Inter-cell Transmit Power Adaptation Algorithm forCoexistence of White Space Applications

Seungil Yoon1, Jongmin Park2, Kyutae Lim1, and Jongman Kim3

1 Georgia Electronic Design Center, School of Electrical and Computer Engineering,

Georgia Institute of Technology, Atlanta, Georgia 30332, Email: {syoon7, ktlim}@ece.gatech.edu2 Qualcomm Inc., San Diego, CA 92121, Email: park@qualcomm.com

3 KORUS Research Center for Informersive Systems, School of Electrical and Computer Engineering,

Georgia Institute of Technology, Atlanta, Georgia 30332, Email: jkim@ece.gatech.edu

Abstract—White space, the unused local TV channels, areready to be used for unlicensed wireless devices. Due to itspropagation characteristics, availability of white space channelscan be limited in a densely populated area. This paper presentsan inter-cell transmit power adaptation (ITPA) algorithm thatenhances the decision procedure of a negotiation-based transmitpower control (TPC) in the selection of a shareable channel andthe decision of the new transmit power level of neighboringwhite space applications (WSAs) on the shareable channel.For the evaluation of the algorithm, we conduct theoreticalanalysis and simulation and prove that the ITPA algorithm canassist the newly-joining WSAs to find shareable channels withneighboring WSAs for the negotiation-based TPC. We expectthat the enhancement in channel assignment contributes to anincrease in the accommodation of newly-joining WSAs althoughall channels are occupied.

Index Terms—white space, inter-cell transmit power control,lower power white space applications, coexistence.

I. INTRODUCTION

In November 2008, Federal Communications Commission

(FCC) approved the rule that allows the use of white space,

unused local TV spectrum, for low power wireless devices un-

less they interfere with incumbent users [1]. Addition of white

space spectrum to mobile devices could extend the availability

of Internet access. However, because of the opportunistic

channel assignment of white space such as dynamic frequency

selection or dynamic frequency sharing according to [2-6],

the number of available white space channels can be limited

in a densely populated area. Due to this insufficiency, the

coexistence of low power unlicensed white space applications

(WSAs) becomes a major issue. Contrary to licensed wireless

systems such as cellular systems that maintain their minimum

transmit power to support the required signal-to-noise ratio

(SNR), WSAs are expected to set up factory-default or FCC

recommended transmit power level. Thus, since WSAs have

a margin to increase or decrease their transmit power on the

condition that they with increased or decreased new transmit

power can support their associated clients, transmit power

control (TPC) is an attractive coexistence approach.

Conventional TPC-based coexistence mechanisms are non-

collaborative mechanisms, where WSAs adjust their transmit

power not to interfere with their neighboring WSAs without

any negotiation of their new transmit power. Although we can

consider to adapt new schemes, introduced in [7] and [8],

WSAs cannot adjust their transmit power precisely with the

absence of collaborative negotiation. For the effective control,

WSAs prefer a collaborative TPC mechanism such as that of

3GPP self-organized network (SON), which operates under the

rules of licensed service providers. However, since low power

WSAs operate in an unlicensed mode, they have no tightly

centralized controllers as the assistant of the collaborative TPC

mechanism. Instead of tightly centralized controllers, we could

consider to use other centralized or distributed controllers,

suggested in [9 -15], but since the controllers have no authority

on channel management, all previous work do not involve the

change of channel configuration such as a current transmit

power. However, we believe that those controllers can assist

heterogeneous white space access points (WSAPs) to negotiate

their new transmit power. Based on this perspective, we sug-

gest inter-cell transmit power adaptation algorithm (ITPA) as

the decision algorithm of the negotiation-based TPC between

WSAPs.

This paper consists of following sections: Section II de-

scribes the proposed ITPA algorithm, and Section III defines

the evaluation metrics for theoretical analysis of the ITPA

algorithm. In addition, Section III presents all equations and

conditions used to evaluate the ITPA algorithm and the evalua-

tion results. Section IV presents the simulation analysis of the

ITPA algorithm-based coexistence mechanism, and Section V

summarizes our work with the future work.

