fully-distributed spectrum sensing: application to

Fully-distributed spectrum sensing:application to cognitive radio

Philippe Ciblat

Dpt Comelec, Télécom ParisTech

Joint work with F. Iutzeler (PhD student funded by DGA grant)

Cognitive radio principle

Spectrum is, at a first glance, entirely used

However, at given time, an assigned subband can be free

⇒ white space

Two kinds of users

− Primary : have paid for using an pre-assigned subband− Secondary : are allowed to use a white space

Insert secondary users into white spaces

How detecting the presence of a primary user ?

Philippe Ciblat Fully-distributed spectrum sensing 2 / 15

Hidden terminal issue

Primary Receiver

Primary Transmitter

Secondary user

Secondary user


Hidden terminal issue

Reception disturbance

Primary Receiver

Primary Transmitter

Secondary user

Secondary user

Problem : a secondary user is disturbing the primary receiver

Solution : secondary users have to cooperate to detect the primary user


Two ways for cooperating

Centralized detection (Fully)-Distributed detection

Fusioncenter

Primary Transmitter

Primary Receiver

Secondary user

Primary Transmitter

Primary Receiver

Secondary user

Detection with more than one sensors

If fusion center is available, centralized (also called distributed) detection

If fusion center is not available, (fully)-distributed detection

− robust against nodes attack− simple network management


System model

{

H0 (absence of primary user) : yk (n) = bk(n) k = 1, · · · ,KH1 (presence of primary user) : yk (n) = xk (n) + bk (n) n = 1, · · · ,Ns

with

secondary user index k and time index n

bk(n) Gaussian with variance σ2k known at secondary user k

{xk (n)}n coming from primary user known at secondary user k

Performance metric

Detection probability : PD = P(H1|H1)

False alarm probability : PFA = P(H1|H0)

Goal : minimizing PFA such that PD ≥ Ptarget

D

Remarks :

If {xk (n)}n unknown but Gaussian ⇒ Energy detector

Hard detection (local decision and then voting) not considered


Reminder on (soft) centralized detection

Optimal test : Log-Likelihood Ratio (LLR)

Λ(y) = log

(

p(y|H1)

p(y|H0)

)

H1

≷H0

µ, with µ chosen for ensuring Ptarget

D

Application to our practical case :

T (y) =1

K

K∑

k=1

tk (yk)H1

≷H0

η, with tk (yk) =yT

k xk

σ2k

and yk = [yk (1), · · · , yk (Ns)]T, xk = [xk (1), · · · , xk (Ns)]

T, (.)T = transpose.

Threshold computation

η =√ςT Q

(−1)(

Ptarget

D

)

+ mT

where Q(−1) is the inverse of the Gaussian tail function, and

mT = Ns

(

1

K

K∑

k=1

SNRk

)

and ςT =Ns

K

(

1

K

K∑

k=1

SNRk

)

.


Fully-distributed detection (I)

Gossiping step of duration NgSensing step of duration Ns

Tk ≈ averageℓ (tℓ)tℓ = yT

ℓ xℓ/σ2

ℓ for each node ℓ

Question : How computing the average of tℓ in a distributed way

⇒ Gossiping (also called consensus) algorithms

Gossiping algorithm description : an example (Pairwise Gossip)

x(0) = [x1(0), · · · , xK (0)]T : initial values

At time t , a node i wakes up and calls one

of its neighbor j . Then

xi(t + 1) = (xi(t) + xj(t))/2

xj(t + 1) = (xi(t) + xj(t))/2

⇒ x(t + 1) = W(t)x(t)t→∞→ xaverage1

T1(y)...

TK (y)

= P

t1(y1)...

tK (yK )

with P = (pkℓ)k,ℓ=1,··· ,K the

gossiping algorithm matrix

after Ng iterations.


Fully-distributed detection (II)

The final test function at node k is

Tk(y) =K∑

ℓ=1

pkℓyTℓxℓ

σ2ℓ

H1

≷H0

ηk ,

where the threshold (for pre-defined Ptarget

D ) is given by

ηk =√ςk Q

(−1) (P

target

D

)

+ mk

with

mk = Ns

K∑

ℓ=1

pkℓSNRℓ and ςk = Ns

K∑

ℓ=1

p2kℓSNRℓ.

Problem

Threshold not computable in a distributed way due to the terms p2kℓ.


Two approaches for threshold computation (I)

Approach 1 : distributed with knowledge of K

η(1)k =

√

ς(1)k Q

(−1) (P

target

D

)

+ mk with ς(1)k =

Ns

K

K∑

ℓ=1

pkℓSNRℓ.

Approach 2 : fully-distributed

Using Sum-Weight-like gossip in order to perform the average and the sum.

z := Qt, w(1) := Q1, w(e) := Qe

where

Q the gossip algorithm matrix after Ng iterations,

e the K -sized vector whose first component is 1 and the others 0.

Each node k calculates the k -th component of

zp = z ⊘ w(1) = Pt → taverage1 and zs = z ⊘ w

(e) = St → tsum1

where

⊘ the elementwise division.

P = diag (1 ⊘ Q1)Q and S = diag (1 ⊘ Qe)Q.


Two approaches for threshold computation (II)

The threshold is then as follows

η(2)k =

√

ς(2)k Q

(−1) (P

target

D

)

+ mk with ς(2)k = Ns

(

∑Kℓ=1 pkℓSNRℓ

)2

∑Kℓ=1 skℓSNRℓ

.

Remarks

Algorithm fully distributed since the number of nodes not required.

New threshold does not ensure the target probability of detection

PD(k) = Q

√

ς(2)k

ςk

Q(−1) (

Ptarget

D

)

.


Numerical illustrations

Setup :

T = Ns + K = 128 with Ns = Ng = 64.

Ptarget

D = 0.99

K = 10

Considered algorithms : energy-based algorithm

centralized detection

pairwise gossip (PG) with centralized threshold

pairwise gossip with Approach 1 based distributed threshold

broadcast sum-weight gossip (BWG) with Approach 2 based distributed

threshold


Performance analysis

PFA and PD versus mean SNR PFA and PD versus Ns

Fully-distributed algorithm performs well

Sensing time equivalent to gossiping time


Hidden terminal context

Hidden terminal configuration PFA and PD versus T

Fast convergence for fully-distributed algorithm

Hidden terminal issue is fixed


Comparison with existing approach

Training based algorithm

Comparison with “A. Sayed, Distributed detection over adaptive networks

using diffusion adaptation, IEEE Trans. Signal Processing, May 2011”.

In this paper, sensing and gossiping steps are interleaved

Outperforming existing approach

More relevant choice of threshold


Conclusion

New fully-distributed detection algorithm

Outperforms existing approaches

Other works :

Max-consensus : asynchronous algorithm

Average-consensus : fast algorithm (BWG) and theoretical analysis

... distributed optimization (to be done)

References :F. Iutzeler and P. Ciblat, “Fully-distributed spectrum sensing : application to cognitive radio”, submitted for publicationto Eusipco, 2013.F. Iutzeler, P. Ciblat, and W. Hachem, “Analysis of Sum-Weight-like algorithms for averaging in Wireless SensorNetworks”, accepted for publication to IEEE Trans. Signal Processing.F. Iutzeler, P. Ciblat, and J. Jakubowicz, “Analysis of max-consensus algorithms in wireless channels”, IEEE Trans.Signal Processing, vol. 60, no. 11, pp. 6103-6107, November 2012.


fully-distributed spectrum sensing: application to

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