Spectrum Sensing - Fundamental Limits and Practical ...sahai/Presentations/...Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90 Utilizing

Spectrum SensingFundamental Limits and Practical Challenges

Anant Sahai Danijela Cabricpresenting joint work with

Robert W. BrodersenNiels Hoven Shridhar Mubaraq Mishra Rahul Tandra

Wireless Foundations and Berkeley Wireless Research CenterDepartment of Electrical Engineering and Computer Science

University of California, Berkeley

Major Support from ITR Award: CNS - 0326503Thanks to Joe Evans at NSF

Dyspan 2005

Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 1 / 90

Spectrum, spectrum, everywhere, but . . .

Available spectrum looks scarce.

Measurements show the allocated spectrum is vastly underutilized.


Utilizing available spectrum: five basic approaches

A new comprehensive commons — eliminate legacy users entirely.



A new comprehensive commons — eliminate legacy users entirely.Preserve some priority for “primary users”

Interference management is Interference management notprimary’s responsibility primary’s responsibility

Secondary has permission Markets UWBSecondary must take care Denials Opportunistic






Ultra-wideband: blanket permissionI “Speak softly, but use a wideband”I Energy limited regime — works because most bands are not used






Ultra-wideband: blanket permissionI “Speak softly, but use a wideband”I Energy limited regime — works because most bands are not used

Secondary takes care: avoid disturbing othersI Denials: primary signals when it is being disturbedI Opportunism: secondary keeps listening for the primary


Spectrum management phases

Future

Scarcity of spectrum

Inefficient spectrum use

Now

Evolutionary steps make senseI Spectrum is locally plentiful, so why disable legacy uses now?I Full utilization before rationing



Future



Now


Markets: “trying to solve tomorrow’s problems today.”I Make sense if resource is scarce. Otherwise, can’t recover fixed costs.I More efficient if “commoditized”I Need to learn demand and competing uses first.



Future



Now



Explicit denials: “your pain for my gain”



Future



Now



Explicit denials: “your pain for my gain”

Focus on opportunism for now.


Objectives

Reclaim underutilizedspectrum

I Peaceful coexistenceI (Hopefully) cheap

devices


Objectives



devices

“If a radio systemtransmits in a band andnobody is listening, does itcause interference?"


Objectives



devices

“If a radio systemtransmits in a band andnobody is listening, does itcause interference?"

I Interference temperatureattempts to quantify this

I Allowable interferencedepends on manyvariables Not just the middle of nowhere!


Big questions

How well must we sense?I How sensitive can I be?I Can I use more power if I’m more sensitive?


Big questions


What coordination is required?I What are the benefits?I How much coordination to realize these benefits?I What if I don’t trust everyone?I If I am more capable, can I avoid having to coordinate?


Big questions


What coordination is required?I What are the benefits?I How much coordination to realize these benefits?I What if I don’t trust everyone?I If I am more capable, can I avoid having to coordinate?

What kind of usage patterns can be supported?

What are the key hardware challenges?


Outline

An overview of the issues involved and some key ideas


Outline

An overview of the issues involved and some key ideasPart I: The basic considerations quantified

I The “sensing link budget”I The energy detector and fundamental limits on its sensitivityI Within-system cooperationI Fairness and cooperation among systems


Outline



Part II: More powerful detectorsI Coherent detectorsI Feature detectors


Outline




Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them


A myriad of factors to consider

Primary power

Amount of protection given primary

Multiple secondaries

Heterogeneous propagation losses

Multipath and shadowing

Coherence times

Primary duty cycles

Secondary power

Cooperation

Competition

Modulation models

Implementation complexity

Robustness

And many more...

We show how to understand these in the spectrum sensing context by buildingup slowly from simple cases to see how everything fits together.


Summary of main points

Uncertainty imposes limits on device sensitivity that can not beovercome by just listening longer.

Shadowing is a major challenge but can be overcome with multi-usercooperative diversity within a system.

Potential interference from other secondaries is a very significantuncertainty, but can be mitigated through mandated local cooperationamong systems.






Non-interference is a system-level, rather than device-level, property andmust be regulated as such.






Non-interference is a system-level, rather than device-level, property andmust be regulated as such.In bands with high-powered primaries, long-range/high-power secondaryuse is possible, but with power comes responsibility.

I Sense more carefullyI Cooperate more among systems






Non-interference is a system-level, rather than device-level, property andmust be regulated as such.In bands with high-powered primaries, long-range/high-power secondaryuse is possible, but with power comes responsibility.

I Sense more carefullyI Cooperate more among systems

Complexity can buy some freedom.


Primary transmitter’s decodability radius

A


We define a protected radius

B


Mice can get close...

B


But keep the lions far away!

B


We can’t protect everyone

B

Demanding complete protection for marginal legacy users will crippleinnovation.


Union of “no talk” zones

B


Fading

A secondary usermight be fadedwhile histransmissionscould still reach anunfaded primaryreceiver.

