GUESS:

Gossiping

Updates

for

Efficient

Spectrum

Sensing

Nabeel

Ahmed

University

of

Waterloo

David

R.

Cheriton

School

of

Computer

Science

David

Hadaller

University

of

Waterloo

David

R.

Cheriton

School

of

Computer

Science

dthadaller@uwaterloo.ca

Srinivasan

Keshav

University

of

Waterloo

David

R.

Cheriton

School

of

Computer

Science

keshav@uwaterloo.ca

ABSTRACT

Wireless

radios

of

the

future

will

likely

be

frequency-agile,

that

is,

supporting

opportunistic

and

adaptive

use

of

the

RF

spectrum.

Such

radios

must

coordinate

with

each

other

to

build

an

accurate

and

consistent

map

of

spectral

utilization

in

their

surroundings.

We

focus

on

the

problem

of

sharing

RF

spectrum

data

among

a

collection

of

wireless

devices.

The

inherent

requirements

of

such

data

and

the

time-granularity

at

which

it

must

be

collected

makes

this

problem

both

interesting

and

technically

challenging.

We

propose

GUESS,

a

novel

incremental

gossiping

approach

to

coordinated

spectral

sensing.

It

reduces

protocol

overhead

by

limiting

the

amount

of

information

exchanged

between

participating

nodes,

is

resilient

to

network

alterations,

due

to

node

movement

or

node

failures,

and

allows

exponentially-fast

information

convergence.

We

outline

an

initial

solution

incorporating

these

ideas

and

also

show

how

our

approach

reduces

network

overhead

by

up

to

a

factor

of

and

results

in

up

to

times

faster

information

convergence

than

alternative

approaches.

Categories

and

Subject

Descriptors

[Distributed

Systems]:

Distributed

applications

General

Terms

Algorithms,

Performance,

Experimentation

INTRODUCTION

There

has

recently

been

a

huge

surge

in

the

growth

of

wireless

technology,

driven

primarily

by

the

availability

of

unlicensed

spectrum.

However,

this

has

come

at

the

cost

of

increased

RF

interference,

which

has

caused

the

Federal

Communications

Commission

(FCC)

in

the

United

States

to

re-evaluate

its

strategy

on

spectrum

allocation.

Currently,

the

FCC

has

licensed

RF

spectrum

to

a

variety

of

public

and

private

institutions,

termed

primary

users.

New

spectrum

allocation

regimes

implemented

by

the

FCC

use

dynamic

spectrum

access

schemes

to

either

negotiate

or

opportunistically

allocate

RF

spectrum

to

unlicensed

secondary

users

Permission

to

make

digital

or

hard

copies

of

all

or

part

of

this

work

for

personal

or

classroom

use

is

granted

without

fee

provided

that

copies

are

not

made

or

distributed

for

profit

or

commercial

advantage

and

that

copies

bear

this

notice

and

the

full

citation

on

the

first

page.

To

copy

otherwise,

to

republish,

to

post

on

servers

or

to

redistribute

to

lists,

requires

prior

specific

Primary

User

Shadowed

Secondary

Users

Secondary

Users

detect

Primary's

Signal

Shadowed

Secondary

User

Figure

Without

cooperation,

shadowed

users

are

not

able

to

detect

the

presence

of

the

primary

user.

that

can

use

it

when

the

primary

user

is

absent.

The

second

type

of

allocation

scheme

is

termed

opportunistic

spectrum

sharing.

The

FCC

has

already

legislated

this

access

method

for

the

GHz

band

and

is

also

considering

the

same

for

TV

broadcast

bands

As

a

result,

a

new

wave

of

intelligent

radios,

termed

cognitive

radios

(or

software

defined

radios),

is

emerging

that

can

dynamically

re-tune

their

radio

parameters

based

on

interactions

with

their

surrounding

environment.

Under

the

new

opportunistic

allocation

strategy,

secondary

users

are

obligated

not

to

interfere

with

primary

users

(senders

or

receivers).

This

can

be

done

by

sensing

the

environment

to

detect

the

presence

of

primary

users.

However,

local

sensing

is

not

always

adequate,

especially

in

cases

where

a

secondary

user

is

shadowed

from

a

primary

user,

as

illustrated

in

Figure

Here,

coordination

between

secondary

users

is

the

only

way

for

shadowed

users

to

detect

the

primary.

In

general,

cooperation

improves

sensing

accuracy

by

an

order

of

magnitude

when

compared

to

not

cooperating

at

all

To

realize

this

vision

of

dynamic

spectrum

access,

two

fundamental

problems

must

be

solved:

Efficient

and

coordinated

spectrum

sensing

and

Distributed

spectrum

allocation.

In

this

paper,

we

propose

strategies

for

coordinated

spectrum

sensing

that

are

low

cost,

operate

on

timescales

comparable

to

the

agility

of

the

RF

environment,

and

are

resilient

to

network

failures

and

alterations.

