Research Article Proportional Fair Power Allocation for Secondary...

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2013 Article ID 272341 8 pageshttpdxdoiorg1011552013272341

Research ArticleProportional Fair Power Allocation for SecondaryTransmitters in the TV White Space

Konstantinos Koufos and Riku Jaumlntti

Communications and Networking Department Aalto University Finland

Correspondence should be addressed to Konstantinos Koufos konstantinoskoufosaaltofi

Received 23 October 2012 Revised 7 February 2013 Accepted 14 February 2013

Academic Editor H Arslan

Copyright copy 2013 K Koufos and R Jantti This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The key bottleneck for secondary spectrum usage is the aggregate interference to the primary system receivers due to simultaneoussecondary transmissions Existing power allocation algorithms for multiple secondary transmitters in the TV white space eitherfail to protect the TV service in all cases or they allocate extremely low power levels to some of the transmitters In this paper wepropose a power allocation algorithm that favors equally the secondary transmitters and it is able to protect the TV service in allcases When the number of secondary transmitters is high the computational complexity of the proposed algorithm becomes hightoo We show how the algorithm could be modified to reduce its computational complexity at the cost of negligible performanceloss The modified algorithm could permit a spectrum allocation database to allocate near optimal transmit power levels to tens ofthousands of secondary transmitters in real time In addition we describe how the modified algorithm could be applied to allowdecentralized power allocation for mobile secondary transmitters In that case the proposed algorithm outperforms the existingalgorithms because it allows reducing the communication signalling overhead between mobile secondary transmitters and thespectrum allocation database

1 Introduction

Themain requirement for secondary spectrum usage is inter-ference control For single secondary transmitter the powerlevel maximizing the secondary transmission rate underprimary system protection constraints has been derived in[1] However the bottleneck for secondary spectrum usageis the aggregate interference to the primary receivers due tosimultaneous secondary transmissions Allocating the powerlevels to multiple secondary transmitters has already drawnconsiderable interest for standardization bodies all over theworld [2ndash4] and also for the academic research community

The SE43 working group in the Electronic Communi-cations Committee (ECC) in Europe announced a powerallocation rule for secondary operation in the TV whitespace (TVWS) hereafter referred to as the SE43 rule [2]Initially the SE43 rule allocates the maximum permittedtransmit power level to each secondary transmitter For 2ndash4simultaneous transmissions the maximum transmit power isdivided with the number of active transmitters In that case

each transmitter generates an equal amount of interferenceat the TV system For a larger number of simultaneoustransmissions a safety protection margin should be utilizedIt has been shown that the existing SE43 rule fails to protectthe TV service in all cases [5]

Power allocation algorithms that satisfy the TV protec-tion constraints have been proposed by the academic researchcommunity [6ndash17] In [6ndash10] all secondary transmittersallocated equal transmit power levels In that case there isa single parameter value to determine and the computationalcomplexity is low The drawback is that the power level forsecondary transmitters located far from the TV coverage areawould be limited due to secondary transmissions that areoriginated close to the TV coverage area The assumptionfor common allocated power level is dropped in [11] wherethe sumpower is maximized In that case the algorithmassociates transmitters located far from the TV coverage areawith a high power level at the cost of transmitters in theproximity of the TV coverage area which remain practicallysilent

2 Journal of Electrical and Computer Engineering

A proportional fair (PF) power allocation rule wouldfavor equally the secondary transmitters by equalizing theirresource consumption The available resource is the max-imum permitted generated interference at the TV systemNote that the SE43 rule resembles a PF power allocationscheme in the limiting scenario with 2ndash4 transmitters Unlikethe SE43 rule the scheme proposed in this paper is ableto protect the TV service in all cases When the numberof secondary transmitters is high the complexity of theproposed scheme may prohibit a real-time implementationin a spectrum allocation database Because of that a sub-optimal method with low complexity is also introducedThe suboptimal method not only allows protecting the TVservice but also enables power allocation to mobile users in adecentralized manner

The ECC report [2] is not the first work targetingfairness in secondary type of networks Fairness in secondaryspectrum allocation and scheduling has been studied in [12ndash14 18ndash21] respectively Also in [15] the minimum secondarySINR is maximized while in [16] the sum rate utility ismaximized In [17] PF power allocation is proposed butthe complexity in large problem instances is not addressedUnfortunately the power allocation algorithms in [15ndash17]assume secondary transmitters with fixed and known loca-tionsThe interference that is originated frommobile users isnot considered

The remainder of this paper is organized as follows InSection 2 we present the TV system model In Section 3we formulate the PF power allocation scheme under TVprotection constraints In Section 4 we propose a subop-timal alternative to the PF scheme that is extended toallow decentralized power allocation for mobile devices inSection 5 In Section 6 we demonstrate the flexibility of theproposed scheme in comparisonwith the current SE43 powerallocation rule In Section 7 we conclude the paper

2 TV System Model

In TV network planning the location probability describesthe percentage of locations within a square area of 100 times

100m2 also known as pixel where the TV reception issatisfactory [2] For satisfactoryTVoperation a target SINR 120574

119905

must bemaintainedwith specific outage probability119874119905due to

the slow fading The outage probability 119874119905is complementary

to the location probability widely used in the definition of TVcoverage contour [2] For evaluating the outage probabilitythe TV coverage area is discretized into pixels Each pixel isconsidered to be a test point where the following conditionshould be satisfied

119874119905ge Pr (120574

119894le 120574119905) (1)

where 120574119894is the SINR at the 119894th TV test point

The probability constraint (1) must be satisfied in thepresence of secondary transmissions too A closed-formexpression for (1) has been derived in [22] assuming thatthe TV signal level and the interference level due to eachsecondary transmitter follow the log-normal distributionwithin a TV test pixel The aggregate secondary interference

becomes a sum of log-normal random variables whosedistribution is not available and approximating methods arecommonly employed In [22] the distribution of the aggregatesecondary interference incorporating also the noise level isapproximated by the log-normal distribution The Fenton-Wilkinson method is used to compute the parameters of theapproximating distribution

Expressing (1) in closedform allows computing the maxi-mum permittedmean secondary interference level which hasbeen defined in [22] as the interference margin The inter-ference margin is a function of the TV system parametersthat is the protection criteria of TV receivers (120574