��

��


Fading margin

A secondary user whocan not distinguishbetween positionsmust be quiet in both.

��

��


What are we giving up?

��

Safe, but might be faded(fading uncertainty)



��


Lights on, but no one home(receiver uncertainty)



��


Lights on, but no one home(receiver uncertainty)

Safe, but not shadowed enough(symmetry uncertainty)


How valuable is the real estate?

0 20 40 60 80 1000

20

40

60

80

100

120

140

160

Distance from primary transmitter (km)

Cap

acity

(M

bps)

Capacity of 100 mW, 10 m range system vs. distance from primary transmitter

isolated secondary systemwith inteference from secondary 50m away

100 kW primary transmitter, 60 km decodable radiusPrimary to secondary decays as r−3.5

Secondary to secondary decays as r−5


Impact of uncertainty: limit on sensitivity

All detectors are based on someaveraged test statistic

If value is high, primary isconsidered presentIf the value is low, it isconsidered absent.

Increasing the amount ofaveraging, increases ourconfidence in the decision.

Unmodeled or non-ergodicuncertainties introduceunresolvable ambiguities.

UncertaintyZone

Signalpresent

TargetSensitivity

σ 2nα

σ 2n1/α ��

��

}Impossible

Noise power

Test statistic


Overcoming fading: multiuser diversity

Cooperation within ageographically distributednetwork of secondary usersavoids dealing with theworst-cases of fading.

Detect the primary collectively!

��

��


New concerns with multiple users

B

More potential secondary usersto keep quiet in the near vicinityof primary receivers.


The challenge of aggregate interference

B

One secondary usermight be acceptable, butwhat about millions?

Limit on the powerdensity

Slower effectiveattenuation withdistance


Overcoming multiuser uncertainty: “sensing MAC”among systems

Secondaries must not confuse uncertain aggregate interference withprimary signal

Nearby secondary users must be quiet during detection

Increasing density of secondary transmissions requires more cooperation


Outline

An overview of the issues involved some key ideasPart I: The basic considerations quantified





The classical link budget

Goal: reliable communicationI At a given rangeI within a given bandwidth

SNRr = Pt + Gantenna + Gcoding

− Lfree−space − Latmospheric − Lshadow − Lmultipath

− Pnoise

− Pinterference

Fundamental limitsI Coding gain bounded by channel capacityI Additional margins needed to deal with uncertainty

“Typical” case: more than enough SNR.


Opportunistic use: new considerations

New constraint: must not interfere with primary users

I Allowable PHI (∼ 1%) at protected primary receiversI Limit on tolerable out-of-system interferenceI Translates to a limit on maximum power, not minimum.

New question: What signal power must we detect to guaranteenon-interference?





New question: What signal power must we detect to guaranteenon-interference?New issues

I Different propagation path lossesF Between primary and secondary usersF Among secondary users

I Multiple opportunistic usersI Heterogeneous transmit powers





New question: What signal power must we detect to guaranteenon-interference?New issues

I Different propagation path lossesF Between primary and secondary usersF Among secondary users

I Multiple opportunistic usersI Heterogeneous transmit powers

“Typical” case: primary signal is absent or weak — very low SNR.


Outline of section

Formalization with path losses only

Basic case: 1 primary, 1 secondary

Multiple secondary transmitters

The “outage view” of multipath and shadowing

Numerical example


Heterogeneous path-losses

Secondary node

Primary receiver

Secondary node

Primary transmitter

Free-space propagation: d−2

Ground reflection: d−4

Absorption term: e−λd

Fit to empirical data: d−α

Antenna height (impacts constants)

Urban/rural (impacts α)

Indoor/outdoor

Receiver placement


The Case of the Single Secondary Transmitter

But we don’t know where we are!

Think in terms of distances,but use local signal strength.


The fundamental constraint

rdecrp

µ

µ determines how much interference above thenoise floor the primary system can tolerate

Q2 + σ2 ≤ σ210µ10

The secondary system must guarantee:

Q2 ≤ (10µ10 − 1)σ2

Q2: (aggregate) receivedsecondary transmitters’powers at primary receiver

µ: dB margin ofprotection

rp: protected radius

rdec: decodable radius for a

primary receiver


Solo secondary sensing link budget

ψ∆rdecrp

µ

r2

At the secondary, the primary signal has dropped by ∆s + ψ.

At the primary receiver, the secondary’s transmission has beenattenuated by g21(r2 − rp).

Sensitivity required vs. desired secondary power

−(ψ + ∆s) ≥ 10 log10 [g12(r2)]

= 10 log10 [g12(rp + (r2 − rp))]

= 10 log10

[g12

(g11

−1(

10µ−∆p

10

)+ g21

−1

((10

µ10 − 1) · σ2

P2

))]

Q2: (aggregate) receivedsecondary transmitters’powers at primaryreceiverµ: dB margin ofprotection

rp: protected radius

rdec: decodable radiusfor a primary receiver

ψ: how much weakerthan the minimaldecodable signal thesecondary’s reception is.

