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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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 2 / 90
Utilizing available spectrum: five basic approaches
A new comprehensive commons — eliminate legacy users entirely.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90
Utilizing available spectrum: five basic approaches
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90
Utilizing available spectrum: five basic approaches
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90
Utilizing available spectrum: five basic approaches
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
Secondary takes care: avoid disturbing othersI Denials: primary signals when it is being disturbedI Opportunism: secondary keeps listening for the primary
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 3 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 4 / 90
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
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 4 / 90
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
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.
Explicit denials: “your pain for my gain”
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 4 / 90
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
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.
Explicit denials: “your pain for my gain”
Focus on opportunism for now.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 4 / 90
Objectives
Reclaim underutilizedspectrum
I Peaceful coexistenceI (Hopefully) cheap
devices
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 5 / 90
Objectives
Reclaim underutilizedspectrum
I Peaceful coexistenceI (Hopefully) cheap
devices
“If a radio systemtransmits in a band andnobody is listening, does itcause interference?"
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 5 / 90
Objectives
Reclaim underutilizedspectrum
I Peaceful coexistenceI (Hopefully) cheap
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!
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 5 / 90
Big questions
How well must we sense?I How sensitive can I be?I Can I use more power if I’m more sensitive?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 6 / 90
Big questions
How well must we sense?I How sensitive can I be?I Can I use more power if I’m more sensitive?
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 6 / 90
Big questions
How well must we sense?I How sensitive can I be?I Can I use more power if I’m more sensitive?
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 6 / 90
Outline
An overview of the issues involved and some key ideas
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 7 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 7 / 90
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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 7 / 90
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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 7 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 8 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 9 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 9 / 90
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.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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 9 / 90
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.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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 9 / 90
Primary transmitter’s decodability radius
A
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 10 / 90
We define a protected radius
B
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 11 / 90
Mice can get close...
B
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 12 / 90
But keep the lions far away!
B
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 13 / 90
We can’t protect everyone
B
Demanding complete protection for marginal legacy users will crippleinnovation.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 14 / 90
Union of “no talk” zones
B
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 15 / 90
Fading
A secondary usermight be fadedwhile histransmissionscould still reach anunfaded primaryreceiver.
����������������
���� ��������������������������
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 16 / 90
Fading margin
A secondary user whocan not distinguishbetween positionsmust be quiet in both.
������������
�� ������������������������
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 17 / 90
What are we giving up?
�� ��������������������������������������
Safe, but might be faded(fading uncertainty)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 18 / 90
What are we giving up?
�� ��������������������������������������
Safe, but might be faded(fading uncertainty)
Lights on, but no one home(receiver uncertainty)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 18 / 90
What are we giving up?
�� ��������������������������������������
Safe, but might be faded(fading uncertainty)
Lights on, but no one home(receiver uncertainty)
Safe, but not shadowed enough(symmetry uncertainty)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 18 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 19 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 20 / 90
Overcoming fading: multiuser diversity
Cooperation within ageographically distributednetwork of secondary usersavoids dealing with theworst-cases of fading.
Detect the primary collectively!
����������������
������ ������������������������
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 21 / 90
New concerns with multiple users
B
More potential secondary usersto keep quiet in the near vicinityof primary receivers.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 22 / 90
The challenge of aggregate interference
B
One secondary usermight be acceptable, butwhat about millions?
Limit on the powerdensity
Slower effectiveattenuation withdistance
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 23 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 24 / 90
Outline
An overview of the issues involved 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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 25 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 26 / 90
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 27 / 90
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 issues
I Different propagation path lossesF Between primary and secondary usersF Among secondary users
I Multiple opportunistic usersI Heterogeneous transmit powers
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 27 / 90
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 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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 27 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 28 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 29 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 30 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 31 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 32 / 90
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)
SNR margin ψ at secondary receiver (dB)
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 33 / 90
Fading
������������
�� ����������������������
0 5 10 15 20 25 30−50
−40
−30
−20
−10
0
10
20
30
40
50Maximum power for secondary transmitter
SNR margin ψ at secondary receiver (dB)
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 34 / 90
Multiple secondaries – What could go wrong?
