Power Allocation in Cognitive Satellite-Vehicular Networks ......channel fading and extend the satellite coverage in land mobile satellite vehicular networks. These studies demonstrated

318 IEEE TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING, VOL. 5, NO. 2, JUNE 2019

Power Allocation in Cognitive Satellite-VehicularNetworks From Energy-Spectral Efficiency

Tradeoff PerspectiveYuhan Ruan , Member, IEEE, Yongzhao Li , Senior Member, IEEE, Cheng-Xiang Wang , Fellow, IEEE,

Rui Zhang, and Hailin Zhang , Member, IEEE

Abstract—With great potential to support multitudinousservices and applications in intelligent transportation systems,cognitive satellite-vehicular networks, an emerging paradigm ofcognitive satellite-terrestrial networks, are attracting increas-ing attentions. To realize friendly coexistence of satellite andvehicular networks as well as efficient resource utilization, weinvestigate power allocation for the cognitive satellite-vehicularnetwork under a realistic 3-D vehicle-to-vehicle channel model.Specifically, by analyzing the characteristics of energy efficiency(EE) and spectral efficiency (SE) performance in different vehic-ular environments, we first develop an EE–SE tradeoff metricwith a preference factor. Based on the developed metric, we for-mulate and analyze a power allocation strategy from the EE–SEtradeoff perspective while guaranteeing the interference powerconstraint imposed by satellite communications. Further, utiliz-ing the obtained optimal transmit power, we derive a closed-formexpression of the outage probability, through which the impactsof the preference parameter and interference constraints on theperformance of vehicular communications can be theoreticallyanalyzed. Finally, numerical results are provided to demonstratethe viability of the EE–SE tradeoff metric and the validity oftheoretical analyses.

Index Terms—Cognitive satellite-vehicular networks, powerallocation, energy-spectral efficiency, interference constraints,outage probability.

I. INTRODUCTION

BENEFITING from the advantages of both satellite andterrestrial systems, hybrid satellite-terrestrial networks

are becoming a promising infrastructure to enhance spectral

Manuscript received October 18, 2018; revised February 9, 2019; acceptedMarch 9, 2019. Date of publication March 14, 2019; date of current versionJune 7, 2019. The authors acknowledge the support from the National KeyR&D Program of China under Grant 2016YFB1200202, the National NaturalScience Foundation of China under Grant 61771365, the Natural ScienceFoundation of Shaanxi Province under Grant 2017JZ022, the PostdoctoralScience Foundation of China under Grant 30101180044, the 111 Project underGrant B08038, the Fundamental Research Funds for the Central Universitiesunder Grant 2242019R30001, and the EU H2020 RISE TESTBED projectunder Grant 734325. The associate editor coordinating the review of thispaper and approving it for publication was A. Zanella. (Corresponding author:Rui Zhang.)

Y. Ruan, Y. Li, R. Zhang, and H. Zhang are with the StateKey Laboratory of Integrated Services Networks, Xidian University,Xi’an 710071, China (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

C.-X. Wang is with the National Mobile Communications ResearchLaboratory, School of Information Science and Engineering, SoutheastUniversity, Nanjing 210096, China, and also with the Purple MountainLaboratories, Nanjing 211111, China (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCCN.2019.2905199

efficiency (SE), extend system coverage, and increase serviceavailability and resilience [1], [2]. However, with the increas-ingly growing number of applications and services in satellitecommunications as well as fifth-generation (5G) communica-tions, the available frequency resources have become scarcedue to the dedicated frequency allocation of standardized wire-less systems [3], [4]. Recently, cognitive radio (CR) whichmakes use of spectrum more intelligently and flexibly haswidely been regarded as an effective means to alleviate thespectrum shortage. In this context, the incorporation of CRtechniques into satellite-terrestrial networks, referred to as cog-nitive satellite-terrestrial networks, have attracted tremendousattention in academic research [5], [6], standardization, e.g.,European Telecommunications Standards Institute (ETSI) [7],and applications, e.g., tactical data links [8].

Until now, numerous researchers have devoted to thespectrum sharing between satellite and terrestrial networks.Maleki et al. [9] presented several basic scenarios and systemmodels for cognitive satellite-terrestrial networks, where satel-lite and terrestrial networks can operate as primary andsecondary systems, respectively, or vice versa. In regard tospectrum sharing, cognitive satellite-terrestrial networks canoperate on various modes, e.g., underlay, overlay, and inter-weave [10], [11]. The underlay mode, in which the cognitivesystem is allowed to share the spectrum licensed to the primarysystem without causing excessive interference at the primaryuser, is especially attractive due to its effective spectrum uti-lization. In this context, various resource allocation schemeswere studied to optimize the performance of cognitive satellite-terrestrial networks [12]–[17]. Specifically, Lagunas et al. [12]proposed a carrier-power-bandwidth allocation scheme tomaximize the satellite throughput. Vassaki et al. [13] intro-duced a power allocation scheme that can optimize theeffective capacity of terrestrial communications for givenquality of service (QoS) requirements while guaranteeingthe outage probability (OP) of satellite communications.Li et al. [14] conducted power allocation to maximizethe achievable rate for cognitive hybrid satellite-terrestrialnetworks with amplify-and-forward (AF) relays. For real-timesatellite applications in cognitive satellite-terrestrial networks,Shi et al. [15] conducted power control to maximize the delay-limited capacity without degrading the communication qualityof the primary terrestrial user. Besides, to enhance the physi-cal layer security for cognitive satellite terrestrial networks,

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RUAN et al.: POWER ALLOCATION IN COGNITIVE SATELLITE-VEHICULAR NETWORKS FROM ENERGY-SE TRADEOFF PERSPECTIVE 319

beamforming based secure transmissions were studiedin [16] and [17].

On the other hand, with the development of industry andeconomy, vehicular communications have been encounteredin many applications, such as wireless mobile ad-hoc peer-to-peer networks and intelligent transportation systems. Tokeep pace with 5G communications and support satellite com-munications in mobile environments, e.g., emergency reliefvehicles, satellite-vehicular communication is becoming a pop-ular research topic. Through simulations, Nguyen et al. [18]evaluated the practical achievable capacity of satellite vehic-ular communications operating in X, Ku, and Ka bands.Cocco et al. [19] employed network coding to combat severechannel fading and extend the satellite coverage in land mobilesatellite vehicular networks. These studies demonstrated thefeasibility and prospect of realizing vehicular communicationsin satellite-terrestrial networks.

Inspired by the benefits of applying CR to satellite-terrestrialnetworks and the development of vehicular communications,in this paper, we focus on a cognitive satellite-vehicularnetwork, which is a visualized and concrete applicationof cognitive satellite-terrestrial networks in mobile envi-ronments. Specifically, the satellite network is regarded asthe primary system and the vehicular network operates asthe secondary system. To realize the coexistence of satel-lite and vehicular networks in the underlay mode, efficientresource allocation is a significant challenge in vehicularenvironments.

