A Crowd Cooperative Spectrum Sensing Algorithm Using a Non-Ideal Channel

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1 algorthms Artcle A Crowd Cooperatve Spectrum Sensng Algorthm Usng a Non-Ideal Channel Xnxn Lv and Q Zhu * Jangsu Key Laboratory of Wreless Communcatons, Nanjng Unversty of Posts and Telecommuncatons, Nanjng , Chna; @163.com * Correspondence: zhuq@njupt.edu.cn; Tel.: Receved: 20 March 2018; Accepted: 16 Aprl 2018; Publshed: 18 Aprl 2018 Abstract: Spectrum sensng s the prerequste of the realzaton of cogntve rado. So t s a sgnfcant part of cogntve rado. In order to stmulate the SUs to sense the spectrum, we combne the ncentve mechansm of crowd-sensng wth cooperatve spectrum sensng effectvely, and put forward a crowd cooperatve spectrum sensng algorthm wth optmal utlty of secondary users (SUs) under non-deal channel whch we defne SUs utlty expectaton functons related to rewards, sensng tme and transmsson power. Then, we construct the optmzaton problem of maxmzng the utltes of SUs by optmzng the sensng tme and the transmsson power, and prove that ths problem s a convex optmzaton problem. The optmal sensng tme and transmsson power are obtaned by usng the Karush-Kuhn-Tucker (KKT) condtons. The numercal smulaton results show that the spectrum detecton performance of algorthm, whch we put forward, s mproved. Keywords: cogntve rado; spectrum sensng; crowd sensng; detectve probablty 1. Introducton In recent years, moble data servces have developed rapdly, and the demand for wreless spectrum resources s growng. Therefore, the technology of cogntve rado was nvented. Spectrum sensng, whch s an mportant part of cogntve rado, s amed to sense whether the prmary user (PU) occupes a specfc frequency spectrum resource at a specfc tme n a partcular locaton. Because of the exstence of path loss and shadow effect, there s a large error n sngle detecton problem. Cooperatve spectrum sensng can solve ths problem [1]. There are fve hard-decson fuson methods for cooperatve spectrum sensng, ncludng and fuson, or fuson, votng fuson, maxmum posteror probablty fuson and Bayesan fuson [2]. Soft-data fuson schemes lke square law selecton fuson, maxmal rato combnaton fuson, square law combnng fuson and selecton combnng are analyzed n [3]. The selecton of SUs wll nfluence the performance of spectrum sensng. In [4], SUs are selected by the sze of the sgnal-to-nose rato. SUs need to send the sgnal-to-nose rato to base staton for selectng, but t wll ncrease the data overhead of the SUs. The dynamc selecton of SUs n sensng system s studed, and a dstrbuted sensng compensaton method s put forward to solve the problem n [5]. Game theory s also appled to spectrum sensng, and the rewards of SUs are related to the reportng results. SUs wll get hgher rewards f ther results are correct, otherwse, they wll get lower rewards [6]. Because the communcaton between SUs and base staton mostly adopts wreless communcaton, there must be error codes and packet loss. In [7], ths phenomenon s analyzed, and the accuracy of data fuson s also calculated. All the papers above assume that the SUs are wllng to partcpate n the sensng. In [8,9], reputaton mechansm s consdered n the cooperatve spectrum sensng. Whle the smartphones have been popular, the robust spectrum sensng and cloud-based archtecture has been studed, [10 12]. The spectrum assgnment methods are also studed n [13 15]. In [16], how the selecton of SUs can Algorthms 2018, 11, 51; do: /a

2 Algorthms 2018, 11, 51 2 of 10 nfluence the performance of spectrum sensng s analyzed. However, because the SUs wll not take part n the sensng wthout some rewards, a certan mechansm s needed to stmulate the SUs. Crowd sensng s a method of collectng samples, and the man way s to collect samples by usng ntellgent equpment. Crowd sensng ncentve mechansm s a mechansm for recrutng and stmulatng the people nvolved n sensng. Ths mechansm can be dvded nto monetary ncentve mechansm and non-monetary ncentve mechansm [17]. At present, most of the research s monetary ncentve mechansm. In [18], the game theory s appled to