PIMRC 2016 Presentation

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Mohamed Seif

PIMRC 2016

Engineering

Motivation CS for Spectrum Sensing Simulation Results
Sparse Spectrum Sensing in
Infrastructure-less Cognitive Radio
Networks via Binary Consensus
Algorithms
Reference:Mohamed Seif, Tamer Elbatt and Karim G. Seddik, "Sparse Spectrum Sensing in
Infrastructure- less Cognitive Radio Networks via Binary Consensus Algorithms", IEEE International
Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Valencia, Spain, Sept.
2016
Kihong Park, KAUST
Author Afﬁliation: Wireless Intelligent Networks Center (WINC), Nile University,
Egypt
September, 2016

Motivation CS for Spectrum Sensing Simulation Results
1 Motivation
2 CS for Spectrum Sensing
3 Simulation Results

Motivation CS for Spectrum Sensing Simulation Results
Sampling Theory
Shannon/Nyquist sampling theorem:
No information loss if we sample
at 2x signal bandwidth
Storage/processing problem

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing
Pioneered by E. Candes, T.Tao and D. Donoho

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing
Pioneered by E. Candes, T.Tao and D. Donoho
Signal acquisition and compression in one step

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing Formulation

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing Formulation
RIP Condition:
(1 − δ) x 2
2 ≤ Φx 2
2 ≤ (1 + δ) x 2
2 . (1)

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing Formulation
Figure: Random measurements by φ (Gaussian).

Motivation CS for Spectrum Sensing Simulation Results
Compressive Sensing Formulation
Figure: Random measurements by φ (Gaussian).
Signal Recovery ( 1 norm recovery):
min
x∈RN
x 1 s.t. y − φx 2 ≤ (2)

Motivation CS for Spectrum Sensing Simulation Results
CS for Spectrum Sensing
frequency
N channel sub-bands
Empty sub-band Occupied sub-band

Motivation CS for Spectrum Sensing Simulation Results
CS for Spectrum Sensing
frequency
N channel sub-bands
Empty sub-band Occupied sub-band
Sparsity in PU occupation

Motivation CS for Spectrum Sensing Simulation Results
CS for Spectrum Sensing
CR3
CR1 CR2
CR4
CRi
Fusion Center
Figure: Fusion based CRN.
Decision making: Majority-Rule, AND-Rule

Motivation CS for Spectrum Sensing Simulation Results
CS for Spectrum Sensing in CRNs
Secondary network:
G(M,E): random graph
Adjacency matrix A(k) ∈ RM×M
:
aij (k) =
⎧⎪⎪
⎨
⎪⎪⎩
1 if ¯τij (k) >= τ, i ≠ j
0 otherwise
(3)
aij modeled as a Bernoulli R.V. with prob.
of success p
CR3
CR1 CR2
CR4
CRi
Figure: Infrastructure-less
CRN.

Motivation CS for Spectrum Sensing Simulation Results
CS for Spectrum Sensing in CRNs
1 1 norm recovery
2 Vector Consensus algorithm
bj (k) = (
1
M
(b(0) +
1
Kp
K−1
∑
t=0
B(t)¯aT
j (t)))
(4)
Convergence will be achieved
lim
k→∞
bj (k) = b∗
(5)
Majority-Rule asymptotic behavior
lim
K→∞
Pd (K) =
N
∑
j=1
M
∑
i=⌈ M
2 ⌉
(
M
i
)(1−π11)M−i
πi
11
(6)
CR3
CR1 CR2
CR4
CRi
Figure: Infrastructure-less
CRN.

