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Fog-Aided Cognitive Radio Networkswith Guard Zone and Interference Cancellation

Based Opportunistic Spectrum AccessChao Jia, Xiaoshi Song, and Xiangbo Meng

Abstract—We investigate the spatial spectrum sharing mecha-nism design in fog-aided cognitive radio (CR) networks with themethods of guard zone and interference cancellation. Particular-ly, it is assumed that the studied CR network is comprised of alibrary of multimedia files F with size F and two types of users,namely the primary and secondary users, with fog computingcapability. The primary users are authorized devices and haveprivilege to preferentially utilize the bandwidth resources. Thesecondary users, on the other hand, are unauthorized devices andcan access the spectrum only if the primary transmissions areunaffected. To constrain the unintended secondary interferenceat the active primary receivers (PRs) while enhance the spectrumaccessibility of the secondary users, the guard zone and inter-ference cancellation based opportunistic spectrum access (GZ-ICOSA) protocol is proposed and analyzed. Under the GZ-IC OSAprotocol, by exploiting the cached content as side information, thef -th file sent by a secondary transmitter (ST) can be effectivelycancelled at the unintended active PRs which cache the samefile. As such, under the GZ-IC OSA protocol, a ST is allowedto transmit the f -th file in F as long as it is outside the unionof the guard zones of all active PRs which cache other filesexcept the f -th file. Assuming decentralized probabilistic caching,under the GZ-IC OSA protocol, we derive the first-order momentmeasure of the access probabilities of primary transmitters (PTs)and STs, respectively. Further, we capture the conditional spatialdistributions of active PTs and STs as piecewise functions withrespect to the radius Rd of the guard zone. Finally, we evaluatethe performance of the proposed GZ-IC OSA protocol in termsof coverage performance and spatial throughput based on thederived conditional spatial distributions.

Index Terms—Fog-aided CR networks, interference cancella-tion, guard zone, opportunistic spectrum access, side information,coverage probability, cache-hit probability, spatial throughput.

I. INTRODUCTION

The rapid growth of smartphone devices and the resultantexplosive demands for bandwidth-hungry multimedia servicesare considered to be the main inducements of the foreseeablecapacity crunch of the next generation 5G systems in thenear future [1]. Particularly, according to Cisco’s annual report[2], the predictions are that the number of mobile deviceslinked to the network will be over 7 billion in 2021 with

This work is supported by the National Natural Science Foundation ofChina under Grants 61701102, 61871107, 61701100, 61501105, and theMajor Research Project for Undergraduate Students of Northeastern Universityin 2017 under Grant ZD1714.

Chao Jia, Xiaoshi Song, and Xiangbo Meng are with the School ofComputer Science and Engineering, Northeastern University, Shenyang, Chi-na, 110819. The corresponding author is Xiaoshi Song (email: songxi-aoshi@cse.neu.edu.cn).

Chao Jia and Xiaoshi Song contributed equally to this work.

the corresponding global data traffic reaching 49 exabytes permonth. As such, one most critical research issue facing byboth the academia and industry is to find disruptive techniquesand innovative architectures such that the above mentionedimpeding mobile data tsunami is effectively addressed.

Cognitive radio (CR), first introduced by Dr. J. Mitola, iswidely believed as an effective technique to enhance the spec-trum efficiency and boost the network throughput of the nextgeneration 5G systems [3]. The fundamental design principleof CR is to endow the mobile devices with the capability ofsensing and analyzing the surrounding radio environment suchthat they can dynamically adjust the transmission strategiesaccordingly and thus improve the utilization of limited yetunder-utilized network resources. With significant develop-ments in the past few years, the CR functionality can beflexibly integrated into various wireless networking paradigmsof 5G system (e.g., D2D communication networks, M2Mcommunication networks [4], V2X communication networks[5], and unmanned aerial vehicle networks [6]) and facilitatea vast amount of sensing based applications.

To further enhance the network performance, fog computingbased wireless caching has recently emerged as an importanttechnology for 5G and 5G beyond systems [7]–[11]. Particu-larly, by maintaining a cache of popular multimedia content atthe wireless edge, e.g. small-cell access points or even hand-held smart devices, fog computing based wireless caching caneffectively offload the redundant traffic at the congested macrobase stations and thereby significantly improves the delayexperience of the end user.

It is worth noting that the CR technology can only alleviatethe traffic congestions over the air, but fails to reduce thestrain on the limited backhaul. Instead, fog computing basedwireless caching can be applied to relieve the heavy burden atthe backhaul. As such, the benefits of CR and fog computingbased wireless caching can be effectively combined. In thispaper, due to such great potentials on enhancing the networkspectrum efficiency, we incorporate the approach of fog com-puting based wireless caching into CR paradigms and expectto achieve a even better network performance. Particularly,we study a fog-aided CR network comprised of a library Fof multimedia files. To protect the primary transmissions fromunintended secondary interference while enhance the spectrumaccessibility of secondary users, a novel OSA protocol, namelythe guard zone and interference cancellation based opportunis-tic spectrum access (GZ-IC OSA) protocol, is proposed. Underthe GZ-IC OSA protocol, by exploiting the cached content as

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side information, the f -th file sent by a secondary transmitter(ST) can be effectively cancelled at the active unintended PRswhich cache the same file. As such, under the GZ-IC OSAprotocol, a ST is allowed to transmit the f -th file in F aslong as it is outside the union of the guard zones of all activePRs which cache other files except the f -th file. Intuitively, theproposed GZ-IC OSA protocol elaborately utilizes the cachedcontent and interference cancellation technique to create “man-made” spectrum holes, and thereby can significantly improvethe spatial reuse gain of the secondary network without suffer-ing a considerable performance loss of the primary network.In the following, related works on CR and wireless cachingare presented. Then, we summarize the main contributions ofthis article.