119905 119874119905) and the

useful TV signal level at the test point Also it depends on thelocations of secondary transmitters and their transmissionpower levels In order to simplify the interference controlprocess a lower bound for the interference margin has beenderived in [22] that is independent of the secondary networkparameters

119868Δ119894

= 10(119878(119889119887)

119894minus120574(119889119887)119905 +119876

minus1(1minus119874119905)sdot120590TV119894)10

minus 119875119873 (2)

where 119868Δ119894

is the available interference margin at the 119894th TVtest point 119878(119889119887)

119894is the TV signal level by using distance-based

pathloss 120590TV119894 in dB is the standard deviation of TV signaldue to slow fading 119876minus1 is the inverse of the Gaussian 119876

function and 119875119873stands for the noise power level at the TV

receiverBy using the concept of interference margin one essen-

tially turns the chance type of constraint (1) into a constraintof the form sum

119873

119895=1119910119894119895

le 119868Δ119894

where 119873 is the number ofsecondary transmitters and 119910

119894119895is the mean interference level

from the 119895th transmitter to the 119894th TV test point The meangenerated interference 119910

119894119895is a function of the secondary

transmission power level 119875119895 the distance-based propagation

pathloss 119871(119889119887)

119894119895 and the mean of the slow fading For log-

normal fading the mean interference level 119910119894119895is

119910119894119895= 119875119895sdot 119890120590211989411989521205852

sdot 10119871(119889119887)

11989411989510

(3)

where 120590119894119895in dB is the slow fading standard deviation due to

the secondary transmission and 120585 = 10 log(10) is a scalingconstantThe standard deviation 120590

119894119895is in general different for

different secondary transmitters andTV test points due to theirregular terrain morphology

3 Proportional Fair Power Allocation Scheme

By using the concept of interference margin the probabilityconstraint (1) is turned into a linear constraintsum

119895119892119894119895sdot119875119895le 119868Δ119894

where 119892119894119895

= 119890120590211989411989521205852

sdot 10119871(119889119887)

11989411989510 is the link gain Therefore the

interference margin can be treated as an available resourceEach transmitter is allowed to take a bite out of the availableresource that is it is allowed to generate some amount ofinterference at the TV test point provided that the meaninterference of secondary transmissions does not exceed theinterference margin

Allocating the transmit power levels can be viewed as aresource sharing problem In order to equalize the resource

Journal of Electrical and Computer Engineering 3

consumption we propose a PF power allocation schemeFor PF power allocation the sum of secondary transmissionpower levels in the log-domain should bemaximized [23] Asa result the power allocation algorithm can be formulated asa constrained optimization problem

Maximize 119875119895ge 0

sum

119895

log (119875119895)

Subject to sum

119895

119892119894119895sdot 119875119895le 119868Δ119894

forall119894

(4)

The optimization function and the constraints are contin-uously differentiable functions of119875

119895TheLagrangian function

is 119871 = sum119895log(119875119895) minus sum119894120582119894(sum119895119892119894119895119875119895minus 119868Δ119894) where 120582

119894ge 0 is the

Lagrangian multiplier The Karush-Kuhn-Tucker conditionsare

120597119871

120597119875119895

= 0 forall119895

120582119894ge 0 sum

119895

119892119894119895119875119895minus 119868Δ119894

le 0

120582119894(sum

119895

119892119894119895119875119895minus 119868Δ119894) = 0 forall119894

(5)

The solution has the form 119875119895

= (sum119894120582119894sdot 119892119894119895)minus1 where

the Lagrangian multiplier 120582119894is positive if the 119894th constraint

is binding Otherwise 120582119894

= 0 The PF scheme allocatesthe transmit power levels so that each transmitter takes anequal fraction out of the aggregate interference margin atthe binding points Unfortunately for complex secondarynetwork geometries and noncontiguous TV coverage areasit is difficult to identify the binding points in advance

One can show that the Hessian matrix of the objectivefunction is negative definite and thus the optimization func-tion is concave Since the constraints are linear functionsof transmit power levels the optimization problem (4) isconvex The globally optimal solution can be found byusing standard convex optimization tools When the numberof constraints and optimization parameters are high thecomputational complexity may prohibit a real-time compu-tation in the spectrum allocation database Note that thedatabasemay need to reallocate the transmission power levelsin frequent time intervals The secondary transmitters canbe mobile or new transmitters can send spectrum accessrequests

4 Simplified Proportional Fair PowerAllocation Scheme

We propose associateing each transmitter with the TV testpoint where its generated interference is maximized In thisway we end up with a subset 119863 of TV test points thatexperience the highest interference levels We call it the setof dominating TV test points Obviously it is sufficient tocontrol the generated interference only at the TV test pointsbelonging to the dominating set

We denote by 119869119894the set of transmitters dominated by

the 119894 isin 119863 TV test point Also let us assume that eachtransmitter generates mean interference level equal to 119901

0at

its dominating point 119910119894119895

= 1199010 119895 isin 119869

119894 119894 isin 119863 Essentially

we propose a PF power allocation scheme for secondarytransmitters belonging to the same set Next we show howto compute the parameter 119901

0

The generated interference at the 119896th TV test point due tothe 119895 isin 119869

119894secondary transmitter can be written as a fraction

of the interference 1199010

119910119896119895

= 1199010sdot exp(

1205902

119896119895minus 1205902

119894119895

21205852

+

119871(119889119887)

119896119895minus 119871(119889119887)

119894119895

120585) 119895 isin 119869

119894 (6)

Themean interference 119868119894at the 119894th TV test point is the sum of

the interference from all secondary transmitters

119868119894= sum

119895

119910119894119895= sum

119895isin119869119894

119910119894119895+ sum

119896 = 119894

sum

119895isin119869119896

119910119896119895 (7)

Since each transmitter 119895 isin 119869119894generates interference equal

to 1199010at the 119894 isin 119863 test point sum

119895isin119869119894119910119894119895

= 1199010sdot |119869119894| where | sdot |

denotes the cardinality of a set Also by using (6) in (7) theaggregate interference 119868

119894can be read as 119868

119894= 1199010sdot 120596119894where

120596119894= |119869119894|+sum119896 = 119894

sum119895isin119869119896

exp((1205902119894119895minus1205902

119896119895)21205852+(119871(119889119887)

119894119895minus119871(119889119887)

119896119895)120585) For

protecting the TV receivers the mean interference should bekept under the margin 119868