We

defer

the

problem

of

spectrum

allocation

to

future

work.

Spectrum

sensing

techniques

for

cognitive

radio

networks

are

broadly

classified

into

three

regimes;

centralized

coordinated

techniques,

decentralized

coordinated

techniques,

and

decentralized

uncoordinated

techniques.

We

advocate

a

decentralized

coordinated

approach,

similar

in

spirit

to

OSPF

link-state

routing

used

in

the

Internet.

This

is

more

effective

than

uncoordinated

approaches

because

making

decisions

based

only

on

local

information

is

fallible

(as

shown

in

Figure

Moreover,

compared

to

tralized

approaches,

decentralized

techniques

are

more

scalable,

robust,

and

resistant

to

network

failures

and

security

attacks

(e.g.

jamming).

Coordinating

sensory

data

between

cognitive

radio

devices

is

technically

challenging

because

accurately

assessing

spectrum

usage

requires

exchanging

potentially

large

amounts

of

data

with

many

radios

at

very

short

time

scales.

Data

size

grows

rapidly

due

to

the

large

number

(i.e.

thousands)

of

spectrum

bands

that

must

be

scanned.

This

data

must

also

be

exchanged

between

potentially

hundreds

of

neighboring

secondary

users

at

short

time

scales,

to

account

for

rapid

changes

in

the

RF

environment.

This

paper

presents

GUESS,

a

novel

approach

to

coordinated

spectrum

sensing

for

cognitive

radio

networks.

Our

approach

is

motivated

by

the

following

key

observations:

Low-cost

sensors

collect

approximate

data:

Most

devices

have

limited

sensing

resolution

because

they

are

low-cost

and

low

duty-cycle

devices

and

thus

cannot

perform

complex

RF

signal

processing

(e.g.

matched

filtering).

Many

are

typically

equipped

with

simple

energy

detectors

that

gather

only

approximate

information.

Approximate

summaries

are

sufficient

for

coordination:

Approximate

statistical

summaries

of

sensed

data

are

sufficient

for

correlating

sensed

information

between

radios,

as

relative

usage

information

is

more

important

than

absolute

usage

data.

Thus,

exchanging

exact

RF

information

may

not

be

necessary,

and

more

importantly,

too

costly

for

the

purposes

of

spectrum

sensing.

RF

spectrum

changes

incrementally:

On

most

bands,

RF

spectrum

utilization

changes

infrequently.

Moreover,

utilization

of

a

specific

RF

band

affects

only

that

band

and

not

the

entire

spectrum.

Therefore,

if

the

usage

pattern

of

a

particular

band

changes

substantially,

nodes

detecting

that

change

can

initiate

an

update

protocol

to

update

the

information

for

that

band

alone,

leaving

in

place

information

already

collected

for

other

bands.

This

allows

rapid

detection

of

change

while

saving

the

overhead

of

exchanging

unnecessary

information.

Based

on

these

observations,

GUESS

makes

the

following

contributions:

A

novel

approach

that

applies

randomized

gossiping

algorithms

to

the

problem

of

coordinated

spectrum

sensing.

These

algorithms

are

well

suited

to

coordinated

spectrum

sensing

due

to

the

unique

characteristics

of

the

problem:

i.e.

radios

are

power-limited,

mobile

and

have

limited

bandwidth

to

support

spectrum

sensing

capabilities.

An

application

of

in-network

aggregation

for

dissemination

of

spectrum

summaries.

We

argue

that

approximate

summaries

are

adequate

for

performing

accurate

radio

parameter

tuning.

An

extension

of

in-network

aggregation

and

randomized

gossiping

to

support

incremental

maintenance

of

spectrum

summaries.

Compared

to

standard

gossiping

approaches,

incremental

techniques

can

further

reduce

overhead

and

protocol

execution

time

by

requiring

fewer

radio

resources.

The

rest

of

the

paper

is

organized

as

follows.

Section

motivates

the

need

for

a

low

cost

and

efficient

approach

to

coordinated

spectrum

sensing.

Section

discusses

related

work

in

the

area,

while

Section

provides

a

background

on

in-network

aggregation

and

randomized

gossiping.

Sections

and

discuss

extensions

and

protocol

details

of

these

techniques

for

coordinated

spectrum

sensing.

Section

presents

simulation

results

showcasing

the

benefits

of

GUESS,

and

Section

presents

a

discussion

and

some

directions

for

future

work.

MOTIVATION

To

estimate

the

scale

of

the

problem,

In-stat

predicts

that

the

number

of

WiFi-enabled

devices

sold

annually

alone

will

grow

to

million

by

Therefore,

it

would

be

reasonable

to

assume

that

a

typical

dense

urban

environment

will

contain

several

thousand

cognitive

radio

devices

in

range

of

each

other.