II. INTER-CELL TRANSMIT POWER ADAPTATION

ALGORITHM

To estimate the power margin that neighboring WSAPs can

afford to adjust, the ITPA algorithm requires three calculation

functions: a distance between two WSAPs, the amount of an

increase in a noise floor, and the expected received signal

strength (RSS) of WSAPs at associated clients.

A. Basic Functions

To calculate a distance between two WSAPs, the algorithm

selects a proper path loss model by referring to location and

channel configuration information. We assume that WSAPs

broadcast not only location information such as an address

or a location type – indoor or outdoor – but also channel

The 8th Annual IEEE Consumer Communications and Networking Conference - Wireless Consumer Communication andNetworking

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configuration information such as their current transmit power,

Ptx, the worst path loss between them and their associated

clients, and their target SNR, Psnr. Let us assume that neigh-

boring WSAPs operate on the ith channel, and newly-joining

WSAPs select the ith channel as their operating channel.

Newly-joining WSAPs can estimate the path loss between

them and neighboring WSAPs using Pl = Ptx − Pmr, where

Pmr is the measured RSS of the signals of neighboring

WSAPs at the center of newly-joining WSAPs. With the

location type of neighboring WSAPs, newly-joining WSAPs

can choose a proper propagation model and a fading model and

then calculate the distance r between newly-joining WSAPs

and neighboring WSAPs using the inverse function of the

following equation: Pl = Ploss(r, f), where Ploss is the

function of path loss models, and f is the center frequency.

The signals of newly-joining WSAPs as interference gener-

ators cause an increase in the noise floor (PN ) of neighboring

WSAP as interference victims, and the increase can be calcu-

lated using the following equation [16]:

�P = �P (Per, PN , d) = 10 log(10

Per10 + 10

PN10

)− PN ,

(1)

where Per is the expected RSS of the signals of newly-joining

WSAPs at the d distance from the center of neighboring WS-

APs. Contrary to the fact that we can acquire practically mea-

sured RSS of the signals of neighboring WSAPs at the center

of newly-joining WSAPs, we can only estimate the expected

RSS of the signals of newly-joining WSAPs at the center of

neighboring WSAPs since newly-joining WSAPs do not really

transmit their signals. Instead, we can estimate the expected

RSS with the following equation: Per = Ptx − Ploss(d, f),where Ptx is the expected transmit power of newly-joining

WSAPs.

The expected RSS of the signals of a newly-joining WSAP

measured by clients associated to neighboring WSAPs should

be less than the sum of Psnr of neighboring WSAPs and

the peak-to-average power ratio (PAPR), PPR. Otherwise,

the clients cannot catch the signals of neighboring WSAPs

because of the interference caused by the signals of newly-

joining WSAPs operating on the same channel. At the clients

associated to the newly-joining APs, the expected RSS of

the signals of the neighboring WSAP at the clients should

be less than the sum of Psnr of the newly-joining WSAP

and PPR. However, since newly-joining WSAPs have no

associated clients yet, the algorithm simply regards that newly-

joining WSAPs have the same clients of neighboring WSAPs.

Thus, the expected RSS of the signals of neighboring WSAPs

at virtual clients, associated to newly-joining WSAPs, should

be less than the sum of Psnr of newly-joining WSAPs and

the PAPR. Now, we can define the desired difference, Pdiff ,

with the following equation:

Pdiff = Psnr + PPR, (2)

where we take the PAPR of 10 dB in this paper, and the

ITPA algorithm uses Pdiff to check the availability of desired

signals.

D1

R

R

nAP ngAP

D2

client

D2D3

RnLngLn

Fig. 1. Reference model of the ITPA algorithm

B. ITPA Algorithm Description

Fig. 1 illustrates the extent to which the ITPA algorithm

works. Let a ngAP denote a neighboring WSAP, and let a nAP

denote a newly-joining WSAP. With Prx that is the measured

RSS of the signals of the ngAP at the nAP and Ptx of the

ngAP, the nAP can estimate the distance, D1, between the

center of the nAP and the center of the ngAP. In addition,

with Plrx that is the lowest estimated RSS at the clients of the

ngAP and Ptx of the ngAP, the nAP can also estimate an active

service coverage, D2, from the center of the ngAP to its clients

that reported Plrx. Instead of a desired service coverage, R,

the ITPA algorithm regards D2 as an actual service coverage.