119894le 119868Δ119894 By enforcing the inequality

to be tight the parameter 1199010can be selected as the minimum

over all test points belonging to the dominating set

1199010= min119894isin119863

119868Δ119894

120596119894

(8)

With the parameter 1199010at hand we can identify the

transmit power level 119875119895after replacing 119910

119894119895by 1199010into (3)

119875119895= 1199010sdot119890minus120590211989411989521205852

sdot10minus119871(119889119887)

11989411989510

119895 isin 119869119894 119894 isin 119863where the value for

the distance-based pathloss 119871(119889119887)119894119895

and the standard deviation120590119894119895must be taken from the test point that dominates the 119895th

transmitter By using (8) and (2) the allocated power level canalso be written as

119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)

119894119895+119876minus1(1minus119874119905)120590TV119894minus(120590

21198941198952120585)minus10log10(120596119894))10

(9)

In Figure 1 it is assumed that both TV test pointsbelonging to the dominating set are also binding that isall their interference margin is filled in by the secondarytransmissions According to the simplified PF scheme eachtransmitter generates mean interference 119901

0at its dominating

test point The remaining interference headroom is filled inby the secondary transmitters dominated by the other testpoint According to the PF scheme the aggregate interferencemargin 119868

Δ1+ 119868Δ2

is divided equally among the secondarytransmitters

The two schemes are characterized by different imple-mentation complexity The complexity to identify the set ofdominating test points in the simplified scheme isO(119873sdot(119873

119901minus


TV coverage area

Dominating test points

119868Δ1

119868Δ2

31199010

41199010

(a) Simplified proportional fair power allocation

TV coverage area


119868Δ1 + 119868Δ2

(b) Proportional fair power allocation

Figure 1 Comparison of simplified PF and PF power allocation schemes

1)) while the complexity to identify the minimum over thecomputed values for 119901

0is O(|119863| minus 1) Since |119863| ≪ 119873

119901the

overall complexity can be approximated byO(119873sdot(119873119901minus1)) In

order to get insight on the complexity for solving (4) by usinginterior-point methods we use the complexity bound O(119873

2sdot

11987332

119901) [24] Besides the lower implementation complexity the

simplified scheme allows power allocation to mobile UE withlower signalling overhead in comparisonwith the PF schemeThis is the topic of the next section

5 Power Allocation for Mobile Users

The power allocation scheme proposed in Section 4 isapplicable to secondary transmitters with fixed and knownlocations for example base stations (BSs) The secondarytransmitters can also be mobile user equipment (UE) If thenumber ofUE is high the communication signaling overheadfor updating their locations in the database at frequent timeintervals would be high too Fortunately the simplified PFalgorithm can be modified to allow decentralized powerallocation with reduced signaling overhead Next we showhow the simplified scheme can group secondary pixels andcontrol the interference from each group instead of doing iton a per-pixel basis UE can move within pixels belonging tothe same groupwithout the need to inform the database abouttheir locations

Following the ECC approach we discretize the secondarydeployment area into pixels We assume that the UE insideeach pixel is distributed according to a Poisson point process(PPP) The density of the process in the 119895th pixel is equal tothe number 119873

119895of UE times the activity factor ] The mean

interference due to the transmissions originating from the 119895thpixel to the 119894th TV test point is [25]

119910119894119895= 119908119895sdot 119875119895sdot 119890120590211989411989521205852

sdot sum

119899

10119871(119889119887)

11989411989511989910

(10)

where the index 119899 is used to integrate over the area 119860119895of

the 119895th pixel 119875119895is the transmit power level for UE located

inside the 119895th pixel and 119908119895= (]119873

119895119860120598)119860119895where 119860

120598is the

integration element The 119908119895describes the average number of

active UE inside the integration element of the 119895th pixel The

119871(119889119887)

119894119895119899stands for the distance-based pathloss between the 119899th

integration element of the 119895th pixel and the 119894th test pointSimilar to the power allocation rule described in

Section 4 we group together pixels dominated by the sametest point The mean interference level from the group 119869

119894to

the 119894th TV test point is 1199010|119869119894| (Note that the parameter value

1199010and the set 119863 of dominating TV test points are in general

different for the secondary transmitters with fixed locationsdescribed in Section 4 and for the secondary pixels describedin this section In order not to introduce unnecessary com-plexity we keep the same notation and provide the relatedexplanation when needed)The interference headroom 119901

0|119869119894|

can be divided among the secondary pixels belonging to thegroup 119869

119894by using any rule For PF allocation each pixel takes

an equal amount of resource 1199010 In that case pixels with low

user density allocate higher power levels to the UE comparedto pixels with high user density One alternative way is todivide the interference headroom 119901

0|119869119894| proportionally to the

user density of pixels belonging to the set 119869119894 In that case the

transmission power level for UE inside the 119895th pixel becomes

119875119895=

1199010sdot10038161003816100381610038161198691198941003816100381610038161003816

sum119895isin119869119894

119908119895

sdot 119890minus120590211989411989521205852

sdot (sum

119899

10119871(119889119887)

11989411989511989910

)

minus1

119895 isin 119869119894 119894 isin 119863

(11)

The parameter 1199010can be calculated based on (8) after

computing the parameter 120596119894as

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816

+ sum

119896 = 119894

sum

119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(12)

The transmission power level 119875119895calculated based on (11)

does not depend on the particular population density in the119895th pixel Only the total amount of UE sum

119895isin119869119894119873119895inside the

group 119869119894has to be known Because of that the UE can freely


move between pixels belonging to the same group withoutthe need to recalculate their transmission power levels atthe database Each UE just has to know the pixel where itbelongs and set its transmission power level based on (11)The database has to recompute the parameter value 119901

0and

the transmission power levels only if the total number of UEin a group of pixels changes

AllowingUEmobilitywithin a group 119869119896 119896 = 119894may violate

the protection criteria at the 119894th TV test point One way toprotect the 119894th test point is to recompute the parameter 120596

119894in

(12) based on the worst case interference scenarioThat refersto the case where all UE inside the group 119869

119896is concentrated

in the pixel generating the highest interference at the 119894th TVtest point In that case the parameter 120596

119894becomes

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816 + sum

119896 = 119894

10038161003816100381610038161198691198961003816100381610038161003816

sdotmax119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(13)