As

a

result,

distributed

spectrum

sensing

and

allocation

would

become

both

important

and

fundamental.

Coordinated

sensing

among

secondary

radios

is

essential

due

to

limited

device

sensing

resolution

and

physical

RF

effects

such

as

shadowing.

Cabric

et

al.

illustrate

the

gains

from

cooperation

and

show

an

order

of

magnitude

reduction

in

the

probability

of

interference

with

the

primary

user

when

only

a

small

fraction

of

secondary

users

cooperate.

However,

such

coordination

is

non-trivial

due

to:

the

limited

bandwidth

available

for

coordination,

the

need

to

communicate

this

information

on

short

timescales,

and

the

large

amount

of

sensory

data

that

needs

to

be

exchanged.

Limited

Bandwidth:

Due

to

restrictions

of

cost

and

power,

most

devices

will

likely

not

have

dedicated

hardware

for

supporting

coordination.

This

implies

that

both

data

and

sensory

traffic

will

need

to

be

time-multiplexed

onto

a

single

radio

interface.

Therefore,

any

time

spent

communicating

sensory

information

takes

away

from

the

device"s

ability

to

perform

its

intended

function.

Thus,

any

such

coordination

must

incur

minimal

network

overhead.

Short

Timescales:

Further

compounding

the

problem

is

the

need

to

immediately

propagate

updated

RF

sensory

data,

in

order

to

allow

devices

to

react

to

it

in

a

timely

fashion.

This

is

especially

true

due

to

mobility,

as

rapid

changes

of

the

RF

environment

can

occur

due

to

device

and

obstacle

movements.

Here,

fading

and

multi-path

interference

heavily

impact

sensing

abilities.

Signal

level

can

drop

to

a

deep

with

just

a

movement

in

receiver

position

cm

at

GHz),

where

λ

is

the

wavelength

Coordination

which

does

not

support

rapid

dissemination

of

information

will

not

be

able

to

account

for

such

RF

variations.

Large

Sensory

Data:

Because

cognitive

radios

can

potentially

use

any

part

of

the

RF

spectrum,

there

will

be

numerous

channels

that

they

need

to

scan.

Suppose

we

wish

to

compute

the

average

signal

energy

in

each

of

discretized

frequency

bands,

and

each

signal

can

have

up

to

discrete

energy

levels.

Exchanging

complete

sensory

information

between

nodes

would

require

bits

per

transmission

(for

channels,

each

requiring

seven

bits

of

information).

Exchanging

this

information

among

even

a

small

group

of

devices

each

second

would

require

time-steps

devices

bits

per

transmission)

Mbps

of

aggregate

network

bandwidth.

Contrast

this

to

the

use

of

a

randomized

gossip

protocol

to

disseminate

such

information,

and

the

use

of

FM

bit

vectors

to

perform

in-network

aggregation.

By

applying

gossip

and

FM

aggregation,

aggregate

bandwidth

requirements

drop

to

(c·logN

time-steps

devices

bits

per

transmission)

Mbps,

since

time-steps

are

needed

to

propagate

the

data

(with

c

for

illustrative

This

is

explained

further

in

Section

Based

on

these

insights,

we

propose

GUESS,

a

low-overhead

approach

which

uses

incremental

extensions

to

FM

aggregation

and

randomized

gossiping

for

efficient

coordination

within

a

cognitive

radio

network.

As

we

show

in

Section

Convergence

time

is

correlated

with

the

connectivity

topology

of

the

devices,

which

in

turn

depends

on

the

environment.

X

A

A

X

B

B

X

Figure

Using

FM

aggregation

to

compute

average

signal

level

measured

by

a

group

of

devices.

these

incremental

extensions

can

further

reduce

bandwidth

requirements

by

up

to

a

factor

of

over

the

standard

approaches

discussed

above.

RELATED

WORK

Research

in

cognitive

radio

has

increased

rapidly

over

the

years,

and

it

is

being

projected

as

one

of

the

leading

enabling

technologies

for

wireless

networks

of

the

future

As

mentioned

earlier,

the

FCC

has

already

identified

new

regimes

for

spectrum

sharing

between

primary

users

and

secondary

users

and

a

variety

of

systems

have

been

proposed

in

the

literature

to

support

such

sharing

Detecting

the

presence

of

a

primary

user

is

non-trivial,

especially

a

legacy

primary

user

that

is

not

cognitive

radio

aware.

Secondary

users

must

be

able

to

detect

the

primary

even

if

they

cannot

properly

decode

its

signals.

This

has

been

shown

by

Sahai

et

al.

to

be

extremely

difficult

even

if

the

modulation

scheme

is

known.

Sophisticated

and

costly

hardware,

beyond

a

simple

energy

detector,

is

required

to

improve

signal

detection

accuracy

Moreover,

a

shadowed

secondary

user

may

not

even

be

able

to

detect

signals

from

the

primary.

