Fully-distributed spectrum sensing: application to cognitive radio

Transcription

1 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)

2 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

3 Hidden terminal issue Secondary user Primary Transmitter Primary Receiver Secondary user Philippe Ciblat Fully-distributed spectrum sensing 3 / 15

4 Hidden terminal issue Secondary user Primary Transmitter Primary Receiver Secondary user Philippe Ciblat Fully-distributed spectrum sensing 3 / 15

5 Hidden terminal issue Secondary user Primary Transmitter Primary Receiver Reception disturbance Secondary user Problem : a secondary user is disturbing the primary receiver Solution : secondary users have to cooperate to detect the primary user Philippe Ciblat Fully-distributed spectrum sensing 3 / 15

6 Two ways for cooperating Centralized detection (Fully)-Distributed detection Primary Transmitter Fusion center Primary Transmitter Primary Receiver Primary Receiver Secondary user 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 Philippe Ciblat Fully-distributed spectrum sensing 4 / 15

7 System model { H0 (absence of primary user) : y k (n) = b k (n) k = 1,, K H 1 (presence of primary user) : y k (n) = x k (n)+b k (n) n = 1,, N s with secondary user index k and time index n b k (n) Gaussian with variance σ 2 k known at secondary user k {x k (n)} n coming from primary user known at secondary user k Performance metric Detection probability : P D = P(H 1 H 1 ) False alarm probability : P FA = P(H 1 H 0 ) Remarks : Goal : minimizing P FA such that P D P target D If {x k (n)} n unknown but Gaussian Energy detector Hard detection (local decision and then voting) not considered Philippe Ciblat Fully-distributed spectrum sensing 5 / 15

8 Reminder on (soft) centralized detection Optimal test : Log-Likelihood Ratio (LLR) ( ) p(y H1 ) H1 Λ(y) = log µ, with µ chosen for ensuring P target D p(y H 0 ) H 0 Application to our practical case : T(y) = 1 K K k=1 t k (y k ) H 1 H 0 η, with t k (y k ) = yt kx k σ 2 k and y k = [y k (1),, y k (N s)] T, x k = [x k (1),, x k (N s)] T, (.) T = transpose. Threshold computation η = ς T Q ( 1)( P target ) D + mt where Q ( 1) is the inverse of the Gaussian tail function, and ( ) ( ) 1 K m T = N s SNR k and ς T = Ns 1 K SNR k. K K K k=1 k=1 Philippe Ciblat Fully-distributed spectrum sensing 6 / 15

9 Fully-distributed detection (I) Sensing step of duration N s Gossiping step of duration N g t l = yl T x l /σl 2 for each node l T k average l (t l ) Question : How computing the average of t l in a distributed way Gossiping (also called consensus) algorithms Gossiping algorithm description : an example (Pairwise Gossip) x(0) = [x 1 (0),, x K (0)] T : initial values At time t, a node i wakes up and calls one of its neighbor j. Then x i (t + 1) = (x i (t)+x j (t))/2 x j (t + 1) = (x i (t)+x j (t))/2 x(t + 1) = W(t)x(t) t x average1 T 1 (y). T K (y) t 1 (y 1 ) = P. t K (y K ) with P = (p kl ) k,l=1,,k the gossiping algorithm matrix after N g iterations. Philippe Ciblat Fully-distributed spectrum sensing 7 / 15

10 Fully-distributed detection (II) The final test function at node k is T k (y) = K l=1 p kl y T lx l σ 2 l H 1 H 0 η k, where the threshold (for pre-defined P target D ) is given by η k = ς k Q ( 1)( P target ) D + mk with K K m k = N s p kl SNR l and ς k = N s pklsnr 2 l. l=1 l=1 Problem Threshold not computable in a distributed way due to the terms p 2 kl. Philippe Ciblat Fully-distributed spectrum sensing 8 / 15

11 Two approaches for threshold computation (I) Approach 1 : distributed with knowledge of K η (1) k = ς (1) k Q ( 1)( P target ) + mk with ς (1) D k = Ns K K p kl SNR l. l=1 Approach 2 : fully-distributed Using Sum-Weight-like gossip in order to perform the average and the sum. where z := Qt, w (1) := Q1, w (e) := Qe Q the gossip algorithm matrix after N g iterations, e the K -sized vector whose first component is 1 and the others 0. Each node k calculates the k-th component of where z p = z w (1) = Pt t average1 and z s = z w (e) = St t sum1 the elementwise division. P = diag(1 Q1) Q and S = diag(1 Qe) Q. Philippe Ciblat Fully-distributed spectrum sensing 9 / 15

12 Two approaches for threshold computation (II) The threshold is then as follows η (2) k = ς (2) k Q ( 1)( P target ) + mk with ς (2) = N s D k ( K l=1 p klsnr l ) 2 K l=1 s klsnr l. Remarks Algorithm fully distributed since the number of nodes not required. New threshold does not ensure the target probability of detection P D (k) = Q ς (2) k Q ( 1)( P target ) D. ς k Philippe Ciblat Fully-distributed spectrum sensing 10 / 15

13 Numerical illustrations Setup : T = N s + K = 128 with N s = N g = 64. P target 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 Philippe Ciblat Fully-distributed spectrum sensing 11 / 15

14 Performance analysis P FA and P D versus mean SNR P FA and P D versus N s Fully-distributed algorithm performs well Sensing time equivalent to gossiping time Philippe Ciblat Fully-distributed spectrum sensing 12 / 15

15 Hidden terminal context Hidden terminal configuration P FA and P D versus T Fast convergence for fully-distributed algorithm Hidden terminal issue is fixed Philippe Ciblat Fully-distributed spectrum sensing 13 / 15

16 Comparison with existing approach Training based algorithm Comparison with A. Sayed, Distributed detection over adaptive networks using diffusion adaptation, IEEE Trans. Signal Processing, May In this paper, sensing and gossiping steps are interleaved Outperforming existing approach More relevant choice of threshold Philippe Ciblat Fully-distributed spectrum sensing 14 / 15

17 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 publication to Eusipco, F. Iutzeler, P. Ciblat, and W. Hachem, Analysis of Sum-Weight-like algorithms for averaging in Wireless Sensor Networks, 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 , November Philippe Ciblat Fully-distributed spectrum sensing 15 / 15