The flexibility introduced with (13) does not come forfree In the worst case the distribution of UE minimizes theinterference at the 119894th TV test point whereas (13) assumesmaximum interference

Thus far the transmission power levels for BS and UEhave been calculated assuming that the full interferencemargin is available to BS and UE respectively When the BSand the UE are simultaneously active the power allocationalgorithm may have the following steps

(1) allocate some fraction 119902 of the interference margin tothe BS 119868(BS)

Δ119894= 119902 sdot 119868

Δ119894 for all 119894

(2) compute the parameter 1199010for the BS transmissions

after replacing 119868Δ119894

by 119868(BS)Δ119894

in (8)(3) compute the BS transmission power levels 119875

119895by using

(9)(4) by using the identified BS transmission power levels

compute the remaining interference margin 119868(UE)Δ119894

=

119868Δ119894

minus sum119895119910119894119895at the TV test points where the 119910

119894119895is

calculated from (3)(5) group the secondary pixels and identify the transmis-

sion power level for UE in each pixel by using (11)Theparameter 119901

0is computed after replacing 119868

Δ119894by 119868(UE)Δ119894

in (8) For supporting UE mobility within groups ofpixels (13) must be used instead of (12)

6 Numerical Illustrations

61 Parameter Settings For testing the proposed powerallocation rule we select a study area in Jyvaskyla in Finlandwhere the Vihtavuori TV transmitter operates at 546MHzThe minimum required median field strength for fixed TV

(km)

(km

)

Use

rs p

er p

ixel

5 10 15 20 25

5

10

15

20

25 1

3

10

30

100

300

1000

Figure 2 Secondary UE density map in the study area

reception at 64QAM and 23 code rate is 525 dbuVm at500MHz [26 pp185] For other frequencies 119891 in MHz thecorrection factor 20 log(119891500) should be added resulting in533 dBuVm at 546MHz

In order to identify the TV coverage area we cover the fullstudy area with square pixels with side equal to 250mA pixelbelongs to the TV coverage area if the median field strengthis higher than 533 dBuVm The TV field strength at thecenter of each pixel has been calculated by using the Longley-Rice propagation model with terrain data implemented inSplat [27] The slow fading standard deviation of the TVsignal is 120590TV119894 = 55 dB for all 119894 The TV self-interferenceis not considered and the noise power level is minus106 dBmThe protection criteria of TV receivers are 120574

119905= 171 dB and

119874119905= 10motivated from [2]For testing power allocation for mobile UE the popu-

lation density map of the area is utilized see Figure 2 Theantenna height for the UE is 15m Their activity factor is10 The locations of secondary BS are fixed and knownThey are placed at a square lattice with 2 km side and theirantenna height is 3m For modeling the distance-basedpropagation pathloss of secondary transmissions we utilizethe modified Hata model for suburban areas [28] The slowfading standard deviation for BS and UE is 120590

119894119895= 8 dB

for all 119894 119895

62 Results First we compare the allocated transmit powerlevels of secondary BS by using PF and simplified PF powerallocation rules For PF rule the power levels are obtainedby solving (4) while for simplified PF rule (9) is utilizedFor illustration purposes the dominating TV test points andthe locations of secondary BS are depicted in Figure 3 forprotection distance equal to 3 km The distributions of BSpower levels for different protection distances are plottedin Figure 4 One can see that the simplified scheme almostachieves the optimal solution In general the PF schemeallocates higher transmission power levels for the BS locatedclose to the TV protection area Also we notice that theset of dominating test points has different cardinality for

6 Journal of Electrical and Computer Engineering(k

m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast

lowastlowastlowastlowast

lowastlowastlowast

lowast lowast lowast

Figure 3 TV protection area (blue-shaded area) secondary BS (redtriangles) and dominating TV test points (yellow stars)

0 5 10 15 20 25 30 35 40 45Transmission power level (dBm)

0

01

02

03

04

05

06

07

08

09

1

CDF

PF 119903119899 = 1 kmSimplified PF 119903119899 = 1 kmPF 119903119899 = 3 kmSimplified PF 119903119899 = 3 km

PF 119903119899Simplified PF 119903119899PF 119903119899 =10 kmSimplified PF 119903119899 = 10 km

= 7km= 7km

Figure 4 Distribution of transmission power levels by using PFand simplified PF schemes for different protection distances Thelocations of secondary transmitters are fixed and known

different protection distances and only a single test point isbinding Hereafter the simplified PF scheme is utilized and itis referred to as the proposed power allocation method

Next we compare the proposed power allocationmethodwith other existing methods If we are to use equal transmitpower for all secondary transmitters [6ndash10] the maximumpermitted levels are 14 26 33 38 dBm for protection dis-tances 1 3 7 10 km respectively As a result the commonpower allocation rule is conservative for secondary transmit-ters located far from the TV coverage area especially whenthe protection distance is small Also if the sumpower ismaximized [11] a single transmitter is essentially favored the

transmitter located furthest away from the TV coverage areahas the smallest link gain and can dominate the sum-powerutility by using high transmit power levelThe power level forthe rest of the transmitters is practically zero As a result thesum-power utility is extremely unfair in our system setup

Next we compare our method with the existing SE43proposal The transmission power level for each BS by usingthe SE43 rule is [2 page 24]

119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)

119894119895+119876minus1(1minus119874119905)radic120590

2TV119894+120590

2119894119895minusSMminusMI)10

(14)

where SM andMI are the safety and the multiple interferenceprotection margin respectively

Instead of using protection margins one can scale thetransmission power of each BS with the total number 119873

of active BS The modified SE43 rule allocates transmissionpower level equal to [29]

119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)

The TV SINR distribution at the test point experiencingthe highest interference level is depicted in Figure 5 forprotection distance 10 km The protection margins for theSE43 rule are taken equal to SM = 10 dB and MI = 6 dBas proposed in the ECC report [2] One can see that theexisting and the modified SE43 rules fail to protect the TVservice The same behaviour is observed for other protectiondistances too One could maintain the TV SINR target byusing for instance a higher value for the safetymargin in (14)This approach requires an iterative type of power allocationalgorithm implemented in the database On the other handthe proposed rule has low complexity and protects the TVsystem in all cases

The proposed rule can also be used to allocate the trans-mission power levels to the UE (11) UE mobility betweenpixels belonging to the same group is allowed if (13) isused instead of (12) This flexibility comes at the cost ofreduced transmission power level at the UE However theloss is negligible especially for a large protection distance seeFigure 6