Although resource allocation schemes in cognitive satellite-terrestrial networks have been extensively investigated, thesestudies mainly analyzed and optimized the performance ofsatellite-terrestrial networks from the perspective of SE.Energy efficiency (EE) is also a vital performance metric inthe design of future environment-friendly satellite commu-nications [20]–[22]. Thus, consideration of both SE and EEis of great importance for green cognitive satellite-terrestrialcommunication networks. Unfortunately, it is well knownthat EE and SE efficient transmission techniques are incon-sistent with each other and there exists a tradeoff betweenEE and SE [23]. Zhang et al. [24] investigated the EE-SE tradeoff by optimizing EE with the SE constraint inhybrid satellite-terrestrial networks. However, in the cognitivesatellite-vehicular network, the mobility of vehicular users andthe vehicular traffic density (VTD) can greatly affect the signalpropagation and subsequently pose new challenges in radioresource management [25]. Therefore, the tradeoff formula-tions as in [24], optimizing either SE or EE, is not suitablefor vehicular communications with different applications anddynamic surrounding circumstances.

Motivated by this need, in this paper, we investigate powerallocation from a novel EE-SE tradeoff perspective in cog-nitive satellite-vehicular networks, where the vehicular link ismodeled as a three-dimensional (3D) vehicle-to-vehicle (V2V)channel to characterize the mobility of vehicular users and theVTD in a realistic vehicular environment [26]. By analyzingthe characteristics of EE-SE performance in different VTDscenarios, we firstly develop a unified EE-SE tradeoff metric.To efficiently manage the co-channel interference caused by

spectrum reuse, we derive and analyze a power allocation strat-egy based on the developed EE and SE tradeoff metric. Themajor contributions of this paper are summarized as follows:

1) A unified EE and SE tradeoff metric is proposedfor power allocation in cognitive satellite-vehicularnetworks. According to the observations of EE-SEperformance in different VTD scenarios, it makes muchsense to optimize SE in a high VTD scenario while pur-sue EE in a low VTD scenario for power allocationin cognitive satellite-vehicular networks. To make theoptimization more tractable than conventional individ-ual optimizations, we condense the SE and EE into asingle utility function with a preference factor. Throughthis preference factor, the priority level of EE and SEcan be flexibly adjusted to adapt to dynamic surroundingcircumstances. In addition, we prove the utility functionis strictly quasi-convex in transmit power.

2) Based on the developed EE-SE tradeoff metric, theoptimal power allocation is derived and analyzed. Firstly,taking the mutual interference into account, we formu-late the power allocation scheme as an optimizationproblem that minimizes the utility function of vehicu-lar communications while guaranteeing the interferencepower constraints imposed by satellite communica-tions. Then, employing the Charnes-Cooper transfor-mation [27], we transform the fractional optimizationproblem into an equivalent convex problem and derivethe optimal solution of the transmit power.

3) Utilizing the derived optimal transmit power, we analyzethe outage performance and obtain a closed-form expres-sion of the OP in cognitive satellite-vehicular networks,where the communication link and interference links aremodeled as 3D V2V channel and generalized-K chan-nels, respectively. Through the obtained closed-formexpression, the impact of the preference parameter andinterference constraints on the performance of vehicularcommunications can be theoretically analyzed.

The remainder of the paper is organized as follows.Section II introduces the system model of the cognitivesatellite-vehicular network. Section III develops a unified EEand SE tradeoff metric and investigates a power allocationscheme. Based on the obtained optimal transmit power, we dis-cuss the tradeoff between EE and SE and theoretically analyzethe outage performance in Section IV. Section V numericallyevaluates the developed power allocation scheme and showthe effect of various parameters on the EE and SE tradeoff.Finally, conclusions are given in Section VI.

II. SYSTEM MODEL

In this paper, we consider a cognitive satellite-vehicularnetwork as illustrated in Fig. 1. Similar to [13], the satellitenetwork acts as the primary system and shares downlink spec-tral resource with the terrestrial vehicular network, referred toas the secondary system. In this case, the secondary vehiculartransmitter (ST) will interfere the primary receiver (PR) whilethe secondary vehicular receiver (SR) will also suffer fromthe interference caused by the primary transmitter (PT). It is


Fig. 1. An underlay cognitive satellite-vehicular network.

assumed that each node is equipped with a single antenna andoperates in a half-duplex mode.1 We denote hss and hpp asthe channel coefficients of ST → SR and PT → PR commu-nication links, respectively, while hps and hsp as the channelcoefficients of PT → SR and ST → PR interfering links,respectively.2

A. Signal Model

For the secondary system, the signal received at the vehic-ular receiver can be expressed as

y =√

Pshssx +√

Pphpsz + n (1)

where Ps and Pp are the transmit powers of the vehicu-lar transmitter and the satellite, respectively, x represents thedesired signal from the vehicular transmitter, z denotes theinterference signal from the satellite communication,3 n rep-resents the complex additive white Gaussian noise (AWGN)with power N0.

Given a system bandwidth W, the spectral efficiency (ΨSE,in bits/s/Hz) of V2V communications can be expressed as

ΨSE =E{C}W

= E{log2(1 + γs)} (2)

where E{·} denotes the expectation operator, C is the instan-

taneous capacity, and γs = Ps|hss|2N0+Pp|hps|2 is the received

signal-to-interference-plus-noise ratio (SINR) at the vehicularreceiver.

Energy efficiency (ΨEE, in bits/Joule/Hz) is defined as theratio of ΨSE to the total power expenditure (Ptot, in Watt)

1Since this paper mainly focuses on managing the interference caused byfrequency reuse in underlay cognitive satellite-vehicular networks and thusassumes that each nodes work in half-duplex mode. The self-interference elim-ination and other key technologies for full-duplex communications [28] areout of the scope of this paper.

2Similar to [29], we assume that these channels are quasi-static and thecorresponding instantaneous channel state information can be obtained byadopting the sparsity structure based channel estimation approach proposedin [30]. How to reduce the amount the feedback to make the proposed powerallocation scheme more feasible in practical implications is left for our futureresearch.

3Although satellite is far away from the vehicular receiver, when thevehicular receiver locates in the beam footprint of the satellite or the chan-nel condition is good between the satellite and the vehicular receiver, theinterference from the satellite cannot be ignored.

and can be formulated as

ΨEE =ΨSE

E{Ptot} (3)

where Ptot consists of radio-frequency power ηPs, circuitpower PC

0 , and static power PS0 , i.e., Ptot = ηPs +PC

0 +PS0 .

Here, η is the transmit power consumption coefficient thatscales up with the transmit power due to amplifier loss.Intuitively, η ∈ [1,∞) is the reciprocal of the power amplifierefficiency which varies in the range of (0, 1] [31]. Since thecircuit and static power consumptions are usually independentof data rate and can be regarded as constants for the transmit-ter, for notational simplicity, we use Ptot = ηPs + P0 in thefollowing, where P0 = PC

0 + PS0 .

B. Channel Model

From Fig. 1 we can observe that the considered cognitivesatellite-vehicular network involves two kinds of channel. Oneis the conventional fixed-to-mobile/fixed channel and the otheris the V2V channel where both the transmitter and receiver arein motion. Specifically, the conventional fixed-to-mobile/fixedlinks consist of one terrestrial link (hsp) and two land mobilesatellite (LMS) links (hpp and hps). As demonstrated, thegeneralized-K model can properly describe not only the sig-nal propagation on terrestrial links [32], but also the channelenvironment of satellite communications [21]. Consideringthe broad suitability of the generalized-K model, we modelthese links uniformly as the generalized-K distribution. Thegeneralized-K distribution is a mixture of Gamma-distributedshadowing and Nakagami-distributed multipath fading effect.

