Non-Intrusive Cognitive Radio Networks based onSmart Antenna Technology

Senhua Huang, Zhi Ding, and Xin LiuUniversity of California Davis

Davis, CA 95616, USAEmail: senhua@ece.ucdavis.edu

Abstract—Cognitive radio has recently been identified as a po-tential relief to spectrum scarcity by improving temporal spectralefficiency. We investigate a flexible non-intrusive cognitive radionetwork based on smart antenna technologies. The proposedscheme exploits transmit beamforming to enable better spectralsharing between primary users and cognitive (secondary) users.As proposed, the cognitive transmitter equipped with antennaarray forms transmit beamforming to keep the interference toprimary receiver below a given threshold. By also adopting smartantennas at primary transmitters, we can significantly boost thesuccessful transmission probability of cognitive users; therebyimproving the spectrum utilization efficiency of the wirelesscommunication networks. 1

I. INTRODUCTION

The rapid growth of wireless technologies and applicationshas made radio spectrum an increasingly scarce commodity.The need for higher spectral efficiency has attracted extensiveresearch interests. At the same time, according to measurementresults reported [1], [2], a large proportion of the licensedspectrum remain mostly unused or under-utilized, indicatingthat the current spectral shortage may be partially relievedby a more flexible user access rather than the presently rigidand static spectral allocation. Cognitive radio, as a promisingtechnology, may lead to better spectral efficiency by permittingopportunistic access of licensed bands by cognitive users whenthe primary licensees are inactive [3], [4], [5].

We have witnessed a surge of recent activities on cognitiveradio research. In [6], a sensing-based opportunistic channelaccess scheme was proposed. In [7], a cognitive approachbased on dynamic spectrum management was proposed toaccess the available spectrum in an opportunistic manner. In[8], cognitive technology is used to enable wide area networksto share the available void frequency spectrum. In [9] and[10], cognitive transmitters are modeled as decision makersthat utilize game theory to optimally control their activities.

In most existing proposals (e.g., [6], [7], [8], [9], [10]),the cognitive transmitter (CT) cannot access the spectrumsimultaneously with the primary transmitter (PT). In [11], theauthors proposed a technique similar to the Gel’fan-Pinskercoding to enable simultaneous transmission by CT and PT. Thedisadvantage of this scheme, however, is that CT must detectthe PT signal before implementing the interference-mitigating

1This work is supported in part by the National Science Foundation GrantCNS-0520126 and Grant CNS-0448613.

coding techniques. This approach would not succeed unlessthe CT is equipped with reliable primary signal detectors.

In this paper, we propose a more flexible opportunisticspectrum access scheme based on spatial diversity and smartantenna technology. The proposed non-intrusive cognitivescheme exploits the spatial void and thus can further improvethe spectral efficiency. Our goal is to jointly integrate theadvantages of cognitive radio and multiple antenna diversity.Our basic idea is that, when CT has multiple antennas, itcan construct its transmission beam pattern such that itsinterference to the primary receiver (PR) is either minimizedor constrained. Combined with transmission power control, theeffective interference to PR can be limited below a predefinedpower threshold. Meanwhile, depending on the relative loca-tion of the cognitive receiver (CR) and the PR, interferencefrom PT to CR can be very small in a large area known asthe “decodable zone”. Therefore, CT and PT can transmit totheir respective receivers with high enough SINR with highprobability when CRs are in the decodable zone.

We organize this paper as follows. We present our systemmodel and describe the problem formulation of the proposedcognitive radio system in Section II. We describe, in SectionIII, an optimal transmit beamforming algorithm that guaranteesthe spectrum access of cognitive radio to be non-intrusiveto primary users while maximizing the achievable signal tointerference and noise ratio (SINR) at the CR. In SectionIV, we use performance analysis and numerical results todemonstrate the benefit of our proposed scheme. Section Vsummarizes our work.

II. SYSTEM MODEL AND PROBLEM DESCRIPTION

We consider a scenario in which two wireless links aredeployed to coexist in a geographical region: one primarycommunication link and one (secondary) cognitive communi-cation link. The primary users are the rightful radio spectrumlicensees, while the cognitive users may have access to theprimary’s spectrum under the condition of non-intrusion. Theentire setup is illustrated in Fig. 1 in which the primarytransmitter (PT) is located at (x0, y0) while the cognitivetransmitter (CT) is located at (x1, y1). They use the samespectral band.