A. Related Works

There have been tremendous research efforts on the mech-anism design of OSA in CR networks [12]–[18] and fogcomputing based wireless caching in 5G RANs [19]–[30],respectively. Particularly, for the study of spectrum sharingin CR networks, in [12] and [13], the authors utilized themulti-armed bandit approach to model the multi-channel OSAproblem and developed decentralized online learning policiesto minimize the system regret. In [14], under the paradigmof CR based VANET, the OSA of STs was studied based onthe framework of game theory. In [15] and [16], the authorsformulated the OSA design problems as partially observableMarkov decision process (POMDP) problems and based onwhich maximize the secondary user’s expected reward orthroughput over a finite horizon. In [17] and [18], the au-thors investigated the signal-strength dependent and distance-dependent OSA protocols in the spatial domain and evaluatedthe successful transmission performance of the CR network.

For the study of fog computing based wireless caching in 5GRANs, in [19]–[21], the authors evaluated the asymptotic per-node throughput capacity of cache-enabled D2D networks. In[22], Song et al. investigated the contention based multimediadeliver strategy in cache-enabled D2D networks. In [23] and[24], the authors considered the content caching at smallcell access points and derived the optimal solutions of thecorresponding content placement problems. In [25]–[28], byassuming that the locations of D2D users follow the Poissoncluster process, cluster-centric content caching policies wereinvestigated based on stochastic geometry to improve theperformance of the cache-enabled D2D networks. In [29] and[30], under the paradigm of heterogeneous networks (HetNet),collaborative multi-tier caching strategies were investigatedto boost the overall throughput by taking the key networkparameters into consideration.

It is worth noting that for the above mentioned relatedworks, neither [12]–[18] nor [19]–[30] considered applyingfog computing based wireless caching in CR networks tosimultaneously obtain the gains of spectrum reuse and edgecaching. To address this issue, several attempts [31]-[34]have been made on the joint design of OSA and wirelesscaching in CR networks. Particularly, in [31], Si et al. in-vestigated the proactive caching of popular video contents

over harvested bands to maximize the spectrum utilizationefficiency in information-centric CR networks. In [32], Zhaoet al. developed the caching techniques in CR networks tosatisfy the delay constraints of secondary transmissions. In[33] and [34], cooperative caching strategies were consideredin CR networks, under which the unlicensed secondary basestations were designed to provide content delivery servicesfor primary users and in exchange obtained more transmissionopportunities.

B. Key Contributions

In this paper, different from [32]-[33], the techniques ofguard zones and interference cancellation are utilized to im-prove the content delivery performance of the fog-aided CRnetworks. We summarize the main technical contributions ofour paper as follows:

• We consider a fog-aided CR network comprised of alibrary F with F files. The primary and secondary usersare modeled as homogeneous Poisson point processes(HPPPs) for the characterization of the spatial averageperformance of the fog-aided CR network. To protectthe active PRs from unintended secondary interferencewhile enhance the spectrum accessibility of the secondaryusers, the GZ-IC OSA protocol is proposed. Particularly,under the GZ-IC OSA protocol, by exploiting the cachedcontent as side information, the f -th file sent by a STcan be effectively cancelled at the active unintended PRswhich cache the same file. As such, under the GZ-IC OSAprotocol, a ST is allowed to transmit the f -th file in Fas long as it is outside the union of the guard zones ofall active PRs which cache other files except the f -th filein F . The GZ-IC OSA protocol thereby can significantlyimprove the spatial reuse gain of the secondary networkwithout suffering a considerable performance loss of theprimary network.

• Under the assumption of decentralized probabilisticcaching, the access probabilities of PTs and STs with theGZ-IC OSA protocol are derived based on the cache-hitanalysis. Further, with the derived access probabilities,we capture the conditional spatial density of active PTsand STs as piecewise functions related to the radius Rd ofthe guard zone. Finally, we evaluate the performance ofthe proposed GZ-IC OSA protocol in terms of coverageprobability and spatial throughput of the fog-aided CRnetwork.

• By numerical simulations, we verify the derived analyti-cal results and illustrate the benefit of the proposed GZ-IC OSA protocol. We also compare the proposed GZ-IC OSA protocol with the exclusive-region only scheme.Particularly, it is shown by the numerical results that theGZ-IC OSA protocol achieves a better performance gainover the guard zone only scheme. It is believed that theoutput of this work may enlighten the design of CR basedoffloading of mobile data streaming from macro basestations to wireless edge access points or D2D nodes infuture wireless networks.

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This paper is organized as follows. We present the networkmodel and the GZ-IC OSA protocol in Section II. In SectionIII, we define the cache-hit probability and based on whichcharacterize the access probability of primary and secondaryusers. In Section IV and V, we capture the conditional spatialdensity of active PTs and STs, and evaluate the performance ofthe proposed GZ-IC OSA protocol in terms of coverage prob-ability and spatial throughput of the fog-aided CR network.Simulation results, performance comparisons, and discussionsare provided in Section VI. Finally, Section VII concludes thepaper.

We summarize the notations of selected symbols in Ta-ble I-B.