∆[p,s]: Signalattenuation between theprimary transmitter andrdec, as measured by aprimary or secondary.

r2: distance fromprimary transmitter tosecondary transmitter


Single transmitter power constraints(g11(r) = g12(r) = r−α1 and g21(r) = r−α2 , µ = 1 dB margin)

0 5 10 15 20 25 30−200

−150

−100

−50

0

50

100

150Maximum power for secondary transmitter, ∆=35 (802.11)

SNR margin ψ at secondary receiver (dB)

Max

sec

onda

ry p

ower

(dB

W)

(a) ∆ = 35 (rdec = 10m)

0 5 10 15 20 25 30−200

−150

−100

−50

0

50

100

150Maximum power for secondary transmitter, ∆=165 (Digital TV)


Max

sec

onda

ry p

ower

(dB

W)

(b) ∆ = 165 (rdec = 51km)

· · · · · · · · · α1 = 3.5, α2 = 5 Secondary signal attenuates faster than primary

α1 = 3.5, α2 = 3.5 Secondary signal attenuates at same rate as primary

− − − α1 = 5, α2 = 3.5 Secondary signal attenuates slower than primary


Fading

��

��

0 5 10 15 20 25 30−50

−40

−30

−20

−10

0

10

20

30

40

50Maximum power for secondary transmitter


Max

sec

onda

ry p

ower

(dB

W)

No shadowing10 dB shadowing

10 dB

If you hear a weak signal, are you far away, or just faded?

The possibility of 10 dB of fading results in a 10 dB shift of the requireddetection margin


Multiple secondaries – What could go wrong?

B

“Keeping Kfour-year olds quiet”

Pmd ≤ 1K PHI


Multiple secondaries – What could go wrong?

B

“Keeping Kfour-year olds quiet”

Pmd ≤ 1K PHI

B

“Conversation in a crowdedrestaurant”

I Each individual transmittertalks quietly

I But the aggregate chatter maybe overwhelming


“Death by a thousand cuts” analysis

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Assume secondaries have limited power, distinctfootprints (Data MAC protocol)

Approximate sea of secondary users by a power density

Circular coast looks like a straight line nearby

Integration changes the decay exponent

I As you move further from the coast you “see”more interferers

I Physical r−4 → r−2 effective.

Q2 =

∫ π2

−π2

∫∞

rn−rpcos(θ)

Dr−α2 r dr dθ

= D · K(α2) · (rn − rp)−α2+2

where K(α2) =

∫ π2

−π2

(cos θ)α2−2 dθ

α2−2 .

For α2 = 6, K(α2) = 14

3!!4!! π ≈ 0.295.


Heterogeneity and competing interests

Primary receiver has acertain margin µ oftolerable interference

We must choose how toallocate this margin tousers at different distances

Far away users can gain atthe expense of nearby users

Policy input required

10 12 14 16 18 20−40

−35

−30

−25

−20

−15

−10

SNR margin to secondary transmitter (ψ dB)

Max

imum

allo

wab

le p

ower

den

sity

(dB

W/m

2 )

Maximum allowable secondary power density (∆=165)

r2, ν=3

r1, ν=3

r0, ν=3

r2, ν=1

r1, ν=1

r0, ν=1

r2, ν=0.1

r1, ν=0.1

r0, ν=0.1

Primary signal decays as r−3.5

Secondary signals decay as r−5

ν: Additional “quiet” margin to allow more power.

I 3 dB ≈ 11 kmI 1 dB ≈ 3.5 km

I 0.1 dB ≈ 0.34 km


Fading revisited

��

��

��

��

Is there a principled way of choosing X dB of fading margin?



−10 −5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fade (dB)

P(b

ette

r th

an x

dB

fade

)

Rayleigh Complementary Cumulative Distribution Function (σ2 = 3.5 dB)

Rayleigh fading modelMany independent scatterers

Magnitude a Rayleigh randomvariable

If primary signal is wideband,could be frequency selective.

Could hurt or help.



−10 −5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fade (dB)

P(b

ette

r th

an x

dB

fade

)

Rayleigh Complementary Cumulative Distribution Function (σ2 = 3.5 dB)

−20 −15 −10 −5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fade (dB)

P(b

ette

r th

an x

dB

fade

)

Lognormal Complementary Cumulative Distribution Function (σ2 = 3.5 dB)

Rayleigh fading modelMany independent scatterers

Magnitude a Rayleigh randomvariable

If primary signal is wideband,could be frequency selective.

Could hurt or help.

Lognormal shadowingLarge number of smallabsorptive losses

Central limit theorem

Not really frequency selective

Can only hurt.


