${\Omega}_{S}$ is the average power of the line-of-sight (LOS) component and

${m}_{S}$ is the Nakagami fading parameter.

Similarly, the interference power

${P}_{i}$ at the base station (BS) in primary terrestrial networks can be calculated as

where

${G}_{t}\left({\theta}^{\prime}\right)$ is the equivalent transmit antenna gain for terrestrial interference link with off-axis angle

${\theta}^{\prime}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}arccos\left(cos\left(\theta \right)cos\left(\psi \right)\right)$ and

$\psi $ denotes the angle between the over horizon projected main lobe of the satellite user and the BS [

36]. In addition,

${G}_{BS}$ is the receive antenna gain at the BS and,

${L}_{p}$ and

${h}_{I}$ are free space loss and the fading channel power gain of the terrestrial interference link, respectively. As for

${h}_{I}$, Nakagami fading distribution is considered and

${h}_{I}$ follows the PDF given by [

16]

where

$\Gamma \left(\xb7\right)$ is the Gamma function [

35],

${m}_{I}$ is the Nakagami fading parameter,

${\Omega}_{I}$ is the average power and

$\epsilon \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{m}_{I}/{\Omega}_{I}$. For brevity, we denote

${G}_{S}={G}_{t}\left(\theta \right){G}_{r}\left(\phi \right){L}_{S}$ and

${G}_{I}={G}_{t}\left({\theta}^{\prime}\right){G}_{BS}{L}_{p}$ in the rest of the paper.

To facilitate the analysis of the average EE limits in cognitive satellite terrestrial networks, it is assumed that the satellite user has perfect channel state information (CSI) about

${h}_{S}$ and

${h}_{I}$ at all fading states. Note that

${h}_{S}$ can be obtained by estimating it at the satellite and sending it back to the satellite user through a feedback link. Furthermore,

${h}_{I}$ can be obtained through cooperation with the BS, or from a third party such as the spectrum manager [

37].

## 5. Conclusions

In this paper, a novel satellite-based WSN is first proposed, which integrates the WSN with the cognitive satellite terrestrial network. Then, the energy-efficient optimal power allocation schemes in cognitive satellite terrestrial networks are proposed for non-real-time and real-time applications, respectively. For both scenarios, AIP constraint is adopted to guarantee the interference power at the primary terrestrial user under a tolerable limit, while ATP and PTP constraints are employed for the transmit power constraint of the satellite user, respectively. In this context, the energy-efficient optimal power allocation problem can be formulated as a nonlinear fractional programming problem, which is solved by combining the Dinkelbach’s method and the Lagrange duality method. Extensive numerical results evaluate the impact of interference power limit, transmit power limits and the interference link quality on the EE of the satellite user. It can be observed that in the same scenario, the optimal EE of the satellite user under ATP constraint is larger than that under PTP constraint. In addition, strong interference link fading is favorable to the performance of the satellite user.