Thus, the expected RSS of the signals of the ngAP at the D2

distance from the center of the ngAP should be greater than

Pmin that also reflects interference caused by the signals of the

nAP. Since Plrx is the worst path loss between the ngAP and

its clients, the algorithm treats an actual distance calculated

with Plrx as the longest distance from the center of the ngAP.

Thus, as depicted in Fig. 1, the strong signals of the ngAP

should reach a location, Lng , where is at the D2 distance

from the center, resulting in providing better QoS to clients

than QoS measured at the client that reported the worst path

loss. However, since we have to tackle the worst case about

the location of clients, the algorithm assumes that Lng locates

on a straight line between the center of the ngAP and the

center of the nAP. Meanwhile, the strong signals of the nAP

should reach a location, Ln, where is at the distance, Rn, from

the center of the nAP. Since the nAP has no real clients, the

algorithm uses a desired service coverage, Rn, to be equal to

D2 of the ngAP. At Ln, the ITPA algorithm estimates �Png

that is the increase in the noise floor of the nAP and Pdiff

of the nAP using (2). The algorithm examines whether the

expected RSS of the signals of the nAP, Pnrx, at Ln is greater

than the sum of Pmin of the nAP and �Png , and If not, the

algorithm declares that the ITPA negotiation cannot proceed

with the ngAP. Otherwise, the algorithm examines whether

the difference of the expected RSS of the signals of the nAP,

Pnrx, and the expected RSS of the ngAP, Png

rx , at Ln is greater

than Pdiff of the nAP. If it is, the ITPA algorithm, which

regards that the nAP can support its potential clients within

a Rn service coverage, includes the channel where the ngAP

operates on in a target list of ITPA negotiation.

488

If the above operation indicates that the nAP can accept

the ITPA-based coexistence, the nAP attempts to investigate

whether the ngAP can accept the activation of the nAP with

revised channel configuration parameters such as new transmit

power of the ngAP on the same channel. At Lng , the ITPA

algorithm estimates �Pn that is the increase in the noise floor

of the ngAP and Pdiff of the ngAP. With them, the algorithm

examines whether the expected RSS of the ngAP, Pngrx , at Lng

is greater than the sum of Pmin of the ngAP and �Pn. If

not, the algorithm declares that the ITPA negotiation cannot

proceed with a given target channel, Ptx of the ngAP, and

Ptx of the nAP. Otherwise, the algorithm examines whether

the difference of the expected RSS of the ngAP, Pngrx , and

the expected RSS of the nAP, Pnrx, at Lng is greater than

Pdiff of the ngAP. If it is, the ITPA algorithm regards that the

ngAP can still serve its clients within the D2 service coverage.

Thus, the algorithm concludes that the ngAP and the nAP can

coexist on the same channel if both APs can accept ITPA-

based coexistence.

The algorithm repeats all above procedures, which examine

whether both the nAP and the ngAP can coexist, with all

possible changeable channel configuration. If the algorithm

finds an affordable configuration of all channels listed in

the spectrum map, the nAP initiates the ITPA negotiation

through the controllers described in Section I, but the detailed

procedures of the ITPA negotiation are beyond the scope in

this paper. The ngAP can break the coexistence of its operating

channel if the ngAP detects a decrease in service quality

below the minimum SNR. This case can occur because of

portable clients, and the ngAP increases its transmit power

while the nAP switches its operating channel to another unused

or reusable channels immediately. Thus, the nAP sharing the

channel of the ngAP must continue to search unused channels

to be able to switch to the new channel immediately.

III. THEORETICAL ANALYSIS

For theoretical analysis, we define two evaluation metrics

for evaluating the performance of the proposed ITPA algo-

rithm. We only consider the forward link of white space since

the majority of data transmission occurs in the forward link.

A. Network and Channel Models

We adopt indoor network environment and media traffic as

the respective reference network model and target application.