crowd sensng ncentve mechansm, and the economc model of crowd sensng applcaton s studed to mprove the qualty of sensng data. In [19], the task assgnment problem of senstve servce qualty s studed, the rewards of partcpants are related to the qualty of sensng data. To ensure that the tasks are completed, each task can be completed by more than one partcpant. In order to reduce the socal cost, a task partcpant cooperaton mechansm s desgned [20]. Partcpants n ths mechansm are nterrelated, so t s easy for partcpants to cooperate, and the sensng cost can be reduced. However, the above lteratures do not concretely translate the crowd sensng nto some applcatons. In cogntve rado network, the SUs need to sense the spectrum to judge whether the prmary user (PU) occupes a specfc frequency spectrum resource. In order to stmulate the SUs to take part n the cooperatve spectrum sensng, we need to combne the crowd sensng ncentve mechansm wth the cooperatve spectrum sensng. The contrbutons of ths paper are summarzed as follows: (1) Under non-deal channel, we propose a system model whch combnes crowd sensng ncentve mechansm wth cooperatve spectrum sensng, and defne SU s utlty expectaton functon whch consders the SUs sensng tme and transmsson power at the same tme. (2) We construct an optmzaton problem about the SU s utlty expectaton, and prove that the optmzaton problem s a convex optmzaton problem. We obtaned the optmal soluton by usng KKT condtons. Ths paper s organzed as follows. In Secton 2, we ntroduce the system model. In Secton 3, we propose a cooperatve spectrum-sensng algorthm based on crowd sensng ncentve mechansm under non-deal channel wth the optmal SUs utltes. The numercal smulaton results and comparsons are gven n Secton 4, and fnally, we draw the conclusons n Secton System Model The system model s shown n Fgure 1. M SUs are evenly dstrbuted wthn the coverage of base staton. The base staton releases the channel to be sensed and reward nformaton. After SUs fnsh the sensng, they send the sensng results to the base staton, and the base staton fuse all the results. SUs use energy detecton for spectrum sensng. The detecton probablty of SU s gven by [21]: p = Q((Q 1 (p f ) t f s γ )/ 2γ + 1), (1) where p f s the target probablty of false alarm, and γ represents the sgnal-to-nose rato of SU. t ndcates the sensng tme. t f s ndcates the samplng ponts, and t can be wrtten as n. The samplng frequency s a constant value. Functon Q s expressed as: Q(x) = 1 e y2 /2 dy. (2) 2π x Take p(u 1 ) as the probablty of the exstence of the PU, and take p(u 0 ) as the probablty that the PU does not exst. So the correct sensng probablty of SU, p c, and the ncorrect sensng probablty of SU, p e, are gven by: p c = p(u 1 )p + p(u 0 )(1 p f ), (3) p n = p(u 1 )(1 p ) + p(u 0 )p f, (4)

3 Algorthms 2018, 11, 51 3 of 10 If the PU exst, the sensng result s 1, otherwse, the result s 0. When SUs sends the results of sensng to the base staton, error codes wll occur. So the correct probablty of the results whch s receved by the base staton from SU s gven by: p rc and the ncorrect probablty s gven by: p rn = p c (1 p e) + p n p e, (5) = p c p e + p n (1 p e ), (6) where p e s the transmsson error rate. Assumng that SUs use 2DPSK modulaton, the error rate of the recever usng non-coherent demodulaton s p e = 1 2 e r [22], where r ndcates the sgnal-to-nose rato of SUs sgnals receved by base staton. In ths paper, we adopt votng fuson method for data fuson. Frst set a threshold m. A hypothess wll be true f more than m SUs support ths hypothess. The detecton probablty and false alarm probablty of votng fuson s expressed by: p D = p F = M j=m M j=m u =j u =j (p ) u (1 p ) 1 u, (7) (p f ) u (1 p f ) 1 u, (8) where u ndcates the sensng result of SU. When threshold m = M/2, the performance of fuson s optmum [21]. 3. Utlty Optmal Algorthm Fgure 1. System scenaro. The base staton frst releases nformaton about the channel to be sensed, the correct reward k and ncorrect reward k for the SUs. The SUs optmze the sensng tme and sgnal transmsson power to obtan the optmal utlty expectaton of the SUs accordng to the utlty expectaton formula. If the utlty expectaton s greater than 0, the SU would execute the sensng and send ts sensng result to the base staton. After the data fuson, the base staton wll offer the rewards to SUs n accordance wth

