tvws_ngmast2015

Sensing-Throughput Tradeoff for Cognitive Radio in TVWhite Spaces

MirMuhammad Lodro, Steve Greedy, Chris Smartt,

DWP Thomas, and Ana Vukovic

George Green Institute for Electromagnetic Research-GGIEMRDepartment of Electrical and Electronic EngineeringThe University of Nottingham, University Park, UK

[email protected]

9th International Conference on Next Generation Mobile Applications, Services andTechnologies,NGMAST 2015, Cambridge, United Kingdom

September 13, 2015

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 SensingSensing-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/VHFpart of the spectrum.

FCC and Ofcomm have legalised these under-utilised UHF/VHF partsof band for secondary user (SU)

TVWS that exists in VHF/UHF part of the TV band is defineddifferently based on space and time. In US non-contiguous TVWSsare located in frequency range of 54-698MHz and a portion offrequency ranging from 470MHz to 790 MHz exists in Europe.

Standards designed to operate in TVWS or using cognitive radio are:I WRAN IEEE 802.22I WLAN IEEE 802.11afI IEEE 802.15.4mI LTE-A+


Introduction

A multi-dimensional Cognitive Radio (CR) exploits the under-utilisedspectrum 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 fixedframe duration the allowable data transmission time reduces.

Figure: Frame Structure


Introduction

Figure: Primary User and Cognitive Radio Network

The purpose is to find optimal sensing time that yields maximumthroughput and meets the PU protection criterion. A higher proba-bility of detection shall guarantee maximum PU protection and lowerprobability 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] = σ2s : Variance of i.i.d PU user

E [|u`(n)|2] = σ2u: Variance of CSCG noise

E [|h`(n)|2] = σ2h: 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)

∑Nn=1 |y`(n)|2 for n = 1, 2, 3, ....,N ` = 1, 2, ...,M

Shorter distance among CR users than the distance from PU to CRuser.

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 = σ2hσ2s /σ

2u (3)


Spectrum Sensing-Throughput with Single Secondary Link

Let C0 and CM represents that throughout for CR when PU is absent andpresent 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

`=1P`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)

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 asfollows: (1− Pf (τ, ξ)P(H0) and (1− Pd(τ, ξ))P(H1)


Sensing-Throughput with Single SU Link

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)

maxτ

R(τ) = R0(τ, ξ) + RM(τ, ξ)

s.t: Pd(τ, ξ) ≥ P̄d

(11)


Sensing-throughput with Single SU Link

It’s clear that the first term in previous equation dominates the secondterm, therefore the total achievable throughput can be given as follows:

maxτ

R(τ) = R0(τ, ξ)

s.t.: Pd(τ, ξ) ≥ P̄d

(12)

For a given sensing time τ , we may choose a detection threshold ξ0 s.t.

Pd(τ, ξ0) = P̄d (13)

We may choose another threshold ξ1 we call it conservative threshold s.t.ξ1 < ξ0 and

Pd(τ, ξ1) > P̄d (14)

Obviously,Pf (τ, ξ1) > Pf (τ, ξ0) (15)


Sensing-throughput Tradefoff with Single SU Link

andR0(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 ofdetection and false alarm respectively at `th CR can be given as follows:

Pd`(τ, ξ`) = Q((

ξ`σ2u(γ + 1)

− 1

)√τ fs

)(21)

Pf`(τ, ξ`) = Q((

ξ`σ2u− 1

)√τ fs

)(22)

Where Q(t) = 12π

∫∞t e−t

2dt 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 notdetected... Every CR performs their decision and send it to the FC:

M∑`=1

V` = (1/M)M∑`=1

|y`(n)|2D1

≷D0

ξ` (25)


Cooperative Sensing-Throughput

Let us say C0 and C1 are the throughputs of the SUs if they are allowed tocontinuously operate in absence and presence of PU. Since a length of τperiod out of the total frame time T is used for sensing, the achievablethroughputs 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 andpresent in the channel respectively. Average achievable throughput of SUis 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 FCdeclares that there is PU. For all the independent decisions, the probabilityof 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 declaresthat there is PU. For all the independent decisions, the probability ofdetection 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 thefinal 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) ≥ P̄d

0 ≤ τ ≤ T

1 ≤ k ≤ N

(33)

Where P̄d is minimum probability of detection that the FC needs toachieve protect the PU. We have already concluded that C0 > CM andhave also concluded that Pf (τ, ξ) < Pd(τ, ξ), therefore at the FC followingis true:

(1− Pf (τ, k ,Ξ)) > (1− Pd(τ, k ,Ξ)) (34)

Additionally, we are interested in under-utilized bands P(H0) ≥ 0.5. Underthis assumption we can say that

R0(τ, k ,Ξ) >> RM(τ, k ,Ξ) (35)


Optimum solution occurs when Pd(τ, k ,Ξ) ≥ P̄d . For same τ and k let usselect two thresholds i.e. conservative threshold Ξ1 and the flexiblethreshold 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)

andR0(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) = P̄d Now, from Pd`(τ, ξ`) = Q((

ξ`σ2u(γ+1)

− 1)√

τ fs)

we can derive threshold as:

Ξ(τ, k) = σ2u(γ + 1)

(1√τ fsQ−1(P̄d(k)) + 1

)(38)

The optimisation problem is reduced to:

max:τ,k

R̂0(τ, k)

s.t.: 0 ≤ τ ≤ T , 1 ≤ k ≤ N(39)


Thus the probabilities of false alarm at each CR and FC respectively canbe written as:

P̂f (τ, k) = Q(α + β√τ) (40)

P̂f (τ, k) =M∑`=k

(M

`

)P̂f (τ, k)`(1− P̂f (τ, k))M−` (41)

Whereα = (γ + 1)Q−1(P̂d(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 10.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized sensing time (τ s)

Probab

ilityof

detection

Pd(τ

s)

γ = 2γ = 4γ = 6γ = 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 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized sensing time τ s

Probab

ilityof

falsealarm

Pf(τ)

γ = 2γ = 4γ = 6γ = 8

Figure: Probability of false alarm vs sensing time


Results(3/4)

−24 −22 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eb/N0 [dB]

Probab

ilityof

Detection

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 35 400

0.5

1

1.5

2

2.5

3

3.5

Sensing time (τ s)

Max.Through

put

SU SNR γs = −2dBSU SNRγs = −4dBSU SNRγs = −6dBSU SNRγs = −8dB

Figure: Maximum Throughput vs sensing-time.


References (1/2)

C. Ghosh, S. Roy, and D. Cavalcanti, Coexistence challenges forheterogeneous cognitive wireless networks in tv whitespaces,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 ofcooperative sensing in cognitive radio networks: a sensing-throughputtradeoff 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 spectrumsharing. IEEE Communica- tions Magazine, vol. 51, no. 10, pp.92?100, 2013.

Ieee standard 802.22 par 2: Cognitive wireless ran mac and phy layerspecifications:policies and procedures for operation in the tv bandsTech. Rep., July 2011.


Reference (2/2)

Ieee p802.11af draft d6, part 11 wireless lan mac and phy layerspecifications-amendement 5: Tv white space operation Tech. Rep.,October 2013.

Ieee p802.15.4m draft d4 part 15.4: Wireless mac and phy layerspecifications for lr-wpans-tv white space between 54 mhz and 862mhz 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, WirelessCommunications, IEEE Transac- tions on, vol. 7, no. 4, pp.1326-1337, 2008.


Thanks You!


tvws_ngmast2015

Documents