Thus, we choose the values of evaluation parameters according

to the characteristics of indoor channel environment and media

traffic service. To support the target bit error rate (BER) of

10−4 for media traffic service, this paper takes target SNRs

of 10, 20 and 30 dB for QPSK, 16/32 QAM and 256 QAM

modulations, respectively [17]. As the channel model, we

adopt Log-normal shadowing [18] and exponential Rayleigh

multi-path fading model [19] to calculate the expected mean

path loss, Ploss, and the expected RSS (ERSS), Prx, which

are expressed as

Ploss(r, f, d0) = L0 + 10η log(r/d0) +X

Prx(Ptx, Ploss) = −(Ptx − Ploss(r, f, d0)) ln(1− τ),(3)

where r is the distance to the center of the AP, and L0, which

is equal to 10 log(c/4πf)2, is the path loss to the reference

distance d0 (= 1 m). f (= 600 MHz) is the channel frequency,

c is the light speed, and Ptx is the transmit power of the

AP. η (= 3) is the log-normal path exponent, X is a zero-

mean Gaussian distribution with standard deviation, σ, and τis a random value between 0 to 1. In the theoretical analysis

and the simulation, the reverse function of (3) is used as the

function to calculate the distance between two APs. According

to the characteristics of indoor radio propagation, PN is 6 - 174

+ 10 log (6 MHz), ρ is from 0.001 to 0.004, and σ has 12 dB

[20]. Rc is the distance of sensing coverage, and this paper

assumes that the nAP can detect ngAPs within Rc (= 180 m, 6

clusters × 30 m average wall distance on IEEE 802.11n Model

F [21]).

B. Expected Success Probability of ITPA Algorithm

We define the probability of interference free (PIF) of the

ngAP at Lng and the PIF of the nAP at Ln. The PIF of

the ngAP is the probability that the expected RSS of the

signals of the ngAP at Lng is greater than not only the

required Pmin but also the expected RSS of the signals of

the nAP at Lng . In addition, the PIF of the nAP at Ln is

the probability that the expected RSS of the signals of the

nAP at Ln is greater than not only the the required Pmin

but also the expected RSS of the signals of the ngAP at

Ln. Because the expected RSS follows the Gaussian distri-

bution, we can estimate the PIF using the following equation:

PA(d, Patx, P

vtx, D) = Q((P ′min − Prx(P

vtx, Ploss))/σ), where

d is the distance to the center of an aggressor WSAP, Patx

is the current transmit power of the aggressor WSAP, Pvtx is

the current transmit power of a victim WSAP, and D is the

distance between two APs. Q(x) = (1/√2π)

∫∞x

e−t2

2 dt is

the Q-function of the normalized Gaussian distribution with

standard deviation, σ.

Thus, the PIF of the nAP is expressed as

PIFn = P (Pnrx > P ′min)× P ((Pn

rx − Pdiff ) > Pngrx ) =

PA(Rn, Pngtx , Pn

tx, D1) × P ′A(Rn, Pngtx , Pn

tx, D1), where Pnrx

is the expected RSS of the signals of the nAP at Ln, and

P ′min(= Pmin+�P (P atx, PN , D− d)) of the nAP is the new

Pmin, where D−d is a distance used to calculate the expected

RSS of the ngAP. Pngrx is the expected RSS of the signals of

the ngAPs at Ln as a noise to the nAP, and P ′A is expressed

as P ′A = 1 − Q(((PN + Pdiff ) − Prx(Ptx, Ploss))/σ).Meanwhile, the PIF of the ngAP is expressed as

PIFng = P (Pngrx > P ′min)× P ((Png

rx − Pdiff ) > Pnrx) =

PA(D2, Pntx, P

ngtx , D1) × P ′A(D2, P

ntx, P

ngtx , D1), where Png

rx

is the expected RSS of the the signals of ngAP at Lng , P ′min

of the ngAP is the sum of Pmin and �Pn, and Pnrx is the

expected RSS of the signals of the nAP at Lng as a noise

to the ngAP. A general formula of the probability of the

success of the ITPA algorithm-based coexistence is expressed

as Ps(Pntx, P

ngtx , Rn, D1, D2) = β × PIFn × PIFng , where

β is a reliability constant of SNR measurements. We assume

that β is 1, and the exact value of β is beyond the scope of

this paper. Since Ps depends on parameters, D1, D2, Pntx,

489

20 30 40 50 60 70 80 90 100 110 120 1300.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Distance, R(m)

S ITP

A :

Ana

lysi

s R

esul

t

n = 50 n = 30 n = 10

(a) SITPA with Psnr = 10 dB.