Motivation CS for Spectrum Sensing Simulation Results
Simulation Parameters
Parameter Symbol Realization
No. channels N 200
No. measurements T 30
No. PU nodes P 4
No. SU nodes M 12
Minimum Distance dmin 10 (m)
Area A 1000 (m) ×1000(m)
Pathloss Exponent α 2

Motivation CS for Spectrum Sensing Simulation Results
Results
0 5 10 15 20 25
0.9
0.95
1
SNR (dB)
P
d
0 5 10 15 20 25
0
2
4
6
8
x 10
−3
SNR (dB)
P
fa
Centralized − Majority Rule
Infrasturcture−less, K=20
Infrasturcture−less, K=10
Infrasturcture−less, K=1000
Centralized − Majority Rule
Infrasturcture−less, K=20
Infrasturcture−less, K=10
Infrasturcture−less, K=1000
Figure: Performance comparison

Motivation CS for Spectrum Sensing Simulation Results
Results
0 5 10 15 20 25
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
SNR (dB)
P
d
Centralized− Majority Rule
Infrastructure−less, p=1
Infrastructure−less, p=0.8
Infrastructure−less, p=0.3
Infrastructure−less, p=0.1
Figure: Effect of link quality

Motivation CS for Spectrum Sensing Simulation Results
Results
0 5 10 15 20 25
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR (dB)
P
d
Centralized − Majority Rule, T=50
Infrasturcture−less, T=50
Infrasturcture−less, T=40
Infrasturcture−less, T=30
Infrasturcture−less, T=20
Figure: Effect of number of measurements

Motivation CS for Spectrum Sensing Simulation Results
Results
1 2 3 4 5 6 7 8 9 10
0.7
0.75
0.8
0.85
0.9
0.95
1
k (iterations)
P
d
(k)
Good connectivity, p=0.8, SNR=10 dB
Poor connectivity, p=0.3, SNR =10 dB
Good connectivity, p=0.8, SNR =5 dB
Poor connectivity, p=0.3, SNR =5 dB
Figure: The convergence of consensus algorithm in terms probability of
detection

Motivation CS for Spectrum Sensing Simulation Results
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PIMRC 2016 Presentation

1. Motivation CS for Spectrum Sensing Simulation Results Sparse Spectrum Sensing in Infrastructure-less Cognitive Radio Networks via Binary Consensus Algorithms Reference:Mohamed Seif, Tamer Elbatt and Karim G. Seddik, "Sparse Spectrum Sensing in Infrastructure- less Cognitive Radio Networks via Binary Consensus Algorithms", IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Valencia, Spain, Sept. 2016 Kihong Park, KAUST Author Afﬁliation: Wireless Intelligent Networks Center (WINC), Nile University, Egypt September, 2016

2. Motivation CS for Spectrum Sensing Simulation Results 1 Motivation 2 CS for Spectrum Sensing 3 Simulation Results

3. Motivation CS for Spectrum Sensing Simulation Results Sampling Theory Shannon/Nyquist sampling theorem: No information loss if we sample at 2x signal bandwidth Storage/processing problem

4. Motivation CS for Spectrum Sensing Simulation Results Sampling Theory Shannon/Nyquist sampling theorem: No information loss if we sample at 2x signal bandwidth Storage/processing problem Solution?

5. Motivation CS for Spectrum Sensing Simulation Results Sampling Theory Shannon/Nyquist sampling theorem: No information loss if we sample at 2x signal bandwidth Storage/processing problem Solution? Yes, Compressive Sensing/Sampling

6. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing

7. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Pioneered by E. Candes, T.Tao and D. Donoho

8. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Pioneered by E. Candes, T.Tao and D. Donoho Signal acquisition and compression in one step

9. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Pioneered by E. Candes, T.Tao and D. Donoho Signal acquisition and compression in one step Sparsity in a certain transform domain (e.g., frequency domain)

10. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Formulation

11. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Formulation

12. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Formulation RIP Condition: (1 − δ) x 2 2 ≤ Φx 2 2 ≤ (1 + δ) x 2 2 . (1)

13. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Formulation Figure: Random measurements by φ (Gaussian).