Finally we consider simultaneous BS and UE trans-missions and the power allocation algorithm described inSection 5 In Figure 7 one can see the distribution of UEtransmit power levels for different fractions 119902 of allocatedinterference margin to the BS When 75 of the margin isallocated to the BS its transmission power levels are between36 dBm and 48 dBm while the UE power levels lie between10 dBm and 30 dBm At the same time the TV SINR target issatisfied at all the dominating test points

7 Conclusions

In this paper we proposed a power allocation algorithm formultiple secondary transmitters in the TVWS that protectsthe TV service in the cochannel The proposed rule canincorporate secondary transmitters with different antenna


5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF

SE43 SM= 10 dBSE43 scaled margin

Figure 5 TV SINR distribution at the dominating test pointexperiencing the highest secondary interference level by usingdifferent power allocation rules and protection distance 10 km

0 10 20 30 40Transmission power level (dBm)

0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)

Figure 6 Distribution of UE transmission power levels by usingthe simplified PF power allocation rule for different protectiondistances The power allocation scheme (12) is compared with thepower allocation scheme supporting mobility within groups ofpixels (13)

heights for instance base stations andmobileUEThe impactof terrain morphology can be considered by using differentslow fading standard deviations for transmitters locatedat different pixels The proposed rule allows reducing thecommunication signaling overhead between the UE and thespectrum allocation database with the reason being that thedatabase groups secondary pixels and controls the aggregate

10 15 20 25 30 35 40Transmission power level (dbm)

0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075

Figure 7 Distribution of UE transmission power levels for differentfractions 119902 of interference margin allocated for BS transmissionsThe simplified PF power allocation rule supporting mobility withingroups of pixels (13) is utilized The protection distance is 10 km

interference from each group instead of doing it on a perpixel basis The proposed rule outperforms the existing SE43rule because it protects the TV service in all cases and resultsin smaller communication signalling overhead However itdoes not consider the scenario where some of the secondarytransmitters fall inside the coverage area of an adjacent TVchannel The SE43 rule takes into account the protection ofadjacent channel TV service by using reference coexistinggeometries The reference geometry rule is conservative par-ticularly at low user densities [30] Extending the proposedrule to incorporate adjacent channel TV protection can be anarea of future work

Acknowledgments

This work was partially supported by the TEKES-fundedproject IMANET+ and by the Academy-of-Finland-fundedproject SMACIW under Grant no 265040

References

[1] X Kang R Zhang and Y C Liang ldquoOptimal power allocationfor cognitive radio under primary userrsquos outage loss constraintrdquoin Proceedings of the IEEE International Conference on Commu-nications (ICC rsquo09) Dresden Germany June 2009

[2] ECC ldquoReport (under public consultation) technical and oper-ational requirements for the possible operation of cognitiveradio systems in the white spaces of the frequency band 470ndash790MHzrdquo Tech Rep 159 2011

[3] Ofcom ldquoDigital dividend geolocation for cognitive accessdiscussion on using geolocation to enable license-exempt accessto the interleaved spectrumrdquo November 2009

[4] ldquoIn the Matter of Unlicensed Operation in the TV BroadcastBands Third Memorandum Opinion and Order FederalCommunications Commission FCC 12-36A1rdquo August 2012


httptransitionfccgovDaily ReleasesDaily Business2012db0405FCC-12-36A1pdf

[5] R Jantti J Kerttula K Koufos and K Ruttik ldquoAggregateinterference with FCC and ECC white space usage rules casestudy in Finlandrdquo in Proceedings of the IEEE InternationalSymposium on Dynamic Spectrum Access Networks (DySPANrsquo11) pp 599ndash602 May 2011

[6] M Vu N Devroye and V Tarokh ldquoOn the primary exclusiveregion of cognitive networksrdquo IEEE Transactions on WirelessCommunications vol 8 no 7 pp 3380ndash3385 2009

[7] N Hoven and A Sahai ldquoPower scaling for cognitive radiordquoin Proceedings of the Wireless Networks Communications andMobile Computing pp 250ndash255 June 2005

[8] S Zaidi D Mclernon M Ghogho and B Zafar ldquoOn outageand interference in 80222 cognitive radio networks underdeterministic network geometryrdquo in Proceedings of the ACMMobicom Beijing Japan September 2009

[9] S Shankar andCCordeiro ldquoAnalysis of aggregated interferenceat DTV receivers in TV bandsrdquo in Proceedings of the 3rdInternational Conference on Cognitive Radio Oriented WirelessNetworks and Communications (CrownCom rsquo08) SingaporeMay 2008

[10] E Larsson and M Skoglund ldquoCognitive radio in a frequency-planned environment some basic limitsrdquo IEEE Transactions onWireless Communications vol 7 no 12 pp 4800ndash4806 2008

[11] K Koufos K Ruttik and R Jantti ldquoControlling the interferencefrom multiple secondary systems at the TV cell borderrdquo inProceedings of the IEEE Personal Indoor and Mobile RadioCommunications (PIMRC rsquo11) pp 645ndash649 Toronto CanadaSeptember 2011

[12] J Tang S Misra and G Xue ldquoJoint spectrum allocation andscheduling for fair spectrum sharing in cognitive radio wirelessnetworksrdquo Computer Networks vol 52 no 11 pp 2148ndash21582008

[13] B Wang and D Zhao ldquoScheduling for long term proportionalfairness in a cognitive wireless network with spectrum under-layrdquo IEEE Transactions on Wireless Communications vol 9 no3 pp 1150ndash1158 2010

[14] L Akter and B Natarajan ldquoModeling fairness in resourceallocation for secondary users in a competitive cognitive radionetworkrdquo in Proceedings of the Wireless TelecommunicationsSymposium (WTS rsquo10) pp 1ndash6 April 2010

[15] L Tang H Wang and Q Chen ldquoPower allocation with max-min fairness for cognitive radio networksrdquo in Proceedings of theGlobal Mobile Congress (GMC rsquo10) October 2010

[16] B Cho K Koufos K Ruttik and R Jantti ldquoPower allocationin the TV white space under constraint on secondary systemselfinterferencerdquo Journal of Electrical and Computer Engineer-ing vol 2012 Article ID 245895 12 pages 2012