We further assume that PT and CT are not co-located, witha separation distance of D =

√(x0 − x1)2 + (y0 − y1)2. The

primary receiver (PR) is randomly distributed within the circle

Fig. 1. Cognitive Radio System Scheme with Smart Antenna Technology

of radius D. This means that the CT is deployed at the edge ofthe primary network. Such a case is reasonable. Often, thereis a spatial variation in the activities of the PR, i.e., in someregions, there is a low probability of PR presence. We deploythe CR in one such circular region. The CRs can be randomlydistributed in this circular region centered at (x1, y1) with a(small) radius d. Here, we use dpp, dpc, dcp and dcc to denotethe distance between PT and PR, PT and CR, CT and PR,CT and CR respectively, as shown in Fig. 1. Clearly, becauseof the constraint on its interference to the PR, the cognitivesystem cannot be arbitrarily deployed. Our goal is to determinethe region where cognitive radio can be deployed using smartantennas.

To better utilize the limited spectrum, cognitive transmitteris equipped with multiple antennas. It can therefore exploitsmart antenna technologies such as beamforming to curb itsinterference to the primary receivers. Here, we assume that theantennas used by cognitive transmitter forms a 2-D uniformcircular array (UCA) with M antenna elements. For simplicity,only azimuth angles are considered in the propagation geome-try. Assuming a relative narrow-band transmission, the antennamanifold vector of the UCA can be written as:

v(ζ) =

⎡⎢⎢⎢⎣

v1(ζ)v2(ζ)

...vM (ζ)

⎤⎥⎥⎥⎦ =

⎡⎢⎢⎢⎣

e−j2π(R/λ)cos(ζ−φ1)

e−j2π(R/λ)cos(ζ−φ2)

...e−j2π(R/λ)cos(ζ−φM )

⎤⎥⎥⎥⎦ , (1)

where R is the array radius, λ is the carrier wavelength, φ i =2πM i, i = 1, · · · , M is the angle of the antenna elements withrespect to the horizontal reference line, and ζ is the directionof transmission beam. As shown in Fig. 1, the direction ofPR with respect to PT and CT are denoted by θpp and θcp,respectively. The direction of CR with respect to PT and CTare characterized by θpc and θcc, respectively.

In this work, we only consider the path loss in the large-scale wireless channel model and denote the path loss factoras α. In addition, we focus on the downlink only and thusassume that there is only one antenna at CR and PR. Inthe non-intrusive network, the PT is not concerned about the

existence of CR and will not adapt its transmission behavior.Hence, the implementation of our cognitive radio must limitits interference to the PR. In other words, as a condition forthe cognitive users to access the primary’s spectrum, the CTmust guarantee that its interference to the PR is limited by apredefined threshold.

We use subscript ()p and ()c to denote the primary userand cognitive user, respectively. The received signals at PRand CR can be written, respectively, as

yp = hppsp + hcpsc + np

yc = hccsc + hpcsp + nc

(2)

where sp and sc are the source signals for PR and CR,respectively, while np and nc represent noises at the PR andthe CR that are white with the same power spectrum N0. Letwi, i = p, c be an M × 1 transmit beamforming vector. Thecorresponding beamforming gain in the direction of θ becomes

Gi(θ) = wHi vi(θ). (3)

Thus, channel gain for each pair of transmitter and receivercan be expressed as

hij = d−αij wH

i vi(θij) = d−αij Gi(θ), i, j = p, c. (4)

Hence, the signal to interference and noise ratio (SINR) atprimary receiver SINRp and at the cognitive receiver SINRc

can be expressed as:

SINRp =Ppd

−αpp |Gp(θpp)|2

N0 + Pcd−αcp |Gc(θcp)|2

,

SINRc =Pcd

−αcc |Gc(θcc)|2

N0 + Ppd−αpc |Gp(θpc)|2

.

(5)

Here Pp and Pc denote the transmitted powers of PT and CT,respectively, subject to the maximum power constraint.