14. Motivation CS for Spectrum Sensing Simulation Results Compressive Sensing Formulation Figure: Random measurements by φ (Gaussian). Signal Recovery ( 1 norm recovery): min x∈RN x 1 s.t. y − φx 2 ≤ (2)

15. Motivation CS for Spectrum Sensing Simulation Results 1 Motivation 2 CS for Spectrum Sensing 3 Simulation Results

16. Motivation CS for Spectrum Sensing Simulation Results CS for Spectrum Sensing frequency N channel sub-bands Empty sub-band Occupied sub-band

17. Motivation CS for Spectrum Sensing Simulation Results CS for Spectrum Sensing frequency N channel sub-bands Empty sub-band Occupied sub-band Sparsity in PU occupation

18. Motivation CS for Spectrum Sensing Simulation Results CS for Spectrum Sensing CR3 CR1 CR2 CR4 CRi Fusion Center Figure: Fusion based CRN. Decision making: Majority-Rule, AND-Rule

19. Motivation CS for Spectrum Sensing Simulation Results CS for Spectrum Sensing in CRNs Secondary network: G(M,E): random graph Adjacency matrix A(k) ∈ RM×M : aij (k) = ⎧⎪⎪ ⎨ ⎪⎪⎩ 1 if ¯τij (k) >= τ, i ≠ j 0 otherwise (3) aij modeled as a Bernoulli R.V. with prob. of success p CR3 CR1 CR2 CR4 CRi Figure: Infrastructure-less CRN.

20. Motivation CS for Spectrum Sensing Simulation Results CS for Spectrum Sensing in CRNs 1 1 norm recovery 2 Vector Consensus algorithm bj (k) = ( 1 M (b(0) + 1 Kp K−1 ∑ t=0 B(t)¯aT j (t))) (4) Convergence will be achieved lim k→∞ bj (k) = b∗ (5) Majority-Rule asymptotic behavior lim K→∞ Pd (K) = N ∑ j=1 M ∑ i=⌈ M 2 ⌉ ( M i )(1−π11)M−i πi 11 (6) CR3 CR1 CR2 CR4 CRi Figure: Infrastructure-less CRN.

21. Motivation CS for Spectrum Sensing Simulation Results 1 Motivation 2 CS for Spectrum Sensing 3 Simulation Results

22. Motivation CS for Spectrum Sensing Simulation Results Simulation Parameters Parameter Symbol Realization No. channels N 200 No. measurements T 30 No. PU nodes P 4 No. SU nodes M 12 Minimum Distance dmin 10 (m) Area A 1000 (m) ×1000(m) Pathloss Exponent α 2

23. Motivation CS for Spectrum Sensing Simulation Results Results 0 5 10 15 20 25 0.9 0.95 1 SNR (dB) P d 0 5 10 15 20 25 0 2 4 6 8 x 10 −3 SNR (dB) P fa Centralized − Majority Rule Infrasturcture−less, K=20 Infrasturcture−less, K=10 Infrasturcture−less, K=1000 Centralized − Majority Rule Infrasturcture−less, K=20 Infrasturcture−less, K=10 Infrasturcture−less, K=1000 Figure: Performance comparison

24. Motivation CS for Spectrum Sensing Simulation Results Results 0 5 10 15 20 25 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 SNR (dB) P d Centralized− Majority Rule Infrastructure−less, p=1 Infrastructure−less, p=0.8 Infrastructure−less, p=0.3 Infrastructure−less, p=0.1 Figure: Effect of link quality

25. Motivation CS for Spectrum Sensing Simulation Results Results 0 5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR (dB) P d Centralized − Majority Rule, T=50 Infrasturcture−less, T=50 Infrasturcture−less, T=40 Infrasturcture−less, T=30 Infrasturcture−less, T=20 Figure: Effect of number of measurements

26. Motivation CS for Spectrum Sensing Simulation Results Results 1 2 3 4 5 6 7 8 9 10 0.7 0.75 0.8 0.85 0.9 0.95 1 k (iterations) P d (k) Good connectivity, p=0.8, SNR=10 dB Poor connectivity, p=0.3, SNR =10 dB Good connectivity, p=0.8, SNR =5 dB Poor connectivity, p=0.3, SNR =5 dB Figure: The convergence of consensus algorithm in terms probability of detection

27. Motivation CS for Spectrum Sensing Simulation Results Thank You!

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PIMRC 2016 Presentation