As

a

result,

simple

local

sensing

approaches

have

not

gained

much

momentum.

This

has

motivated

the

need

for

cooperation

among

cognitive

radios

More

recently,

some

researchers

have

proposed

approaches

for

radio

coordination.

Liu

et

al.

consider

a

centralized

access

point

(or

base

station)

architecture

in

which

sensing

information

is

forwarded

to

APs

for

spectrum

allocation

purposes.

APs

direct

mobile

clients

to

collect

such

sensing

information

on

their

behalf.

However,

due

to

the

need

of

a

fixed

AP

infrastructure,

such

a

centralized

approach

is

clearly

not

scalable.

In

other

work,

Zhao

et

al.

propose

a

distributed

coordination

approach

for

spectrum

sensing

and

allocation.

Cognitive

radios

organize

into

clusters

and

coordination

occurs

within

clusters.

The

CORVUS

architecture

proposes

a

similar

clustering

method

that

can

use

either

a

centralized

or

decentralized

approach

to

manage

clusters.

Although

an

improvement

over

purely

centralized

approaches,

these

techniques

still

require

a

setup

phase

to

generate

the

clusters,

which

not

only

adds

additional

delay,

but

also

requires

many

of

the

secondary

users

to

be

static

or

quasi-static.

In

contrast,

GUESS

does

not

place

such

restrictions

on

secondary

users,

and

can

even

function

in

highly

mobile

environments.

BACKGROUND

This

section

provides

the

background

for

our

approach.

We

present

the

FM

aggregation

scheme

that

we

use

to

generate

spectrum

summaries

and

perform

in-network

aggregation.

We

also

discuss

randomized

gossiping

techniques

for

disseminating

aggregates

in

a

cognitive

radio

network.

FM

Aggregation

Aggregation

is

the

process

where

nodes

in

a

distributed

network

combine

data

received

from

neighboring

nodes

with

their

local

value

to

generate

a

combined

aggregate.

This

aggregate

is

then

communicated

to

other

nodes

in

the

network

and

this

process

repeats

until

the

aggregate

at

all

nodes

has

converged

to

the

same

value,

i.e.

the

global

aggregate.

Double-counting

is

a

well

known

problem

in

this

process,

where

nodes

may

contribute

more

than

once

to

the

aggregate,

causing

inaccuracy

in

the

final

result.

Intuitively,

nodes

can

tag

the

aggregate

value

they

transmit

with

information

about

which

nodes

have

contributed

to

it.

However,

this

approach

is

not

scalable.

Order

and

Duplicate

Insensitive

(ODI)

techniques

have

been

proposed

in

the

literature

We

adopt

the

ODI

approach

pioneered

by

Flajolet

and

Martin

(FM)

for

the

purposes

of

aggregation.

Next

we

outline

the

FM

approach;

for

full

details,

see

Suppose

we

want

to

compute

the

number

of

nodes

in

the

network,

i.e.

the

COUNT

query.

To

do

so,

each

node

performs

a

coin

toss

experiment

as

follows:

toss

an

unbiased

coin,

stopping

after

the

first

head

is

seen.

The

node

then

sets

the

ith

bit

in

a

bit

vector

(initially

filled

with

zeros),

where

i

is

the

number

of

coin

tosses

it

performed.

The

intuition

is

that

as

the

number

of

nodes

doing

coin

toss

experiments

increases,

the

probability

of

a

more

significant

bit

being

set

in

one

of

the

nodes"

bit

vectors

increases.

These

bit

vectors

are

then

exchanged

among

nodes.

When

a

node

receives

a

bit

vector,

it

updates

its

local

bit

vector

by

bitwise

OR-ing

it

with

the

received

vector

(as

shown

in

Figure

which

computes

AVERAGE).

At

the

end

of

the

aggregation

process,

every

node,

with

high

probability,

has

the

same

bit

vector.

The

actual

value

of

the

count

aggregate

is

then

computed

using

the

following

formula,

AGGF

M

where

j

represents

the

bit

position

of

the

least

significant

zero

in

the

aggregate

bit

vector

Although

such

aggregates

are

very

compact

in

nature,

requiring

only

O(logN)

state

space

(where

N

is

the

number

of

nodes),

they

may

not

be

very

accurate

as

they

can

only

approximate

values

to

the

closest

power

of

potentially

causing

errors

of

up

to

More

accurate

aggregates

can

be

computed

by

maintaining

multiple

bit

vectors

at

each

node,

as

explained

in

This

decreases

the

error

to

within

m),

where

m

is

the

number

of

such

bit

vectors.

Queries

other

than

count

can

also

be

computed

using

variants

of

this

basic

counting

algorithm,

as

discussed

in

(and

shown

in

Figure

Transmitting

FM

bit

vectors

between

nodes

is

done

using

randomized

gossiping,

discussed

next.

