An algorithm for dynamic spectrum allocation
in shadowing environment and with communication
constraints
Konstantinos Koufos
Helsinki University of Technology
Communications Laboratory
Instructor : Lic. Tech. Kalle Ruttik
Supervisor : Professor Riku Jäntti
CONTENTS
 Motivation
 Background work
 System Model
 Proposed algorithm
 Power detection
 Distributed power detection
 Results
 Conclusions
 Future work
MOTIVATION
 Measurements show that the spectrum is underutilised (TV Broadcast)
─ Rightful owners leave it partially unused (temporarily,spatially)
 Sporadically used spectrum could be accessed by other users too
 This access is called Dynamic Spectrum Allocation (DSA)
 DSA access : Efficient and Adaptive
BACKGROUND WORK
How much efficient DSA could be?
 Accessibility control to the open spectrum
 Applications of game theory on available frequency channels
How much adaptive DSA could be?
 Co-existence – Interference control
 Two step decision
 What is the worst case scenario?
SYSTEM MODEL I
1. Three system components
2. Three critical power levels
3. Semi-mobile secondary users
4. The noise level is known s n2
5. No deterministic components
6. Unknown coding and modulation
7. Power detection
8. δ,ε,ω are known and positive (WHY?)
9. Outage req. for primary users: Routage
SYSTEM MODEL II
Collaborative spectrum sensing benefits
Send measurements to the fusion centre
 The fusion centre decides and broadcasts
 Two schemes are studied
─ Centralized
─ Decentralized
 Decentralized scheme is more challenging
─ less capacity and power requirement
─ cooperation between fusion and sensors
for system wise optimization
PROPOSED ALGORITHM I
Power detection of the primary signal
Output : decision threshold T1
Power identification of the primary signal
Output : decision threshold T2
Where T1 and T2 depends on?
: The primary signal is assumed to be absent if it at most δ dB above the
noise level.
Second step : The transmission does not probably generate interference if the primary
signal is at most ε dB above the noise level.
First step
PROPOSED ALGORITHM II
1. Obtain an estimate within [T1,T2]
2. Interference estimation
•
•
unknow attenuation
unknown distance to the transmitter
3. Worst case interference estimation
Block diagram
RULE
Initiate transmission provided the
generated interference is negligible
compared to the noise level
POWER DETECTION
The primary signal is assumed to be absent if it is at most δ dB above the noise level
H 0 : s n2 = N0 2 Ч10s NF
(
10
H1 : s 12 = s n2 Ч 1 + 10d 10
)
The distribution of the measured samples is assumed to be Gaussian:
(
ж
ц
зз X i2 ч
ч
ч
exp зч
2
з
2
ч
2
s
з
ч
2ps n
nш
и
1
)
p X i | H0 =
(
)
p X i | H1 =
(
)
1
p X | H0 =
i.i.d
N
(2ps )
2
2
n
ж
ц
зз X i2 ч
ч
ч
exp з2ч
з
2
ч
2
s
зи
ч
2ps 1
1 ш
1
(
)
1
p X | H1 =
(
N
2ps 12
)
2
ж
зз 1
exp зззз 2s 2
n
зи
ж
зз 1
exp зззз 2s 2
1
зи
N
е
i= 1
N
е
i= 1
To decide optimally we use Bayes test and Neymann-Pearson approach
( )Ј
l ў(X )@
p (X | H )
p X | H1
H0
0
H1
N
h
What is the distribution of
( )
lў X =
е
i= 1
l ў?
ж
ц
ж 2ч
цч
2 2 з
ч
з
2
s
s
s
N
з
ч
ч
ч
X i2 Ј 2 n 1 2 ззln h ln зз n2 ч
= g
ч
ч
з
з
ч
ч
2
s
s
s
H1 1
чч
зи 1 ш
n з
ч
зи
ш
H0
How do we fix
g?
ц
ч
ч
ч
ч
ч
ш
ч
X i2 ч
ч
ц
ч
ч
ч
X i2 ч
ч
ч
ч
ч
ш
DISTRIBUTED POWER DETECTION
Procedure
Independent users sense the spectrum, calculate LLR and send it to the fusion
Centralized scheme
• The complete LLR is communicated
• The fusion adds the received LLRs and compares the result with a threshold
• Centralized scheme is equivalent to a single sensor system with more
degrees of freedom when there is no shadowing.
