some fundamental limitations for cognitive radiosahai/presentations/cognitive... · some...

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Some Fundamental Limitations

for Cognitive Radio

Anant Sahai

Wireless Foundations, UCB EECS

[email protected]

Joint work with Niels Hoven and Rahul Tandra

Work supported by the NSF ITR program

November 1 at BWRC Cognitive Radio Workshop

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Outline

1. Why cognitive radios?

2. Fundamental need to detect very weak primary signals

3. Knowledge of modulation does not help but knowledge of pilot

signals does

4. Receiver uncertainty and quantization’s impact on detection

5. Conclusions


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Apparent spectrum allocations

• Traditional spectrum allocation picture

• Apparent spectrum scarcity


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Apparent spectrum usage

Actual measurements show that < 20% of spectrum is used, but:

• Some users listen for very weak signals

– GPS

– Weather radar and remote sensing

– Radio astronomy

– Satellite communications

• Spectrum use can vary with space and time on all scales.


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Cognitive radio justification

Wireless interference is primarily a local phenomenon.

“If a radio system transmits in a band and nobody else is

listening, does it cause interference?”


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Ambitious Goal

Would like to take advantage of plentiful spectrum without requiring

a lot of regulation or assumed coordination among users.


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Objectives

• Protect primary users of the spectrum

– Socially important services may deserve priority on band

– Legacy systems may not be able to change

• Allow for secondary users to use otherwise unused bands

– Not the UWB approach: “speak softly but use a wide band”

– May have to coordinate/coexist with other secondary users

See what happens for the case of a single secondary user first.


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Primary decodability region


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Primary protected region

B

A

Users at the very edge of the currently decodable region will do

worse under any changes to the exclusive-use model.


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“No talk” zones

B

A

Mice can get close...


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“No talk” zones

B

A

But keep the lions far away!


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If the protected region nears the decodability

bound...

A

B


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The “no talk” zones grow dramatically

A

B


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Union of “no talk” zones

A

B

Need to be able to detect an undecodable transmission if either the

protected radius or the allowed secondary power is large.


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Fundamental Tradeoffs

Assume 1d2 attenuation of signals:

rcensored =

√

√

√

√

Ps

Pp

(22R−1)r2

protected

− σ2

Ps = r2censored

[

Pp

(22R − 1)r2protected

− σ2

]

• To allow secondary power to increase, we must be able to

detect weak primary signals in order to protect primary

receivers from interference.

• To protect primary receivers with already marginal reception,

the censored radius must grow and so even weaker primary

signals must be able to be detected.


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Censored radius vs. interferer power and

protected radius

1000 1500 2000 2500 3000 3500 4000 4500 50000

5

10

15

20

25

Protected radius (m)

Allo

wa

ble

in

terf

ere

r p

ow

er

(W)

Effects as protected radius nears decodability bound (censored radius = 10 meters)

0 1000 2000 3000 4000 50000

5

10

15

20

25

30

Protected radius (m)

Ce

nso

red

ra

diu

s (

m)

Effects as protected radius nears decodability bound (200 mW secondary user)

0 200 400 600 800 10000

5

10

15

20

25

30

Interferer power (mW)

Ce

nso

red

ra

diu

s (

m)

Censored zones for mice and lions (4.5 km from transmitter)


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Shadowing

C

A secondary user might be in a local shadow while his

transmissions could still reach an unshadowed primary receiver.


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Shadowing

C

1

2

Secondary user can not distinguish between positions (1) and (2)

— must be quiet in both: must detect even weaker primary

signals.


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Cognitive radio is still potentially useful

Even while protecting primary users, a large geographic area may

still be available for secondary users in any given band.


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Lessons so far

• “Don’t transmit if you can decode” is a poor rule

• Could do much better if we could detect undecodable signals

– Better protect primary users

– Allow longer range and higher rate secondary uses

• How hard is this?


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Model

• Hypothesis testing problem: is the primary signal out there?

H0 : Y [n] = W [n]

Hs : Y [n] = W [n] + x[n]

• Moderate Pfa, Pmd targets.

• Potentially very low SNR at the detector: will need many

samples to distinguish hypotheses.

• Proxy for difficulty: How long must we listen?


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Assume perfect knowledge

• x[n] known exactly at receiver

• Optimal detector is a matched filter

N∑

k=1

y[n]x[n]

‖x‖Hs

≷H0

‖x‖2

The power of processing gain: we only require O(1/SNR) samples


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Assume minimal knowledge

• Only know power and signal is like white Gaussian noise

• No processing gain available

• Optimal detector is an energy detector (radiometer)

N∑

k=1

y[n]2Hs

≷H0

N

(

σ2 +P

2

)

• We require O(1/SNR2) samples


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Energy detector vs. Coherent detector

−60 −55 −50 −45 −40 −35 −30 −25 −202

4

6

8

10

12

14

SNR (in dB)

log 10

N

Energy and the Coherent detectorEnergy DetectorCoherent Detector

Slope = −2

Slope = −1


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Undecodable BPSK

What if we had a little more information?

• Power is low.

• Modulation scheme (BPSK) is known

• Assume perfect synchronization to both the carrier frequency

and symbol timing.

H0 : Y [n] = W [n]

Hs : Y [n] = W [n] + X[n]√

P

X[n] ∼ iid. Bernoulli(1/2)


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Undecodable BPSK cont.

−5 −4 −3 −2 −1 0 1 2 3 4 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.50.5 f

1(x|a =−0.25)

0.5 f1(x|a= 0.25)

f1(x)

f0(x)

SNR ≈ −12 dB

P−1/2

P−1/2

• Optimal detector turns out to be like the energy detector at

low SNR



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Numerical plots for number of required samples..

