Some Fundamental Limits on Cognitive Radio - Semantic Scholar
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Some Fundamental Limits on Cognitive Radio
Niels Hoven, Rahul Tandra, and Prof. Anant Sahai Wireless Foundations, EECS University of California at Berkeley February 11, 2005
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Spectrum: Allocation vs Usage
• Apparent spectrum scarcity • Actual measurements show that > 70% of spectrum is unused. • Enough free spectrum for DVD-res cameras every few feet! &
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That was then, this is now... • Primitive analog hardware
• Digital wideband hardware
• Devices fixed to bands
• More flexible spectrum view
• Interference a severe challenge
• Heterogeneous applications
• Long range applications
– Different priorities – Range of spatial scales
• Bands allocated by law
• Require interoperability
• Enforce by licensing devices
• Enforcement more difficult
What architectures will be needed to better exploit spectrum? What’s the minimal change in regulation? &
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Cognitive Radio Justification
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
• 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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– Not the UWB approach: “speak softly but use a wide band” – Primary band usage may vary in time – May have to scavenge many discontinuous bands – May have to coordinate/coexist with other secondary users
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Justification Cont. A
A
B
B
Mice can get close... A
A
B
But keep the lions far away!
&
The “no talk” zones grow dramatically
B
Union of “no talk” zones.
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Shadowing 1
2
C
C
A secondary user might be in a local shadow while his transmissions could still reach an unshadowed primary receiver. &
Secondary user can not distinguish between positions (1) and (2) - must be quiet in both.
Multiuser diversity should increase our chances of an accurate measurement.
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A Fundamental tradeoff Interferer Power vs Detectable SNR α 1 γ +M γ −β α − det −α − dec 2 Pp 10 10 Ps = Pp rp 10 − σ · 10 − rp σ2
• Glossary Maximum interferer power vs. detectable SNR
– γdec : Minimum SIN R for decodability at the primary receiver.
– β: SN R loss in detectability due to shadowing. – M : Margin of protection given to the primary receivers.
60
50
40
30
20
10
0
−10 −40
&
No shadowing −10dB shadowing
70
Max interferer power at any range(dB)
– γdet : Minimum SN R at which the secondary can detect the primary transmission.
80
−35
−30
−25
−20 −15 Detectable SNR (dB)
−10
−5
0
%
'
$
Censored radius vs. interferer power and protected radius Allowable intereferer power (4.5 km from transmitter)
Effects as protected radius nears decodability bound (censored radius = 10 meters) 25
1000
900
800
700 Interferer power (mW)
Allowable interferer power (W)
20
15
10
600
500
400
300
5
200
100
0 1000
1500
2000
2500 3000 3500 Protected radius (m)
4000
4500
5000
Protecting marginal users forces the cognitive radio to squeak.
&
0
0
5
10
15 Censored radius (m)
20
25
30
Larger censored regions allow the cognitive radios to roar.
%
'
$
Model • Hypothesis testing problem: is the primary signal out there?
H0 : Y [n] = W [n] Hs : Y [n] = W [n] + x[n]
• Moderate Pf a , Pmd targets • Potentially very low SNR at the detector: will need many samples to distinguish hypothesis • How long must we listen? &
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'
$
Signal detection Low SNR
BPSK −− Detector Performance 14 Energy Detector Undecodable BPSK BPSK with Pilot signal Sub−optimal scheme Deterministic BPSK
12
• The optimal detector behaves like an energy detector. • If one exists, just detecting a pilot signal is nearly optimal.
8
log
10
N
10
6
• Signals without pilots are difficult to detect.