4 Algorthms 2018, 11, 51 4 of 10 the correctness of the decson receved, f the result of SU s the same wth the result of the fuson decson, SU can get the correct reward k, otherwse the reward s k. The reward expectaton of SU s gven by: re = k p rc The utlty expectaton of SU can be expressed by: + k p rn. (9) utlty = re { c t c s s = k [p(u 1 )p + p(u 0 )(1 p f )](1 p e ) + [p(u 1 )(1 p ) } +p(u 0 )p f ]p e + k { [p(u 1 )p + p(u 0 )(1 p f )]p e + [p(u 1 )(1 p ) + p(u 0 )p ](1 p e )} c t c s s, (10) where s ndcates the sgnal transmsson power of SU. c and c s represent the cost of unt sensng tme and the cost of unt transmsson power, respectvely. In order to mprove the effcency of spectrum sensng, a SU wll not take part n the spectrum sensng f the detecton probablty s less than 0.5, because the sensng result does not have reference value. Hence a SU wll take part n the spectrum sensng when the detecton probablty s greater than 0.5. It s known from the propertes of Q functon that f the detecton probablty s greater than 0.5, the argument of the Q functon n (2) s less than 0,.e., Q 1 (p f ) t f s γ 2γ + 1 < 0. (11) The goal of ths paper s that the SU can obtan the optmal utltes by optmzng the sensng tme and the transmsson power, and the optmzaton problem can be expressed as follows: P1 : mn ( utlty ) (12) {t,s } s.t. t + 1 ( Q 1 2 (p f ) ) < 0, (13) f s γ s < 0, (14) where the constrant condton (13) s derved from (11), and (14) ndcates that the transmsson power of the SU s greater than 0. As long as the optmzaton problem s proved to be a convex optmzaton problem, the optmal sensng tme and transmsson power can be obtaned through the KKT condtons [23]. Proposton 1. Optmzaton problem P1 s a convex optmzaton problem. The proof s gven n Appendx A. Set X = (t, s ), and h k (X ) < 0, k = 1, 2 represents 2 constrants on convex optmzaton problem. We defne the Lagrangan equaton as follows: L = utlty + 2 k=1 µ k h(x ). (15) Thus, the KKT condton for the convex optmzaton problem s gven by: L X = 0, (16) µ k 0 k = 1, 2, (17)

5 Algorthms 2018, 11, 51 5 of 10 h k (X ) < 0 k = 1, 2. (16) Accordng to (15), we can get µ k = 0, k = 1, 2. Hence (14) can be expressed by: (utlty ) γ t = 1 2 (k k )(1 2p e )[ 2 4πγ +2π (t f s ) 1/2 e m2 /2 k b c f s ] c = 0 (utlty ) s = 1 n (k k )(p p f )e s /n c s = 0. (18) The optmal sensng tme and emsson power can be obtaned by solvng Equaton (17). In summary, the algorthm of crowd cooperatve spectrum sensng s as follows (Algorthm 1): Algorthm 1 Crowd Cooperatve Spectrum Sensng Algorthm under Non-Ideal Channel. 1: for all SUs do 2: Solve the Equatons (17) and get the optmal sensng tme t and emsson power s ; 3: Calculate the utlty accordng to (10); 4: f utlty > 0 5: SU take part n the spectrum sensng and send the result to the base staton; 6: The base staton receves the sensng result R from SU ; 7: end f 8: end for 9: The base staton fuses the results from SUs and gets the fuson result R; 10: for all SUs partcpatng n the sensng do 12: f R = R 13: SU gets correct reward k; 14: else 15: SU gets ncorrect reward k ; 16: end f 17: end for 4. Computer Smulatons In ths paper, we smulate the correct detecton probablty and the SUs average utlty wth MATLAB R2012a, and compare the smulaton results wth the results of [4]. In the smulaton scenaro, 6 SUs are randomly dstrbuted n the crcle wth a radus of 100 m. The coordnate of the PU s (0,0), and the base staton s coordnate s (200,200) m. The samplng frequency of the SU f s s set to 10 khz. The sensng tme cost c s set to 0.1 per mllsecond, and the transmsson power cost c s s set to 0.01 per mllwatts. The ncorrect reward k s 1/10 of the correct reward k, and the target false alarm probablty of SUs s set to 0.1. The transmsson of sgnal s based on the emprcal path loss model n large scale fadng, and the fadng coeffcent s 