Gossip

Protocols

Gossip-based

protocols

operate

in

discrete

time-steps;

a

time-step

is

the

required

amount

of

time

for

all

transmissions

in

that

time-step

to

complete.

At

every

time-step,

each

node

having

something

to

send

randomly

selects

one

or

more

neighboring

nodes

and

transmits

its

data

to

them.

The

randomized

propagation

of

information

provides

fault-tolerance

and

resilience

to

network

failures

and

outages.

We

emphasize

that

this

characteristic

of

the

protocol

also

allows

it

to

operate

without

relying

on

any

underlying

network

structure.

Gossip

protocols

have

been

shown

to

provide

exponentially

fast

on

the

order

of

O(log

N)

where

N

is

the

number

of

nodes

(or

radios).

These

protocols

can

therefore

easily

scale

to

very

dense

environments.

Convergence

refers

to

the

state

in

which

all

nodes

have

the

most

up-to-date

view

of

the

network.

Two

types

of

gossip

protocols

are:

Uniform

Gossip:

In

uniform

gossip,

at

each

timestep,

each

node

chooses

a

random

neighbor

and

sends

its

data

to

it.

This

process

repeats

for

O(log(N))

steps

(where

N

is

the

number

of

nodes

in

the

network).

Uniform

gossip

provides

exponentially

fast

convergence,

with

low

network

overhead

Random

Walk:

In

random

walk,

only

a

subset

of

the

nodes

(termed

designated

nodes)

communicate

in

a

particular

time-step.

At

startup,

k

nodes

are

randomly

elected

as

designated

nodes.

In

each

time-step,

each

designated

node

sends

its

data

to

a

random

neighbor,

which

becomes

designated

for

the

subsequent

timestep

(much

like

passing

a

token).

This

process

repeats

until

the

aggregate

has

converged

in

the

network.

Random

walk

has

been

shown

to

provide

similar

convergence

bounds

as

uniform

gossip

in

problems

of

similar

context

INCREMENTAL

PROTOCOLS

Incremental

FM

Aggregates

One

limitation

of

FM

aggregation

is

that

it

does

not

support

updates.

Due

to

the

probabilistic

nature

of

FM,

once

bit

vectors

have

been

ORed

together,

information

cannot

simply

be

removed

from

them

as

each

node"s

contribution

has

not

been

recorded.

We

propose

the

use

of

delete

vectors,

an

extension

of

FM

to

support

updates.

We

maintain

a

separate

aggregate

delete

vector

whose

value

is

subtracted

from

the

original

aggregate

vector"s

value

to

obtain

the

resulting

value

as

follows.

AGGINC

Here,

a

and

b

represent

the

bit

positions

of

the

least

significant

zero

in

the

original

and

delete

bit

vectors

respectively.

Suppose

we

wish

to

compute

the

average

signal

level

detected

in

a

particular

frequency.

To

compute

this,

we

compute

the

SUM

of

all

signal

level

measurements

and

divide

that

by

the

COUNT

of

the

number

of

measurements.

A

SUM

aggregate

is

computed

similar

to

COUNT

(explained

in

Section

except

that

each

node

performs

s

coin

toss

experiments,

where

s

is

the

locally

measured

signal

level.

Figure

illustrates

the

sequence

by

which

the

average

signal

energy

is

computed

in

a

particular

band

using

FM

aggregation.

Now

suppose

that

the

measured

signal

at

a

node

changes

from

s

to

s

The

vectors

are

updated

as

follows.

s

s:

We

simply

perform

(s

s)

more

coin

toss

experiments

and

bitwise

OR

the

result

with

the

original

bit

vector.

s

s:

We

increase

the

value

of

the

delete

vector

by

performing

(s

s

coin

toss

experiments

and

bitwise

OR

the

result

with

the

current

delete

vector.

Using

delete

vectors,

we

can

now

support

updates

to

the

measured

signal

level.

With

the

original

implementation

of

FM,

the

aggregate

would

need

to

be

discarded

and

a

new

one

recomputed

every

time

an

update

occurred.

Thus,

delete

vectors

provide

a

low

overhead

alternative

for

applications

whose

data

changes

incrementally,

such

as

signal

level

measurements

in

a

coordinated

spectrum

sensing

environment.

Next

we

discuss

how

these

aggregates

can

be

communicated

between

devices

using

incremental

routing

protocols.

Incremental

Routing

Protocol

We

use

the

following

incremental

variants

of

the

routing

protocols

presented

in

Section

to

support

incremental

updates

to

previously

computed

aggregates.

Update

Received

OR

Local

Update

Occurs

Recovered

Susceptible

Time-stamp

Expires

Initial

State

Additional

Update

Received

Infectious

Clean

Up

Figure

State

diagram

each

device

passes

through

as

updates

proceed

in

the

system

Incremental

Gossip

Protocol

(IGP):

When

an

update

occurs,

the

updated

node

initiates

the

gossiping

procedure.