4
2
0 −60
−50
−40
−30
−20
−10
0
SNR (in dB)
p = 1/5 p = 1/4
p = 1/4 p = 1/5
p = 1/3
p = 1/3
p = 1/5
p = 6/7 [−1 , 0 ]
p = 1/4
p = 1/4
p = 1/7 [6 , 0]
p = 1/3
p = 1/5 p = 1/5
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Noise Uncertainty Low−noise amplifier
Frequency down− converter
Intermediate frequency amplifier
A/D Converter
Receiving antenna
Demodulator
• In practice there is always uncertainty about the noise. • Sources of uncertainty: – Thermal noise in components (Non-uniform, time-varying) – Noise due to transmissions by other users ∗ Unintentional (Close-by) ∗ Intentional (Far-away) &
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'
$
Noise Uncertainty: Conservative Model • Noise can be modeled as “Approximately Gaussian” to incorporate uncertainty. – Like Gaussian noise, but x dB uncertainty in moments. – EN 2k−1 = 0. [Symmetry property] – EN 2k ∈ [EW 2k , α EW 2k ], where W ∼ N (0, σ 2 ) and α = 10x/10 . • What are the consequences? – SNR walls
• Theorem: For the case of detection of a weak BPSK signal, the ‘2k-th moment detector’ encounters a threshold (wall) below which detection is impossible. The threshold for detection as a function of the noise uncertainty x is given by: (x/10) SN R2k = 10 log [10 − 1] − 10 log10 k 10 wall
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$
Noise Uncertainty: Threshold Behavior • Moment detector performance
• Noise uncertainty vs SNR wall 0
8 2nd Moment Detector 4th Moment Detector 6th Moment Detector 8th Moment Detector 10th Moment Detector Envelope of detectors Energy Detector
7
−5
−10
(in dB)
6
−15
wall
log10 N
5
SNR
−20
4
−25
3
−30
2
1 −18
2nd Moment Detector 4th Moment Detector 6th Moment Detector 8th Moment Detector 10th Moment Detector
−35
−16
&
−14
−12
−10 −8 Nominal SNR (in dB)
−6
−4
−2
0
0
0.5
1
1.5
2
2.5
3
Noise Uncertainty (in dB)
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$
Noise uncertainty + Quantization • Our abstraction
• Things get worse under quantization Secondary
Data Demodulation
Noise S
Sampler
– Bounded dynamic range on quantization bins – Moment uncertainty model for noise
Q Quantizer
Signal Detection
&
• Assumptions:
• There exists an SNR threshold below which detection is absolutely impossible. %
'
$
BPSK example • Detection can be absolutely impossible for 2-bit quantizer – Adversarial noise can make the distributions identical under both hypotheses if √ ¶ √ ¶¸ µ ¶ · µ µ d1 1 d1 + P d1 − P Q = Q +Q σ0 2 σ1 σ1 • Wall always exists for any detector. 14
12
x=0.001 dB
x=0.1 dB
x=1 dB
log10 N
10
8
6
4
2
0 −40
−35
−30
−25
−20
−15
−10
−5
0
Nominal SNR
&
%
'
$
Conclusions • Cognitive radio can enable significant spectrum reuse. • To function, we 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. • If not, some infrastructure and/or collaboration will be needed to support cognitive radio deployment. • Similar limits apply to secondary markets. &
%
$
Some Fundamental Limits on Cognitive Radio
Niels Hoven, Rahul Tandra, and Prof. Anant Sahai Wireless Foundations, EECS University of California at Berkeley February 11, 2005
&
%
'
$
Spectrum: Allocation vs Usage
• Apparent spectrum scarcity • Actual measurements show that > 70% of spectrum is unused. • Enough free spectrum for DVD-res cameras every few feet! &
%
'
$
That was then, this is now... • Primitive analog hardware
• Digital wideband hardware
• Devices fixed to bands
• More flexible spectrum view
• Interference a severe challenge
• Heterogeneous applications
• Long range applications
– Different priorities – Range of spatial scales
• Bands allocated by law
• Require interoperability
• Enforce by licensing devices
• Enforcement more difficult
What architectures will be needed to better exploit spectrum? What’s the minimal change in regulation? &
%
'
$
Cognitive Radio Justification
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
• Wireless interference is primarily a local phenomenon. • If a radio system transmits in a band and nobody else is listening, does it cause interference?
&
– Not the UWB approach: “speak softly but use a wide band” – Primary band usage may vary in time – May have to scavenge many discontinuous bands – May have to coordinate/coexist with other secondary users
%
'
$
Justification Cont. A
A
B
B
Mice can get close... A
A
B
But keep the lions far away!
&
The “no talk” zones grow dramatically
B
Union of “no talk” zones.
%
'
$
Shadowing 1
2
C
C
A secondary user might be in a local shadow while his transmissions could still reach an unshadowed primary receiver. &
Secondary user can not distinguish between positions (1) and (2) - must be quiet in both.
Multiuser diversity should increase our chances of an accurate measurement.
%
'
$
A Fundamental tradeoff Interferer Power vs Detectable SNR α 1 γ +M γ −β α − det −α − dec 2 Pp 10 10 Ps = Pp rp 10 − σ · 10 − rp σ2
• Glossary Maximum interferer power vs. detectable SNR
– γdec : Minimum SIN R for decodability at the primary receiver.
– β: SN R loss in detectability due to shadowing. – M : Margin of protection given to the primary receivers.
60
50
40
30
20
10
0
−10 −40
&
No shadowing −10dB shadowing
70
Max interferer power at any range(dB)
– γdet : Minimum SN R at which the secondary can detect the primary transmission.