2.5. The transmsson power of the prmary user s 40 mw, and the program runs 3000 tmes to get the average values. Fgures 2 and 3 show the changes n the average utlty and correct sensng probablty of SUs wth the reward k. In Fgure 2, the SUs average utlty of the algorthm ncreases wth remuneraton, and s greater than of the comparson algorthm. The reason s that ths algorthm s a utlty expectaton optmal algorthm. By maxmzng the sensng tme and sgnal transmsson power, the utltes expectaton of the SUs get the maxmum value. However, the contrast algorthm dd not consder the SUs sensng tme and transmsson power, so the detectve probablty and error rate cannot be changed whch means t can not get the optmal values. Therefore, the average utlty of the SUs s greater than the contrast algorthm. From Fgure 3, t can be seen that the correct probablty of sensng s also ncreasng wth the reward, and the correct probablty of ths algorthm s hgher than that of the contrast algorthm. The reason s that wth the ncrease of the reward, the number of people nvolved n sensng wll ncrease, whch can mprove the correct probablty. Because the average utlty of ths algorthm s greater than the contrast algorthm, the number of people nvolved n the sensng wll be more than the contrast algorthm, so the correct probablty s hgher than the contrast algorthm.

6 Algorthms 2018, 11, 51 6 of 10 Fgure 2. The change of the SUs average utlty wth the correct reward. Fgure 3. The change of the correct probablty wth the correct reward. Fgures 4 and 5 represent the changes n the average utlty and correct probablty of the SUs wth the transmsson power of the PU, and the reward k s set to 0.6. In Fgure 4, the two curves are begnnng to grow more clearly, and then more slowly. The reason s that when the transmsson power of the PU s low, the SUs acceptance of sgnal-to-nose rato s low, the detecton error s large, so the utltes are low. Wth the promoton of the power of the PU, the accuracy of the SUs s mproved, so the utltes of the SUs are also mproved. Because the reward k s constant, when the detecton probabltes ncrease, the utltes of the SUs are close to the maxmum utlty that can be obtaned, so the curves are relatvely gentle behnd. In can be seen from Fgure 4 that the secondary user s average utlty of ths algorthm s greater than that of the contract algorthm. The reason s that ths algorthm s a utlty expectaton optmal algorthm. By maxmzng the sensng tme and sgnal transmsson power, we can get the maxmum utlty expectatons of the SUs, so the average utlty of the SUs s hgher than that of the contrast algorthm. From Fgure 5, we can see that two curves ncrease monotonously wth the transmsson power of the prmary users. The correct probablty of the algorthm s greater than that of the contrast algorthm. The reason s that the secondary user

7 Algorthms 2018, 11, 51 7 of 10 utlty of the algorthm s hgher than that of the contrast algorthm, so the number of partcpants s more, and the probablty of correctness s hgher. Fgure 4. The change of the SUs average utlty wth the transmsson power of PU. Fgure 5. The change of the correct probablty wth the transmsson of PU. 5. Conclusons We apply the crowd sensng ncentve mechansm to cooperatve spectrum sensng under non-deal channel, and propose a cooperatve spectrum sensng algorthm based on crowd sensng ncentve mechansm under non-deal channel wth the optmal SUs utltes. Frst, the utlty expectaton functon of the SUs s set up, and the maxmum utlty expectaton s obtaned by optmzng the sensng tme and sgnal transmsson power. The base staton compares the receved SUs judgment results wth the fuson decson results, f the same, the secondary users can get a hgher reward, otherwse the reward s low, so as to stmulate the SUs sensng ntatve and the performance of spectrum sensng s mproved. Fnally, the smulaton shows that whle the utlty of the SU s gettng the optmal value, the accuracy of spectrum sensng s also mproved. The key nsght of our algorthm s that spectrum sensng and crowd sensng ncentve mechansm can be combned to stmulate the SUs and mprove the sensng performance.

