Performance Analysis of Energy Detector in Relay Based Cognitive Radio Networks

Saman AtapattuChintha Tellambura

Hai Jiang

Outline

Introduction System model Detection analysis Upper bound ROC curves Conclusions

Radio Spectrum Primary user / license

holder Occupancy of spectrum

(below 1 GHz) is around 6~10%.

Spectrum holes Spectrum under

utilization

Maximum Amplitudes

Frequency (MHz)

Am

pli

du

e (

dB

m)

Heavy Use

Sparse Use

Heavy Use

Medium Use

Less than 6-10% OccupancyLess than 6-10% Occupancy

Cognitive Radio

“A radio that can change its transmitter parameters based on the environment in which it operates”.

Cognitive radio Secondary network Unlicensed users

Spectrum Sensing…?

Spectrum Sensing

Multipath fading & shadowing. Hidden terminal problem.

PU should not be effected by secondary activities. Reliability

Decision based on the received signal

Ho = Primary user is absent (idle)

H0: Y [n] = W [n]H1 = Primary user is in operation (busy)

H1: Y [n]= h X [n] + W [n]

Cooperative Spectrum Sensing (CCS)

Mitigate multipath fading & shadowing by spatial diversity.

Avoid hidden terminal problem.

Shadowing Shadowed node

Cooperative nodes

Improve reliability and detection capability.

Sensing Techniques

Matched filter: SU has a prior knowledge of the

PU, coherent detection.

Cyclostationary detection: PU exhibits strong

cyclostationary properties.

Covariance detection: the statistical covariance matrices of the signal and noise.

Energy detection: the received signal strength.

Sensing Techniques

Matched filter: SU has a prior knowledge of the

PU, coherent detection.

Cyclostationary detection: PU exhibits strong

cyclostationary properties.

Covariance detection: the statistical covariance matrices of the signal and noise.

Energy detection: the received signal strength.

Non-coherent Low complexity

Relay-based CCS

Data fusion AF relaying in cooperative communications

Relay Fixed gain (blind/semi blind)Variable gain

Combining MRC/ SLC

Filtering Energy detector Multipath fading

Rayleigh/ Nakagami-m Ri to CC (i=1, …, n) channel

Orthogonal (TDMA) Relay links Relay links + Direct link

System Model

Energy Detector

Output is compared to the predefined threshold. Non-coherent, optimal, low signal processing.

Binary hypothesis

Performance Metrics

Test statistic

False alarm probability:

Detection probability:

Detection Analysis Detection:

Average detection probability:

Detection Analysis Detection:

Average detection probability:

Contour integration: Residue theorem

Moment generating function (MGF)

MGF Variable gain

Fixed gain

Upper Bound for Pd

Case 1: Multiple-relay Case 2: Multiple-relay + Direct link

SNR:

MGF:

Upper bound: Case 1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1, 2

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1, 2

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1, 2, 3, 4, 5

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

Exact (simulations)Upper Bound (analytical)

n = 1, 2, 3, 4, 5

ROC curves for different number of cognitive relays (n)

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

n = 1 + direct linkn = 3 + direct link

Direct link SNR = -5 dB

ROC curves for relay links + direct link

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

n = 1 + direct linkn = 3 + direct link

Direct link SNR = -5, -3 dB

ROC curves for relay links + direct link

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

n = 1 + direct linkn = 3 + direct link

Direct link SNR = -5, -3, 0 dB

ROC curves for relay links + direct link

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

n = 1 + direct linkn = 3 + direct link

Direct link SNR = -5, -3, 0, 3 dB

ROC curves for relay links + direct link

u=2, average SNR = 5 dB and fixed gain C=1.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pf

Pd

n = 1 + direct linkn = 3 + direct link

Direct link SNR = -5, -3, 0, 3 dB

n =1

n =3

ROC curves for relay links + direct link

u=2, average SNR = 5 dB and fixed gain C=1.7

Conclusions

The MGF of received SNR of the primary user’s signal is utilized to analyze the average detection probability.

Tighter upper bound is derived.

Sensing capability is increased with spatial diversity.

Direct link has major impact of the detection capability.

Analysis can be extended to multihop relaying.

References[1] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE

J. Select. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005.

[2] H. Jiang, L. Lai, R. Fan, and H. V. Poor, “Optimal selection of channel sensing order in cognitive radio,” IEEE Trans. Wireless Commun., vol. 8, no. 1, pp. 297–307, Jan. 2009.

[3] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inform. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[4] G. Ganesan and Y. Li, “Cooperative spectrum sensing in cognitive radio, part I: Two user networks,” IEEE Trans. Wireless Commun., vol. 6, no. 6, pp. 2204–2213, June 2007.

[5] F. F. Digham, M.-S. Alouini, and M. K. Simon, “On the energy detection of unknown signals over fading channels,” IEEE Trans. Commun., vol. 55, no. 1, pp. 21-24, Jan. 2007.

[6] C. Tellambura, A. Annamalai, and V. K. Bhargava, “Closed form and infinite series solutions for the MGF of a dual-diversity selection combiner output in bivariate Nakagami fading,” IEEE Trans. Commun., vol. 51, no. 4, pp. 539–542, Apr. 2003.

Thank you

Questions