Symbol NotationSymbol Meaningµfa , µ

fa Density of active PRs caching the f -th file/caching

other file except the f -th file in Fqf , qf The probability that the request from a PR can not be

served locally but only be served by its respective PTα Path-loss exponentγ Zipf parameterPp, Ps Transmission power of PTs, STsF File libraryF Size of file library Fpf Probability that receivers request for file fcf Probability that transmitters/receivers cache file fRd The radius of the guard zoneθp, θs SIR target for the primary, secondary networkQe Access probability for STs under GZ-IC OSA protocolλe Density of active STs under GZ-IC OSA protocolλfe , λ

fe Density of active STs which transmit the f -th file/other

file except the f -th file under GZ-IC OSA protocolRp,Tp Typical active PR, PTRs,Ts Typical active SR, STΦx

e (r) Point process formed by the active STs on a circleof radius r centered at location x ∈ R2 underGZ-IC OSA protocol

Ψxe (r) Point process formed by the active PRs on a circle

of radius r centered at location x ∈ R2 underGZ-IC OSA protocol

Υxe (r) Point process formed by the active PTs on a circle

of radius r centered at location x ∈ R2underGZ-IC OSA protocol

λxe (r) Density of Φxe (r)

ψxe (r) Density of Ψx

e (r)υxe (r) Density of Υx

e (r)

Cfp , Cfs Coverage probability for the primary/secondary network withrespect to file f under GZ-IC OSA protocol

τp, τs Spatial throughput for the primary/secondary networkunder GZ-IC OSA protocol

II. NETWORK MODEL

In this paper, we consider a fog-aided CR network com-prised of a library F of F equal-sized files. The primaryand secondary users are assumed to have fog computingcapability and modeled as HPPPs for the characterization ofthe spatial average performance of the fog-aided CR network.Particularly, the PTs and STs are assumed to be distributed onR2 according to two independent HPPPs of intensities µp andλ0, respectively, with the corresponding transmit power givenby Pp and Ps. Further, the distance between each PT-PR/ST-SR pair is given by dp or ds.

We consider Rayleigh fading channels and denote the cor-responding power gain as h ∼ exp(1). Then, for an arbitrarylocation x ∈ R2, the received power of the signal sent froma PT or ST at location y is given by Pph|y − x|−α orPsh|y−x|−α, where |y−x|−α denotes the propagation pathloss with exponent α ≥ 2.

The popularity of the f -ranked file1 is modeled by the Zipfdistribution [21] as

pf =1/fγ

ΣFj=11/jγ, (1)

with the shape parameter γ ≥ 0 reflecting the skewness.Further, we consider the decentralized probabilistic cachingstrategy [35] for both primary and secondary users, and denotethe corresponding caching probability of the f -ranked file ascf , where

∑Ff=1 cf = 1. Throughout this paper, we assume

that the cache memory of each PT/ST and PR/SR is M = 1file2. Further, we restrict our analysis to the case that a requestfrom an arbitrary PR/SR can be served either locally or by itsrespective PT/ST, but no one else.

For the primary network, if the content requested by thePR is not cached locally but found at its respective PT, thetagged PT-PR pair is then allowed to utilize the spectrumfor data transmission. For the secondary network, to protectthe primary transmissions from the unintended secondaryinterference while enhance the spectrum accessibility of thesecondary users, the GZ-IC OSA protocol is proposed, whichis described in details as follows.• GZ-IC OSA Protocol: In this protocol, each active PR

is assumed to broadcast a unique beacon signal on adedicated control channel to indicate the correspondingcaching status at the beginning of each time slot. Underthe assumption of perfect CR sensing, the STs are thenable to identify the beacon signals sent from differentPRs and retrieve the corresponding content caching in-formation. Further, it is assumed that the locations of thePRs are known as a priori to STs. To protect the primarytransmissions, guard zones of radius Rd around the PRsare employed. Particularly, if the tagged ST is outsidethe union of the guard zones of all PRs, it can directlyaccess the spectrum. Otherwise, let B denote the set ofthe corresponding potentially interfered PRs (i.e., the PRswith the guard zones covering the tagged ST). Then, withthe technique of interference cancellation, the tagged STis allowed to access the spectrum only if the file it intendsto send is cached at the local storage of all PRs in B. Wecall this OSA protocol the “Guard Zone and InterferenceCancellation Based Opportunistic Spectrum Access (GZ-IC OSA)” protocol.

Particularly, under the GZ-IC OSA protocol, by exploitingthe cached content as side information, the f -th file sent by aST can be effectively cancelled at the unintended active PRswhich cache the same file. As such, under the GZ-IC OSA

1Throughout this paper, with an abuse of notation, we assume that ‘thef-ranked file’ has the same meaning as ‘the f-the file’ and ‘file f’.

2It is worth noting that though we simply consider the case of M = 1 inthis paper, by applying a similar approach, our analysis can be easily extendedto the general case of M ≥ 1.

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protocol, a ST is allowed to transmit an arbitrary file f aslong as it is outside the union of the guard zones of all activePRs which cache other files except file f .

III. ACCESS PROBABILITY

In this section, we evaluate the access probability of PTs andSTs, respectively, under the GZ-IC OSA protocol. Particularly,for the primary network, to derive the access probability ofPTs, we first consider two types of PRs, i.e., the PRs whichcache file f , and the PRs which cache other files except filef . Let qf and q̄f be the nonlocal cache-hit probabilities (i.e.,the probability that the request from a PR can not be servedlocally but only be served by its respective PT) of the firstand second types of PRs, respectively. Then, we characterizeqf and q̄f as follows.