8 Algorthms 2018, 11, 51 8 of 10 Acknowledgments: Ths work s supported by Natonal Natural Scence Foundaton of Chna ( , ). Author Contrbutons: The manuscrpt was wrtten by Xnxn Lv under the gudance of Q Zhu. All authors revewed the manuscrpt. Conflcts of Interest: The authors declare no conflct of nterest. Appendx A Proof for Proposton 1: It s obvous that the feasble doman of the optmzaton problem P1 s a convex set, and then we prove that the objectve functon s a convex functon. The necessary and suffcent condton for a functon to be a convex functon s that the Laplasse operator s not less than 0 [23],.e., ( utlty) 0 (A1) For the sake of smplcty, wthout losng the generalty, we set p(u 1 ) = p(u 0 ) = 0.5,.e., the probablty of the exstence of the man user s 0.5. (10) can be smplfed as follows: utlty = 0.5 [(k k )(p 2p p e + 2p f p e + 1 p f )] c t c s s. (A2) So the Laplasse operator of the objectve functon can be expressed as follows: ( utlty ) = 2 ( utlty ) t 2 Frst calculate 2 ( utlty ), and we can get: t ( utlty ) s 2. (A3) 2 ( utlty ) t 2 j = 1 2 (k k )(1 2p e )( 2 1 s (t f s ) 3/2 e m2 /2 + m s (t f s ) 1/2 e m2 /2 1 2 (t f s) 1/2 γ 2γ ), (A4) +1 where m = Q 1 (p f ) t f s γ, s = 1 2γ γ 4πγ + 2π. Because the sgnal-to-nose rato γ s postve and therefore s > 0. Because (t f s ) 3/2 e m2 /2 > 0, so 1 2 s (t f s ) 3/2 e m2 /2 < 0,.e., m 0. So m s (t f s ) 1/2 e m2 /2 1 2 (t f s ) 1/2 γ j 2γj + 1 > 0. (A5) Accordng to the defnton and (5), we can get k k > 0 and p e 0.5. So 2 ( utlty ) n 2 j 0. (A6) Then calculate 2 ( utlty ), and we can get: s 2 2 ( utlty ) s 2 = ( pl n ) 2 (k k )(p p f )e s pl/n, (A7) where n ndcates nose power, and pl ndcates path loss. Set target false alarm probablty p f less than 0.5. Because 1 n 2 e s /n > 0, we can get: 2 ( utlty ) s 2 0. (A8)

9 Algorthms 2018, 11, 51 9 of 10 Thus, we can get: ( utlty ) = 2 ( utlty ) t ( utlty ) s 2 0. (A9) Hence objectve functon s a convex functon. Optmzaton problem P1 s a convex optmzaton problem. Proof complete. References 1. Mshra, S.M.; Saha, A.; Brodersen, R.W. Cooperatve Sensng among Cogntve Rados. In Proceedngs of the IEEE Internatonal Conference on Communcatons, Istanbul, Turkey, June 2006; IEEE: New York, NY, USA, 2006; pp L, B.; Q, Z. Cooperatve Spectrum Sensng Algorthm Based on Data Fuson. J. NJUPT 2009, 29, [CrossRef] 3. Nallagonda, S.; Kumar, Y.R.; Shlpa, P. Analyss of Hard-Decson and Soft-Data Fuson Schemes for Cooperatve Spectrum Sensng n Raylegh Fadng Channel. In Proceedngs of the Advance Computng Conference, Istanbul, Turkey, June 2006; IEEE: New York, NY, USA, 2017; pp Ma, Y.; Gao, Y.; Zhang, X.; Cuthbert, L. Optmzaton of collaboratng secondary users n a cooperatve sensng under nose uncertanty. In Proceedngs of the IEEE Internatonal