TVWS_NGMAST2015

Sensing-Throughput Tradeoﬀ for Cognitive Radio in TV
White Spaces
MirMuhammad Lodro, Steve Greedy, Chris Smartt,
DWP Thomas, and Ana Vukovic
George Green Institute for Electromagnetic Research-GGIEMR
Department of Electrical and Electronic Engineering
The University of Nottingham, University Park, UK
mir.m.lodro@ieee.org
9th International Conference on Next Generation Mobile Applications, Services and
Technologies,NGMAST 2015, Cambridge, United Kingdom
Mir Lodro (UoN) Sensing-Throughput for Cognitive Radio September 13, 2015 1 / 35

Contents
1 Introduction
2 Conventions
3 Assumptions
4 System Model
5 Cooperative Sensing
Sensing-Throughput Tradeoﬀ

Introduction
EM spectrum is costly commodity in the world. All of us know this!
EM spectrum due to digital dividend is under-utilised in UHF/VHF
part of the spectrum.
FCC and Ofcomm have legalised these under-utilised UHF/VHF parts
of band for secondary user (SU)
TVWS that exists in VHF/UHF part of the TV band is deﬁned
diﬀerently based on space and time. In US non-contiguous TVWSs
are located in frequency range of 54-698MHz and a portion of
frequency ranging from 470MHz to 790 MHz exists in Europe.
Standards designed to operate in TVWS or using cognitive radio are:
WRAN IEEE 802.22
WLAN IEEE 802.11af
IEEE 802.15.4m
LTE-A+

Introduction
A multi-dimensional Cognitive Radio (CR) exploits the under-utilised
spectrum in time, space, frequency and code (underlay).
A CR doesn’t introduce intolerable interference to secondary user (SU)
and a non-secondary user (non-SU) which are as follows:
Primary Transmitter and Primary User,
Wireless Microphone
Another Cognitive Radio Network (CRN)

Introduction
Longer Sensing time improves the sensing performance, but for a ﬁxed
frame duration the allowable data transmission time reduces.

Introduction
Longer Sensing time improves the sensing performance, but for a ﬁxed
frame duration the allowable data transmission time reduces.
Figure: Frame Structure

Introduction
Figure: Primary User and Cognitive Radio Network

Introduction
Figure: Primary User and Cognitive Radio Network
The purpose is to ﬁnd optimal sensing time that yields maximum
throughput and meets the PU protection criterion. A higher proba-
bility of detection shall guarantee maximum PU protection and lower
probability of false alarm shall increase the CR throughput.

Conventions
Hypotheses
H0: Absence of PU
H1: Presence of PU
s(n): PU signal
y (n): Sampled signal received at th CR
u (n): Sampled noise received at th CR
E[|s(n)|2] = σ2
s : Variance of i.i.d PU user
E[|u (n)|2] = σ2
u: Variance of CSCG noise
E[|h (n)|2] = σ2
h: Variance of Rayleigh-distributed channel gain

Conventions
ξ : the threshold at th CR
Ξ: the threshold at Fusion Center (FC)
P(H0): the probability of PU when it is inactive
P(H1): the probability of PU when it is active
Pd (..., ..., ...): the probability of detection at th CR
Pf (..., ..., ...): the probability of false alarm at th CR
Pd (..., ..., ...): the probability of detection at FC
Pf (..., ..., ...): the probability of false alarm at FC

Assumptions
Each CR users employs energy detection and undergoes ﬂat fading.
fs sampling requency and τ =sensing time
Each CR measures the power during its sensing period:
V = (1/N) N
n=1 |y (n)|2 for n = 1, 2, 3, ...., N = 1, 2, ..., M
Shorter distance among CR users than the distance from PU to CR
user.
s(n),h (n) and u (n) are independent of eachother

System Model
Sampled received signal at th CR node: y (n) = s(n) + u (n)
Under hypotheses H0 and H1 respectively
y (n) = u (n) (1)
y (n) = h (n)s(n) + u (n) (2)
Average SNR at each CR:
γ = σ2
hσ2
s /σ2
u (3)