Lemma 3.1: Under the GZ-IC OSA protocol, the nonlocalcache-hit probabilities qf and q̄f are given by

qf = cf

F∑i=1,i6=f

cipi, (2)

and

q̄f =

F∑j=1,j 6=f

qj , (3)

respectively.Proof: Given pf and cf , (2) and (3) can be immediately

obtained.Remark 3.1: Let qc denote the average nonlocal cache-hit

probability of PRs. Then, it can be easily verified that

qc =

F∑f=1

qf . (4)

Remark 3.2: Based on Remark 3.1, the access probabilityof PTs is then given by the cache hit probability qc.

Let Ψfp and Ψ

f

p denote the sets of active PRs of the first typeand second type, respectively. Then, based on Lemmas 3.1,the spatial distributions of Ψf

p and Ψf

p are characterized in thefollowing corollary.

Corollary 3.1: Ψfp and Ψ

f

p follow two independent HPPPswith respective densities µfa and µfa given by

µfa = µp · qf , (5)

andµfa = µp · q̄f , (6)

respectively.Proof: Based on Lemma 3.1, (5) and (6) can be imme-

diately obtained by independent thinning of HPPP.Remark 3.3: Let Ψp denote the set of all active PRs. Then,

it can be easily verified from Corollary 3.1 that Ψp = Ψfp∪Ψ

f

p

follows a HPPP with density µa given by

µa = µfa + µfa

= µp ·F∑f=1

qf

= µp · qc. (7)

For the secondary network, let Qfe denote the access prob-ability that the STs (which cache the file f ) are able tolaunch the transmission of the f -ranked content and serve therequests of their associated SRs. Based on Lemma 3.1 andCorollary 3.1, we characterize Qfe as follows.

Lemma 3.2: The access probability Qfe of STs which cachethe file f under the GZ-IC OSA protocol is given by

Qfe = e−µ̄faπR

2d · ζf , (8)

whereζf = cf (1− cf )pf . (9)

Proof: According to the GZ-IC OSA protocol, a ST whichcaches the f -ranked file can initiate the content delivery onlyif it is outside the guard zones of all active PRs which cacheother files except file f and its associate SR (which does notcache file f ) requests the file f . Based on this fact, by notingthat the density of active PRs which cache other files exceptfile f is µfa , (8) is derived.

Remark 3.4: We denote Φfe as the point process formed bythe active STs which transmit the f -ranked file under the GZ-IC OSA protocol. Further, we denote λfe as the density of Φfe .Then, from Lemma 3.2, we can obtain that λfe = λ0Q

fe .

Let Qe denote the average access probability of STs. Then,Qe is derived in the following theorem by using Lemma 3.2.

Theorem 3.1: The access probability Qe for STs under theproposed GZ-IC OSA protocol is given by

Qe =

F∑f=1

e−µ̄faπR

2d · ζf . (10)

Proof: With Lemma 3.2, (10) can be immediately ob-tained based on the fact that Qe =

∑Ff=1Q

fe .

Remark 3.5: We denote Φe as the point process formed bythe active STs under the GZ-IC OSA protocol. Further, wedenote λe as the density of Φe. Then, from Theorem 3.1, wecan obtain that λe = λ0Qe.

Remark 3.6: Let Φf

e denote the point process formed by theactive STs which cache other files except the f -th files underthe GZ-IC OSA protocol. Further, let λ

f

e denote the densityof Φ

f

e . Then, based on Remarks 3.4 and 3.5, λf

e = λe − λfe .Remark 3.7: Under the proposed GZ-IC OSA protocol, the

access of the spectrum of nearby STs are dependent. As such,Φe, Φfe , and Φ

f

e do not follow HPPPs.Based on the derived access probability of PTs and STs, we

evaluate the performance of the proposed GZ-IC OSA protocolin terms of coverage probability in the following two sections.

IV. COVERAGE PERFORMANCE IN PRIMARY NETWORK

We define the coverage probability Cp of the primarynetwork as

Cp = Pr {SIRp ≥ θp} , (11)

where SIRp denotes the received signal-to-interference ratio(SIR) at the tagged PR and θp denotes the SIR target. Toanalyze τp, without loss of generality, a typical PR denotedby Rp is placed at the origin of the Euclidean plain. Further,

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the associated PT of Rp, which is denoted by Tp, is placedat dp away from the origin.

For the primary network, by Slivnyaks theorem [36], theconditional spatial distribution of the active PRs/PTs remainsas that of Ψp. For the secondary network, we focus on thecircle of radius r centered at the origin and denote Φ

Rpe (r)

as the point process formed by the active STs on this circle.Then, conditioned on that Rp caches the f -th file, we derivethe density λRp

e (r) of ΦRpe (r) in the following lemma.

Lemma 4.1: Conditioned on that Rp caches the f -th file,λRpe (r) is given by

λRpe (r) =

{λfe , r ≤ Rd,λe, r > Rd.