III. NON-INTRUSIVE OPTIMAL BEAMFORMING

Because the cognitive system is non-intrusive, the primarytransmission dose not need adjustment. We consider twofixed transmission strategies at the PT: one that uses omni-directional antenna, the other that adopts the following trans-mit beamforming algorithm:

minwp

maxθpi �∈[θpp−Δθ,θpp+Δθ]

|Gp(θpi)|,subject to |Gp(θpp)| = 1

(6)

where Δθ is the designed half-power beamwidth of the trans-mit beamforming of PT. The second strategy is a beamformingalgorithm that minimizes the transmission gain outside anarrow beamwidth while maintaining a unit gain in the PRdirection. This beamforming algorithm for PT is reasonable,since it can reduce inter-cell interference for the primarysystem. Obviously, the omni-directional case sets a tighterbound on the performance of CR because the interference isgreater than the case when the PT uses transmit beamforming.

The CT, however, has to guarantee that its interferenceto the primary receiver is below a limit or a threshold I0,in order to gain access and remain non-intrusive. Thus, the

cognitive radio must be aware of the approximate locationof the primary receiver. This knowledge may be acquired invarious ways. Firstly, it can be obtained through database. Forinstance, the primary users may be static computer stationswith fixed locations. Secondly, several cognitive users canestimate the distance and angle of arrival of PR by monitoringthe uplink communication between primary users. Thirdly,this information can be obtained by deploying a number ofmeasurement devices in coverage area. Normally, the locationinformation of PR is not accurate due to the estimation errorand possible scatters around the PR. Hence, the CT must limitthe worst case interference on the PR under the threshold I0.Here, we consider the uncertainty on the angle information ofPR θcp only, and use Δφ to denote this angle ambiguity. Thedistance is known accurately. The information of CR’s locationcan be obtained by feedback channel and measurement in theuplink channel of cognitive users. Given the (approximate)PR location or angle, the optimal CT beamforming can beoptimized via

maxwc

SINRc

subject to

Pcd−αcp |Gc(θcp)|2 ≤ I0

|Gc(θcc)| = 1|Gc(θcj)| ≤ 1/2, θcj �∈ [θcc − Δθ, θcc + Δθ]Pc ≤ Pmax,

(7)

where Pcd−αcp |Gc(θcp)|2 ≤ I0 is the interference constraint on

the CT, |Gc(θcj) ≤ 1/2| is a constraint on the sidelobe leakageof the CT antenna beam, and the maximum transmission powerof the CT Pmax is determined by dcc and SNR requirementof the CR γc as Pmax = γcN0d

αcc. For given wc, we define

gc = maxθcp−Δφ≤θ≤θcp+Δφ

Gc(θ), (8)

which indicates the worst interference gain to the PR. As aresult, we have the interference constraint on the CT as:

Pcd−αcp g2

c ≤ I0 (9)

From (5), because the PT can not be required (due to non-intrusiveness) to minimize |Gp(θpc)|2, we have to increasePc to increase SINRc. However, when Pc increases, the in-terference on the PR will increase. Thus, the performance ofSINRc is tightly related to gc, and we rewrite the optimizationproblem (7) as follows:

minwc

maxθcp−Δφ≤θci≤θcp+Δφ

|Gc(θci)|subject to

|Gc(θcc)| = 1|Gc(θcj)| ≤ 1/2, θcj �∈ [θcc − Δθ, θcc + Δθ].

(10)

As shown in [12], (6) and (10) are convex optimizationproblems and thus can be solved very efficiently using al-gorithms such as interior point methods. Also notice that,when θcc ∈ [θcp − Δφ, θcp + Δφ], we have gc = 1. After

determining the optimal beamforming vector w c for CT, theCT’s transmission power can be written as

Pc = min {I0|gc|−2dαcp, γcN0d

αcc} (11)

Consequently, the SINR at PR and CR can be written as

SINRp ≥ Ppd−αpp

N0 + I0=

γp

1 + c

SINRc = min {c (dcp/dcc)α|gc|−2

1 + γp(dpp/dpc)α|Gp(θpc)|2 ,

Pmaxd−αcc

N0 + Ppd−αpc |Gp(θcp)|2

}

= min {c (dcp/dcc)α|gc|−2

1 + γp(dpp/dpc)α|Gp(θpc)|2 ,

γc

1 + γp(dpp/dpc)−α|Gp(θcp)|2 }

(12)

where c = I0/N0 denotes the ratio of endurable interference atPR to the noise power, and γp = Ppd

−αpp /N0 is the SNR of the

PR. Obviously, the larger the I0, the greater the SINRc, whilethe smaller the SINRp. Thus, I0 can be regarded as a trade-off parameter balancing the performance of primary users andcognitive users.