[17] D Li and J Gross ldquoDistributed TV spectrum allocation forcognitive cellular network under game theoretical frameworkrdquoin Proceedings of the Dynamic Spectrum Access Networks (IEEEDySPAN rsquo12) October 2012

[18] H Zheng and C Peng ldquoCollaboration and fairness in oppor-tunistic spectrum accessrdquo in Proceedings of the IEEE Interna-tional Conference on Communications (ICC rsquo05) Seoul KoreaMay 2005

[19] Y Xing R Chandramouli S Mangold and S NandagopalanldquoDynamic spectrum access in open spectrum in wireless net-worksrdquo IEEE Journal on Selected Areas in Communications vol24 no 3 pp 627ndash637 2006

[20] J Bater H P Tan K N Brown and L Doyle ldquoModellinginterference temperature constraints for spectrum access incognitive radio networksrdquo in Proceedings of the IEEE Interna-tional Conference on Communications (ICC rsquo07) pp 6493ndash6498June 2007

[21] Z Ma Z Cao and W Chen ldquoA fair opportunistic spectrumaccess (FOSA) scheme in distributed cognitive radio networksrdquoin Proceedings of the IEEE International Conference on Commu-nications (ICC rsquo08) pp 4054ndash4058 May 2008

[22] K Ruttik K Koufos and R Jantti ldquoModeling of the secondarysystemrsquos generated interference and studying of its impact onthe secondary system designrdquo Radioengineering vol 19 no 4pp 488ndash493 2010

[23] F P Kelly A K Maulloo and D Tan ldquoRate control forcommunication networks shadow prices proportional fairnessand stabilityrdquo Journal of theOperational Research Society vol 49no 3 pp 237ndash252 1998

[24] A Nemirovski Interior Point Polynomial Time Methods inConvex Programming Lecture Notes Georgia Institute of Tech-nology 2004

[25] K Koufos K Ruttik and R Jantti ldquoAggregate interferencefrom WLAN in the TV white space by using terrain-basedchannel modelrdquo in Proceedings of the IEEE Cognitive RadioOriented Wireless Networks and Communications (CrownComrsquo12) Stockholm Sweden June 2012

[26] Final Acts of the Regional Radiocommunication Conference forPlanning of the Digital Terrestrial Broadcasting Service in Partsof Regions 1 and 3 in the Frequency Bands 174ndash230MHz and470ndash862MHz (RRC-06) ITU-R 2006

[27] ldquoRF Signal Propagation Loss and Terrain analysistool for the spectrum between 20MHz and 20GHzrdquohttpwwwqslnetkd2bdsplathtml

[28] ldquoMonte carlo radio simulation methodologyrdquo ERC Report 68Naples Italy 2000

[29] ldquoSE43(11)63 draft report Method of IM value setting in ECCReport 159rdquo httpwwwceptorgeccgroupseccwg-se

[30] L Shi K W Sung and J Zander ldquoControlling aggregateinterference under adjacent channel interference constraint inTV white spacerdquo in Proceedings of the IEEE Cognitive RadioOriented Wireless Networks amp Communications (CrownComrsquo12) Stockholm Sweden June 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



A proportional fair (PF) power allocation rule wouldfavor equally the secondary transmitters by equalizing theirresource consumption The available resource is the max-imum permitted generated interference at the TV systemNote that the SE43 rule resembles a PF power allocationscheme in the limiting scenario with 2ndash4 transmitters Unlikethe SE43 rule the scheme proposed in this paper is ableto protect the TV service in all cases When the numberof secondary transmitters is high the complexity of theproposed scheme may prohibit a real-time implementationin a spectrum allocation database Because of that a sub-optimal method with low complexity is also introducedThe suboptimal method not only allows protecting the TVservice but also enables power allocation to mobile users in adecentralized manner

The ECC report [2] is not the first work targetingfairness in secondary type of networks Fairness in secondaryspectrum allocation and scheduling has been studied in [12ndash14 18ndash21] respectively Also in [15] the minimum secondarySINR is maximized while in [16] the sum rate utility ismaximized In [17] PF power allocation is proposed butthe complexity in large problem instances is not addressedUnfortunately the power allocation algorithms in [15ndash17]assume secondary transmitters with fixed and known loca-tionsThe interference that is originated frommobile users isnot considered

The remainder of this paper is organized as follows InSection 2 we present the TV system model In Section 3we formulate the PF power allocation scheme under TVprotection constraints In Section 4 we propose a subop-timal alternative to the PF scheme that is extended toallow decentralized power allocation for mobile devices inSection 5 In Section 6 we demonstrate the flexibility of theproposed scheme in comparisonwith the current SE43 powerallocation rule In Section 7 we conclude the paper

2 TV System Model

In TV network planning the location probability describesthe percentage of locations within a square area of 100 times

100m2 also known as pixel where the TV reception issatisfactory [2] For satisfactoryTVoperation a target SINR 120574

119905

must bemaintainedwith specific outage probability119874119905due to

the slow fading The outage probability 119874119905is complementary

to the location probability widely used in the definition of TVcoverage contour [2] For evaluating the outage probabilitythe TV coverage area is discretized into pixels Each pixel isconsidered to be a test point where the following conditionshould be satisfied

119874119905ge Pr (120574

119894le 120574119905) (1)

where 120574119894is the SINR at the 119894th TV test point

The probability constraint (1) must be satisfied in thepresence of secondary transmissions too A closed-formexpression for (1) has been derived in [22] assuming thatthe TV signal level and the interference level due to eachsecondary transmitter follow the log-normal distributionwithin a TV test pixel The aggregate secondary interference

becomes a sum of log-normal random variables whosedistribution is not available and approximating methods arecommonly employed In [22] the distribution of the aggregatesecondary interference incorporating also the noise level isapproximated by the log-normal distribution The Fenton-Wilkinson method is used to compute the parameters of theapproximating distribution

Expressing (1) in closedform allows computing the maxi-mum permittedmean secondary interference level which hasbeen defined in [22] as the interference margin The inter-ference margin is a function of the TV system parametersthat is the protection criteria of TV receivers (120574

119905 119874119905) and the

useful TV signal level at the test point Also it depends on thelocations of secondary transmitters and their transmissionpower levels In order to simplify the interference controlprocess a lower bound for the interference margin has beenderived in [22] that is independent of the secondary networkparameters

119868Δ119894

= 10(119878(119889119887)