20 30 40 50 60 70 80 90 100 110 120 1300.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Distance, R(m)

S ITP

A :

Ana

lysi

s R

esul

t

n = 50 n = 30 n = 10

(b) SITPA with Psnr = 30 dB.

10 20 300.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

R= 30 R= 60 R= 90 R= 120

SNR (dB)

S ITPA

: A

naly

sis

Res

ult

(c) SITPA for n = 50.

Fig. 2. Analysis results of the expected success rate of the ITPA algorithm (SITPA) with Ptx = 20 dBm.

Pngtx , and Rn, with given Pn

tx, Pngtx , and Rn, the probability

of the success of the ITPA algorithm-based coexistence varies

by D1 and D2. We adopt the uniform distribution as the

probability density function (pdf) for the distribution of the

clients associated to the WSAP. The pdf for the distance D2

is expressed as fRP (D2, Rm) = (2D2/R2m), 0 ≤ D2 ≤ Rm,

where Rm is the maximum service coverage [22]. Thus, the

expected probability of the success of the ITPA negotiation

with a given D1 is expressed as

E(Ps(D1, D2)) =

∫ R

0

fRP (r,R)Ps(Pntx, P

ngtx , Rn, D1, r) dr.

(4)

The variance of D1 depends on the AP density, ρ, and the

maximum distance of sensing coverage, Rc. Using ω = ρR2c =

αn, where ω is the average number of active neighboring

APs, n is the number of white space channels, and α is a

reusable index, we can estimate ρ where the newly-joining

AP requires the ITPA algorithm with given n, Rc, and α.

We estimate ρ using P (Ne ≥ αN) = 1 − P (Ne < αN) =

1 − e−ω∑αN−1

j=0ωj

j! , where P (Ne ≥ αN) is the probability

that the detected number, Ne, of neighboring APs is greater

than αN . In other words, P (Ne ≥ αN) is the probability that

newly-joining APs require the ITPA algorithm. With α ≈ 1.3,

which we acquired through a simulation, the calculated ρvalues for αn are 1.3e-004, 4.1e-004, and 7.0e-004 for n= 10, 30, and 50 respectively. We use the calculated ρvalues to calculate the expected distance D1 with the lth

neighboring ngAP, E(Dl1). In the calculation of E(Dl

1), we

use the pdf of the lth nearest neighbor [23], which is ex-

pressed as E(Dl1) =

∫∞0

r fl(r)dr =∫∞0

r ((2πlρlr2l−1)/(l−1)!)e−πρr2dr = (1/

√ρ)(((2n)!n)/((2n n!)2), where fl(r)

is the pdf of the l th nearest ngAP within a given ra-

dius, r , and ρ is one of three values matched to αn.

With Ps and E(Dl1), the expected probability of the suc-

cess of the ITPA algorithm-based coexistence with the

lth neighbor AP is expressed as E(Ps(E(Dl1), D2)) =

(1/R2)∫ R

02r Ps(P

ntx, P

ngtx , Rn, E(Dl

1), r) dr. Thus, the ex-

pected success probability of ITPA algorithm is expressed as

SITPA = 1−αn∏l=1

(1− E(Ps(E(Dl1), D2))). (5)

As depicted in Fig. 2(a) and (b), all cases with a lower

Psnr show better results than the cases with a higher Psnr.