The key role of Pmd: the “outage view”

Pmd = P(good fade) · P(missing a good signal) + P(bad fade)

bad fadesgood fades

can detect give up

sensitivity

Our ability to detect is limited by the probability of a bad fade




bad fadesgood fades

can detect give up

sensitivity


Pfade fade (dB)10% -16 dB1% -21 dB

0.1% -26 dB0.01% -31 dB

(Assuming lognormal+Rayleigh fading, σ =3.5 dB each)




bad fadesgood fades

can detect give up

sensitivity


Pfade fade (dB)10% -16 dB1% -21 dB

0.1% -26 dB0.01% -31 dB

(Assuming lognormal+Rayleigh fading, σ =3.5 dB each)

But deep fade “probabilities” are uncertain and poorly modeled.


Sensing budget evaluated

Protocol Tx power Footprint Density (W/m2) Add’l Sensitivity With fading"WiMax" 1 W 1 km2 1 · 10−6 -0.17 dB -31.17 dB

"Bluetooth" 2.5 mW 20 m2 1.3 · 10−4 -1.23 dB -32.23 dB"WiFi" 100 mW 300 m2 3.3 · 10−4 -1.68 dB -32.68 dB

Fading is the dominant term.

If 23dB SNR at decodable radius, need to robustly detect at least 8 dBbelow noise floor.

Is this possible?


Outline



Part II: More powerful detectorsI Coherent detectorI Feature detectors



Big question: sensing the primary

fc+W/2fc−W/2

UnknownActivity

UnknownActivityBand of Interest

Spectrum picture

Look for the primary in the ‘band of interest’Within band model:

I White or unknown signal, X(t)I Independent white noise, W(t)

First step: sample the band of interest at Nyquist rate


Hypothesis testing problem formulation

Distinguish between the following hypotheses:

H0 : Y[n] = W[n]

H1 : Y[n] = W[n] + X[n]

Basic assumptions:I X[n]’s are i.i.d. signal samplesI W[n]’s are i.i.d. noise samples

Target error probabilities:I PFA: Probability of false alarmI PMD: Probability of missed detection

Key Resource: Dwell Time N of the detector


Performance measures for detection

Dwell time of the detector

I Limited by primary duty cycle, sharing with others, etc.I Sample complexity of detectors

DefinitionSample complexity captures how N varies with SNR for given PFA and PMD






RobustnessI What uncertainties are unavoidableI How does the detector perform despite the uncertainty






RobustnessI What uncertainties are unavoidableI How does the detector perform despite the uncertainty

Computational/Implementational complexity


Simplest detector: Energy detector

Recall:I Signal, X[n] could be anything, including whiteI Noise, W[n] is white Gaussian

Received energy used for detection

Test statistic:

T(y) =N∑

n=1

Y2[n]

Decision rule:

T(y)H1

≷H0

γ(N)


Error probability analysis

False alarm probability

PFA = P(T(y) > γ|H0)

= P

T(y)σ2 − N√

2N>

γ

σ2 − N√

2N

≈ Q( γ

σ2 − N√

2N

)

Probability of detection

PD = P(T(y) > γ|H1)

= P

T(y)σ2 − λ − N√

4λ + 2N>

γ

σ2 − λ − N√

4λ + 2N

≈ Q( γ

σ2 − λ − N√

4λ + 2N

)

Receiver does not know signal power λI Only has knowledge of σ2

I Set threshold γ based on PFA

Evaluate PMD for different values of λ to get sensitivity.Eliminate γ to get sample complexity:

N ≈ 2[Q−1(PFA) −Q−1(PD)

]2SNR−2


Understanding robustness: noise uncertainty

Frequency

converterdown−

Low−noise

amplifier

Intermediatefrequencyamplifier

A/DConverter

Detector

Receivingantenna

Noise is usually assumed to be GaussianSources of uncertainty:

I Non-linearity of componentsI Thermal noise in components (Non-uniform, time-varying)



Frequency

converterdown−

Low−noise

amplifier


A/DConverter

Detector

Receivingantenna


I Non-linearity of componentsI Thermal noise in components (Non-uniform, time-varying)I Noise due to transmissions by other users

F Unintentional (Close-by)F Intentional (Far-away)



Frequency

converterdown−

Low−noise

amplifier


A/DConverter

Detector

Receivingantenna


I Non-linearity of componentsI Thermal noise in components (Non-uniform, time-varying)I Noise due to transmissions by other users

F Unintentional (Close-by)F Intentional (Far-away)F Opportunistic


Impact of uncertainty: energy detector

Actual noise power,σ2

a ∈ [ 1ασ2

n, ασ2n]

If

P + σ2a ≤ ασ2

n

⇒ P ≤ α2 − 1α

σ2n

Energy detector fails to detectthe signal

UncertaintyZone

Signalpresent

TargetSensitivity

σ 2nα

σ 2n1/α ��

��

}Impossible

Noise power

Test statistic


SNR wall for energy detectorSNRwall for the energy detector is given by

SNRwall = 10 log10

(α2 − 1

α

)

where, α = 10(x/10)

0 0.5 1 1.5 2 2.5 3−14

−12

−10

−8

−6

−4

−2

0

2Position of SNR wall for radiometer

Noise uncertainty x (in dB)

SNR wa

ll (in

dB)

−3.3 dB


Realistic model for noise uncertaintyEven if we calibrate, there is always residual uncertainty about the noise.