For the generalized-K model, the PDF of |hi |2(i = pp,ps, sp) can be written as

f|hi |2(x ) =2bϕi+εi

i

Γ(εi )Γ(ϕi )x

(ϕi+εi

2

)−1Kϕi−εi

(2bi

√x)

(4)

where Kϕi−εi (·) is the modified Bessel function of the second

kind with order (ϕi − εi ) and bi =√

ϕiεiΩi

. Here, εi ≥ 0.5and ϕi ≥ 0 are the multipath and shadowing parameters,respectively, Ωi is the mean of the received local power.Since the generalized-K distribution has a relatively simplemathematical form, it allows an integrated performance anal-ysis of digital communication systems operating in compositemultipath/shadowing fading environments.

Apart form the conventional fixed-to-mobile/fixed links, theconsidered network also involves in V2V links in the sec-ondary vehicular communications, where both the transmitterand receiver may have high mobility. In this paper, we adopta simple vehicle-mobility model where vehicles move in astraight line with a constant velocity. Under this situation,the traditional channel model where either the transmitter orthe receiver is assumed motionless is no longer applicable.Therefore, we adopt the 3D V2V channel model proposedin [26] to accurately capture the effect of the velocity and VTDon the channel characteristics. In this model, the radio propa-gation environment is characterized by 3D effective scatteringwith line-of-sight (LoS) and non-LoS (NLoS) componentsbetween the vehicular transmitter and receiver. Specifically, the


NLoS components can be further classified as single bounced(SB) rays representing signals reflected only once during thepropagation process and double bounced (DB) rays represent-ing signals reflected more than once. Noteworthily, differentfrom physical scatterers, an effective scatterer may includeseveral physical scatterers which are unresolvable in delay andangle domains. Moreover, this channel model utilizes a two-sphere model to mimic the moving scatterers, such as othervehicles, and an elliptic-cylinder model to depict the station-ary roadside environments, such as buildings and trees. Thegeometry of the single- and double-bounced two-sphere modeland other related details can be found in [26].

The channel coefficient4 hss at the carrier frequency f isa superposition of three types of components, which can beexpressed as

hss = hLoS +I∑

i=1

hSBi+ hDB (5)

where hLoS, hSBi, and hDB are the LoS component, SB

component, and DB component, respectively. In this model,I = 3, which means there are three subcomponents for SBrays, i.e., SB1 from the transmitter sphere, SB2 from thereceiver sphere, and SB3 from the elliptic-cylinder. Accordingto [26], the probability density function (PDF) of |hss|2 canbe expressed as

f|hss|2(x ) = (1 + K )e−K e−(1+K )x I0(2√

K (1 + K )x)

(6)

where K is the Ricean factor and I0(x ) is the zero-ordermodified Bessel function of the first kind.

III. POWER ALLOCATION IN COGNITIVE

SATELLITE-VEHICULAR NETWORKS FROM

EE-SE TRADEOFF PERSPECTIVE

In this section, we investigate a power allocation strategy forcognitive satellite-vehicular networks. According to the dis-tinct performance characteristics in different VTD scenarios,a unified EE-SE tradeoff metric is firstly developed to facili-tate the applicability and tractability of resource management.By proving the utility function being strictly quasi-convexin transmit power, we propose an optimal power allocationscheme for vehicular communications to minimize the utilityfunction under the interference power constraints imposed bysatellite communications. Moreover, with the Charnes-Coopertransformation, the optimal solution for the transmit poweris derived.

A. A Unified Spectral-Energy Efficiency Tradeoff Metric

To design a delicate power allocation strategy from theEE-SE tradeoff perspective, first, we need to analyze theperformance characteristics of EE and SE in cognitive satellite-vehicular networks. In vehicular communications, high VTDand low VTD scenarios are two typical scenarios corre-sponding to communication occurs in urban and rural areas,respectively. In a high VTD scenario with dozens of vehi-cles per square kilometer, the received power comes from all

4Time index is omitted in this paper for notation simplicity.

Fig. 2. EE versus SE in cognitive satellite-vehicular networks with differentVTD scenarios (dss = 300 m, v = 10 m/s, P0 = 150 mW, γ̄p = 8 dB,Ith = −90 dBm).

directions reflected by moving vehicles and DB rays dominatedue to dense moving vehicles. In a low VTD scenario withless than ten vehicles per square kilometer, the received powercomes mainly from specific directions identified by main sta-tionary roadside scatterers and LoS component. It is interestingto note that the Ricean factor K specified in (6) in a low VTDscenario is larger than that in a high VTD scenario, indicat-ing that a better channel performance can be achieved in alow VTD scenario compared with the high VTD case. Asillustrated in [26] and [33], the VTD has a great impact onall channel statistical properties, which eventually affect theperformance of EE and SE.

In the following, to explicitly reveal the impact of VTDon EE and SE, we plot the achievable EE versus SE forV2V communications in different VTD scenarios in Fig. 2.As expected, the EE increases at the beginning and decreasesafterwards in both scenarios, verifying the tradeoff betweenEE and SE. However, the slopes of two curves that EE versusSE are distinguishing. For example, as can be seen in Fig. 2,for the high VTD scenario, a small degradation in EE (20%)around its peak value results in a significant gain in SE (80%).While for the low VTD scenario, we can achieve a consider-able gain in EE (46%) with a small degradation in SE (20%).These observations illustrate that it would make much senseto optimize SE in high VTD scenario while optimize EE inlow VTD scenario.

The above observations and discussions reveal differentpreference of EE and SE in various vehicular scenarios.However, the existing literature mainly optimized either EEor SE with the requirement of the other one as the same whenconducting power allocation, which is only suitable for specificcommunication scenarios and cannot deal with the dynamicchanges of circumstances. Moreover, both EE and SE areconsidered as two key performance indicators for 5G commu-nication systems. As such, EE and SE should jointly be max-imized as a multi-objective optimization problem (MOOP).Here, we need to note two phenomena. Firstly, due to thefact that EE and SE functions are correlated and the curve of


EE-SE relation turns to a bell shape, maximizing EE and SEare conflicting objectives and can hardly be achieved simulta-neously. Secondly, from Fig. 2 we can see that for vehicularcommunications, VTD has impacts on the system preferenceof EE and SE. To facilitate the applicability and tractabilityof resource management, we aim to develop a power alloca-tion scheme which is capable to adapt to diverse propagationcharacteristics of vehicular environments.

Inspired by the green communication trend and the diver-sity of preferences in different VTD scenarios, we adopt theweighted sum method to convert the MOOP into a new EE-SEtradeoff framework with a synthetic objective. Considering theunit for EE is bits/Joule/Hz while the unit for SE is bits/s/Hz,to get rid of the different measurements and orders of magni-tude of EE and SE, we first normalize the EE and SE with thecorresponding maximum achievable EE value, i.e., ΨEE

MAX,and SE value, i.e., ΨSE

MAX, respectively. Here, ΨEEMAX and

ΨSEMAX represent the maximum values achievable on the fea-

sible region of transmit power, i.e., P ∈ [0, Ith/|hsp |2]. In thisway, the SE and EE can be regarded as quantities without anassociated physical unit. From Fig. 2 we can see that, it makesmuch sense to maximize EE(Ps) = ΨEE

ΨEEMAX

in a low VTD

scenario while turns to SE(Ps) = ΨSE

ΨSEMAX

in a high VTD sce-

nario. In other words, it is equivalent to minimize EE−1(Ps)and SE−1(Ps), respectively. By denoting ω and 1 − ω as therelative preference factors of EE and SE, we formulate theunified metric as

F(ω,Ps) = (1 − ω)ΨSE

MAX

ΨSE+ ω

ΨEEMAX

ΨEE. (7)

It can be seen that through the preference factor ω, the prioritylevel of EE and SE can be flexibly changed to adapt to dif-ferent VTD scenarios, thus various vehicular environments. Itis worthy noting that although different VTD scenarios havedifferent preference of EE and SE from the perspective ofenhancing system resource efficiency, we cannot obtain anoptimal w value. This is because in practical applications, w isthe priori articulation of preference for EE and SE provided bysystem operator, based on the specific situation of the systemresources. To make the subsequent power allocation tractable,we give the following theorem.