(12)

Proof: Under the GZ-IC OSA protocol, for STs outsidethe circle of radius r centered at the origin, their averageaccess probability follows directly from Theorem 3.1 and isthereby given by Qe. On the other hand, for STs inside thecircle of radius r centered at the origin, due to the fact thatRp caches the f -th file, only the one which is requested totransmit the f -th file and outside the guard zones of Ψ

f

p canperform the content delivery. Based on this fact, according toLemma 3.2, the corresponding probability is given by Qfe . Assuch, λRp

e (r) = λ0Qfe for r ≤ Rd and λ

Rpe (r) = λ0Qe for

r > Rd.Obviously, due to the fact that the access of nearby STs in

ΦRpe (r) may be dependent, Φ

Rpe (r) is not a HPPP. As such,

for the tractability of Cp, we approximate ΦRpe (r) as a HPPP

and derive the coverage performance Cfp of the typical PRwhich caches the f -ranked content in F as follows.

Theorem 4.1: Conditioned on that Rp caches the f -rankedfile, under the HPPP assumption of Φ

Rpe (r), Cfp is given by

Cfp = exp

{− 2π2

α sin(

2πα

)µaθ 2αp d

2p

}

× exp

−2π

∫ ∞Rd

λf

e

1 +Pprα

θpPsdαp

rdr

. (13)

Proof: See Appendix A.Based on Theorem 4.1, we then obtain Cp in following

corollary.Corollary 4.1: Conditioned on that Rp caches the f -ranked

file, under the HPPP assumption of ΦRpe (r), Cp is given by

Cp =

F∑f=1

qf × exp

{− 2π2

α sin(

2πα

)µaθ 2αp d

2p

}

× exp

−2π

∫ ∞Rd

λf

e

1 +Pprα

θpPsdαp

rdr

. (14)

Proof: With Lemma 3.1 and (13), (14) is immediatelyobtained.

Remark 4.1: Let τp denote the spatial throughput of theprimary network with the GZ-IC OSA protocol. Then, based

on Theorem 4.1, τp is given by

τp =

F∑f=1

(µfa · Cfp + cf · pf · µp

), (15)

whereF∑f=1

cf · pf · µp denotes the spatial throughput of the

PRs which can serve the requests locally.

V. COVERAGE PROBABILITY IN SECONDARY NETWORK

We define the coverage probability Cs of the secondarynetwork as

Cs = Pr {SIRs ≥ θs} , (16)

where SIRs denotes the received SIR at the tagged SR and θsdenotes the SIR target. To analyze τs, similar as the primarynetwork case, a typical SR denoted by Rs is placed at theorigin of the Euclidean plain. Further, the associated ST ofRs, which is denoted by Ts, is placed at ds away from theorigin.

For the primary network, we first focus on the circle ofradius r centered at the origin and denote ΨTs

e (r) as thepoint process formed by the active PRs on this circle. Then,conditioned on that Ts is delivering the f -ranked content, wederive the density ψTs

e (r) of ΨTse (r) in the following lemma.

Lemma 5.1: Conditioned on that Ts is delivering the f -ranked content, ΨTs

e (r) is a HPPP with density ψTse (r) given

by

ψTse (r) =

{µfa , r ≤ Rd,µa, r > Rd.

(17)

Proof: Conditioned on that Ts is transmitting the f -thfile, a PR within the guard zone of Ts is active only if itcaches the same file as the typical ST transmits, such that theinterference from Ts can be effectively cancelled. Due to thisfact, the density of active PRs within a distance of Rd fromTs is µfa . On the other hand, for PRs outside the circle ofradius Rd centered at Ts, their activation does not affected bythe typical ST. As such, the corresponding density is given byµa. This thus obtains the piece-wise density function given by(17).

Based on ΨTse (r), we aim to characterize the conditional

spatial distribution of the active PTs. Particularly, we denoteΥTse (r) as point process of the active PTs on the same circle

as ΨTse (r) and denote υTse (r) as the corresponding density.

Then, with (17), we derive υTse (r) as follows.Lemma 5.2: Conditioned on that Ts is delivering the f -

ranked content, ΥTse (r) is HPPP with its density υTse (r) given

by {µa ≥ υTse (r) ≥ µfa , r ≤ Rd + dp,

υTse (r) = µa, r > Rd + dp.(18)

Proof: According to Lemma 5.1, conditioned on that Ts

is delivering the f -ranked content, for r ≤ Rd + dp, υTse (r)is upper and lower bounded by µa ≥ υTse (r) ≥ µfa . Further,for r ≥ Rd + dp, υTse (r) = µa is obtained based on the factthat ψTs

e (r) = µa for r ≥ Rd.With ΥTs

e (r), we further consider the conditional spatialdistribution of active PTs around Rs. Particularly, we focus

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on the circle of radius r centered at Rs and denote ΥRse (u) as

the active PTs on this circle. Further, by noting that ΥRse (u)

is a non-HPPP, we denote υRse (u) as the average intensity of

ΥRse (u). Then, we derive υRs

e (u) as follows.Lemma 5.3: Conditioned on that Ts is delivering the f -

ranked content, υRs(u) is given by{µa ≥ υRs

e (u) ≥ µfa , u ≤ Rd + dp + ds,

υRse (u) = µa, u > Rd + dp + ds.

(19)

Proof: (19) is immediately obtained by applying Lem-ma 5.2 and the fact that the distance between Rs and Ts isds.

For the secondary network, we focus on the active STs on acircle of radius r centered at Rs and denote the correspondingpoint process as ΦRs

e (r). Similar as ΥRse (u), ΦRs

e (r) is nota HPPP. Let λRs

e (r) denote the average density of ΦRse (r).