Spectrum Sensing-Throughput with Single Secondary Link
Let C0 and CM represents that throughout for CR when PU is absent and
present respectively which can be mathematically deﬁned as follows:
C0 = log2 1 +
Ps
N0
= log2(1 + SNRs) (4)
and

Spectrum Sensing-Throughput with Single Secondary Link
Let C0 and CM represents that throughout for CR when PU is absent and
present respectively which can be mathematically deﬁned as follows:
C0 = log2 1 +
Ps
N0
= log2(1 + SNRs) (4)
and
CM = log2 1 +
Ps
M
=1 P + N0
= log2 1 +
Ps
1 + M
=1
P
N0
= log2 1 +
SNRs
1 + SNR
(5)

Sensing-Throughput with Single SU Link
We are interested in frequency band where P(H0) ≥ 0.5. Obviously,
C0 > CM because CR experiences interference from PU in second scenario.
When PU is absent the achievable throughput of the secondary link is
1 −
τ
T
C0 (6)

We are interested in frequency band where P(H0) ≥ 0.5. Obviously,
C0 > CM because CR experiences interference from PU in second scenario.
When PU is absent the achievable throughput of the secondary link is
1 −
τ
T
C0 (6)
and in presence of PU the achievable throughput for CR is
1 −
τ
T
CM (7)
The probabilities with which above two equations are guaranteed are as
follows: (1 − Pf (τ, ξ)P(H0) and (1 − Pd (τ, ξ))P(H1)

Therefore, the throughput at CR in absence of PU is
R0(τ, ξ) = 1 −
τ
T
C0(1 − Pf (τ, ξ))P(H0) (8)

Therefore, the throughput at CR in absence of PU is
R0(τ, ξ) = 1 −
τ
T
C0(1 − Pf (τ, ξ))P(H0) (8)
and the throughput at CR in presence of PU is
RM(τ, ξ) = 1 −
τ
T
CM(1 − Pd (τ, ξ))P(H1) (9)
Hence the total throughput can be given as follows:
R(τ, ξ) = R0(τ, ξ) + RM(τ, ξ) (10)
max
τ
R(τ) = R0(τ, ξ) + RM(τ, ξ)
s.t: Pd (τ, ξ) ≥ ¯Pd
(11)

Sensing-throughput with Single SU Link
It’s clear that the ﬁrst term in previous equation dominates the second
term, therefore the total achievable throughput can be given as follows:
max
τ
R(τ) = R0(τ, ξ)
s.t.: Pd (τ, ξ) ≥ ¯Pd
(12)
For a given sensing time τ, we may choose a detection threshold ξ0 s.t.
Pd (τ, ξ0) = ¯Pd (13)
We may choose another threshold ξ1 we call it conservative threshold s.t.
ξ1 < ξ0 and

Sensing-throughput with Single SU Link
It’s clear that the ﬁrst term in previous equation dominates the second
term, therefore the total achievable throughput can be given as follows:
max
τ
R(τ) = R0(τ, ξ)
s.t.: Pd (τ, ξ) ≥ ¯Pd
(12)
For a given sensing time τ, we may choose a detection threshold ξ0 s.t.
Pd (τ, ξ0) = ¯Pd (13)
We may choose another threshold ξ1 we call it conservative threshold s.t.
ξ1 < ξ0 and
Pd (τ, ξ1) > ¯Pd (14)
Obviously,
Pf (τ, ξ1) > Pf (τ, ξ0) (15)

Sensing-throughput Tradefoﬀ with Single SU Link
and
R0(τ, ξ1) < R0(τ, ξ0) (16)
RM(τ, ξ1) < RM(τ, ξ0) (17)
Hence the total throughput can be given as:

Sensing-throughput Tradefoﬀ with Single SU Link
and
R0(τ, ξ1) < R0(τ, ξ0) (16)
RM(τ, ξ1) < RM(τ, ξ0) (17)
Hence the total throughput can be given as:
R0(τ, ξ1) + RM(τ, ξ1) < R0(τ, ξ0) + RM(τ, ξ1) (18)

Probabilities of Detection and False Alarm at CR
Probability of false alarm can be given by:
Pf (τ, ξ) = Pr(V > ξ|H0) =
∞
ξ
p0(x)dx (19)
and the probability of detection
Pd (τ, ξ) = Pr(V > ξ|H1) =
∞
ξ
p1(x)dx (20)

Probabilities of Detection and False Alarm at CR
When PU signal is complex-valued PSK modulated, then the probability of
detection and false alarm respectively at th CR can be given as follows:
Pd (τ, ξ ) = Q
ξ
σ2
u(γ + 1)
− 1 τfs (21)
Pf (τ, ξ ) = Q
ξ
σ2
u
− 1 τfs (22)
Where Q(t) = 1
2π
∞
t e−t2
dt is known as Q-function and measures the
right-tail probability of Gaussian distribution.