Theorem 1: For any fixed weight ω, the utility functionF(ω,Ps) is strictly quasi-convex in Ps.

Proof: The proof is presented in Appendix A.

B. The Optimal Power Allocation Derivation

Based on the developed utility function, a power allocationscheme is then proposed for better coexistence of the vehic-ular and satellite communications. In the power allocation,we minimize the utility function of vehicular communicationswhile restricting the interference power imposed at the satellitereceiver below a predefined threshold, i.e., Ith. Considering theservices in vehicular communications are mostly determinedby instant SINR [34], we adopt the peak interference constraintto restrict the resultant interference power under a predefined

value. Thus, the optimization problem can be formulated as

minimizePs(ω,γ,hsp)≥0

F(ω,Ps

(ω, γ, hsp

))

subject to Ps(ω, γ, hsp

)∣∣hsp

∣∣2 ≤ Ith (8)

where γ = |hss|21+γ̄p|hps|2 with γ̄p = Pp/N0.

Since we consider the diverse preferences of different vehic-ular scenarios and interference constraints imposed by satellitecommunications, the transmit power of vehicular communica-tions Ps is a function of ω, γ, and hsp, i.e., Ps(ω, γ, hsp).

In the following, we first provide a solution for theoptimization problem without the interference constraint, i.e.,

minimizePs(ω,γ)≥0

(1 − ω)ΨSEMAX + ωΨEE

MAXEγ{ηPs(ω, γ) + P0}Eγ{log2(1 + Ps(ω, γ)γ/N0)} .

(9)

By denoting g(Ps(ω, γ)) and f (Ps(ω, γ)) as the numeratorand denominator, respectively, (9) can be equalized to

maximizePs(ω,γ)≥0

f (Ps(ω, γ))g(Ps(ω, γ))

. (10)

As observed, the objective function in (10) is a ratioof two functions with respect to Ps(ω, γ). According toCharnes-Cooper transformation [27], we apply suitable vari-able transformation to reformulate the optimization problemto an equivalent problem. By applying the transformationx = Ps

G(Ps)and t = 1

G(Ps), we have


tf(x

t

)

subject to tg(x

t

)≤ 1. (11)

Theorem 2: If (x∗, t∗) is an optimal solution for (11), thenx∗t∗ is an optimal solution for (10).

Proof: The proof is presented in Appendix B.Then, the optimization in (9) can be written as


tEγ{log2(1 + Ps(ω, γ)γ/N0)}

subject to t((1 − ω)ΨSE

MAX + ωΨEEMAXEγ{ηPs(ω, γ) + P0}

) ≤ 1.

(12)

In the following, we focus on solving the optimizationproblem (12). As the objective function in (12) is a logarithmicfunction with respect to Ps(ω, γ,), thus it is concave accordingto [35]. Besides, the constraint is an affine function and thus,the feasible set defined by constraint is a convex set. Therefore,the Karush-Kuhn-Tucker (KKT) conditions are both sufficientand necessary for the optimality of (12) [35]. We employ theLagrange multiplier method to obtain the optimal solution ofthe transmit power. Then, the partial Lagrangian of problem(12) is given by

L(Ps(ω, γ), t , �) = tEγ{log2(1 + Ps(ω, γ)γ/N0)}+ �

(1 − t

((1 − ω)ΨSE

MAX + ωΨEEMAXEγ

× {ηPs(ω, γ) + P0}))

(13)


where � > 0 is the Lagrangian parameter. Then, the KKTcondition ∂L(Ps(ω,γ),t ,�)

∂Ps(ω,γ)= 0 can be written as

tγln 2(Ps(ω, γ)γ + N0)

− t�ωηΨEEMAX = 0. (14)

Hence, the power allocation can be found as

P̃s =[

1αω

− N0

γ

]+

(15)

where α = ln 2�ηΨEEMAX and [x ]+ = max(0, x ). The optimal

value of � can be found from the following equation

Eγ

{log2

(1 + P̃sγ/N0

)}− �

((1 − ω)ΨSE

MAX

+ ωΨEEMAX

(ηEγ

{P̃s

}+ P0

))= 0. (16)

Note that (16) only depends on � and is independent from t.The involved mean values can be derived as

E

[P̃s

]= Q1

(αω)−1

(αωN0)ε̃ps

G2232

×[

(1 + K )αωN0

b2ps

∣∣∣∣1 − ϕ̃ps, 1 + ϕ̃ps, 2 + ε̃ps

ε̃ps, 1 + p + ε̃ps

]

(17)

and

E

[

log2

(

1+P̃sγ

N0

)]

= Q1

L∑

l=0

(−1)lΓ(l+1)

l(αωN0)ε̃ps

× G2232

[(1+K )αωN0

b2ps

∣∣∣∣1−ϕ̃ps, 1+ϕ̃ps, 1+ε̃ps

ε̃ps−l , 1+p+ε̃ps

]

. (18)

where ε̃ps = ϕps+εps

2 and ϕ̃ps = ϕps−εps

2 .Proof: The derivation can be found in Appendix C.Assume that we have obtained the transmit power allo-

cated for the interference unconstrained optimization. Whenthe interference constraint is considered, since hsp remainsunchanged for each specific transmission slot, the interferencereceived at the satellite receiver is determined by the transmitpower. In this situation, the interference constraint in (8) canbe equalized to a transmit power constraint, i.e., Ps(ω, γ) ≤Ith/|hsp|2. Then, the solution for the problem (8) can bedivided into two regions:

1) P̃s ≤ Ith/|hsp|2: In this case, the added interferenceconstraint does not affect the optimal solution and hence,the optimal power of (8) is the same as that of (9), i.e.,P∗

s = P̃s.2) P̃s > Ith/|hsp|2: If the transmit power for minimiz-

ing the unconstrained utility function is beyond theinterference level allowed by satellite communications, itwould be invalid for practical system application. In thiscase, to protect satellite communications, the optimaltransmit power should be limited by the interferenceconstraint, i.e., P∗

s = Ith/|hsp|2.

In summary, the optimal transmit power of (8) can beexpressed as

P∗s = min

([1

αω− N0

γ

]+

,Ith∣∣hsp

∣∣2

)

. (19)

By using the synthetic objective discussed in (7), the solutionin (19) means the optimal transmit power that maximizes thesystem resource efficiency [39] under a given system config-uration, i.e., a given w. In other words, the optimal solutionof the transmit power provides a proper guideline for systemoperator to optimize the system resource.