Then, conditioned on that Ts is delivering the f -rankedcontent, we derive the average density λRs

e (r) as follows.Lemma 5.4: Conditioned on that Ts is delivering the f -

ranked content, λRse (r) is given by{

λe ≥ λRse (r) ≥ λfe , r ≤ 2Rd + ds,

λRse (r) = λe, r > 2Rd + ds.

(20)

Proof: Conditioned on that Ts is delivering the f -rankedcontent, according to Lemma 5.1, the access probability ofSTs is bounded between Qe and Qfe for r ≤ 2Rd + ds. Assuch, λe ≥ λRs

e (r) ≥ λfe for r ≤ 2Rd + ds. On the otherhand, for r > 2Rd + ds, the access probability of STs equalsto Qe. Therefore, λRs

e (r) = λfe for r > 2Rd+ds. (20) is thusobtained.

For the same reason as discussed in the primary networkcase, ΦRs

e (r) is not a HPPP. Then, to obtain tractable analyticalresults of Cfs , we approximate ΦRs

e (r) as a HPPP. Based onthis approximation, conditioned on that Ts is delivering thef -ranked content, we evaluate the coverage performance Cfsof Rs in the following theorem.

Theorem 5.1: Conditioned on that Ts is delivering the f -ranked content, under the HPPP assumption of ΦRs

e (r), Cfs isupper and lower bounded by

Cfs ≤ exp

{−2π

∫ Rd+dp+ds

0

µfa1 + Psrα

θsPpdαs

rdr

}

× exp

{−2π

∫ 2Rd+ds

0

λfe1 + rα

θsdαs

rdr

}

× exp

{−2π

∫ ∞Rd+dp+ds

µa

1 + Psrα

θsPpdαs

rdr

}

× exp

{−2π

∫ ∞2Rd+ds

λe1 + rα

θsdαs

rdr

}, (21)

and

Cfs ≥ exp

{− 2π2

α sin(

2πα

) (µa(PpPs

) 2α

+ λe

)θ

2αs d

2s

}, (22)

respectively.Proof: See Appendix B.

With Theorem 5.1, we then obtain Cs in following corollary.

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����

����

���

�

�

Acces

s Prob

ability

of ST

s

��

R d = 1 A n a l y t i c a l R d = 1 S i m u l a t i o n R d = 1 . 5 A n a l y t i c a l R d = 1 . 5 S i m u l a t i o n R d = 2 A n a l y t i c a l R d = 2 S i m u l a t i o n

Fig. 1. Access probability in fog-aided CR network under the GZ-IC OSAprotocol.

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0 0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8

0 . 1 0

0 . 1 2

0 . 1 4

0 . 1 6

0 . 1 8

0 . 2 0 λ 0 = 0 . 1 G Z - I C O S A P r o t o c o l A p p r o x i m a t i o n λ 0 = 0 . 1 G Z - I C O S A P r o t o c o l S i m u l a t i o n λ 0 = 0 . 2 G Z - I C O S A P r o t o c o l A p p r o x i m a t i o n λ 0 = 0 . 2 G Z - I C O S A P r o t o c o l S i m u l a t i o n

�

�

Cover

age Pr

obabil

ity of

Prim

ary Ne

twork

� p

Fig. 2. Cp for λ0 = 0.1 and 0.2, respectively.

Corollary 5.1: Conditioned on that Ts is delivering the f -ranked content, under the HPPP assumption of ΦRs

e (r), Cs isupper and lower bounded by

Cs ≤F∑f=1

Qfe × exp

{−2π

∫ Rd+dp+ds

0

µfa1 + Psrα

θsPpdαs

rdr

}

× exp

{−2π

∫ 2Rd+ds

0

λfe1 + rα

θsdαs

rdr

}

× exp

{−2π

∫ ∞Rd+dp+ds

µa

1 + Psrα

θsPpdαs

rdr

}

× exp

{−2π

∫ ∞2Rd+ds

λe1 + rα

θsdαs

rdr

},

(23)

and

Cs ≥F∑f=1

Qfe × exp

{− 2π2θ

2αs d2

s

α sin(

2πα

) (µa(PpPs

)2α

+λe

)}, (24)

respectively.

7

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0 0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8

0 . 1 0

0 . 1 2 G Z - I C O S A P r o t o c o l U p p e r B o u n d ( A p p r o x i m a t i o n ) G Z - I C O S A P r o t o c o l L o w e r B o u n d ( A p p r o x i m a t i o n ) G Z - I C O S A P r o t o c o l S i m u l a t i o n

�

�

Cover

age Pr

obabil

ity of

Secon

dary N

etwork

� p

(a) λ0 = 0.1

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0 0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8 G Z - I C O S A P r o t o c o l U p p e r B o u n d ( A p p r o x i m a t i o n ) G Z - I C O S A P r o t o c o l L o w e r B o u n d ( A p p r o x i m a t i o n ) G Z - I C O S A P r o t o c o l S i m u l a t i o n

�

�

Cover

age Pr

obabil

ity of

Secon

dary N

etwork

� p

(b) λ0 = 0.2

Fig. 3. Cs for λ0 = 0.1 and 0.2, respectively.

Proof: With Lemma 3.2 and Theorem 5.1, (23) and (24)are immediately obtained.

Remark 5.1: Let τs denote the spatial throughput of thesecondary network with the GZ-IC OSA protocol. Then, basedon Theorem 5.1, τs is given by

τs = λ0

F∑f=1

(Qfe · Cfs + cf · pf

),

where λ0

F∑f=1

cf ·pf denotes the spatial throughput of the SRs

which can sever their requests locally.