Symposum on Personal Indoor and Moble Rado Communcatons, London, UK, 8 11 September 2013; IEEE: New York, NY, USA, 2013; pp Zhang, Y.; Xu, Y.; Wu, Q.; Feng, S.; Anpalagan, A. Near Optmal Dstrbuted Cooperatve Spectrum Sensng and Access: A Beneft-and-Compensaton Approach. In Proceedngs of the IEEE Vehcular Technology Conference, Toronto, ON, Canada, September 2017; IEEE: New York, NY, USA, 2017; pp Chen, B.; Zhang, B.; Yu, J.L.; Zhu, H. An ndrect recprocty based ncentve framework for cooperatve spectrum sensng. In Proceedngs of the IEEE Internatonal Conference on Communcatons, Pars, France, May 2017; IEEE: New York, NY, USA, 2017; pp Zhu, R.; Zhang, X.; Lu, X.; Shu, W.; Mao, T.; Jalaan, B. ERDT: Energy-Effcent Relable Decson Transmsson for Intellgent Cooperatve Spectrum Sensng n Industral IoT. IEEE Access 2015, 3, [CrossRef] 8. Benedetto, F.; Gunta, G. A Theoretcal Analyss of Asymptotcal Performance of Cooperatve Spectrum Sensng n the Presence of Malcous Users. IEEE Wrel. Commun. Lett. 2017, 99. [CrossRef] 9. Benedetto, F.; Tedesch, A.; Gunta, G.; Coronas, P. Performance mprovements of reputaton-based cooperatve spectrum sensng. In Proceedngs of the Internatonal Symposum on Personal, Indoor, and Moble Rado Communcatons, Valenca, Span, 4 8 September 2016; IEEE: New York, NY, USA, 2016; pp Dng, G.; Song, F.; Wu, Q.; Zou, Y.; Zhang, L.; Feng, S.; Yao, Y.-D. Robust Spectrum Sensng wth Crowd Sensors. IEEE Trans. Commun. 2014, 9, [CrossRef] 11. Wu, Q.; Dng, G.; Du, Z.; Sun, Y.; Jo, M.; Vaslakos, A.V. A Cloud-Based Archtecture for the Internet of Spectrum Devces over Future Wreless Networks. IEEE Access 2017, 4, [CrossRef] 12. Dng, G.; Wang, J.; Wu, Q.; Yao, Y.D.; Song, F.; Tsftss, T.A. Cellular-base-staton-asssted devce-to-devce communcatons n tv whte space. IEEE J. Sel. Areas Commun. 2015, 34, [CrossRef] 13. Ser, J.D.; Alonso, A.; Gl-Lopez, S.; Garay, M. On the desgn of an heurstcally optmzed multband spectrum sensng approach for cogntve rado systems. In Proceedngs of the 2012 IEEE 17th Internatonal Workshop on Computer Aded Modelng and Desgn of Communcaton Lnks and Networks (CAMAD), Barcelona, Span, September 2012; pp Ser, J.D.; Matnmkko, M.; Gl-López, S.; Mustonen, M. Centralzed and dstrbuted spectrum channel assgnment n cogntve wreless networks: A Harmony Search approach. Appl. Soft Comput. 2012, 12, [CrossRef] 15. Tragos, E.Z.; Zeadally, S.; Fragkadaks, A.G.; Srs, V.A. Spectrum Assgnment n Cogntve Rado Networks: A Comprehensve Survey. IEEE Commun. Surv. Tutor. 2013, 15, [CrossRef] 16. Sobron, I.; Martns, W.A.; de Campos, M.L.R.; Elez, M. Incumbent and LSA Lcensee Classfcaton through Dstrbuted Cogntve Networks. IEEE Trans. Commun. 2016, 1, [CrossRef]

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