We provide an example beam-pattern of CT in Fig. 2. Itshows that, the beamforming gain in the direction of the PRcan be made very small. The performance of the cognitivebeamforming algorithm (10) is also numerically evaluated toyield the results of Figures 3(a) 3(b). The relationship betweenangle ambiguity and gc is shown in Fig. 3(a). We observethat gc increases when Δφ increases, as expected. Fig. 3(b)demonstrates the relationship between the angle separationΔθc = θcc − θcp and gc, given Δφ = 10o.

0 50 100 150 200 250 300 350−80

−70

−60

−50

−40

−30

−20

−10

0

θci

|Gs(θ

ci)|

in d

B

Beamforming Pattern of Cognitive Tx

Cognitive RxPrimary Rx

Fig. 2. An example of CT’s beamforming pattern

IV. PERFORMANCE ANALYSIS AND NUMERICAL RESULTS

To characterize the performance of the new cognitive radiosystem equipped with smart antennas, we study the probabilitydistribution of Pr{SINRc ≥ T }. First, we note that thedistances and the angles are independent random variables inour model. From (6) and (10), the solution to the beamformingproblem is determined by the angles information and con-straints, i.e., θcp, θcc, θpp, θcc, Δφ and half-power beamwidthΔθ.

5 10 15 20 25 30 35 40−80

−70

−60

−50

−40

−30

−20

−10

0

|gc| (

dB)

Δ φ

M = 16Δ θ = 15o

θcc

= 60o

θcp

= 100o

(a) Angle Ambiguity Versus gc

0 20 40 60 80 100 120 140 160 180−180

−160

−140

−120

−100

−80

−60

−40

−20

0

|gc| (

dB)

Δ θc

M = 16Δ φ = 10o

θ cc

= 60o

Δ θ = 15o

(b) Angle Separation Versus gc

Fig. 3. Relationship between Angle Ambiguity, Angle Separation and gc

When PT uses omni-directional antenna, we have gp = 1.Thus, we can obtain a lower bound on the performance ofSINRc. Additionally, if there is no power constraint on CT,i.e., Pmax = ∞, we can obtain an upper bound on SINR c.Consequently,

SINRc = c(dcp/dcc)αg−2

c

1 + γp(dpp/dpc)α. (13)

We consider two different cases: one for the scenario with afixed location primary receiver, and one for the scenario witha fixed cognitive receiver.

A. Fixed Location Primary Receiver

Fixing the location of PR also fix parameters dpp, dcp, andθcp. Then, because gc = f(θcc − θcp) becomes a functionof only θcc, SINRc becomes a function of only dcc, θcc anddpc, Note that dcc and θcc are independent and uniformlydistributed random variables with dcc ∼ U(dmin, dmax) andθcc ∼ U(0, 2π) (U denotes uniform distribution). Here, weset dmax = D and dmin = 10m, which justifies the large-scale wireless channel model. The probability can be furtherexpanded into

PT = Pr{c (dcp/dcc)αg−2c

1 + γp(dpp/dpc)α≥ T }

= Pr{dαccg

2c + (

dcc

dpc)αg2

cγpdαpp ≤ dα

cpc

T}.