Other

nodes

only

begin

gossiping

once

they

receive

the

update.

Therefore,

nodes

receiving

the

update

become

active

and

continue

communicating

with

their

neighbors

until

the

update

protocol

terminates,

after

O(log(N))

time

steps.

Incremental

Random

Walk

Protocol

(IRWP):

When

an

update

(or

updates)

occur

in

the

system,

instead

of

starting

random

walks

at

k

random

nodes

in

the

network,

all

k

random

walks

are

initiated

from

the

updated

node(s).

The

rest

of

the

protocol

proceeds

in

the

same

fashion

as

the

standard

random

walk

protocol.

The

allocation

of

walks

to

updates

is

discussed

in

more

detail

in

where

the

authors

show

that

the

number

of

walks

has

an

almost

negligible

impact

on

network

overhead.

PROTOCOL

DETAILS

Using

incremental

routing

protocols

to

disseminate

incremental

FM

aggregates

is

a

natural

fit

for

the

problem

of

coordinated

spectrum

sensing.

Here

we

outline

the

implementation

of

such

techniques

for

a

cognitive

radio

network.

We

continue

with

the

example

from

Section

where

we

wish

to

perform

coordination

between

a

group

of

wireless

devices

to

compute

the

average

signal

level

in

a

particular

frequency

band.

Using

either

incremental

random

walk

or

incremental

gossip,

each

device

proceeds

through

three

phases,

in

order

to

determine

the

global

average

signal

level

for

a

particular

frequency

band.

Figure

shows

a

state

diagram

of

these

phases.

Susceptible:

Each

device

starts

in

the

susceptible

state

and

becomes

infectious

only

when

its

locally

measured

signal

level

changes,

or

if

it

receives

an

update

message

from

a

neighboring

device.

If

a

local

change

is

observed,

the

device

updates

either

the

original

or

delete

bit

vector,

as

described

in

Section

and

moves

into

the

infectious

state.

If

it

receives

an

update

message,

it

ORs

the

received

original

and

delete

bit

vectors

with

its

local

bit

vectors

and

moves

into

the

infectious

state.

Note,

because

signal

level

measurements

may

change

sporadically

over

time,

a

smoothing

function,

such

as

an

exponentially

weighted

moving

average,

should

be

applied

to

these

measurements.

Infectious:

Once

a

device

is

infectious

it

continues

to

send

its

up-to-date

bit

vectors,

using

either

incremental

random

walk

or

incremental

gossip,

to

neighboring

nodes.

Due

to

FM"s

order

and

duplicate

insensitive

(ODI)

properties,

simultaneously

occurring

updates

are

handled

seamlessly

by

the

protocol.

Update

messages

contain

a

time

stamp

indicating

when

the

update

was

generated,

and

each

device

maintains

a

Number

of

Measured

Signal

Changes

Executiontime(ms)

Incremental

Gossip

Uniform

Gossip

(a)

Incremental

Gossip

and

Uniform

Gossip

on

Clique

Number

of

Measured

Signal

Changes

ExecutionTime(ms).

Incremental

Random

Walk

Random

Walk

(b)

Incremental

Random

Walk

and

Random

Walk

on

Clique

Number

of

Measured

Signal

Changes

ExecutionTime(ms).

Random

Walk

Incremental

Random

Walk

(c)

Incremental

Random

Walk

and

Random

Walk

on

Power-Law

Random

Graph

Figure

Execution

times

of

Incremental

Protocols

Number

of

Measured

Signal

Changes

OverheadImprovementRatio.

(NormalizedtoUniformGossip)

Incremental

Gossip

Uniform

Gossip

(a)

Incremental

Gossip

and

Uniform

Gossip

on

Clique

Number

of

Measured

Signal

Changes

OverheadImprovementRatio.

(NormalizedtoRandomWalk)

Incremental

Random

Walk

Random

Walk

(b)

Incremental

Random

Walk

and

Random

Walk

on

Clique

Number

of

Measured

Signal

Changes

OverheadImprovementRatio.

(NormalizedtoRandomWalk)

Random

Walk

Incremental

Random

Walk

(c)

Incremental

Random

Walk

and

Random

Walk

on

Power-Law

Random

Graph

Figure

Network

overhead

of

Incremental

Protocols

cal

time

stamp

of

when

it

received

the

most

recent

update.

Using

this

information,

a

device

moves

into

the

recovered

state

once

enough

time

has

passed

for

the

most

recent

update

to

have

converged.

As

discussed

in

Section

this

happens

after

O(log(N))

time

steps.

Recovered:

A

recovered

device

ceases

to

propagate

any

update

information.

At

this

point,

it

performs

clean-up

and

prepares

for

the

next

infection

by

entering

the

susceptible

state.

Once

all

devices

have

entered

the

recovered

state,

the

system

will

have

converged,

and

with

high

probability,

all

devices

will

have

the

up-to-date

average

signal

level.