IV. ANALYSIS OF THE OPTIMAL TRANSMIT POWER

In the previous section, we have investigated a power alloca-tion strategy from the EE-SE tradeoff perspective and obtainedthe optimal transmit power solution expressed as a functionof the preference factor. In this section, we conduct somediscussions on the derived optimal transmit power. Firstly,the influence of the preference factor on the transmit poweris analyzed. Moreover, utilizing the derived optimal transmitpower, we theoretically analyze the performance of the cog-nitive satellite-vehicular networks in terms of OP, providingtheoretical insights on the impacts of the preference parameterand interference constraints.

A. The Effect of ω on the Optimal Transmit Power

From (19) we can see that the optimal transmit power P∗s

is dependent on the interference constraint (Ith), the chan-nel gains (|hss|2, |hsp|2, |hps|2), and the preference factor ω,among which ω is the decisive parameter in terms of thetradeoff between EE and SE. In the following, we focus ondiscussing the impact of ω on P∗

s , where ω can be dividedinto three regions:

1) when ω < 1α (N0

γ + Ith|hsp|2 )−1, the ratio of EE in utility

function is too small to affect the transmit power allo-cation. In this case, the power allocation scheme can beregarded as an optimization problem maximizing SE.Thus, the transmit power equals to the maximum valuebounded by interference constraints, i.e., P∗

s = Ith|hsp|2 .

2) when 1α (N0

γ + Ith|hsp|2 )−1 ≤ ω ≤ γ

αN0, we have P∗

s =1

αω − N0γ . In this case, we should adjust the trans-

mit power according to channel fading under the givenpreference factor ω.

3) when ω > γαN0

, we have P∗s = 0. Here, extremely

poor link quality between vehicular users, such asserve fading, long distance, or serious interference fromsatellite, may result in vehicular communications beingterminated. In this case, the reused resource for vehic-ular users can be reallocated to increase the spectrumaccess probability.

B. Outage Performance Based on the OptimalTransmit Power

To visualize the effect of the power allocation scheme onthe transmission performance, we investigate the performance


of the secondary vehicular system in terms of OP based onthe derived solution in (19). The OP, Pout, is defined as theprobability that the instantaneous end-to-end SINR falls belowa threshold Θth, i.e.,

Pout = Pr(γs ≤ Θth) (20)

where γs = P∗s γ/N0. From (19), we can get

γs =P∗

s |hss|2Pp

∣∣hps∣∣2 + N0

= min

([γ

αωN0− 1

]+

,Ithγ

∣∣hsp∣∣2N0

)

.

(21)

As for any random variables a and b, we have min(a, b) = aif b ≥ a and min(a, b) = b if b ≤ a. Therefore, Pout can becalculated as

Pout = Pr

(γ

αωN0−1 ≤ Ithγ

|hsp|2N0

,γ

αωN0−1 ≥ 0,

γ

αωN0−1 ≤ Θth

)

+ Pr

(γ

αωN0−1 ≥ Ithγ

|hsp|2N0

,Ithγ

|hsp|2N0

≤ Θth

). (22)

By carrying out some algebraic manipulations on (22), Pout

can be expressed as the sum of the following probabilities

Ξ1 = Pr

(αωN0|hsp|2

|hsp|2 − αωIth≤ γ ≤ ΘthN0|hsp|2

Ith

)

=

∫ ∞

0

∫ ΘthN0y

Ith

αωN0yy−αωIth

fγ(x)f|hsp|2 (y)dxdy (23)

Ξ2 = Pr

(|hsp|2 ≥ αω(Θth + 1)

ΘthIth, αωN0 ≤ γ ≤ αωN0|hsp|2

|hsp|2 − αωIth

)

=

∫ ∞

αω(Θth+1)ΘthIth

∫ αωN0yy−αωIth

αωN0

fγ(x)f|hsp|2 (y)dxdy (24)

Ξ3 = Pr

(|hsp|2 ≤ αω(Θth + 1)

ΘthIth, αωN0 ≤ γ ≤ αωN0(Θth + 1)

)

=

∫ αω(Θth+1)ΘthIth

0

∫ αωN0(Θth+1)

αωN0

fγ(x)f|hsp|2 (y)dxdy. (25)

According to the integral property, we firstly calculatethe integrals of fγ(x ) with [0, αωN0], [0, αωN0(Θth + 1)],[0, ΘthN0y

Ith], and [0, αωN0y

y−αωIth], which are denoted as Δ1, Δ2,

Δ3, and Δ4, respectively. Then, we can get

Δ1 =∫ αωN0

0fγ(x )dx = Q1

∫ αωN0

0x−ε̃ps−1

× G1221

[(1 + K )

b2ps

x∣∣∣∣1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps

]

dx . (26)

Using the integral relationship in [36, eq. (7.811.2)], Δ1 canbe computed as

Δ1 =Q1

(αωN0)ε̃psG13

32

[(1 + K )αωN0

b2ps

∣∣∣∣∣1 + ε̃ps, 1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps, ε̃ps

]

.

(27)

Similarly, we can obtain

Δ2 =Q1

(αωN0(Θth + 1))ε̃ps

× G1332

[αωN0(1 + K )(Θth + 1)

b2ps

∣∣∣∣∣1 + ε̃ps, 1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps, ε̃ps

]

(28)

and

Δ3 =I

ε̃psth Q1

(ΘthN0y)ε̃psG13

32

×[

(1 + K )ΘthN0

b2psIth

y

∣∣∣∣∣1 + ε̃ps, 1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps, ε̃ps

]

. (29)

To make the derivation of Δ4 tractable, we approximatethe PDF of generalized-K model using a Gamma distributedformat with a shape parameter ϑ and a scale parameterη [40], i.e.,

fγ̄p|hps|2(x ) =xϑps−1e

− xηpsγ̄p

Γ(ϑps

)(ηpsγ̄p

)ϑps, x > 0 (30)

where ϑps = ϕpsεps

ϕps+εps+1 and ηps = Ωps/ϑps. In this way,fγ(x ) can be simplified as

fγ(x ) = Q2xp(

1ηpsγ̄p

+ (1 + K )x)−ϑps−p−1

(31)

with Q2 = e−K

Γ(ϑps)(ηpsγ̄p)ϑps

∑Lp=0

K p(1+K )p+1Γ(ϑps+p+1)

(p!)2.

Then, with the aid of [36, eq. (3.194.1)], we can get

Δ4 = Q2(ηpsγ̄p)ϑps+p+1

p + 1

(αωN0y

y − αωIth

)p+1

× 2F1

(ϑps + p + 1, p + 1; p + 2;− (1 + K )ηpsγ̄pαωN0y

y − aIth

)

(32)

where 2F1(a, b; c; z ) is the Hypergeometric functionand can be expressed as the sum of L series, i.e.,

2F1(a, b; c; z ) =∑L

r=0(a)r (b)r z

r

(c)r r ![36, eq. (9.100)].

Here, (a)r = Γ(a + r)/Γ(a) is the Pochhammer symbol.Thus, Δ4 can be expressed as

Δ4 = Q2

L∑

r=0

(ϑps + p + 1)r (−1)r (1 + K )r

(p + r + 1)r !(ηpsγ̄p)r+ϑps+p+1

× (αωN0)r+p+1

(y

y − αωIth

)r+p+1

(33)

Then, from (23) we can get

Ξ1 =∫ ∞

0(Δ3 − Δ4)f|hsp|2(y)dy . (34)

By substituting (29) and (33) into (34) and applying[36, eq. (7.813.1)], the analytical expression of Ξ1 can beobtained. In the similar way, Ξ2 and Ξ3 can also be derived.Detailed derivations are omitted here due to the limited space.