Receiver knows the noise distribution only up to an uncertainty set Wx.

Realistic model

Noise cloud includes a range of Gaussians with variance ∈ [ 1α

σ2n , ασ2

n ] as well as othersimilar distributions.

Wa ∈ W̃x iff

EW2ka ∈

[1αk

EW2kn , α

kEW2k

n

], α = 10x/10

Implication: Energy detector like wall for all detectors

TheoremConsider detecting a weak BPSK signal with the noise distribution lying in W̃x. Under thismodel, there exists an absolute SNR wall (snr∗wall) for any possible robust detector.

snr∗wall = mink>0

snr(2k)wall = α − 1


Example of noise distribution overlap

Signal looks like noise: fWa+X = fWn


Position of SNR wallRealistic model

0 2 4 6 8 10 12 14 16 18 20−20

−15

−10

−5

0

5

10

15

20

Noise uncertainty x (in dB)

SN

Rw

all (

in d

B)

Energy detector wallAbsolute SNR wall

Figure: SNR∗wall as a function of x


Conclusions

Noise uncertainty is always presentI At least about 1-2 dB of device level uncertainty

F Cannot see 3 dB below the noiseI Easily 10-20 dB of interference level uncertainty

F Cannot see below it at all!

E.g.: In a 6MHz TV band, Digital TV receiver sensitivity = -85dBm.I We must have -117dBm sensitivity to deal with rare fading.I Thermal Noise at -106dBm !

What can we do to mitigate this?


Outline






How can cooperation help?

Fading is the dominant challenge

Multipath varies significantly onthe scale of λ4 (10cm at 800MHz).

Shadowing varies significantly onthe scale 20-500m

Use multiple radios as a proxyfor multiple antennas!

��

��


How can cooperation help?

Fading is the dominant challenge

Multipath varies significantly onthe scale of λ4 (10cm at 800MHz).

Shadowing varies significantly onthe scale 20-500m

Use multiple radios as a proxyfor multiple antennas!Analogy: Deck of cards wherered cards signify bad fades.

I Probability that I get a red card:Very High (50%)!

I Probability that all users getred cards: Very Low

��

��


Cooperative diversity quantified

If PHI = 1%, K = 100, then PMD,system = 0.01% !

What if our system had many (M) independent radios?

PD,radio ≤ 1 − M

√PHI

K

I For M = 10, PD,radio = 60% Just have to work in the best 60% cases.

Robustness comes from being able to write off the worst possible fades.No longer need to model them as precisely!


How much does cooperation buy us?Transmit Power (dBm)

Loss due to distance

Sensitivity Threshold with no cooperation (eg -110dBm)

Loss due to multipath & shadowing

Realizable sensitivity with cooperation (eg -85dBm) Potential

Gain from cooperation

Cooperation helps us approach the nominal distance dependent path loss

100

101

102

103

104

105

−130

−120

−110

−100

−90

−80

−70

−60S

ensi

tivi

ty (

dB

m)

Number of Users (log scale)

Multipath OnlyShadowing OnlyMultipath and Shadowing

Path Loss

Probability of Misdetection = .01%

Cooperation model: Each user sends a 1 bit decision to a controller10 - 20 users are needed to obtain realistic receiver sensitivity levels.


Beware of Multipath Gains!

CR #2 CR #3

CR #2 CR #3

CR #1

Primary Transmitter

pdf

Energy (dBm)

CR #1

Primary Transmitter

pdf

Energy (dBm)

Rayleigh Fading

Rician Fading

Cannot rely on multipath gains - might have a single weak path

Cooperation should only be used to mitigate bad multipath


What are the limits on cooperation?

Complexity of getting everyone on board

I Control channel bandwidth may be limited during the setup stageI Delay in relaying decisions may make decisions obsolete.





Independence issuesI How does correlation effect cooperation?I How to quantify independence?





Independence issuesI How does correlation effect cooperation?I How to quantify independence?

Trust issues

I What if users lie about sensing decisions?I What if radios fail in unknown ways and/or are malicious?


Dealing with channel correlation

Multipath is not correlatedI Radio placements on the scale of wavelength are essentially random.

Shadowing is correlated if two radios are blocked by the same obstacle

One model: Correlation decays exponentially with distance.

CR #1

Primary Transmitter

CR #2

CR #3

Correlated Shadowing

Independent Shadowing


The few, the independent, . . .

Can a large number ofcorrelated users make upfor lack of independence ?No !!

It is better to increasedistance spread of usersthan to increase the count. 0 50 100 150 200

−87

−86

−85

−84

−83

−82

−81

Number of users considered

Th

resh

old

(dB

m)

Distance Spread = 50mDistance Spread = 500mDistance Spread = 1kmDistance spread = 2.5km


The few, the independent, . . .

Can a large number ofcorrelated users make upfor lack of independence ?No !!