VI. NUMERICAL RESULTS

In this section, we validate our derived analytical results andillustrate the benefit of the proposed GZ-IC OSA protocol bymeans of extensive simulations. We assume that the simula-tion results are obtained by averaging over 10,000 realizationsof the CR networks over the spatial domain. Particularly,in each realization, a set of locations of the primary andsecondary users is independently and uniformly generated in

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0 0 0

0 . 0 0 2

0 . 0 0 4

0 . 0 0 6

0 . 0 0 8

0 . 0 1 0

0 . 0 1 2 λ 0 = 0 . 1 G Z - I C O S A P r o t o c o l S i m u l a t i o n λ 0 = 0 . 1 G Z o n l y S i m u l a t i o n λ 0 = 0 . 2 G Z - I C O S A P r o t o c o l S i m u l a t i o n λ 0 = 0 . 2 G Z o n l y S i m u l a t i o n

�

�

Spatia

l Thro

ughput

of Pr

imary

Netwo

rk

� p

Fig. 4. Simulated values of τp under the GZ-IC OSA or GZ only protocol,for λ0 = 0.1 and 0.2, respectively.

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 00 . 0 0 0

0 . 0 0 2

0 . 0 0 4

0 . 0 0 6

0 . 0 0 8

0 . 0 1 0

�

�

Spatia

l Thro

ughput

of Se

condar

y Netw

ork

� p

λ 0 = 0 . 1 G Z - I C O S A P r o t o c o l S i m u l a t i o n λ 0 = 0 . 1 G Z o n l y S i m u l a t i o n λ 0 = 0 . 2 G Z - I C O S A P r o t o c o l S i m u l a t i o n λ 0 = 0 . 2 G Z o n l y S i m u l a t i o n

Fig. 5. Simulated values of τs under the GZ-IC OSA or GZ only protocol,for λ0 = 0.1 and 0.2, respectively.

a circular area of radius 100 m centered at the origin. Further,for each realization, we conduct 10,000 independent trials overthe time domain to simulate the effects of random channelpower coefficients and user requests. In the following, unlessspecified otherwise, the parameters of the simulations aregiven as follows: F = 5, Pp = 5 W, Ps = 2 W, dp = ds = 2m, θp = θs = 3, Rd = 1 m, α = 4, and cf = pf .

The average access probability Qe of STs is illustrated inFig. 1, when Rd =1, 1.5, and 2, respectively. Particularly,the theoretical and simulation plots of Qe presented in Fig. 1validate the accuracy of our analysis given by Theorem 3.1.Fig. 1 also shows that the access probability of STs with GZ-IC OSA protocol is a decreasing function with respect to µp aswell as Rd. Intuitively, this is because that the increase of µpand/or Rd will reduce the available spatial spectrum resourcesfor the secondary network.

Figs. 2 and 3 plot Cp and Cs of the fog-aided CR network,respectively, when λ0 = 0.1 and 0.2. It is observed fromFigs. 2 and 3 that the analytical results of Cp and Cs derivedin Corollaries 4.1 and 5.1 are valid, which thereby indicates

8

that the HPPP approximations on ΦRpe (r) and ΦRs

e (r) areeffective.

Figs. 4, 5, and 6 compare the performance of the proposedGZ-IC OSA protocol with the guard zone (GZ) only protocolin terms of spatial throughput. Particularly, Fig. 4 plots thesimulated value of τp under the GZ-IC OSA protocol and theGZ only protocol, respectively, when λ0 = 0.1 and 0.2. It isshown by Fig. 4 that the GZ-IC OSA protocol outperforms theGZ only protocol with respect to τp. Intuitively, this is due tothe fact that compared with the GZ only scheme, the GZ-IC OSA protocol effectively eliminates a substantial amountof unintended secondary interference received at the PRs byutilizing the cached content as side information and therebyachieves a better performance of τp. It is also observed fromFig. 4 that τp is a concave function with respect to µp underboth schemes. Intuitively, when µp is small, τp is dominated byµp instead of Cp. Therefore, τp is an increasing function of µpwhen µp is small. On the other hand, when µp is sufficientlylarge, τp is dominated by Cp instead of µp. Notice that Cpdecreases with µp. As such, τp is a decreasing function withrespect to µp. Fig. 5 plots the simulated value of τs under theGZ-IC OSA protocol and the GZ only protocol, respectively,when λ0 = 0.1 and 0.2. Different from the case of τp, the GZonly protocol outperforms the GZ-IC OSA protocol on τs. Thisis due to the fact that compared with the GZ only protocol,the GZ-IC OSA protocol increases the access probability ofSTs which thereby intensifies the collisions in the secondarynetwork. Finally, Fig. 6 plots the simulated results of thesum spatial throughput of the fog-aided CR network, whenλ0 = 0.1 and 0.2. It is shown by Fig. 6 that the GZ-IC OSAprotocol achieves a better overall performance than the GZonly protocol.