Finally, by summing up Ξ1, Ξ2, and Ξ3, a closed-formexpression of Pout can be obtained as shown in (35), as shownat the bottom of the next page, where Υ(·, ·) and Γ(·, ·) are thelower and upper incomplete Gamma functions, respectively.

V. RESULTS AND ANALYSIS

In this section, numerical results are provided to evaluatethe proposed power allocation scheme and corroborate ourtheoretical analysis. In the simulations, we employ the pathloss model PL = 128.1 + 37.6 log10(d[in Km]) for terrestriallinks and set η = 1.2, Θth = 1 dB, N0 = −114 dBm, and


Fig. 3. EE and SE versus preference factor ω for various P0 in a lowVTD scenario with hsp experiencing ILS fading (dss = 300 m, v = 5 m/s,γ̄p = 5 dB, Ith = −95 dBm).

dsp = 500 m. For the generalized-K fading channels, using amoment matching technique, the corresponding parameter ϕi

can be linked to ϕi = 1eσ2−1

, where σ is the standard devia-tion of the log-normal shadowing and increases as the amountof fading increases. Considering the terrestrial link usuallyexperiences a severer shadowing than the satellite downlink,we assume hps follows the infrequent light shadowing (ILS)fading, while hsp follows the ILS fading or the average shad-owing (AS) fading. Specifically, according to [41], we setσi = 0.115, εi = 3,Ωi = 1 in ILS fading, while σi = 0.345,εi = 2, Ωi = 1 in AS fading. Besides, the 3D V2V channelparameters are the same as configured in [26, Sec. IV].

We firstly conduct simulations to investigate the effects ofthe preference factor ω on the corresponding EE and SE.Taking low VTD scenario as an example, Fig. 3 presentsthe SE (on the left-hand-side y-Axis) and EE (on the right-hand-side y-Axis) versus the preference factor ω for variouscircuit power consumptions, P0. It can be seen that the SEdecreases while the EE gradually increases with increasing ω.This phenomenon can be explained by the fact that increas-ing ω raises the importance of EE and diminishes the priorityof SE, which coincide with our design intention. Especially,in the case of ω = 0 and ω = 1, the optimization reducesto the maximization of SE and EE, respectively. Additionally,different from EE, the expression of SE is independent ofP0. Thus, the SE curves with various P0 values overlap atthe beginning while the EE curves have different endpoints.It is interesting to note that when ω ∈ [0, 0.1], EE and SEalmost remain constant for P0 = 50 mW. This is because in

Fig. 4. EE and SE versus preference factor ω for various velocities vin a low VTD scenario with hsp experiencing ILS fading (dss = 300 m,P0 = 100 mW, γ̄p = 5 dB, Ith = −95 dBm).

Fig. 5. SE versus interference threshold Ith for various preference factors ωwith hsp experiencing ILS fading (dss = 300 m, v = 5 m/s, P0 = 100 mW,γ̄p = 5 dB).

this region, the optimal transmit power is beyond the max-imum allowable power bounded by interference constraints.Moreover, when P0 = 100 mW, we can achieve a higherSE while lower EE compared with P0 = 50 mW. This isbecause as P0 gets larger, the optimal transmit power wouldincrease. To illustrate the impact of V2V channel characteris-tics on system performance, we plot the SE and EE versus thepreference factor ω for various vehicle velocities in Fig. 4.As observed, both the performance of SE and EE degradeas the velocity increases, which reveals that a larger velocityrepresents a poor communication link condition.

Pout =Q1

Γ(ϑsp)

(Ith

ΘthN0ηsp

)ε̃ps

G1442

[(1 + K )ΘthN0ηsp

b2psIth

∣∣∣∣1 − ϑsp + ε̃ps, 1 + ε̃ps, 1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps, ε̃ps

]− Q2Q3(−αωIth)ϑsp

Γ(ϑsp)ηϑspsp Γ(r + p + 1)

× G2112

[−αωIth

ηsp

∣∣∣∣−r − p − ϑsp

−ϑsp, 0

]+

Q2Q3

Γ(ϑsp)e−αωIth

ηsp

r+p+ϑsp∑

q=0

(r + p + ϑsp

q

)Γ

[ϑsp − q ,

1

ηsp

((Θth + 1)αω

ΘthIth− αωIth

)]

×(

αωIthηsp

)q

− Q1Δ1

Γ(ϑsp)Γ

(ϑsp,

(Θth + 1)αω

ΘthIthηsp

)+ (Δ2 − Δ1)

γ(ϑsp,

(Θth+1)αωηspΘthIth

)

Γ(ϑsp)(35)


Fig. 6. EE versus interference threshold Ith for various preference factors ωwith hsp experiencing ILS fading (dss = 300 m, v = 5 m/s, P0 = 100 mW,γ̄ p = 5 dB).

Then, we present the SE and EE versus the interferencethreshold Ith for various preference factors ω in Fig. 5 and Fig. 6,respectively. For both figures, communication occurring in highVTD scenario experiences a worse performance than that inlow VTD scenario, either in terms of SE or EE. This is dueto the fact that in high VTD scenario, the received power isreflected by dense moving vehicles, which result in a smallerRicean factor. Moreover, In the case of ω = 0 where the unifiedtradeoff optimization reduces to the SE maximization problem,the optimal transmit power is exactly the maximum allowablepower bounded by interference power constraints. Thus, as theinterference constraint gets looser, i.e., Ith becomes larger, theoptimal transmit power increases, resulting in a continuouslygrowing in SE and simultaneously losing EE. When ω = 1, theunified tradeoff optimization reduces to an EE maximizationproblem. In this case, from the figures we can observe thatthe maximum EE value can be achieved until Ith reachesto −95 dBm which corresponds to the transmit power P∗

EE.Therefore, when Ith < −95 dBm, SE and EE increase as Ithincreases, while when Ith > −95 dBm, system always operatesat the global optimal power P∗

EE. As a result, EE stabilizes atits maximum value and SE remains at ΨSE(P∗

EE).Finally, we evaluate the outage performance based on the

obtained optimal transmit power. Fig. 7 and Fig. 8 presentthe OP versus the satellite transmit power-to-noise ratio γ̄p

and interference threshold Ith, respectively. For both figures,the outage performance in low VTD scenario outperformsthat in high VTD scenario, which verifies our illustration inSection III. Moreover, we can observe that the theoreticalresults agree well with Monte Carlo simulations, confirmingthe accuracy of our derivations and simulations. For Fig. 7, asexpected, the OP increases as γ̄p increases. Moreover, whenthe weight added on EE increases, i.e., ω gets larger, theoptimal transmit power will decrease, which results in a pooroutage performance. This phenomenon reveals that for a givensystem, there is a tradeoff between the reliability and energyefficiency. It is interesting to note that as ω increase from 0.2to 0.8 and finally to 1, the gaps between the correspondingcurves get larger either in low VTD or high VTD scenarios,

Fig. 7. OP versus satellite transmit power-to-noise ratio γ̄p for various ωwith hsp experiencing ILS fading (dss = 300 m, v = 10 m/s, P0 = 100 mW,Ith = −80 dBm).