Due

to

the

cumulative

nature

of

FM,

even

if

all

devices

have

not

converged,

the

next

update

will

include

all

previous

updates.

Nevertheless,

the

probability

that

gossip

fails

to

converge

is

small,

and

has

been

shown

to

be

For

coordinated

spectrum

sensing,

non-incremental

routing

protocols

can

be

implemented

in

a

similar

fashion.

Random

walk

would

operate

by

having

devices

periodically

drop

the

aggregate

and

re-run

the

protocol.

Each

device

would

perform

a

coin

toss

(biased

on

the

number

of

walks)

to

determine

whether

or

not

it

is

a

designated

node.

This

is

different

from

the

protocol

discussed

above

where

only

updated

nodes

initiate

random

walks.

Similar

techniques

can

be

used

to

implement

standard

gossip.

EVALUATION

We

now

provide

a

preliminary

evaluation

of

GUESS

in

simulation.

A

more

detailed

evaluation

of

this

approach

can

be

found

in

Here

we

focus

on

how

incremental

extensions

to

gossip

protocols

can

lead

to

further

improvements

over

standard

gossiping

techniques,

for

the

problem

of

coordinated

spectrum

sensing.

Simulation

Setup:

We

implemented

a

custom

simulator

in

C++.

We

study

the

improvements

of

our

incremental

gossip

protocols

over

standard

gossiping

in

two

dimensions:

execution

time

and

network

overhead.

We

use

two

topologies

to

represent

device

connectivity:

a

clique,

to

eliminate

the

effects

of

the

underlying

topology

on

protocol

performance,

and

a

BRITE-generated

power-law

random

graph

(PLRG),

to

illustrate

how

our

results

extend

to

more

realistic

scenarios.

We

simulate

a

large

deployment

of

devices

to

analyze

protocol

scalability.

In

our

simulations,

we

compute

the

average

signal

level

in

a

particular

band

by

disseminating

FM

bit

vectors.

In

each

run

of

the

simulation,

we

induce

a

change

in

the

measured

signal

at

one

or

more

devices.

A

run

ends

when

the

new

average

signal

level

has

converged

in

the

network.

For

each

data

point,

we

ran

simulations

and

confidence

intervals

(error

bars)

are

shown.

Simulation

Parameters:

Each

transmission

involves

sending

bits

of

information

to

a

neighboring

node.

To

compute

the

AVERAGE

aggregate,

four

bit

vectors

need

to

be

transmitted:

the

original

SUM

vector,

the

SUM

delete

vector,

the

original

COUNT

vector,

and

the

COUNT

delete

vector.

Non-incremental

protocols

do

not

transmit

the

delete

vectors.

Each

transmission

also

includes

a

time

stamp

of

when

the

update

was

generated.

We

assume

nodes

communicate

on

a

common

control

channel

at

Mbps.

Therefore,

one

time-step

of

protocol

execution

corresponds

to

the

time

required

for

nodes

to

sequentially

send

bits

at

Mbps.

Sequential

use

of

the

control

channel

is

a

worst

case

for

our

protocols;

in

practice,

multiple

control

channels

could

be

used

in

parallel

to

reduce

execution

time.

We

also

assume

nodes

are

loosely

time

synchronized,

the

implications

of

which

are

discussed

further

in

Finally,

in

order

to

isolate

the

effect

of

protocol

operation

on

performance,

we

do

not

model

the

complexities

of

the

wireless

channel

in

our

simulations.

Incremental

Protocols

Reduce

Execution

Time:

Figure

compares

the

performance

of

incremental

gossip

(IGP)

with

uniform

gossip

on

a

clique

topology.

We

observe

that

both

protocols

have

almost

identical

execution

times.

This

is

expected

as

IGP

operates

in

a

similar

fashion

to

uniform

gossip,

taking

O(log(N))

time-steps

to

converge.

Figure

compares

the

execution

times

of

incremental

random

walk

(IRWP)

and

standard

random

walk

on

a

clique.

IRWP

reduces

execution

time

by

a

factor

of

for

a

small

number

of

measured

signal

changes.

Although

random

walk

and

IRWP

both

use

k

random

walks

(in

our

simulations

k

number

of

nodes),

IRWP

initiates

walks

only

from

updated

nodes

(as

explained

in

Section

resulting

in

faster

information

convergence.

These

improvements

carry

over

to

a

PLRG

topology

as

well

(as

shown

in

Figure

where

IRWP

is

times

faster

than

random

walk.

Incremental

Protocols

Reduce

Network

Overhead:

Figure

shows

the

ratio

of

data

transmitted

using

uniform

gossip

relative

to

incremental

gossip

on

a

clique.

For

a

small

number

of

signal

changes,

incremental

gossip

incurs

times

less

overhead

than

uniform

gossip.

