Performance of Energy Detection:A Complementary AUC Approach

Saman Atapattu, Chintha Tellambura & Hai Jiang

Electrical and Computer Engineering University of Alberta

CANADA

GLOBECOM 2010

2

Outline

Introduction Spectrum sensing Energy detection

Research work Cooperative spectrum sensing

Analysis

Results

3

Spectrum Sensing Cognitive radio: environment awareness & spectrum intelligence [1].

Dynamic spectrum access Spectrum sensing

Spectrum sensing: to identify the spectrum holes.

Cooperative spectrum sensing: to mitigate multipath fading, shadowing/hidden terminal problem.

busy

Idle

(spectrum hole)

4

Spectrum Sensing

Primary user has two states, idle or busy. Noise Noise + signal

Binary Hypothesis:

Performance metrics: False alarm (Pf): efficiency Missed-detection (Pm): reliability Detection (Pd): 1-Pm

Higher Pd (lower Pm) and lower Pf are preferred.

5

Spectrum Sensing Techniques

Matched Filter Perfect knowledge Dedicated receiver structure

Eigenvalue Detection Max-Min eigenvalues Computational complexity Difficulty of threshold selection

Cyclostationary Detection Cyclostationary property High sampling rate Complex processing algorithm

Energy Detection [2]

MF

Eigenvalue

Cyclo

ED

ComplexityAc

cura

cy

6

Energy Detection Energy of the received signal.

Digital implementation:

Test statistic:

Noise (AWGN), Signal (deterministic/random), Channel. Compared with threshold.

( )2

Noise pre-filter Squaring device Integrator

Test statistics Y(t) ∑ ADC

Analog-to-digital converter

7

Performance Measurements Average Pd:

Pd vs. SNR

ROC (receiver operating characteristic) curve: Pd vs. Pf

(1, 1)

False alarm probability

Detection probability

(0, 0)

Thres

hold

0

8

Detec

tion

capa

bility

AUC (area under ROC curve) [3]: probability that choosing correct decision is more likely than choosing incorrect decision. AUC vs. SNR

8

Research Work

Complementary AUC (CAUC) Area under the complementary ROC (Pm vs Pf)

CAUC = 1-AUC, varies from 0.5 to 0 Good representation for diversity order

System Model Data fusion strategy AF relaying Square-law combining (SLC) Rayleigh fading

ROC analysis in [4]. rn

hprn hr dn

r1

ri

r2

hpr1 1hr d

2hr d2

hpr

hprihr di

p d

relay linkdirect link

hpd

p: primary user

ri: i-th cognitive relay

d: fusion center

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Analysis

AUC for instantaneous SNR in [3].

CAUC:

Average CAUC:

where

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Results Average CAUC for relay based-cooperative spectrum

sensing network. easy to extend for diversity techniques.

Sensing Diversity Order:

For high SNR Without direct path:

With direct path:

Nakagami-m fading:

Diversity techniques:

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Results ROC curves

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Pf

Pd

Simulation

Analytical

n = 1, 2, 3, 4, 5

(SNR=5dB)

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Results CAUC curves

(SNR=5dB)

-20 -10 0 10 20 30

10-10

10-5

Average SNR (dB)

Lo

g [

Ave

rag

e C

AU

C]

Without direct path n = 1Only direct path

With direct path n = 1

With direct path n = 2

With direct path n = 3

With direct path n = 4With direct path n = 5

n = 1, 2, 3, 4, 5

-20 -10 0 10 20 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Average SNR (dB)

Ave

rag

e C

AU

C

Without direct path (n = 1) Only direct path

With direct path (n = 1)

With direct path (n = 2)

With direct path (n = 3)

With direct path (n = 4)With direct path (n = 5)

n = 1, 2, 3, 4, 5

semi-log scale log-log scale

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Results CAUC curves

(SNR=5dB)

-10 -5 0 5 10 15 20

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Average SNR (dB)

Lo

g[A

vera

ge

CA

UC

]

SC

SLC

MRC

L = 5

L = 1

L = 2

-10 -5 0 5 10 15 20 25 3010

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Average SNR (dB)

Lo

g[A

vera

ge

CA

UC

]

m = 1

m = 2

m = 3m = 4

m = 5

m = 1, 2, 3, 4, 5

Nakagami-m Diversity techniques

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Contribution

Introduced Complementary Area under ROC Curve (CAUC)

Derived CAUC for relay-based cooperative spectrum sensing network.

Showed that Diversity order:

Cooperative network: n or (n+1) Nakagami fading: m Diversity techniques: L

Proposed methodology and results can be useful for other wireless research topics.

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Reference

1. S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE JSAC, vol. 23, no. 2, pp. 201–220, Feb. 2005.

2. 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.

3. S. Atapattu, C. Tellambura, and H. Jiang, “Analysis of area under the ROC curve of energy detection,” IEEE Trans. Wireless Commun., vol. 9, no. 3, pp. 1216–1225, Mar. 2010.

4. S. Atapattu, C. Tellambura, and H. Jiang, “Relay based cooperative spectrum sensing in cognitive radio networks,” in IEEE Global Telecommn. Conf. (GLOBECOM), Dec. 2009.

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Thank You !