Fig. 8. OP versus interference threshold Ith for various dss and shadowingcases (v = 10 m/s, ω = 0.5, γ̄p = −5 dB, P0 = 100 mW).

which implies that the effect of the preference factor becomesmore pronounced.

For Fig. 8, we can observe that the stricter the interferencepower constraint is, i.e., Ith gets smaller, the larger the OPis, which verifies the fact that there is a balance between theperformance of the primary and secondary systems. Moreover,when the vehicular transceivers are close to each other, i.e., dss

gets smaller, the channel condition will be improved and sub-sequently the outage performance. Furthermore, for a certaininterference power constraint, when the interference link fromthe vehicular transmitter to the satellite receiver experiencesseverer fading, the optimal transmit power increases. Thus, theoutage performance with AS shadowing outperforms that withILS shadowing.

VI. CONCLUSION

In this paper, we have proposed a power allocationscheme from the EE and SE tradeoff perspective in cognitivesatellite-vehicular networks, where a 3D V2V channel modelhas been adopted. According to the distinct performance char-acteristics in different VTD scenarios, we have proposed aunified EE and SE tradeoff metric with a preference factor,


through which the priority level of EE and SE can be flex-ibly changed to adapt to various vehicular circumstances.By proving the utility function being strictly quasi-convexin transmit power, we have derived and analyzed a powerallocation strategy under the interference power constraintsimposed by satellite communications. Utilizing the obtainedoptimal transmit power, we have theoretically analyzed theoutage performance of vehicular communications and dis-cussed the impact of the preference factor on the optimaltransmit power. Finally, numerical results have demonstratedthat the developed EE-SE tradeoff metric can adapt to variousvehicular circumstances and the interference power constraintis an effective method for co-channel interference managementin cognitive systems.

APPENDIX APROOF OF THEOREM 1

We rewrite F(ω,Ps) as

F(ω,Ps) =A + BPs

log2(1 + νPs)(36)

where A = (1 − ω)ΨSEMAX + ωP0ΨEE

MAX, B = ωηΨEEMAX,

and ν = γN0

. From (36), we can get the first derivative ofF(ω,Ps) as

∂F(ω,Ps)∂Ps

=Blog2(1 + νPs) − ν(A+BPs)

ln 2(1+νPs)

(log2(1 + νPs))2

=h(Ps)

(log2(1 + νPs))2(37)

where h(Ps) = h1(Ps) − h2(Ps) with h1(Ps) =Blog2(1 + νPs) and h2(Ps) = ν(A+BPs)

ln 2(1+νPs).

For Ps ∈ [0,+∞), we have

∂h(Ps)∂Ps

=ν2(A + BPs)ln 2(1 + νPs)2

. (38)

Since A > 0, B > 0, and Ps > 0, h ′(Ps) is larger than zero forPs ∈ [0,+∞). As h(Ps) is continuous, there is at most oneintersection point between h1(Ps) and h2(Ps). Moreover, letus assume that P̄ ≥ 0. If h1(P̄) ≥ h2(P̄), we have h1(Ps) >h2(Ps) for Ps ≥ P̄ .

In addition, we have h(0) = h1(0)−h2(0) = − νAln 2 < 0 and

there is one intersection point P̃s between h1(Ps) and h2(Ps).For 0 ≤ Ps < P̃ , we have h(Ps) < 0. Thus, F(ω,Ps) isstrictly decreasing for 0 ≤ Ps < P̃ . For Ps > P̃ , we haveh(Ps) > 0. Thus, F(ω,Ps) is strictly increasing for Ps > P̃ .The minimum value of F(ω,Ps) can be obtained at Ps = P̃ .Therefore, F(ω,Ps) is strictly quasi-convex in Ps ∈ [0,+∞).Hence, Theorem 1 follows.

APPENDIX BPROOF OF THEOREM 2

We denote F (x , t) = f ( xt )ϕ(t) and G(x , t) = g( x

t )ϕ(t).For ϑ > 0, we have G(x , t) = ϑ. As (x∗, t∗) is an optimalsolution of the optimization problem (11), we have

F (x∗, t∗) ≥ F (x , t). (39)

Let us assume that Ps = x∗t∗ is not the optimal solution of

the problem (10). Thus, we have another value P∗s �= x∗

t∗ thatmaximizes the objective function of (10), i.e.,

f (P∗s )

g(P∗s )

> f(

x∗t∗

)/g(

x∗t∗

). (40)

As the power consumption function is positive for all val-ues of Ps, we have g(P∗

s ) = δϑ(δ > 0). If we consider thatx = P∗

s ϕ−1(1/δ) and t = ϕ−1(1/δ), then (x, t) is a feasiblesolution for (11), i.e.,

G(x , t) = g(P∗s )ϕ(t) = ϑ. (41)

Therefore, we can get the following expression

f (P∗s )

g(P∗s )

=f (P∗

s )ϕ(t)g(P∗

s )ϕ(t)=

F (x , t)G(x , t)

=F (x , t)

ϑ. (42)

We also have

f (x∗/t∗)gf (x∗/t∗) =

ϕ(t∗)f (x∗/t∗)ϕ(t∗)g(x∗/t∗) =

F (x∗, t∗)G(x∗, t∗) =

F (x∗, t∗)ϑ

.

(43)

From (40), (42), and (43), we can conclude that

F (x∗, t∗) < F (x , t) (44)

which contradicts the assumption that F (x∗, t∗) ≥ F (x , t).Thus, Ps = x∗

t∗ is an optimal solution of (10). This completesthe proof of Theorem 2.

APPENDIX CDERIVATION OF (17) AND (18)

From the expression of P̃s specified in (15),

Eγ [log2(1 + P̃sγN0

)], denoted by Ψ̄SE, can be calculated as

Ψ̄SE = Eγ

[log2

(v

αωN0

)]∣∣∣∣γ≥αωN0

=∫ ∞

αωN0

log2

(x

αωN0

)fγ(x )dx . (45)

To calculate the integral in (45), we need to derive the PDF

of γ firstly. From γ = |hss|21+γ̄p|hpd|2 , fγ(x ) can be written as

fγ(x ) =∫ ∞

0(y + 1)fγ̄p|hps|2(y)f|hss|2(x (y + 1))dy . (46)

By substituting (4) and (6) into (46) and expanding theseries expression for I0(x ) [36, eq. (8.447.1)], (46) can beexpressed as

fγ(x ) =2bϕps+εps

ps (1 + K )e−K

Γ(ϕps

)Γ(εps

)(γ̄p

)ε̃ps

L∑

p=0

K p(1 + K )p

(p!)2xp

×∫ ∞

0yp+ε̃pse−(1+K )xyKϕps−εps

(2bps

√y)

︸︷︷︸J

dy

(47)

where ε̃ps = ϕps+εps

2 . In the above derivation, we assumethat the interference dominates the noise, which is reasonablein an interference-limited scenario [37]. To derive the integral


in (47), we express Kϕps−εps(2bps√

y) in terms of Meijer-jfunction [38, eq. (14)], i.e.,

Kϕps−εps

(2bps

√y)

=12G20

02

[b2psy

∣∣∣∣·

ϕ̃ps,−ϕ̃ps

](48)

where ϕ̃ps = ϕps−εps

2 . Then, by substituting (48) into (47)and using [36, eq. (7.813.1)], J can be obtained as

J =12((1 + K )x )−p−ε̃ps−1G21

12

[b2ps

(1 + K )x

∣∣∣∣−p − ε̃ps

ϕ̃ps,−ϕ̃ps

]

.