80
−35
−30
−25
−20 −15 Detectable SNR (dB)
−10
−5
0
%
'
$
Censored radius vs. interferer power and protected radius Allowable intereferer power (4.5 km from transmitter)
Effects as protected radius nears decodability bound (censored radius = 10 meters) 25
1000
900
800
700 Interferer power (mW)
Allowable interferer power (W)
20
15
10
600
500
400
300
5
200
100
0 1000
1500
2000
2500 3000 3500 Protected radius (m)
4000
4500
5000
Protecting marginal users forces the cognitive radio to squeak.
&
0
0
5
10
15 Censored radius (m)
20
25
30
Larger censored regions allow the cognitive radios to roar.
%
'
$
Model • Hypothesis testing problem: is the primary signal out there?
H0 : Y [n] = W [n] Hs : Y [n] = W [n] + x[n]
• Moderate Pf a , Pmd targets • Potentially very low SNR at the detector: will need many samples to distinguish hypothesis • How long must we listen? &
%
'
$
Signal detection Low SNR
BPSK −− Detector Performance 14 Energy Detector Undecodable BPSK BPSK with Pilot signal Sub−optimal scheme Deterministic BPSK
12
• The optimal detector behaves like an energy detector. • If one exists, just detecting a pilot signal is nearly optimal.
8
log
10
N
10
6
• Signals without pilots are difficult to detect.
4
2
0 −60
−50
−40
−30
−20
−10
0
SNR (in dB)
p = 1/5 p = 1/4
p = 1/4 p = 1/5
p = 1/3
p = 1/3
p = 1/5
p = 6/7 [−1 , 0 ]
p = 1/4
p = 1/4
p = 1/7 [6 , 0]
p = 1/3
p = 1/5 p = 1/5
&
%
'
$
Noise Uncertainty Low−noise amplifier
Frequency down− converter
Intermediate frequency amplifier
A/D Converter
Receiving antenna
Demodulator
• In practice there is always uncertainty about the noise. • Sources of uncertainty: – Thermal noise in components (Non-uniform, time-varying) – Noise due to transmissions by other users ∗ Unintentional (Close-by) ∗ Intentional (Far-away) &
%
'
$
Noise Uncertainty: Conservative Model • Noise can be modeled as “Approximately Gaussian” to incorporate uncertainty. – Like Gaussian noise, but x dB uncertainty in moments. – EN 2k−1 = 0. [Symmetry property] – EN 2k ∈ [EW 2k , α EW 2k ], where W ∼ N (0, σ 2 ) and α = 10x/10 . • What are the consequences? – SNR walls
• Theorem: For the case of detection of a weak BPSK signal, the ‘2k-th moment detector’ encounters a threshold (wall) below which detection is impossible. The threshold for detection as a function of the noise uncertainty x is given by: (x/10) SN R2k = 10 log [10 − 1] − 10 log10 k 10 wall
&
%
'
$
Noise Uncertainty: Threshold Behavior • Moment detector performance
• Noise uncertainty vs SNR wall 0
8 2nd Moment Detector 4th Moment Detector 6th Moment Detector 8th Moment Detector 10th Moment Detector Envelope of detectors Energy Detector
7
−5
−10
(in dB)
6
−15
wall
log10 N
5
SNR
−20
4
−25
3
−30
2
1 −18
2nd Moment Detector 4th Moment Detector 6th Moment Detector 8th Moment Detector 10th Moment Detector
−35
−16
&
−14
−12
−10 −8 Nominal SNR (in dB)
−6
−4
−2
0
0
0.5
1
1.5
2
2.5
3
Noise Uncertainty (in dB)
%
'
$
Noise uncertainty + Quantization • Our abstraction
• Things get worse under quantization Secondary
Data Demodulation
Noise S
Sampler
– Bounded dynamic range on quantization bins – Moment uncertainty model for noise
Q Quantizer
Signal Detection
&
• Assumptions:
• There exists an SNR threshold below which detection is absolutely impossible. %
'
$
BPSK example • Detection can be absolutely impossible for 2-bit quantizer – Adversarial noise can make the distributions identical under both hypotheses if √ ¶ √ ¶¸ µ ¶ · µ µ d1 1 d1 + P d1 − P Q = Q +Q σ0 2 σ1 σ1 • Wall always exists for any detector. 14
12
x=0.001 dB
x=0.1 dB
x=1 dB
log10 N
10
8
6
4
2
0 −40
−35
−30
−25
−20
−15
−10
−5
0
Nominal SNR
&
%
'
$
Conclusions • Cognitive radio can enable significant spectrum reuse. • To function, we 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. • If not, some infrastructure and/or collaboration will be needed to support cognitive radio deployment. • Similar limits apply to secondary markets. &
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