119894minus120574(119889119887)119905 +119876

minus1(1minus119874119905)sdot120590TV119894)10

minus 119875119873 (2)

where 119868Δ119894

is the available interference margin at the 119894th TVtest point 119878(119889119887)

119894is the TV signal level by using distance-based

pathloss 120590TV119894 in dB is the standard deviation of TV signaldue to slow fading 119876minus1 is the inverse of the Gaussian 119876

function and 119875119873stands for the noise power level at the TV

receiverBy using the concept of interference margin one essen-

tially turns the chance type of constraint (1) into a constraintof the form sum

119873

119895=1119910119894119895

le 119868Δ119894

where 119873 is the number ofsecondary transmitters and 119910

119894119895is the mean interference level

from the 119895th transmitter to the 119894th TV test point The meangenerated interference 119910

119894119895is a function of the secondary

transmission power level 119875119895 the distance-based propagation

pathloss 119871(119889119887)

119894119895 and the mean of the slow fading For log-

normal fading the mean interference level 119910119894119895is

119910119894119895= 119875119895sdot 119890120590211989411989521205852

sdot 10119871(119889119887)

11989411989510

(3)

where 120590119894119895in dB is the slow fading standard deviation due to

the secondary transmission and 120585 = 10 log(10) is a scalingconstantThe standard deviation 120590

119894119895is in general different for

different secondary transmitters andTV test points due to theirregular terrain morphology

3 Proportional Fair Power Allocation Scheme

By using the concept of interference margin the probabilityconstraint (1) is turned into a linear constraintsum

119895119892119894119895sdot119875119895le 119868Δ119894

where 119892119894119895

= 119890120590211989411989521205852

sdot 10119871(119889119887)

11989411989510 is the link gain Therefore the

interference margin can be treated as an available resourceEach transmitter is allowed to take a bite out of the availableresource that is it is allowed to generate some amount ofinterference at the TV test point provided that the meaninterference of secondary transmissions does not exceed theinterference margin

Allocating the transmit power levels can be viewed as aresource sharing problem In order to equalize the resource




sum

119895

log (119875119895)

Subject to sum

119895

119892119894119895sdot 119875119895le 119868Δ119894

forall119894

(4)




119894ge 0 is the


120597119871

120597119875119895

= 0 forall119895

120582119894ge 0 sum

119895

119892119894119895119875119895minus 119868Δ119894

le 0

120582119894(sum

119895

119892119894119895119875119895minus 119868Δ119894) = 0 forall119894

(5)











0at


= 1199010 119895 isin 119869



0




119910119896119895

= 1199010sdot exp(

1205902

119896119895minus 1205902

119894119895

21205852

+

119871(119889119887)

119896119895minus 119871(119889119887)

119894119895

120585) 119895 isin 119869

119894 (6)



119868119894= sum

119895

119910119894119895= sum

119895isin119869119894

119910119894119895+ sum

119896 = 119894

sum

119895isin119869119896

119910119896119895 (7)



119895isin119869119894119910119894119895

= 1199010sdot |119869119894| where | sdot |



119894= 1199010sdot 120596119894where

120596119894= |119869119894|+sum119896 = 119894

sum119895isin119869119896

exp((1205902119894119895minus1205902

119896119895)21205852+(119871(119889119887)

119894119895minus119871(119889119887)

119896119895)120585) For





1199010= min119894isin119863

119868Δ119894

120596119894

(8)



119894119895by 1199010into (3)

119875119895= 1199010sdot119890minus120590211989411989521205852

sdot10minus119871(119889119887)

11989411989510





119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


21198941198952120585)minus10log10(120596119894))10

(9)


0at its dominating


Δ1+ 119868Δ2



119901minus


TV coverage area


119868Δ1

119868Δ2

31199010

41199010


TV coverage area


119868Δ1 + 119868Δ2




0is O(|119863| minus 1) Since |119863| ≪ 119873

119901the



2sdot

11987332








119910119894119895= 119908119895sdot 119875119895sdot 119890120590211989411989521205852

sdot sum

119899

10119871(119889119887)

11989411989511989910

(10)




119895119860120598)119860119895where 119860

120598is the



119871(119889119887)




119894to




0|119869119894|








119875119895=

1199010sdot10038161003816100381610038161198691198941003816100381610038161003816

sum119895isin119869119894

119908119895

sdot 119890minus120590211989411989521205852

sdot (sum

119899

10119871(119889119887)

11989411989511989910

)

minus1

119895 isin 119869119894 119894 isin 119863

(11)



120596119894=

10038161003816100381610038161198691198941003816100381610038161003816

+ sum

119896 = 119894

sum

119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(12)



119895isin119869119894119873119895inside the




0and




119894in




119894becomes

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816 + sum

119896 = 119894

10038161003816100381610038161198691198961003816100381610038161003816

sdotmax119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(13)




Δ119894= 119902 sdot 119868

Δ119894 for all 119894



by 119868(BS)Δ119894


119895by using



=

119868Δ119894


119894119895is




Δ119894by 119868(UE)Δ119894




(km)

(km

)

Use

rs p

er p

ixel

5 10 15 20 25

5

10

15

20

25 1

3

10

30

100

300

1000




119905= 171 dB and



119894119895= 8 dB

for all 119894 119895



m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast


lowastlowastlowast




0

01

02

03

04

05

06

07

08

09

1

CDF



= 7km= 7km






119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590


(14)




119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)




7 Conclusions



5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












sum

119895

log (119875119895)

Subject to sum

119895

119892119894119895sdot 119875119895le 119868Δ119894

forall119894

(4)




119894ge 0 is the


120597119871

120597119875119895

= 0 forall119895

120582119894ge 0 sum

119895

119892119894119895119875119895minus 119868Δ119894

le 0

120582119894(sum

119895

119892119894119895119875119895minus 119868Δ119894) = 0 forall119894

(5)











0at


= 1199010 119895 isin 119869



0




119910119896119895

= 1199010sdot exp(

1205902

119896119895minus 1205902

119894119895

21205852

+

119871(119889119887)

119896119895minus 119871(119889119887)

119894119895

120585) 119895 isin 119869

119894 (6)



119868119894= sum

119895

119910119894119895= sum

119895isin119869119894

119910119894119895+ sum

119896 = 119894

sum

119895isin119869119896

119910119896119895 (7)