(49)

Utilizing the property of Meijer-j function shown in[36, eq. (9.31.2)], fγ(x ) can be given by

fγ(x ) = Q1x−ε̃ps−1G1221

[(1 + K )

b2ps

x∣∣∣∣1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps

]

(50)

with Q1 = bϕps+εpsps e−K

Γ(ϕps)Γ(εps)(γ̄p)ε̃ps

∑Lp=0

K p(1+K )−ε̃ps

(p!)2.

Then, we focus on deriving Ψ̄SE in (45). Considering thefact that the integral in (45) is mathematically intractable, weexpand the log function into the sum of L series and substitutefγ(x ) in (50) into (45). Then, Ψ̄SE can be calculated as

Ψ̄SE = Q1

L∑

l=0

(−1)l(αωN0)−l

l

∫ ∞

αωN0

x−ε̃ps−1(x − αωN0)l

× G1221

[(1 + K )

b2ps

x∣∣∣∣1 − ϕ̃ps, 1 + ϕ̃ps

1 + p + ε̃ps

]

dx . (51)

With the aid of [36, eq. (7.811.3)], the analytical expressionof Ψ̄SE can be finally derived as shown in (18).

From the expression of P̃s specified in (15), the averagetransmit power can be expressed as

Eγ

[P̃s

]= Eγ

[1

αω− N0

x

]∣∣∣∣γ≥αωN0

=∫ ∞

αωN0

(1

αω− N0

x

)fγ(x )dx . (52)

With the similar derivation steps of Ψ̄SE, the analyticalexpression of Eγ [P̃s] can be calculated as shown in (17).

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Yuhan Ruan received the B.S. and Ph.D. degreesin telecommunications engineering from XidianUniversity, Xi’an, China, in 2013 and 2018, respec-tively. She was a visiting Ph.D. student withHeriot-Watt University, Edinburgh, U.K., from 2016to 2017, under the supervision of Prof. C.-X. Wang.She is currently a Post-Doctoral Fellow with XidianUniversity. Her research interests are in the fieldsof satellite-terrestrial networks, cooperative commu-nications, cognitive radio techniques, and energyefficient wireless networks.

Yongzhao Li (M’04–SM’17) received the B.S.,M.S., and Ph.D. degrees in electronic engineeringfrom Xidian University, Xi’an, China, in 1996, 2001,and 2005, respectively. In 1996, he joined XidianUniversity, where he is currently a Full Professorwith the State Key Laboratory of Integrated ServicesNetworks and also currently serves as the Vice Deanof the Graduate School. He was a Research Professorwith the University of Delaware, Delaware, USA,from 2007 to 2008, and the University of Bristol,Bristol, U.K., in 2011. He has published over

50 journal papers and 20 conference papers. His research interests includewideband wireless communications, signal processing for communications,and spatial communications networks. He was a recipient of the Best PaperAward of IEEE ChinaCOM’08 International Conference in 2008. Due tohis excellent contributions in education and research, he was awarded bythe Program for New Century Excellent Talents in University, Ministry ofEducation, China, in 2012.

Cheng-Xiang Wang (S’01–M’05–SM’08–F’17)received the B.Sc. and M.Eng. degrees in commu-nication and information systems from ShandongUniversity, China, in 1997 and 2000, respectively,and the Ph.D. degree in wireless communicationsfrom Aalborg University, Denmark, in 2004.

He was a Research Assistant with the HamburgUniversity of Technology, Hamburg, Germany, from2000 to 2001, a Visiting Researcher with SiemensAG Mobile Phones, Munich, Germany, in 2004, anda Research Fellow with the University of Agder,

Grimstad, Norway, from 2001 to 2005. He has been with Heriot-WattUniversity, Edinburgh, U.K., since 2005, where he was promoted to aProfessor in 2011. In 2018, he joined Southeast University, China, as aProfessor. He has authored 3 books, 1 book chapter, and over 350 papersin refereed journals and conference proceedings, including 23 Highly CitedPapers. He has also delivered 17 invited keynote speeches/talks and 6 tuto-rials in international conferences. His current research interests includewireless channel measurements and modeling, (B)5G wireless communica-tion networks, and applying artificial intelligence to wireless communicationnetworks.

Dr. Wang was a recipient of nine best paper awards from IEEEGLOBECOM 2010, IEEE ICCT 2011, ITST 2012, IEEE VTC 2013-Spring,IWCMC 2015, IWCMC 2016, IEEE/CIC ICCC 2016, and WPMC 2016,and the Highly Cited Researcher Award by Clarivate Analytics in 2017 and2018. He has served as the TPC member, the TPC chair, and the generalchair for over 80 international conferences. He is currently an ExecutiveEditorial Committee Member for the IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS. He has served as an Editor for nine international journals,including the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from2007 to 2009, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY

from 2011 to 2017, and the IEEE TRANSACTIONS ON COMMUNICATIONS

from 2015 to 2017. He was a Guest Editor for the IEEE JOURNAL

ON SELECTED AREAS IN COMMUNICATIONS, Special Issue on VehicularCommunications and Networks (Lead Guest Editor), Special Issue onSpectrum and Energy Efficient Design of Wireless Communication Networks,and Special Issue on Airborne Communication Networks. He was also aGuest Editor for the IEEE TRANSACTIONS ON BIG DATA, Special Issue onWireless Big Data. He is a Fellow of IET and an IEEE CommunicationsSociety Distinguished Lecturer in 2019 and 2020.

Rui Zhang received the B.S., M.S., and Ph.D.degrees in telecommunications engineering fromXidian University, Xi’an, China, in 2012, 2015, and2018, respectively. He was a visiting student withHeriot-Watt University, Edinburgh, U.K., from 2016to 2017, under the supervision of Prof. C.-X. Wang.His current research interests focus on device-to-device communications, vehicle-to-vehicle commu-nications, radio resource allocation techniques, andenergy efficient wireless networks.

Hailin Zhang (M’98) received the B.S. and M.S.degrees from Northwestern Polytechnic University,Xi’an, China, in 1985 and 1988, respectively, and thePh.D. degree from Xidian University, Xi’an, in 1991.Since 1991, he has been with Xidian University,where he is currently a Senior Professor and a Ph.D.Adviser with the School of TelecommunicationsEngineering. He is currently the Director of the KeyLaboratory in Wireless Communications Sponsoredby China Ministry of Information Technology, aKey Member of the State Key Laboratory of

Integrated Services Networks, one of the State Government SpeciallyCompensated Scientists and Engineers, a Field Leader in telecommunica-tions and information systems with Xidian University, and the AssociateDirector for National 111 Project. He has recently published 78 papers intelecommunications journals and proceedings. His current research interestsinclude key transmission technologies and standards on broadband wirelesscommunications for 4G, 5G, and next generation broadband wireless accesssystems.

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Power Allocation in Cognitive Satellite-Vehicular Networks ......channel fading and extend the satellite coverage in land mobile satellite vehicular networks. These studies demonstrated