Cooperative Sensing
Pd (τ, k, ξ) =
M
=k
M
Pd (τ, ξ) (1 − Pd (τ, ξ))M−
(23)
Pf (τ, k, ξ) =
M
=k
M
Pf (τ, ξ) (1 − Pf (τ, ξ))M−
(24)
D1 = 1 represents that PU is detected and D0 = 0 represents PU not
detected... Every CR performs their decision and send it to the FC:
M
=1
V = (1/M)
M
=1
|y (n)|2
D1
D0
ξ (25)

Cooperative Sensing-Throughput
Let us say C0 and C1 are the throughputs of the SUs if they are allowed to
continuously operate in absence and presence of PU. Since a length of τ
period out of the total frame time T is used for sensing, the achievable
throughputs of the SUs under these scenarios are:
R0(τ, k, ξ) = C0P(H0) 1 −
τ
T
(1 − Pf (τ, k, ξ)) (26)
RM(τ, k, ξ) = C0P(H1) 1 −
τ
T
(1 − Pd (τ, k, ξ)) (27)
Where P(H0) and P(H1) are the probabilities of the PU being absent and
present in the channel respectively. Average achievable throughput of SU
is given as:
R(τ, k, ξ) = R0(τ, k, ξ) + RM(τ, k, ξ) (28)

Decision Fusion Strategies

Fusion Rule: OR Rule
If one of the SU says that there is PU, then the ﬁnal decision at FC
declares that there is PU. For all the independent decisions, the probability
of detection and probability of false alarm at FC are:
Pd (τ, k, ξ) = 1 −
M
=1
(1 − Pd (τ, k, ξ)) (29)
Pf (τ, k, ξ) = 1 −
M
=1
(1 − Pf (τ, k, ξ)) (30)

Fusion Rule: AND Rule
If all the SUs says that there is PU, then the ﬁnal decision at FC declares
that there is PU. For all the independent decisions, the probability of
detection and probability of false alarm at FC are:
Pd (τ, k, Ξ) =
M
=1
Pd (τ, k, Ξ) (31)
Pf (τ, k, Ξ) =
M
=1
Pf (τ, k, Ξ) (32)

k-out-of-N or Majority Rule
If half or more CRs decide in favour of the presence of the PU then the
ﬁnal decision at FC is presence of PU.

Back to Sensing-Throughput Tradeoﬀ

Formulation of Optimization Problem
max:
τ
R(τ, k, Ξ)
s.t.: Pd (τ, k, Ξ) ≥ ¯Pd
0 ≤ τ ≤ T
1 ≤ k ≤ N
(33)
Where ¯Pd is minimum probability of detection that the FC needs to
achieve protect the PU. We have already concluded that C0 > CM and
have also concluded that Pf (τ, ξ) < Pd (τ, ξ), therefore at the FC following
is true:
(1 − Pf (τ, k, Ξ)) > (1 − Pd (τ, k, Ξ)) (34)
Additionally, we are interested in under-utilized bands P(H0) ≥ 0.5. Under
this assumption we can say that
R0(τ, k, Ξ) >> RM(τ, k, Ξ) (35)

Optimum solution occurs when Pd (τ, k, Ξ) ≥ ¯Pd . For same τ and k let us
select two thresholds i.e. conservative threshold Ξ1 and the ﬂexible
threshold Ξ0 at FC such that Ξ1 < Ξ0. Obviously,
Pd (τ, k, Ξ1) > Pd (τ, k, Ξ0)
Pf (τ, k, Ξ1) < Pf (τ, k, Ξ0)
(36)
and
R0(τ, k, Ξ1) < R0(τ, k, Ξ0)
R(τ, k, Ξ1) < R(τ, k, Ξ0)
(37)