B
“Keeping Kfour-year olds quiet”
Pmd ≤ 1K PHI
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 35 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 35 / 90
“Death by a thousand cuts” analysis
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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 36 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 37 / 90
Fading revisited
�����
�����
�����
�����
Is there a principled way of choosing X dB of fading margin?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 38 / 90
Multipath and shadowing
−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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 39 / 90
Multipath and shadowing
−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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 39 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 40 / 90
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
Pfade fade (dB)10% -16 dB1% -21 dB
0.1% -26 dB0.01% -31 dB
(Assuming lognormal+Rayleigh fading, σ =3.5 dB each)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 40 / 90
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
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 40 / 90
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 41 / 90
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
Part II: More powerful detectorsI Coherent detectorI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 42 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 43 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 44 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 45 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 45 / 90
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
Computational/Implementational complexity
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 45 / 90
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)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 46 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 47 / 90
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)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 48 / 90
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)I Noise due to transmissions by other users
F Unintentional (Close-by)F Intentional (Far-away)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 48 / 90
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)I Noise due to transmissions by other users
F Unintentional (Close-by)F Intentional (Far-away)F Opportunistic
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 48 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 49 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 50 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 51 / 90
Example of noise distribution overlap
Signal looks like noise: fWa+X = fWn
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 52 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 53 / 90
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 54 / 90
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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 55 / 90
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!
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�� ����������������������
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 56 / 90
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
��������������������
�� ����������������������
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 56 / 90
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!
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 57 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 58 / 90
Beware of Multipath Gains!
CR #2 CR #3
CR #2 CR #3
CR #1
Primary Transmitter
Energy (dBm)
CR #1
Primary Transmitter
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 59 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 60 / 90
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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 60 / 90
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?
Trust issues
I What if users lie about sensing decisions?I What if radios fail in unknown ways and/or are malicious?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 60 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 61 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 62 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 62 / 90
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%
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 63 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 64 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 64 / 90
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.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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 64 / 90
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.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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 64 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 65 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 66 / 90
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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 67 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 68 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 69 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 69 / 90
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 Have everyone nearby be quiet during sensing.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 69 / 90
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 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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 69 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 70 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 70 / 90
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.Increasing density of secondary transmissions requires more cooperation.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 70 / 90
How to evaluate power / cooperation tradeoffs
Must satisfy two constraintsI Non-interference to primary receiversI Fairness among secondary users
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 71 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 71 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 71 / 90
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.
3. Set “shut-up” radius rs to reduce uncertainty Imax = D 2πα22−2 rs
2−α22
enough to allow robust detection at target level.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 71 / 90
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
Secondary system density (dBW/m2)
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
Secondary system density (dBW/m2)
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 72 / 90
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
Part II: More powerful detectorsI Coherent detectorsI Feature detectors
Part III: Hardware considerationsI Fundamental hardware limitationsI Ways around them
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 73 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 74 / 90
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.I Have deterministic pilot tones.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 74 / 90
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.I Have deterministic pilot tones.I Have guard bands and do not occupy all degrees of freedom.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 74 / 90
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.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?
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 74 / 90
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)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 75 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 76 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 77 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 78 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 79 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 80 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 81 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 82 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 83 / 90
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)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 83 / 90
Noise uncertainty: closer look
Noise = receiver/background noise + secondary interference,σ2 = σ2
0 + σ2i
Effect of interferenceInterference is uncertain
Dominating term in noise uncertainty
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 84 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 84 / 90
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%)
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 85 / 90
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 86 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 87 / 90
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’
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 88 / 90
Coherence buys freedom from secondary-MAC
−60 −55 −50 −45 −40 −35 −30 −25 −200
20
40
60
80
100
120
Secondary system density (dBW/m2)
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
Secondary system density (dBW/m2)
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
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 89 / 90
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.
Anant Sahai, Danijela Cabric (UC Berkeley) Wireless Foundations and BWRC Dyspan 2005 90 / 90