−60 −50 −40 −30 −20 −10 00

2

4

6

8

10

12

14

SNR (in dB)

log 10

NEnergy DetectorUndecodable BPSKCoherent Detector

BPSK −− Detector Performance


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General symbol constellations

• Is the story bad only for BPSK?

H0 :−→Y [n] =

−→W [n]

Hs :−→Y [n] =

−→W [n] +

−→X [n]

−→x [n] = −→c i , i ∈ {1, 2, . . . , 2LR}−→w [n] ∼ N (0, σ2IL)

• Assumptions

– Short symbols ~ci of length L.

– 2LR symbols known to the receiver

– Symbol constellation is zero-mean

– Symbols independent

– Very little energy in any individual symbol


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Examples of zero-mean symbol constellations

p = 1/4

p = 1/4 p = 1/4

p = 1/4

p = 1/5

p = 1/5

p = 1/5

p = 1/5

p = 1/5

p = 1/3

p = 1/3

p = 1/3 p = 6/7 p = 1/7

[−1 , 0 ] [6 , 0]

Also includes symbols multiplied by short PRN sequences, short

OFDM packets, etc.


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Result

• Optimal detector is like an energy detector at low SNR


−60 −50 −40 −30 −20 −10 010

2

104

106

108

1010

1012

1014

SNR (dB)

log

10 N

Asymmetric Constellation − Detector Performance

Optimal DetectorEnergy Detector


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The importance of the zero-mean assumption

p2

p1

[−1 , 0 ] [2 , 0]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3x 10

6

p1

N

Energy DetectorOptimal DetectorDeterministic Detector

The peak occurs when the constellation has zero mean.


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Assume a weak pilot signal alongside the BPSK

−60 −50 −40 −30 −20 −10 00

2

4

6

8

10

12

14

SNR (in dB)

log 10

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

BPSK −− Detector Performance


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The story so far

• Without help from the primary user, the secondary users

require a long time to detect free bands.

– Less agility

– Overhead in searching for unused bands

• It gets a whole lot worse.

– Noise uncertainty

– Quantization


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Receiver chain structure

down−converter

Frequency Intermediatefrequencyamplifier Converter

A/Damplifier

Low−noise

Demodulator

Receivingantenna


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Noise uncertainty

• Let residual noise uncertainty be x dB within the band.

• Receiver faces an SNR within

[SNRnominal, SNRnominal + x]

• Pnoise ∈ [Pnominal, α · Pnominal] , α = 10(x/10)

• Therefore, the energy detector fails if:

Pnoise ≥ Pnominal + Psignal

⇒ SNRnominal ≤ 10 log10 [10(x/10)− 1]


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Energy detector with noise uncertainty

−40 −35 −30 −25 −20 −15 −10 −5 00

2

4

6

8

10

12

14

Nominal SNR

log

10 N

x = 0.1 dBx = 0.001 dB x = 1 dB


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“Wall” position as a function of uncertainty

SNRwall = 10 log10 [10(x/10)− 1]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−40

−35

−30

−25

−20

−15

−10

−5

SNR sensitivity (in dB)

Det

ecta

bilit

y th

resh

old

(in d

B)


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Quantization: Our abstraction

Secondary

DemodulationData

SignalDetection

SSampler Quantizer

Q

Noise


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SNR loss from quantization

−45 −44 −43 −42 −41 −40 −39 −38 −37 −36 −35

8.5

9

9.5

10

10.5

SNR (in dB)

log

10 N

non−coherent detector6−bin non−coherent detector4−bin non−coherent detectorContinuous Energy detector

−45 −44 −43 −42 −41 −40 −39 −38 −37 −36 −354.6

4.8

5

5.2

5.4

5.6

5.8

SNR (in dB)

log

10 N

Coherent detector 2−bin Coherent detector4−bin Coherent detector6−bin Coherent detectorContinuous Coherent detector

Quantization SNR loss SNR loss

bins (coherent detector) (non-coherent detector)

2 bins 2 dB ∞

4 bins 0.5 dB 1.4 dB

6 bins 0.3 dB 0.7 dB


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Noise uncertainty under quantization

• Detection can be absolutely impossible for 2-bit quantizer

under noise variance uncertainty alone.

– Can make the distributions identical under both hypotheses

if

Q

(

d1

σ0

)

=1

2

[

Q

(

d1 +√

P

σ1

)

+ Q

(

d1 −√

P

σ1

)]

– σ2i is noise variance under hypothesis i

– d1 is the quantization bin boundary

• Wall always exists for any detector.


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Quantized detector with noise uncertainty:

2-bit quantizer

−40 −35 −30 −25 −20 −15 −10 −5 00

2

4

6

8

10

12

14

Nominal SNR

log

10 N

x=0.1 dB x=1 dBx=0.001 dB


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Conclusions

• Cognitive radios must be able to detect the presence of

undecodable signals

– Just knowing the modulation scheme and codebooks is

nearly useless: stuck with energy detector performance.

– Even small noise uncertainty causes serious limits in

detectability.

– Quantization makes matters even worse.

• Primary users should transmit pilot signals or sirens.

• If not, some serious “infrastructure” will be needed to support

cognitive radio deployment.


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Key future questions

• Multiuser situations

– Control channel use and coordination

– Distributed reliable environmental proofs

– Efficiency and robustness

• How to ensure forward compatibility

– Can future computational capabilities help systems

engineered today?

– Poorly engineered systems today will hinder future systems.

• Congestion is still potentially possible in the future.


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