For example, for n = 50 and R = 60m, SITPA with

Psnr = 10 dB is about 60% while SITPA with Psnr = 30 dB

is less than 20%. With Psnr = 20 dB, as depicted in Fig. 2(c),

SITPA for all n cases except R = 30 m is less than or about

50%. The previous results are reasonable since a higher Psnr

will increase Pmin of neighboring ngAPs so that a newly-

joining AP is hard to acquire the approval of sharing their

already used channel since the signals of the newly-joining AP

become a critical interference to the ngAPs. We can observe a

similar pattern with the cases having more available channels.

However, although more channels can increase the success

of ITPA-base coexistence, with a higher Psnr, SITPA is less

than 50% as depicted in Fig. 2(b). Previous results reveal

that the ITPA algorithm-based coexistence is appropriate to

accommodate newly-joining APs requiring a lower Psnr or

a higher Psnr with a short service distance. In fact, WSAPs

providing high quality service will be reluctant to allow other

WSAPs to share their white space channels, and thus, they

are not likely cooperative about coexistence. Instead, other

WSAPs satisfying with a lower Psnr like 20 or 10 dB seem

to be cooperative in spectrum sharing. Also, newly-joining

WSAPs can have plenty of shareable channels in some areas

where we have n = 30 or 50. In this case, the ITPA-based

coexistence can enhance the success of activating the newly-

joining WSAPs after all channels are occupied.

IV. SIMULATION ANALYSIS

We implement the ITPA algorithm in MatlabTM.

A. Simulation Scenario

The simulation uniformly distributes all APs and randomly

activates one new nAP. The selected AP, nAP, performs

spectrum sensing, and the nAP calculates the expected RSS of

490

0.000 0.002 0.004 0.006 0.008 0.0100.0

0.2

0.4

0.6

0.8

1.0

the AP density (�)

(b)

The

suc

css

rate

of

chan

nel a

ssig

nmen

t Ss, n=30 Si1,n=30 Si2,n=30 Ss, n=50 Si1,n=50 Si2,n=50

(a)

Fig. 3. The success rate of channel assignment with Ptx = 20 dBm, R =90 m, and Psnr = 10 dB.

all activated ngAPs measured at the nAP. If the expected RSS

is less than or equal to PN of the nAP, the simulation declares

the success of finding its operating channel. Otherwise, the

simulation executes the ITPA algorithm with a new transmit

power, Ptx = 10 or 20 dBm.

B. The Success of Newly-joining AP Activation

We estimate the following three variables:

• Ss: the success rate of spectrum sensing.

• Si1: Ss plus the success of the ITPA with Ptx = 20 dBm.

• Si2: Si1 plus the success of the ITPA with Ptx = 10 dBm.

Let Tn denote the total number of APs. The number of

spectrum sensing attempts is equal to Tn. If the number of

the success of spectrum sensing is Ts, Ss is expressed as

Ss = Ts/Tn. If the number of the success of the ITPA

algorithm with Ptx = 20 dBm is Ts1, Si1 is expressed as

Si1 = (Ts + Ts1)/Tn. If the number of the success of the

ITPA algorithm with Ptx = 10 dBm is Ts2, Si2 is expressed

as Si2 = (Ts+Ts1+Ts2)/Tn. Fig. 3 illustrates the simulation

results with Psnr = 10 dB and R = 90m. With n = 30, Si2 is

greater than Ss by 30% as depicted in the (a) label of Fig. 3.

With n = 30, the difference decreases since Ss has a higher

success rate of channel assignment during spectrum sensing

with more available channels. With n = 50, as the AP density

increases, the difference between Ss and Si2 increases. For

instance, at ρ = 0.004, the difference for n = 50, is greater

than 40% as depicted in the (b) label of Fig. 3. Thus, while

the total success rate decreases as the AP density increases,

our approach can improve the total success rate compared to

the general approach only relying on searching unoccupied

channels.

V. CONCLUSIONS

The ITPA algorithm aims to increase channel reusability of

white space by adjusting the transmit power and the service

coverage of white space applications. Theoretical analysis

and simulation results show that the ITPA algorithm can

assist newly-joining APs to activate their service even after

spectrum sensing results report that all channels are occupied.

As a future work, we will enhance the ITPA algorithm-based

coexistence mechanism that can operate on heterogenous white

space applications.

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