It is better to increasedistance spread of usersthan to increase the count. 0 50 100 150 200

−87

−86

−85

−84

−83

−82

−81

Number of users considered

Th

resh

old

(dB

m)

Distance Spread = 50mDistance Spread = 500mDistance Spread = 1kmDistance spread = 2.5km

Need long range cooperation within opportunistic systems.


Known failures are easy

Some users may not contribute to sensing.

Such known failures just reduce the effective number of users in thesystem

100

101

102

103

104

105

−100

−95

−90

−85

−80

−75

−70

−65S

ensi

tivi

ty(d

Bm

)

Number of users considered (log scale)

No LiarsPercentage of "Always no" liars = 25%Percentage of "Always no" liars = 50%


Dealing with unpredictable adversaries

Malicious adversaries are impossible to predict reliably — need tobudget for worst case.

Assume M users with a known fraction α behaving unpredictably.





PFA : Set threshold at βM (β > α) — declare Primary present only if βMnodes say Yes.





PFA : Set threshold at βM (β > α) — declare Primary present only if βMnodes say Yes.PMD : What if the adversaries now behave as Always No liars?

I Reduces actual users to M(1 − α) of which βM must declare Yes.I For β

1−αof them to detect, threshold must be such that PD,radio ≥ β

1−α.





PFA : Set threshold at βM (β > α) — declare Primary present only if βMnodes say Yes.PMD : What if the adversaries now behave as Always No liars?

I Reduces actual users to M(1 − α) of which βM must declare Yes.I For β

1−αof them to detect, threshold must be such that PD,radio ≥ β

1−α.

Distrust limits diversity gains


The impact of distrust

0 50 100 150 200−88

−86

−84

−82

−80

−78

−76

−74

Number of users

Sen

siti

vity

(dB

m)

Percent liars=0%Percent liars=1%, Detection Threshold=2%Percent liars=5%, Detection Threshold=6%Percent liars=10%, Detection Threshold=11%Percent liars=20%, Detection Threshold=22%

Diversity gains with α fraction untrusted users are bounded by thoseachievable by a trusted population of 1

αtrusted users.

To achieve these gains, we need M » 1α

when α large.


Within-system cooperation summary

Low-moderate fading is all that can be realistically modeled.

Cooperation allows independent radios to target individual sensitivitylevels based on low-moderate fading margins while maintaining systemrobustness.

We prefer a few distant users to many nearby users.

Untrusted radios introduce a bound on achievable sensitivity reductions.


Outline

An overview of the issues involved and some key ideasPart I: The basic considerations

I The “sensing link budget”I Limits on sensitivity for an energy detectorI Within-system cooperationI Fairness and among-system cooperation




The story so far

Opportunistic use can be high-power with long range, as long as thepower-density is controlled appropriately.

Opportunism requires a system, not a device, in order to deal with fading.

I Needs to be regulated as a system.I Has an internal incentive to cooperate with trusted nodes on a larger

geographical scale.I Has a mild disincentive to collaborate with non-trusted nodes nearby.

So far, only considered secondary-to-primary interference.


Conceptualizing secondary-to-secondary interference

Secondary-to-secondary interference complicates detectionI Radiometer cannot distinguish between secondary signals and the primary

signalI Doesn’t know if secondaries from other systems are present nearby.





View 1: FairnessI Don’t want the first opportunistic user to exclude all other secondariesI Possible options

F Mandate honest sharing of detection results.






F Mandate honest sharing of detection results.F Have everyone nearby be quiet during sensing.






F Mandate honest sharing of detection results.F Have everyone nearby be quiet during sensing.

View 2: Maximize steady state utilizationI Maintain good utilization as systems hop around.I No need to have overly interference-free bands when no primary users are

around.


Mandated “sensing MAC” among systems

During sensing, secondary-to-secondary interference is uncertain andinduces an SNRwall

I Problematic because we are uncertain how many secondaries are talking.I Higher permitted densities induce more uncertainty.I Wall must be kept below required sensitivity.





Keep nearby secondary users quiet during detection.





Keep nearby secondary users quiet during detection.Increasing density of secondary transmissions requires more cooperation.


How to evaluate power / cooperation tradeoffs

Must satisfy two constraintsI Non-interference to primary receiversI Fairness among secondary users




1. Use non-interference due to aggregate interference to pick no-talk radiusfor a given power density D.





2. Use fading-margin and primary-to-secondary attenuation to pick a targetdetection level.





2. Use fading-margin and primary-to-secondary attenuation to pick a targetdetection level.

3. Set “shut-up” radius rs to reduce uncertainty Imax = D 2πα22−2 rs

2−α22

enough to allow robust detection at target level.