(14)

Using the relationship of D−dcc < dpc < D +dcc, we canobtain an upper/lower bound of this probability P +

T and P−T ,

respectively, as

P−T = Pr{dα

ccg2c + (

dcc

D − dcc)αγpd

αppg

2c ≤ dα

cpc

T}

= Pr{g2c (d2

cc + γpdαpp

dαcc

(D − dcc)α) ≤ dα

cpc

T}

=∫∫

S−:{(dcc,θcc):g2c (d2

cc+γpdαpp

dαcc

(D−dcc)α )≤ dαcpc

T }ds

(15)

P+T = Pr{dα

ccg2c + (

dcc

D + dcc)αγpd

αppg

2c ≤ d2

cpc

T}

= Pr{g2c (d2

cc + γpdαpp

dαcc

(D + dcc)α) ≤ dα

cpc

T}

=∫∫

S+:{(dcc,θcc):g2c (d2

cc+γpdαpp

dαcc

(D+dcc)α )≤ dαcpc

T }ds.

(16)

Notice that P−T and P +

T are monotonically increasing functionsof dcc, because their first order derivative is greater than 0 for0 < dcc < D. This means that for a given θcc, if we have(d∗, θcc) in S− and S+, then any (dcc, θcc) with dcc < d∗

will also be in S− and S+.If we define the decodable zone of CR as

S :=∫∫

S:(dcc,θcc):SINRc≥T

ds,

then the integration regions S− in (15) and S+ (16) areactually the lower and upper bounds on the decodable zone,respectively. In fact, for every θcc and consequently gc, wehave a lower bound and an upper bound on d ∗ as solutions tothe following equations with constraint 0 < d∗ < D:

d∗lbα + γp

dαpp

(D − d∗lb)αd∗lb

α =dα

cpc

T g2c

d∗ubα + γp

dαpp

(D + d∗ub)αd∗ub

α =dα

cpc

T g2c

.

(17)

To illustrate how tight the bounds are, Monte-Carlo simula-tions are used to generate the decodable zone of CR. We setγc = 10,and γp = 10. Interference threshold to the PR fromCT is fixed at I0 = 0.1N0, thus we have SINRp ≥ 10

1.1 = 9.1.The path loss factor is set as α = 2.

When the PT uses omni-directional antenna, we obtain thedecodable zones for T = 6dB, shown as shaded regions inFig. 4 with γc = 10dB and γc = 20dB respectively. The unitsof the two axes are meters. The lower/upper bound S − and S+

are also shown in Fig. 4 as bold lines for comparison purpose.From Fig. 4, we see that when the maximum transmissionpower is very large, the bounds we obtain in (17) are verytight. The difference of shaded areas between Fig. 4(a) and4(b) can be regarded as power-limited area. In this area, theinterference from the PT is the main constraint of the SINRc

performance. When the PT uses transmit beamforming withweight vector calculated from (6), the decodable zones of CR

0 500 1000 1500 2000 2500 3000 3500 4000 45000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 10dB

T = 6dB

PR PTS+

S−

CT

(a) Decodable zone of CR with γc = 10dB

0 500 1000 1500 2000 2500 3000 3500 4000 45000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 20dB

T = 6dB

PR PTS+

S−

(b) Decodable zone of CR with γc = 20dB

Fig. 4. Decodable Zone of CR when PT uses omni-directional antenna

with γc = 10dB and γc = 20dB are shown in Fig. 5(a) and Fig.5(b). We see that, when the PT uses transmit beamforming,the decodable zones of CR increases dramatically. This resultsfrom the fact that the interference from the PT is greatlyreduced if the PT uses smart antenna technique to steer itsmain-lobe to the direction of the PR. Therefore the SINR c willincrease without increasing the maximum transmission powerof the CT.

B. Fixed Location Cognitive Receiver

By fixing the location of CR, probability ρ(dcc, θcc) =Pr{SINRc ≥ T } describes the performance SINRc of the givenCR with the PR randomly located at the region centered atthe PT. ρ(dcc, θcc) can also be regarded as the probabilityof certain CR falling into the decodable zone and achievesuccessful transmission. In different location of CR, the prob-ability Pr{SINRc ≥ T } is different. The total improvementon spectral efficiency ρ0 can thus be expressed as

ρ0 =∫∫

A:{dcc∈[dmin,dmax],θcc∈[0,2π)}ρ(dcc, θcc) dA (18)

