Performance Evaluation of Censoring-Enabled Systems for Sequential Detection in Large Wireless Sensor Networks
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1 Performance Evaluation of Censoring-Enabled Systems for Sequential Detection in Large Wireless Sensor Networks Mohammed Karmoose Karim Seddik 2 Ahmed Sultan Electrical Engineering Dept, Alexandria University 2 American University in Cairo (AUC) Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection in/ Large 20
2 Motivation 2 System Model 3 System Model 4 Performance analysis 5 Numerical evaluation Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection2 in/ Large 20
3 Motivation Sensor s limited power source Censoring as a means to save energy - increase lifetime However, there could be more in censoring in hard-decision framework Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection3 in/ Large 20
4 Motivation H H One with high LLR Zero with low LLR Zero with low LLR One with high LLR Zero with low LLR Zero with low LLR Sends a Sends a - Sends a - Sends a Censors Censors FC FC Decides in favor of H0 Decides in favor of H Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection4 in/ Large 20
5 Motivation We consider sequential topology: Nodes are sequentially polled until a decision is made by the FC We characterize performance metrics: average error probability, average incurred delay Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection5 in/ Large 20
6 System Model Data Model: H 0 : x n N ( 0, σ0 2 ) H : x n N ( 0, σ) 2. Local Decisions: Log-Likelihood Ratio Test l j (x j ) γ u(x j ) = 0 γ 0 < l j (x j ) < γ l j (x j γ ) 0 l j (x j ) = log ( Pr(x j) Pr 0(x j) ohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection6 in/ Large 20
7 System Model Wireless channel impairment u(x i ) û(x i ) Decision Variable Z J = J j= û(x j) Global decision H u 0 = H 0 Request more decisions Z J α Z J β β Z J α ohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection7 in/ Large 20
8 System Model FC-Aware: FC is aware of nodes that censor transmission Only ± could be erroneously received by the FC Binary Symmetric Channel (BSC) Assume AWGN channel: p = Q ( σ ) N - p p p p - ohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection8 in/ Large 20
9 System Model FC-Unaware: FC is not aware of nodes that censor transmission All decisions could be erroneously received by the FC Ternary Symmetric Channel 0 0 Assume AWGN channel: ( ) γ p 00 = Q σ N ( ) ( ) γ + γ p 00 = Q Q σ N σ N ( ) + γ p 00 = Q σ N - - -γ Decide - Decide 0 γ - Decide ohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection9 in/ Large 20
10 Performance Analysis {Z n, n > }: One-dimensional Random Walk process with two absorbing barriers Probability of error: Pr 0 (Z n α) and Pr (Z n β) Average delay (average stopping time): E 0 (J) = E 0 (Z J ) /E 0 (û) E (J) = E (Z J ) /E (û) ohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection0 in/ Large 20
11 Performance Analysis Probability of error: Chernoff bound: [ ( )] γ(r0 ) Pr 0 (Z n α) exp α `γ(r 0 ) r 0 exp ( r α) ) where `γ(r 0 ) = α/n, γ(r) = ln gû(r), gû(r) = E (e (rû) is the Moment Generating Function of the random variable Û, and r is the solution to the equation γ(r) = 0 Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection in/ Large 20
12 Performance Analysis By applying the bound [Apx: A]: ( P E/H0 ( P E/H0 P E/H0 ) α ( p u (0), P p u (0) E/H ) α (, P E/H p (0) u p (0) u ( p (0) p (0) ) α, P E/H ( p () p () p () u p () u p () u p () ) β (Conventional) ) β (FC-aware) u ) β (FC-unaware) Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection2 in/ Large 20
13 Performance Analysis Average stopping time [Apx: B]: ( E 0 (J) β+(α+β) 2p u (0) ( E 0 (J) β+(α+β) E 0 (J) E0(ZJ) p (0) p (0) 2p (0) u ) p u (0) α p u (0) p (0) u p (0) u ) α, E (J) E(ZJ) (, E (J) α (α+β) 2p u( (), E (J) α (α+β) p () p () 2p () u p u () p u () p u () p u () ) β ) β (Conventional) (FC-aware) (FC-unaware) where E 0 (Z J ) β + (α + β) E (Z J ) α (α + β) ( ( p (0) ) α p (0) ) β p () p () Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection3 in/ Large 20
14 Numerical Evaluation Conventional Censoring Unaware censoring 0 2 P e SNR (db) Figure: Bound on the error probability for all systems Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection4 in/ Large 20
15 Numerical Evaluation Conventional Censoring Unaware censoring J SNR (db) Figure: Bound on the expected number of observations for both systems Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection5 in/ Large 20
16 Numerical Evaluation Thresholds Conventional Threshold Threshold 0 Threshold Unaware Threshold 0 Unaware SNR (db) Figure: Optimal thresholds for all systems Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection6 in/ Large 20
17 Numerical Evaluation Conventional Unaware censoring 0 2 P e SNR (db) Figure: Error probability for the conventional system and the FC-unaware system with equal average stopping time Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection7 in/ Large 20
18 Numerical Evaluation Conventional Unaware censoring 60 J SNR (db) Figure: Average stopping time for the conventional system and the FC-unaware system with fixed error probability Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection8 in/ Large 20
19 Conclusion and Future Work Conclusion: Proved that censoring enhances system performance in hard-decision framework Characterized performance gains in sequential distributed detection systems Future Work: Consider the implementation issues of such a technique Expand for other wireless networks than WSNs Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection9 in/ Large 20
20 Thank you Mohammed Karmoose, Karim Seddik, Ahmed Performance Sultan (Alex. Evaluation Univ.) of Censoring-Enabled Systems for Sequential Detection20 in/ Large 20
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