Decentralized scheme
• A single bit decision is transmitted to the fusion
• Unlike centralized scheme two decision thresholds have to be set :
( )
( )
R (K , g )Ј R
F
minimize: RFmiss K , g + Rfalse
K, g
subject to:
F
miss
outage
RESULTS I
DETECTION FOR SINGLE USER
9
8
x 10
1
P(L | H0)
P(L | H1)
7
0.9
detection
Threshold
Detection Probability PS
p(L)-chi-squared
6
5
4
3
2
1
0
0.8
0.7
0.6
N
N
N
N
0.5
0.4
=
=
=
=
6&
20 &
20 &
6&
=
=
=
=
2dB
2dB
1dB
1dB
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Decision Variable L
2
0
0.1
0.2
0.3
0.4
0.5
0.6
Probability of false alarm
-9
x 10
0
0.7
0.8
0.9
1
PS
false
10
 = 1dB
 = 2dB
1
=0
S
0.8
Erroneous decisions Pe
Detection Probability PS
detection
0.9
0.7
 = 1dB
0.6
0.5
N
N
N
N
0.4
0.3
=
=
=
=
6
10
20
40
-1
10
0.2
0.1
=
0
0
0.1
-2
0.2
0.3
0.4
0.5
0.6
0.7
Probability of false alarm P S
false
0.8
0.9
1
10
10
15
20
25
30
35
40
Number of Samples N
45
50
55
60
RESULTS II
DETECTION WITH SHADOWING
Due to the obstacles along the propagation path the signal level is not deterministic
at a particular transmitter-receiver separation
We assume that the signal level is distributed log-normally
p (s 2 | H1 ) =
2ц
ж
зз (10log10 s 2 - 10log10 s 12 ) ч
ч
ч
exp ззч
ч
2
2
2
з
ч
2s SF
2ps SF s
ззи
ч
ш
Ґ
1
p (Lў| H1 ) =
т
p (L ў| s 2 )Чp (s 2 | H1 )d s 2
0
All the samples experience the same shadowing
9
6
1
x 10
0.9

0.7
SF
= 3dB
No slow fading
p(L')-chi-squared
Detection Probability PS
detection
5
0.8
0.6
0.5
0.4
P(L' | H0)
4
P(L' | H1) &  SF = 3dB
P(L' | H1) & No slow fading
3
2
0.3
0.2
1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Probability of false alarm
0.7
PS
false
0.8
0.9
1
0
0
0.2
0.4
0.6
0.8
1
1.2
Decision Variable L'
1.4
1.6
1.8
2
-9
x 10
RESULTS III
DISTRIBUTED DETECTION
For single user the shadowing samples are correlated
Low threshold
The user should consider the probability of deep fading
Assume independent shadow fading among the secondary users
The mean and the variance of the shadowing distribution is common for all
The effect of shadowing could be averaged out
without shadowing
with shadowing
0
10
0
10
-1
10
10
Probability of false alarm
Probability of false alarm
-1
-2
10
-3
10
-4
10
-5
10
10
Centralized  = 1dB
Centralized  = 2dB
Decentralized  = 1dB
Decentralized  = 2dB
Single Sensor
12
14
16
18
-2
10
-3
10
-4
10
Centralized
Centralized
Decentralized
Decentralized
Single sensor
Single sensor
-5
10
-6
20
22
24
26
Number of collected samples per sensor
28
30
10
6
8
 = 1dB
 = 2dB
 = 1dB
 = 2dB
 = 2dB
 = 1dB
10
12
14
Number of Samples N
16
18
20
CONCLUSIONS
1. A three step algorithm for DSA access was proposed based on the generated
interference at the cell border
2. The first step was presented
3. The performance depends on the outage requirement, on the SNR and
on the number of power samples
4. For a single user in the presence of shadowing almost no spectrum reuse
5. The performance was greatly improved by collecting measurements made by
multiple independent users and jointly process them at a fusion centre
6. The performance was affected by the amount of information conveyed from
the sensors to the fusion
7. Two extremes were studying providing useful performance bounds for
any practical distributed detection scheme
FUTURE WORK
1. Sequential distributed detection.
2. Under shadow fading numerical integration was used to evaluate the distribution
of the test statistic in the presence of primary signal. The log-normal distribution
could be upper bounded by strair function and analytical solutions could be
retrieved instead.
3. Correlated shadow fading could be considered
4. Joint optimization of the three algorithm steps