119895isin119869119894119910119894119895

= 1199010sdot |119869119894| where | sdot |



119894= 1199010sdot 120596119894where

120596119894= |119869119894|+sum119896 = 119894

sum119895isin119869119896

exp((1205902119894119895minus1205902

119896119895)21205852+(119871(119889119887)

119894119895minus119871(119889119887)

119896119895)120585) For





1199010= min119894isin119863

119868Δ119894

120596119894

(8)



119894119895by 1199010into (3)

119875119895= 1199010sdot119890minus120590211989411989521205852

sdot10minus119871(119889119887)

11989411989510





119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


21198941198952120585)minus10log10(120596119894))10

(9)


0at its dominating


Δ1+ 119868Δ2



119901minus


TV coverage area


119868Δ1

119868Δ2

31199010

41199010


TV coverage area


119868Δ1 + 119868Δ2




0is O(|119863| minus 1) Since |119863| ≪ 119873

119901the



2sdot

11987332








119910119894119895= 119908119895sdot 119875119895sdot 119890120590211989411989521205852

sdot sum

119899

10119871(119889119887)

11989411989511989910

(10)




119895119860120598)119860119895where 119860

120598is the



119871(119889119887)




119894to




0|119869119894|








119875119895=

1199010sdot10038161003816100381610038161198691198941003816100381610038161003816

sum119895isin119869119894

119908119895

sdot 119890minus120590211989411989521205852

sdot (sum

119899

10119871(119889119887)

11989411989511989910

)

minus1

119895 isin 119869119894 119894 isin 119863

(11)



120596119894=

10038161003816100381610038161198691198941003816100381610038161003816

+ sum

119896 = 119894

sum

119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(12)



119895isin119869119894119873119895inside the




0and




119894in




119894becomes

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816 + sum

119896 = 119894

10038161003816100381610038161198691198961003816100381610038161003816

sdotmax119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(13)




Δ119894= 119902 sdot 119868

Δ119894 for all 119894



by 119868(BS)Δ119894


119895by using



=

119868Δ119894


119894119895is




Δ119894by 119868(UE)Δ119894




(km)

(km

)

Use

rs p

er p

ixel

5 10 15 20 25

5

10

15

20

25 1

3

10

30

100

300

1000




119905= 171 dB and



119894119895= 8 dB

for all 119894 119895



m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast


lowastlowastlowast




0

01

02

03

04

05

06

07

08

09

1

CDF



= 7km= 7km






119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590


(14)




119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)




7 Conclusions



5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










TV coverage area


119868Δ1

119868Δ2

31199010

41199010


TV coverage area


119868Δ1 + 119868Δ2




0is O(|119863| minus 1) Since |119863| ≪ 119873

119901the



2sdot

11987332








119910119894119895= 119908119895sdot 119875119895sdot 119890120590211989411989521205852

sdot sum

119899

10119871(119889119887)

11989411989511989910

(10)




119895119860120598)119860119895where 119860

120598is the



119871(119889119887)




119894to




0|119869119894|








119875119895=

1199010sdot10038161003816100381610038161198691198941003816100381610038161003816

sum119895isin119869119894

119908119895

sdot 119890minus120590211989411989521205852

sdot (sum

119899

10119871(119889119887)

11989411989511989910

)

minus1

119895 isin 119869119894 119894 isin 119863

(11)



120596119894=

10038161003816100381610038161198691198941003816100381610038161003816

+ sum

119896 = 119894

sum

119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(12)



119895isin119869119894119873119895inside the




0and




119894in




119894becomes

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816 + sum

119896 = 119894

10038161003816100381610038161198691198961003816100381610038161003816

sdotmax119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(13)




Δ119894= 119902 sdot 119868

Δ119894 for all 119894



by 119868(BS)Δ119894


119895by using



=

119868Δ119894


119894119895is




Δ119894by 119868(UE)Δ119894




(km)

(km

)

Use

rs p

er p

ixel

5 10 15 20 25

5

10

15

20

25 1

3

10

30

100

300

1000




119905= 171 dB and



119894119895= 8 dB

for all 119894 119895



m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast


lowastlowastlowast




0

01

02

03

04

05

06

07

08

09

1

CDF



= 7km= 7km






119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590


(14)




119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)




7 Conclusions



5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0and




119894in




119894becomes

120596119894=

10038161003816100381610038161198691198941003816100381610038161003816 + sum

119896 = 119894

10038161003816100381610038161198691198961003816100381610038161003816

sdotmax119895isin119869119896

exp(

1205902

119894119895minus 1205902

119896119895

21205852

+10

120585(log10sum

119899

10119871(119889119887)

11989411989511989910

minuslog10sum

119899

10119871(119889119887)

11989611989511989910

))

(13)




Δ119894= 119902 sdot 119868

Δ119894 for all 119894



by 119868(BS)Δ119894


119895by using



=

119868Δ119894


119894119895is




Δ119894by 119868(UE)Δ119894




(km)

(km

)

Use

rs p

er p

ixel

5 10 15 20 25

5

10

15

20

25 1

3

10

30

100

300

1000




119905= 171 dB and



119894119895= 8 dB

for all 119894 119895



m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast


lowastlowastlowast




0

01

02

03

04

05

06

07

08

09

1

CDF



= 7km= 7km






119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590


(14)




119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)




7 Conclusions



5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










m)

(km) 5 10 15 20 25

5

10

15

20

25

lowastlowastlowast


lowastlowastlowast




0

01

02

03

04

05

06

07

08

09

1

CDF



= 7km= 7km






119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590


(14)




119875119895= min119894isin119863

10(119878(119889119887)

119894minus120574(119889119887)119905 minus119871

(119889119887)


2TV119894+120590

2119894119895minus10 log10(119873))10

(15)




7 Conclusions



5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 10 15 20 25 30 35 400

01

02

03

04

05

06

07

08

09

1

SINR (dB)

CDF

PFSimplified PF




0

01

02

03

04

05

06

07

08

09

1

CDF

minus10

119903119899 = 1 km (11)119903119899 = 1 km (12)119903119899 = 3 km (11)119903119899 = 3 km (12)

119903119899 = 7 km (11)119903119899 = 7 km (12)119903119899 = 10 km (11)119903119899 = 10 km (12)




0010203040506070809

1

CDF

119902 = 0

119902 = 05

119902 = 075



Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Proportional Fair Power Allocation for Secondary...

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