Since dpc, dcc and θcc are fixed, SINRc is a function of dcp,θcp and dpp. However, since gc = f(θcp) in the expression(13) is a function of θcp, which depends on both of θpp anddpp, we are unable to separate g2

c from dpp. Instead, Monte-Carlo method is used to determine the Pr{SINRc ≥ T }.Regions in which CR satisfies Pr{SINRc ≥ T } > p aremarked by dots in Fig. 6 and Fig. 7 for γc = 10dB andγc = 15dB, respectively. If we deploy the CRs in the shadedregions, at least ρ0 = p × ShadedArea

TotalArea in spectral efficiency

0 500 1000 1500 2000 2500 3000 3500 4000 45000

500

1000

1500

2000

2500

3000

3500

4000

4500

CT

S−S+PT(Tx BF)PR

γc = 10dB

T = 6dB

(a) Decodable Zone of CR with γc = 10dB

0 500 1000 1500 2000 2500 3000 3500 4000 45000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 20dB

T = 6dB

PRPT(Tx BF) S+

S−

CT

(b) Decodable Zone of CR with γc = 20dB

Fig. 5. Decodable Zone of CR when PT uses transmit beamforming

can be achieved. From simulations, we show that, 13.45%,42.48%, 40.63%, and 45.15% increases in spectrum efficiencycan be achieved as shown in Figures 6(a), 6(b), 7(a) and 7(b),respectively.

From Fig. 6 and Fig. 7, we observe that, SINRc is mostlimited by the interference from the PT. Thus, when the PTuses transmit beamforming technique, the interference fromthe PT to the CR is reduced and thus the shaded regionexpands significantly. Another way to increase the shadedregion is to relax the transmission power constraint of the CT,which can be also observed from the simulation results. Noticethat, even when we increase the transmission power of the CT,the interference to the PR is still limited to I0. Therefore,by applying smart antenna techniques, we can achieve atradeoff between the implementation complexity/power andthe wireless spectrum.

From the presented performance analysis and numericalresults, we can see that the proposed cognitive radio networkbased on smart antenna technology (transmit beamforming)enables cognitive users to have access to the primary users’spectrum simultaneously with the primary users. The size ofdecodable zone of CR relative to the entire coverage area ofthe CT represents the improvement on spectrum efficiency.Cognitive receivers that are out of the decodable zone shouldswitch to another spectral band or wait until the primarycommunication link ceases transmission or migrates away. Inconjunction with sensing-based opportunistic spectrum accessschemes and frequency hand-over techniques, the proposedapproach can significantly enhance the spectral efficiency by

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 10dB

T = 6dBp = 0.5

PT(Tx BF)

(a) PT uses transmit beamforming

0 1000 2000 3000 40000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 10dB

T = 6dBp = 0.5

PT

(b) PT uses omni-directional antenna

Fig. 6. Regions of CR with Pr{SINRc ≥ T} > p for γc = 10dB

utilizing both spatial and temporal spectral vacancy.

V. CONCLUSION

In this paper, we presented a cognitive radio system basedon smart antenna technologies to achieve non-intrusiveness toprimary licensees. This system allows simultaneous operationof primary users and cognitive users while suppressing theinterference generated by the cognitive radios to the primaryusers under a tolerable limit. We improved the overall spectralefficiency by positioning the cognitive system in areas thathave low or no primary activity. We also determined the de-codable zones for cognitive radio based on different transmitterpower constraints and verified the tightness of a lower/upperbound of the decodable zone.

Future works may include the investigation of transmissionstrategies and performance analysis to (small scale) time-varying fading channels, and consideration of inaccuracy ondistance information. The deployment of multiple antennasin systems where multiple cognitive nodes coexist is alsoof interest. Another possible direction is to develop efficienthybrid MAC layer protocol to jointly exploiting the spectralvacancy in both the spatial and temporal domains.

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−1000 0 1000 2000 3000 4000 50000

500

1000

1500

2000

2500

3000

3500

4000

4500

γc = 15dB

T = 6dBp = 0.5

PT(Tx BF)

(a) PT uses transmit beamforming

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500

1000

1500

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2500

3000

3500

4000

4500

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PT

(b) PT uses omni-directional antenna

Fig. 7. Regions of CR with Pr{SINRc ≥ T} > p for γc = 15dB

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