This

is

because

in

the

early

steps

of

protocol

execution,

only

devices

which

detect

signal

changes

communicate.

As

more

signal

changes

are

introduced

into

the

system,

gossip

and

incremental

gossip

incur

approximately

the

same

overhead.

Similarly,

incremental

random

walk

(IRWP)

incurs

much

less

overhead

than

standard

random

walk.

Figure

shows

a

fold

reduction

in

overhead

for

small

numbers

of

signal

changes

on

a

clique.

Although

each

protocol

uses

the

same

number

of

random

walks,

IRWP

uses

fewer

network

resources

than

random

walk

because

it

takes

less

time

to

converge.

This

improvement

also

holds

true

on

more

complex

PLRG

topologies

(as

shown

in

Figure

where

we

observe

a

reduction

in

network

overhead.

From

these

results

it

is

clear

that

incremental

techniques

yield

significant

improvements

over

standard

approaches

to

gossip,

even

on

complex

topologies.

Because

spectrum

utilization

is

characterized

by

incremental

changes

to

usage,

incremental

protocols

are

ideally

suited

to

solve

this

problem

in

an

efficient

and

cost

effective

manner.

DISCUSSION

AND

FUTURE

WORK

We

have

only

just

scratched

the

surface

in

addressing

the

problem

of

coordinated

spectrum

sensing

using

incremental

gossiping.

Next,

we

outline

some

open

areas

of

research.

Spatial

Decay:

Devices

performing

coordinated

sensing

are

primarily

interested

in

the

spectrum

usage

of

their

local

neighborhood.

Therefore,

we

recommend

the

use

of

spatially

decaying

aggregates

which

limits

the

impact

of

an

update

on

more

distant

nodes.

Spatially

decaying

aggregates

work

by

successively

reducing

(by

means

of

a

decay

function)

the

value

of

the

update

as

it

propagates

further

from

its

origin.

One

challenge

with

this

approach

is

that

propagation

distance

cannot

be

determined

ahead

of

time

and

more

importantly,

exhibits

spatio-temporal

variations.

Therefore,

finding

the

optimal

decay

function

is

non-trivial,

and

an

interesting

subject

of

future

work.

Significance

Threshold:

RF

spectrum

bands

continually

experience

small-scale

changes

which

may

not

necessarily

be

significant.

Deciding

if

a

change

is

significant

can

be

done

using

a

significance

threshold

β,

below

which

any

observed

change

is

not

propagated

by

the

node.

Choosing

an

appropriate

operating

value

for

β

is

application

dependent,

and

explored

further

in

Weighted

Readings:

Although

we

argued

that

most

devices

will

likely

be

equipped

with

low-cost

sensing

equipment,

there

may

be

situations

where

there

are

some

special

infrastructure

nodes

that

have

better

sensing

abilities

than

others.

Weighting

their

measurements

more

heavily

could

be

used

to

maintain

a

higher

degree

of

accuracy.

Determining

how

to

assign

such

weights

is

an

open

area

of

research.

Implementation

Specifics:

Finally,

implementing

gossip

for

coordinated

spectrum

sensing

is

also

open.

If

implemented

at

the

MAC

layer,

it

may

be

feasible

to

piggy-back

gossip

messages

over

existing

management

frames

(e.g.

networking

advertisement

messages).

As

well,

we

also

require

the

use

of

a

control

channel

to

disseminate

sensing

information.

There

are

a

variety

of

alternatives

for

implementing

such

a

channel,

some

of

which

are

outlined

in

The

trade-offs

of

different

approaches

to

implementing

GUESS

is

a

subject

of

future

work.

CONCLUSION

Spectrum

sensing

is

a

key

requirement

for

dynamic

spectrum

allocation

in

cognitive

radio

networks.

The

nature

of

the

RF

environment

necessitates

coordination

between

cognitive

radio

devices.

We

propose

GUESS,

an

approximate

yet

low

overhead

approach

to

perform

efficient

coordination

between

cognitive

radios.

The

fundamental

contributions

of

GUESS

are:

an

FM

aggregation

scheme

for

efficient

innetwork

aggregation,

a

randomized

gossiping

approach

which

provides

exponentially

fast

convergence

and

robustness

to

network

alterations,

and

incremental

variations

of

FM

and

gossip

which

we

show

can

reduce

the

communication

time

by

up

to

a

factor

of

and

reduce

network

overhead

by

up

to

a

factor

of

Our

preliminary

simulation

results

showcase

the

benefits

of

this

approach

and

we

also

outline

a

set

of

open

problems

that

make

this

a

new

and

exciting

area

of

research.

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O

spatially decaying aggregate
coordinate spectrum sense
incremental algorithm

spectrum sensing
rf interference
rf spectrum
cognitive radio
spectrum allocation
coordinated sensing
fm aggregation
incremental gossip protocol
opportunistic spectrum sharing
innetwork aggregation
gossip protocol