Power / cooperation tradeoffs for α12 = −3.5

−60 −55 −50 −45 −40 −35 −30 −25 −200

5000

10000

15000

Secondary system density (dBW/m2)

Req

uire

d co

oper

atio

n ra

dius

(m

)

Cooperation / Power Tradeoffs (Digital TV)

No cooperation: −25 dB fadingCooperation: −10 dB fading

Bluetooth WiFi

(a) α22 = −5

−60 −55 −50 −45 −40 −35 −30 −25 −200

500

1000

1500

2000

2500


Req

uire

d co

oper

atio

n ra

dius

(m

)

Bluetooth WiFi

(b) α22 = −5 zoom

−60 −55 −50 −45 −40 −35 −30 −25 −200

50

100

150

200

250

300

350

400

450

500


Req

uire

d co

oper

atio

n ra

dius

(m

)

Bluetooth WiFi

(c) α22 = −6

“Double whammy” with increased opportunistic power density.I Must detect weaker primaryI Increased interference uncertainty

The aggregate interference from all potential secondaries must be weakerthan the weak primary signal.Requires among-system coordination across a large local area, even afterwithin-system cooperation has reduced fading margins.


Outline

An overview of the issues involved and some key ideasPart I: The basic considerations

I The “sensing link budget”I Limits on sensitivity for an energy detectorI Within-system cooperationI Fairness and among-system cooperation




The need for more complex detectors

The energy detector works for all possible primary signals withoutknowing what they are.

If the primary is zero-mean, white, and occupies all degrees of freedom,nothing more is possible.

But physical signals are not that general.





But physical signals are not that general.I Have deterministic pilot tones.





But physical signals are not that general.I Have deterministic pilot tones.I Have guard bands and do not occupy all degrees of freedom.





But physical signals are not that general.I Have deterministic pilot tones.I Have guard bands and do not occupy all degrees of freedom.

Can we exploit these to improve performance and robustness?


Coherent detection

fc+W/2fc−W/2

UnknownActivity

UnknownActivity

Pilot tone

Spectrum picture

Band of Interest

Look for the primary pilot in the ‘band of interest’

Pilots come up in different situations:

I Denial pilot (very critical)I Permissive pilot (non-critical)

Within band model:I White or unknown signal, X(t)I Independent white noise, W(t)


Hypothesis testing model: Coherent detection

Distinguish between the following hypotheses:

H0 : Y[n] = W[n]

H1 : Y[n] = W[n] +√

(1 − θ)X[n] +√

θXp[n]

Basic assumptions:I Signal samples X[n]’s are white or orthogonal to the pilot.I Noise samples W[n]’s are white.I Xp[n] is a known pilot toneI θ is the fraction of total power allocated to pilot tone

Possible detection strategies:I Energy detector (radiometer)I Coherently detect pilot tone


Matched filter analysis

Correlate received signal with a unit vector in pilot’s direction

T(y) =1N

N∑

n=1

Y[n]X̂p[n]

x̂p is a unit vector in the direction of the pilot

Test statistic under both hypotheses:

H0 : T(y) = 1N

∑Nn=1 W[n]X̂p[n] ∼ N (0,

1N

σ2)

H1 : T(y) = 1N

∑Nn=1{

√θXp[n] +

√(1 − θ)X[n] + W[n]}X̂p[n] ∼ N (

√θP,

1N

σ2)

Here P = 1N

∑Nn=1 X2[n], is the average signal power, σ2 is the noise

power.

Decision rule: T(y)H1

≷H0

γ(σ2), Threshold γ is set based on PFA


Error probability for matched filter

False alarm

PFA = P(T(y) > γ|H0)

= P

T(y)√σ2

N

>γ√σ2

N

|H0

= Q

γ√σ2

N

Missed detection

PD = P(T(y) > γ|H1)

= P

T(y) −√θP√

σ2

N

>γ −

√θP√

Pσ2

N

|H1

= Q

γ −

√θP√

σ2

N

Eliminating γ,

N = [Q−1(PD) −Q−1(PFA)]2θ−1SNR−1


Matched filter performance

X[n] are BPSK modulatedI X[n] ∼ Bernoulli ( 1

2 ), taking values in {√

P,−√

P}θ = 0.01, ie. 1% energy in the pilot

−60 −50 −40 −30 −20 −10 00

2

4

6

8

10

12

14

SNR (in dB)

log 10

N

Energy Detector Undecodable BPSKBPSK with Pilot signal Sub−optimal schemeDeterministic BPSK

BPSK −− Detector Performance


Easy uncertainties

Unknown but steady frequency and time offsetsEffect on pilot:

I Xp[n] = A cos(2πfsn + φ)I fs and φ unknownI Phase offset is easy to deal with

Approach: Search in many binsImplementation and computational complexity

I Need to compute an N-point FFTI Search for the maximum over fsI Computationally more involved than the energy detector

FFT 1N | |

2

sfover

Choosemaximum

H1

H2

>>X[n] γ


Analysis of easy uncertainties

False alarm probability

PFA = 1 −(

1 − exp(−γ

σ2

))L

≈ 1 −(

1 − L exp(−γ

σ2

))

= LPFA(bin)

where L = N2 − 1 is the number of frequency

bins

Probability of detection

PD = Qχ′

22( NSNR

2 )

(2γ

σ2

)

Eliminating, γ, we get

PD = Qχ′

22( NSNR

2 )

(2 ln

LPFA

)

Need to tighten PFA, linearly with the number of bins we search

Effective frequency uncertainty scales with dwell time N


Easy uncertainty: Impact on dwell time

−30 −28 −26 −24 −22 −20 −18 −16 −14 −12 −102

3

4

5

6

7

8

SNR (in dB)

log 10

N

Matched filterMatched filter with frequency offsetRadiometer

New O(log N) term in the threshold.

