Performance of Energy Detection:
A Complementary AUC Approach
Saman Atapattu, Chintha Tellambura & Hai Jiang
Electrical and Computer Engineering
University of Alberta
CANADA
GLOBECOM 2010
Outline

Introduction
 Spectrum
sensing
 Energy detection

Research work
 Cooperative

Analysis

Results
spectrum sensing
2
Spectrum Sensing

Cognitive radio: environment awareness & spectrum intelligence [1].


Dynamic spectrum access
Spectrum sensing
busy
Idle
(spectrum hole)


Spectrum sensing: to identify the spectrum holes.
Cooperative spectrum sensing: to mitigate multipath fading,
shadowing/hidden terminal problem.
3
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.
4
Spectrum Sensing Techniques

Matched Filter

Perfect knowledge
 Dedicated receiver structure
Eigenvalue Detection

Max-Min eigenvalues
 Computational complexity
 Difficulty of threshold selection
Accuracy

MF
Eigenvalue
Cyclo
ED

Cyclostationary Detection

Cyclostationary property
 High sampling rate
 Complex processing algorithm

Complexity
Energy Detection [2]
5
Energy Detection

Energy of the received signal.

Digital implementation:
Y(t)
Noise pre-filter

ADC
( )2
∑
Analog-to-digital converter
Squaring device
Integrator
Test
statistics
Test statistic:


Noise (AWGN), Signal (deterministic/random), Channel.
Compared with threshold.
6
Performance Measurements
Average Pd:
(1, 1)
(0, 0)

n
tio
0
et
ec
ld
ho
es
Th
r
ROC (receiver operating
characteristic) curve:
 Pd vs. Pf
8

Pd vs. SNR
D

Detection probability
ca
pa
bi
lit
y

False alarm probability
AUC (area under ROC curve) [3]: probability that choosing correct
decision is more likely than choosing incorrect decision.
 AUC vs. SNR
7
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
r1
System Model




hr1 d
hpr1
Data fusion strategy
AF relaying
Square-law combining (SLC)
Rayleigh fading
hpr2
r2
hpd
hr i d
hpri
ri
p
hprn

ROC analysis in [4].
hr 2 d
relay link
direct link
d
hrn d
rn
p: primary user
ri: i-th cognitive relay
d: fusion center
8
Analysis

AUC for instantaneous SNR in [3].

CAUC:

Average CAUC:

where
9
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:
10
Results
ROC curves
1
0.8
0.6
n = 1, 2, 3, 4, 5
Pd

0.4
0.2
Simulation
Analytical
0
0
0.2
0.4
0.6
0.8
1
Pf
(SNR=5dB)
11
Results

CAUC curves
semi-log scale
log-log scale
0.5
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)
0.45
0.4
0.35
-5
Log [Average CAUC]
Average CAUC
10
0.3
0.25
0.2
n = 1, 2, 3, 4, 5
-10
10
0.15
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
0.1
0.05
0
-20
-10
0
10
Average SNR (dB)
20
30
-20
-10
0
10
Average SNR (dB)
20
30
(SNR=5dB)
12
Results
CAUC curves

Nakagami-m
Diversity techniques
-1
-1
10
10
-2
-2
10
10
-3
10
-3
10
Log[Average CAUC]
Log[Average CAUC]
L=1
-4
10
m = 1, 2, 3, 4, 5
-5
10
-6
10
-4
10
L=2
-5
10
L=5
-6
10
-7
10
m
m
m
m
m
-8
10
-9
10
-10
-5
=
=
=
=
=
-7
1
2
3
4
5
10
-8
10
0
(SNR=5dB)
5
10
15
Average SNR (dB)
20
25
30
-10
SC
SLC
MRC
-5
0
5
10
Average SNR (dB)
15
20
13
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.
14
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.
15
Thank You !
16