Censoring for Improved Sensing Performance in Infrastructure-less Cognitive Radio Networks

Transcription

1 Censoring for Improved Sensing Performance in Infrastructure-less Cognitive Radio Networks Mohamed Seif 1 Mohammed Karmoose 2 Moustafa Youssef 3 1 Wireless Intelligent Networks Center (WINC),, Egypt 2 Electrical Engineering Department, Alexandria University, Egypt 3 Wireless Research Center, Egypt-Japan University of Science and Technology, Egypt March 19, 2015

2 Outline 1 Motivation and related work 2 System Model 3 System Analysis 4 Numerical Evaluation 5 Summary

3 Related Work Sensor has limited power source Censoring as a means to save energy - increase lifetime

4 Related Work In [1], censoring was considered in a hard decision framework, where sensors apply one-bit quantization to their local measurements before transmission It was proven that censoring enhances the performance in terms of error probability of the global decision besides the energy savings 1 : Karim G Seddik, Ahmed K Sultan, and Amr A El-Sherif,?Censoring for improved performance of distributed detection in wireless sensor networks,? in 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE, 2011, pp. 181?185.

5 Related Work In [2]-[3], Censoring was applied to different topologies like TDMA, TBMA (Type Based Multiple Access), and sequential 2 : Mohammed Karmoose, Karim G Seddik, and Hassan El Kamchouchi,?Censoring for type-based multiple access scheme in wireless sensor networks,? in Vehicular Technology Conference (VTC Fall). IEEE, 2012, pp. 1?6. 3 : Mohammed Karmoose, Karim G. Seddik, and Ahmed Sultan,?Performance evaluation of censoring-enabled systems for sequential detection in large wireless sensor networks,? in 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 2014.

6 Related Work These related works have a common assumption that a fusion center is present for coordination among the transmitting SUs Contribution: We propose a censoring based hard-decision without a fusion center We characterize the proposed system in terms of average error probability, energy expenditure and network overhead

7 Network Model M SUs are opportunistically transmitting in the presence of a PU 1 Primary User Range A node i is connected to node j at time k if τ ij C τ which is channel to noise ratio of link ɛ ij j M CSMA/CA protocol is assumed between SU nodes 3 3 j j Figure: CRN model

8 Spectrum Sensing Each SU is equipped with energy detector as shown in the figure The received signal at SU i can be expressed as: f s T r i ( t ) 2 ( ) x i (0 ) b (0 ) dt i 0 Figure: Energy detector r iˆt œ n iˆt Given H 0 h iˆt sˆt n iˆt Given H 1 Where, h i ˆt : complex-gaussian channel gain between PU and the ith SU sˆt : signal transmitted by the PU n i ˆt : AWGN at the ith SU PU inactive Censored PU active Decide -1 Decide 0 Decide 1 Figure: Thresholds

9 Local Decisions We allow nodes to censor transmission A node employs a two-threshold decision making process as shown in the figure The detection process can be expressed as: f s T r i ( t ) 2 ( ) x i (0 ) b (0 ) dt i 0 Figure: Energy detector b iˆ0 Where, 1, x iˆ0 C η 1 0, η 0 B x η 1 1, x η 0 PU inactive Censored PU active Decide -1 Decide 0 Decide 1 Figure: Thresholds x i ˆ0 : output of the energy detector

10 Binary Consensus Algorithm After the local decision phase: Each SU transmits its local decision to the available neighbor for K times Primary User Range 1 j M Upon the terminations of the algorithm (i.e. at k K ), each SU make a final decision based on the obtained decisions j j Figure: CRN cluster

11 Binary Consensus Algorithm To model the connectivity between SUs among the network, the adjacency matrix Aˆk is defined as: Primary User Range 1 j M a ijˆk 1 if τ ijˆk A τ, i x j 0 otherwise j j Figure: CRN cluster

12 Binary Consensus Algorithm The combining function of obtained decisions, and the decision function can be mathematically expressed as: 1 Primary User Range F ˆbˆn, n 0,,k 1 bˆk 1, K, Dˆbˆn, n 0,,K K1 DecŒ Q M ˆbˆ0 Aˆt bˆt Kp t 0 where, bˆk b 1ˆk,..., b M ˆk T be the vector of local decisions at time step k at M SUs and, 1, if x C 0 Decˆx œ 0, if j 3 j j M Figure: CRN cluster

