PIMRC 2016 Presentation

Motivation CS for Spectrum Sensing Simulation Results

Sparse Spectrum Sensing inInfrastructure-less Cognitive Radio

Networks via Binary ConsensusAlgorithms

Reference:Mohamed Seif, Tamer Elbatt and Karim G. Seddik, "Sparse Spectrum Sensing inInfrastructure- less Cognitive Radio Networks via Binary Consensus Algorithms", IEEE InternationalSymposium 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


1 Motivation

2 CS for Spectrum Sensing

3 Simulation Results


Sampling Theory

Shannon/Nyquist sampling theorem:

No information loss if we sampleat 2x signal bandwidthStorage/processing problem

Solution?

Yes, Compressive Sensing/Sampling


Sampling Theory



Solution?



Sampling Theory



Solution?



Compressive Sensing

Pioneered by E. Candes, T.Tao and D. DonohoSignal acquisition and compression in one stepSparsity in a certain transform domain (e.g., frequencydomain)


Compressive Sensing

Pioneered by E. Candes, T.Tao and D. Donoho

Signal acquisition and compression in one stepSparsity in a certain transform domain (e.g., frequencydomain)


Compressive Sensing

Pioneered by E. Candes, T.Tao and D. DonohoSignal acquisition and compression in one step

Sparsity in a certain transform domain (e.g., frequencydomain)


Compressive Sensing

Pioneered by E. Candes, T.Tao and D. DonohoSignal acquisition and compression in one stepSparsity in a certain transform domain (e.g., frequencydomain)


Compressive Sensing Formulation



RIP Condition:

(1 − δ) ∥x∥22 ≤ ∥Φx∥22 ≤ (1 + δ) ∥x∥22 . (1)



RIP Condition:

(1 − δ) ∥x∥22 ≤ ∥Φx∥22 ≤ (1 + δ) ∥x∥22 . (1)



Figure: Random measurements by φ (Gaussian).

Signal Recovery (`1 norm recovery):

minx∈RN∥x∥1 s.t.∥y − φx∥2 ≤ ε (2)



Figure: Random measurements by φ (Gaussian).

Signal Recovery (`1 norm recovery):

minx∈RN∥x∥1 s.t.∥y − φx∥2 ≤ ε (2)


1 Motivation




CS for Spectrum Sensing

frequencyN channel sub-bands

Empty sub-band Occupied sub-band

Sparsity in PU occupation



frequencyN channel sub-bands

Empty sub-band Occupied sub-band

Sparsity in PU occupation



CR3

CR1 CR2

CR4

CRi

Fusion Center

Figure: Fusion based CRN.

Decision making: Majority-Rule, AND-Rule


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 ≠ j0 otherwise

(3)

aij modeled as a Bernoulli R.V. with prob.of success p

CR3

CR1 CR2

CR4

CRi

Figure: Infrastructure-lessCRN.


CS for Spectrum Sensing in CRNs

1 `1 norm recovery

2 Vector Consensus algorithm

bj(k) = (1M(b(0) + 1

Kp

K−1

∑t=0

B(t)aTj (t)))

(4)

Convergence will be achieved

limk→∞

bj(k) = b∗ (5)

Majority-Rule asymptotic behavior

limK→∞

Pd(K ) =N

∑j=1

M

∑i=⌈M

2 ⌉(Mi )(1−π11)M−iπi

11

(6)

CR3

CR1 CR2

CR4

CRi

Figure: Infrastructure-lessCRN.


1 Motivation




Simulation Parameters

Parameter Symbol RealizationNo. channels N 200No. measurements T 30No. PU nodes P 4No. SU nodes M 12Minimum Distance dmin 10 (m)Area A 1000 (m) ×1000(m)Pathloss Exponent α 2


Results

0 5 10 15 20 250.9

0.95

1

SNR (dB)

Pd

0 5 10 15 20 250

2

4

6

8x 10

−3

SNR (dB)

Pfa

Centralized − Majority RuleInfrasturcture−less, K=20Infrasturcture−less, K=10Infrasturcture−less, K=1000

Centralized − Majority RuleInfrasturcture−less, K=20Infrasturcture−less, K=10Infrasturcture−less, K=1000

Figure: Performance comparison


Results

0 5 10 15 20 250.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

SNR (dB)

Pd

Centralized− Majority RuleInfrastructure−less, p=1Infrastructure−less, p=0.8Infrastructure−less, p=0.3Infrastructure−less, p=0.1

Figure: Effect of link quality


Results

0 5 10 15 20 250.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR (dB)

Pd

Centralized − Majority Rule, T=50Infrasturcture−less, T=50Infrasturcture−less, T=40Infrasturcture−less, T=30Infrasturcture−less, T=20

Figure: Effect of number of measurements


Results

1 2 3 4 5 6 7 8 9 100.7

0.75

0.8

0.85

0.9

0.95

1

k (iterations)

Pd(k

)

Good connectivity, p=0.8, SNR=10 dBPoor connectivity, p=0.3, SNR =10 dBGood connectivity, p=0.8, SNR =5 dBPoor connectivity, p=0.3, SNR =5 dB

Figure: The convergence of consensus algorithm in terms probability ofdetection


Thank You!

Engineering

PIMRC 2016 Presentation