Threshold
For a given pair of τ and k we are able to determine threshold that can
satisfy Pd (τ, k, Ξ) = ¯Pd Now, from Pd (τ, ξ ) = Q ξ
σ2
u(γ+1)
− 1
√
τfs
we can derive threshold as:
Ξ(τ, k) = σ2
u(γ + 1)
1
√
τfs
Q−1
( ¯Pd (k)) + 1 (38)

Threshold
For a given pair of τ and k we are able to determine threshold that can
satisfy Pd (τ, k, Ξ) = ¯Pd Now, from Pd (τ, ξ ) = Q ξ
σ2
u(γ+1)
− 1
√
τfs
we can derive threshold as:
Ξ(τ, k) = σ2
u(γ + 1)
1
√
τfs
Q−1
( ¯Pd (k)) + 1 (38)
The optimisation problem is reduced to:
max:
τ,k
ˆR0(τ, k)
s.t.: 0 ≤ τ ≤ T, 1 ≤ k ≤ N
(39)

Thus the probabilities of false alarm at each CR and FC respectively can
be written as:
ˆPf (τ, k) = Q(α + β
√
τ) (40)
ˆPf (τ, k) =
M
=k
M ˆPf (τ, k) (1 − ˆPf (τ, k))M−
(41)
Where
α = (γ + 1)Q−1( ˆPd (k)) and β = γ
√
fs

Results(1/4)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized sensing time (τs)
ProbabilityofdetectionPd(τs)
γ = 2
γ = 4
γ = 6
γ = 8
Figure: Probability of detection vs normalised sensing time

Results(2/4)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized sensing time τs
ProbabilityoffalsealarmPf(τ)
γ = 2
γ = 4
γ = 6
γ = 8
Figure: Probability of false alarm vs sensing time

Results(3/4)
−24 −22 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Eb/N0 [dB]
ProbabilityofDetection
Pf = 10−1
Pf = 10−2
Pf = 10−3
Pf = 10−4
Figure: Probability of detection vs Eb/N0

Results(4/4)
0 5 10 15 20 25 30 35 40
0
0.5
1
1.5
2
2.5
3
3.5
Sensing time (τs)
Max.Throughput
SU SNR γs = −2dB
SU SNRγs = −4dB
SU SNRγs = −6dB
SU SNRγs = −8dB
Figure: Maximum Throughput vs sensing-time.

References (1/2)
C. Ghosh, S. Roy, and D. Cavalcanti, Coexistence challenges for
heterogeneous cognitive wireless networks in tv white
spaces,Wireless Communications, IEEE, vol. 18, no. 4, pp. 22?31,
2011.
E. C. Y. Peh, Y.-C. Liang, Y. L. Guan, and Y. Zeng, Optimization of
cooperative sensing in cognitive radio networks: a sensing-throughput
tradeoﬀ view,Vehicular Technology, IEEE Transactions on, vol. 58,
no. 9, pp. 5294?5299, 2009.
A. B. Flores, R. E. Guerra, E. W. Knightly, P. Eccle- sine, and S.
Pandey, Ieee 802.11 af: a standard for tv white space spectrum
sharing. IEEE Communica- tions Magazine, vol. 51, no. 10, pp.
92?100, 2013.
Ieee standard 802.22 par 2: Cognitive wireless ran mac and phy layer
speciﬁcations:policies and procedures for operation in the tv bands
Tech. Rep., July 2011.

Reference (2/2)
Ieee p802.11af draft d6, part 11 wireless lan mac and phy layer
specifications-amendement 5: Tv white space operation Tech. Rep.,
October 2013.
Ieee p802.15.4m draft d4 part 15.4: Wireless mac and phy layer
specifications for lr-wpans-tv white space between 54 mhz and 862
mhz physical layer, Tech. Rep., October 2013.
Y.-C. Liang, Y. Zeng, E. C. Peh, and A. T. Hoang,
Sensing-throughput tradeoff for cognitive radio networks, Wireless
Communications, IEEE Transac- tions on, vol. 7, no. 4, pp.
1326-1337, 2008.

Thanks You!

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