13 Average Error Probability For a one threshold system, the local decision probabilities of the ith node under hypothesis H 1 and H 0 : π 11 Prˆb i ˆ0 1SH 1 e η 2 Œe η 2ˆ γ1 e η 2 TB2 Q n 0 TB2 Q n 0 1 γ 1 n! ˆ γ 1 η γ n n! Ž 2ˆ γ 1 Γ l ˆTB, η 2 π 10 prˆb i ˆ0 1SH 0 1 ΓˆTB where, η: the local threshold at each SU TB: time bandwidth product γ: average SNR Γˆx and Γ l ˆx, y are the Gamma and lower incomplete Gamma functions, respectively. TB1

14 Average Error Probability For the censoring (i.e. two-threshold) system, we define the local decision probabilities of the ith node under hypothesis H j, j 0, 1 as: π 1j Prˆb i ˆ0 1SH j Prˆx i ˆ0 A η 1 SH j π 1j Prˆb i ˆ0 1SH j Prˆx i ˆ0 B η 0 SH j π 0j Prˆb i ˆ0 0SH j 1 ˆπ c 1j πc 1j.

15 Average Error Probability Censoring System Global detection and false probabilities expressions are: P d ˆK P M M! P c 0 n P fa ˆK P M M! P c 0 n c Mc n! c!ˆmnc! πn 11 πc 01 πmnc 11 1 n QŒ 1 n QŒ ¾ˆ1p ˆMc ¾ˆ1p ˆM1c pk pk c Mc n!c!ˆmnc! πn 10 πc 00 πmnc 10 1 n QŒ 1 n QŒ Where, n: number of ones in vector at time k c: number of censored node at time k M: number of SU nodes p: probability of link connectivity Then, ¾ˆ1p ˆMc P eˆk π H0 P faˆk π H1 ˆ1 P d ˆK pk ¾ˆ1p ˆM1c pk

16 Energy Expenditure Let E be the energy consumed by a node to transmit a decision (either 1 or 1) to neighboring nodes Then, the average consumed a node in our proposed scheme is E av p H0 ˆ1 π 00 p H1 ˆ1 π 01 Ž E B E, which is less than the average energy consumed in conventional scheme E.

17 Network Overhaed Given that C is the number of nodes which made a decision to censor transmission in a network The average number of censoring nodes at any time can be expressed as: E ˆC p H0 E0ˆC p H 1 E1ˆC where, E ˆX is the expectation of X and Ej ˆX is the conditional expectation of X given H j.

18 Network Overhaed The average number of censoring nodes is equal to E ˆC ˆp H0 π 00 p H1 π 01 M The average number of transmitted message per node in this case is ˆ1 ˆp H0 π 00 p H1 π 01 M K M ˆ1 ˆp H0 π 00 p H1 π 01 K B K which is less than the average transmitted messages in conventional scheme K.

19 Average Error Probability Average Error Probability Conventional p = 0.8 γ = 2 db Censoring p = 0.8 γ = 2 db Conventional p = 0.2 γ = 2 db Censoring p = 0.2 γ = 2 db Conventional p = 0.8 γ = 4 db Censoring p = 0.8 γ = 4 db Algorithm Runtime (K) Figure: Average probability of error - M 51, TB 5 and K 10.

20 Energy Expenditure Average Energy Expenditure (E av ) Conventional Censoring p = 0.8 γ = 2 db Censoring p = 0.2 γ = 2 db Censoring p = 0.8 γ = 4 db Algorithm Runtime (K) Figure: Energy Expenditure - M 51, TB 5 and K 10.

21 Network Overhead Network Overhead Conventional Censoring p = 0.8 γ = 2 db Censoring p = 0.2 γ = 2 db Censoring p = 0.8 γ = 4 db Algorithm Runtime (K) Figure: Network overhead - M 51, TB 5 and K 10.

22 Summary We proposed a distributed detection framework for infrastructure-less CRNs which allows SUs nodes to censor transmissions. We characterize the proposed system in terms of average error probability, energy expenditure and network overhead Showed the attained gains in these terms when applying the proposed scheme

23 Thank You!