VII. CONCLUSION

This paper investigated the spatial spectrum sharing mech-anism design in fog-aided CR networks by utilizing thetechniques of guard zone and interference cancellation. Par-ticularly, to protect the active PRs from unintended secondaryinterference while enhance the spectrum accessibility of thesecondary users, the GZ-IC OSA protocol is proposed andanalyzed. Under the GZ-IC OSA protocol, by exploiting thecached content as side information, the f -th file sent bya ST can be effectively cancelled at the unintended activePRs which cache the same file. Therefore, under the GZ-IC OSA protocol, a ST is allowed to transmit the f -rankedcontent in F as long as it is outside the union of the guardzones of all active PRs which cache other files except the f -th file. Under the assumption of decentralized probabilisticcaching, the access probabilities of PTs and STs with theGZ-IC OSA protocol are derived based on the cache-hitanalysis. Further, with the derived access probabilities, wecapture the conditional spatial density of active PTs and STs aspiecewise functions related to the radius Rd of the guard zone.Then, with the conditional spatial distribution, we evaluatethe performance of the proposed GZ-IC OSA protocol interms of coverage probability and spatial throughput of thefog-aided CR network. By numerical simulations, we verify

0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 5 0 . 3 0 0 . 3 5 0 . 4 0 0 . 4 5 0 . 5 00 . 0 0 0

0 . 0 0 3

0 . 0 0 6

0 . 0 0 9

0 . 0 1 2

0 . 0 1 5

�

�

Sum

Spatia

l Thro

ughput

of Fo

g-Aide

d CR N

etwork

� p

λ 0 = 0 . 1 G Z - I C O S A S i m u l a t i o n λ 0 = 0 . 1 G Z o n l y S i m u l a t i o n λ 0 = 0 . 2 G Z - I C O S A S i m u l a t i o n λ 0 = 0 . 2 G Z o n l y S i m u l a t i o n

Fig. 6. Simulated values of the sum spatial throughput of fog-aided CRnetwork under the GZ-IC OSA or GZ only protocol, for λ0 = 0.1 and 0.2,respectively.

the derived analytical results. We also compare the proposedGZ-IC OSA protocol with the guard zone only scheme. It isshown by the numerical results that the GZ-IC OSA protocolachieves a better performance gain over the exclusive-regiononly scheme. It is believed that the output of this work andthe analytical framework may enlighten the novel design ofCR based offloading in both academia and industry.

APPENDIX APROOF OF THEOREM 4.1

Proof: Conditioned on that Rp caches the f -ranked file,the SIR received at Rp is given as

SIRp =Pph0d

−αp∑

i∈Πp

Pphi|Xi|−α +∑j∈Πs

Psgj |Yj |−α. (25)

where Πp and Πs denote the set of active PTs and STs, h0, hiand gj are independently and exponentially distributed channelfading power of unit mean. Then, under the HPPP assumptionof Φ

Rpe (r), based on Lemma 4.1, Cfp is given as

Cfp = Pr {SIRp ≥ θp}

= Pr

Pph0d−αp∑

i∈Πp

Pphi|Xi|−α +∑j∈Πs

Psgj |Yj |−α≥ θp

= EX

∏i∈Πp

Eh

[e−θphi|Xi|

−α

d−αp

]× EY

∏j∈Πs

Eg

[e

−θpPsgj |Yz|−α

Ppd−αp

]= exp

{− 2π2

α sin(

2πα

)µaθ 2αp d

2p

}

× exp

−2π

∫ ∞Rd

λf

e

1 +Pprα

θpPsdαp

rdr

, (26)

9

which completes the proof.

APPENDIX BPROOF OF THEOREM 5.1

Proof: Conditioned on that Ts is delivering the f -rankedfile, the SIR received at Rs is given as

SIRs =Psg0d

−αs∑

i∈Πp

Pphi|Xi|−α +∑j∈Πs

Psgj |Yj |−α, (27)

where Πp and Πs denote the set of active PTs and STs, h0, hiand gj are independently and exponentially distributed channelfading power of unit mean. Then, under the HPPP assumptionof ΦRs

e (r), Cfs is given by

Cfs = Pr {SIRs ≥ θs}

= exp

{−2π

∫ ∞0

υRse (r)

1 + rα

θsdαs

rdr

}

× exp

{−2π

∫ ∞0

λRse (r)

1 + Psrα

θsPpdαs

rdr

}. (28)

By applying Lemma 5.2 and 5.4 to (28), we obtain thelower and upper bounds on Cfs as given by (21) and (22),respectively.

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Chao Jia is currently an undergraduate student withthe School of Computer Science and Engineering,Northeastern University, Shenyang, China. His re-search interests include stochastic geometry and itsapplication in wireless caching networks.

Xiaoshi Song (S’08-M’14) received the B.E. degreein electrical engineering from Dalian University ofTechnology, Dalian, China, in 2008, and the Ph.D.degree in information and communication engineer-ing from Beijing University of Posts and Telecom-munications, Beijing, China, in 2014. Since 2014,he has joined the School of Computer Science andEngineering of Northeastern University, Shenyang,China, as an Assistant Professor. He was a visitingPh. D student at the University of California, Irvine,USA, from 2011 to 2013, and a visiting scholar

at the University of Hong Kong, Hong Kong, China, from July 2014 toOct. 2014. He has served as the peer reviewer for IEEE Wireless Com-munications Magazine, IEEE Journal on Selected Areas in Communications,IEEE Transactions on Wireless Communications, and IEEE Transactions onCommunications. His research interests include stochastic geometry and itsapplications in large-scale wireless networks, multiuser information theory,and wireless communication.

Xiangbo Meng received the B.E. degree in commu-nication engineering from Northeastern University,Shenyang, China, in 2018. He is now pursuing hisPh. D degree at the University of Notre Dame, USA.His research interests include stochastic geometry,cognitive radio networks, and energy harvesting.