Impact on dwell time is not too bad


Medium uncertainty: White noise level uncertainty

Detection problem:

H0 : Y[n] = W[n]

H1 : Y[n] = W[n] +√

θXp[n] +√

(1 − θ)X[n]

W[n] ∈ Wx = [σ2low, σ2

high]

Assume x dB uncertainty in noise level


Medium uncertainty: White noise level uncertainty

Detection problem:

H0 : Y[n] = W[n]

H1 : Y[n] = W[n] +√

θXp[n] +√

(1 − θ)X[n]

W[n] ∈ Wx = [σ2low, σ2

high]

Assume x dB uncertainty in noise levelMain idea: Coherent processing gain can overcome noise leveluncertainty

T(y) =1N

N∑

n=1

Y[n]X̂p[n]H1

≷H0

γ(σ2)


Noise uncertainty: closer look

Noise = receiver/background noise + secondary interference,σ2 = σ2

0 + σ2i

Effect of interferenceInterference is uncertain

Dominating term in noise uncertainty


Noise uncertainty: closer look

Noise = receiver/background noise + secondary interference,σ2 = σ2

0 + σ2i

Effect of interferenceInterference is uncertain

Dominating term in noise uncertainty

Proposed remedy

Robustly estimate σ2i

Significant reduction in noiseuncertainty


Setting threshold: learning based approach

In-band measurement

UnknownActivity

Pilot

tone

−W/2fc f

c+W/2

Noise +Interferencelevel

MeasurementZone

UnknownActivity Band of Interest

}

Noise prediction error

Measurement zoneNoise at

Pilot frequencyNoise at

Prediction Error Measurement

Noise}

Sources of prediction error:I Long-term frequency selectivity in secondary signalsI Coherence bandwidth for secondary signalsI Practical guess (1 − 5%)


Fundamentally challenging uncertainties

Realistic model:

H0 : Y[n] = W[n]

H1 : Y[n] = W[n] +

L−1∑

l=0

hl[n]X̃[n − l]

where X̃[n] =√

θXp[n] +√

(1 − θ)X[n]

Assumptions:I Fast multipath fading: hl ∼ CN(0, 1)I W[n] ∈ Wx: Noise uncertainty set


Fast fading

Assume known channel coherence time, TcI Fading is assumed constant during this coherence timeI Matched filter (coherent processing) can be applied in each coherent blockI Test statistic:

T(y) =1N

N−1∑

n=0

[1√Nc

Nc∑

k=1

Y[n]X̂p[nNc + k]

]2

I Nc: Length of single coherence block

Reduced to the energy detector case,I Processing gain due to the coherence time TcI Less interference uncertainty.


Summary: robust gains from coherent processing

Primary coherence time: [100 µs, 10 ms]⇒ [20, 40]dB: Processing gain for both wall and dwell time.

Interference prediction error: [1, 10]%⇒ [10, 20] dB: In-band measurement gain for wall only

Pilot energy: θ = [0.01, 0.1]⇒ [−20,−10] dB loss for both wall and dwell time

Effective SNR wall: [10, 50] dB lowerDwell times: [0, 30] dB better

System could be ‘Wall limited’ or ‘Dwell limited’


Coherence buys freedom from secondary-MAC

−60 −55 −50 −45 −40 −35 −30 −25 −200

20

40

60

80

100

120


Req

uire

d co

oper

atio

n ra

dius

(m

)

WiFi Bluetooth

1 % pilot power

10% pilot power

(a) α22 = −5

−60 −55 −50 −45 −40 −35 −30 −25 −200

5

10

15

20

25

30

35

40

45

50


Req

uire

d co

oper

atio

n ra

dius

(m

)

1 % pilot power

10% pilot power

Bluetooth WiFi

(b) α22 = −6

Primary transmitter power: 100 kW, Protection margin µ = 1 dB

Primary Attenuation: α12 = −3.5, Post-cooperation fading margin = 10 dB

Coherent processing gain 104

Interference prediction error = 1%, Residual device uncertainty = 1 dB


Extensions and Implications

Universality over coherence times is possibleI Search strategy over coherence times and offsets.I Increases computational complexity.I Better dwell times when primary channel is more coherent.

ImplicationsI Secondary waveforms must avoid using confusing pilots.I Coherent processing can drastically reduce the need to cooperate with

other systems unless seriously dwell-time limited.I Not enough of a gain to eliminate the need for within-system cooperation.


Spectrum Sensing - Fundamental Limits and Practical ...sahai/Presentations/...Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90 Utilizing

Documents