Adaptive Phase Synchronisation Algorithm for Collaborative Beamforming in Wireless Sensor Networks

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1 213 7th Asa Modellng Symposum Adaptve Phase Synchronsaton Algorthm for Collaboratve Beamformng n Wreless Sensor Networks Chen How Wong, Zhan We Sew, Renee Ka Yn Chn, Aroland Krng, Kenneth Tze Kn Teo Modellng, Smulaton & Computng Laboratory, Materal & Mneral Research Unt School of Engneerng and Informaton Technology Unverst Malaysa Sabah Kota Knabalu, Malaysa msclab@ums.edu.my, ktkteo@eee.org Abstract Collaboratve beamformng (CB) s a cooperatve technque that utlzes a group of dstrbuted wreless nodes to collectvely transmt a common message wth proper phase weghts to an ntended drecton. As a result, CB sgnfcantly extends the communcaton range of the sensor node n wreless sensor networks (WSNs). Each sensor node n CB has an ndependent local oscllator. It becomes a vtal problem to acheve CB as the dstrbuted nodes are unaware of ther phase relatonshp. Therefore, an effcent phase synchronsaton algorthm s needed as the dstrbuted nodes are unaware of ther phase relatonshp. In ths paper, an teratve phase synchronsaton algorthm usng (1+1)-evoluton strategy (ES) s proposed to acheve CB n WSNs. Evaluatons have been carred out through smulaton and the results show that the proposed algorthm s more energy effcent n comparson to the exstng phase synchronsaton algorthm. Keywords-wreless sensor networks; collaboratve beamformng; phase synchronsaton I. INTRODUCTION Collaboratve beamformng (CB), also referred to as dstrbuted beamformng [1], s a beamformng based transmsson technque n wreless sensor networks (WSNs). Va CB, a group of the dstrbuted wreless sensor nodes ntrnscally acts as a set of vrtual antenna array and transmt a common message towards the drecton of the desred destnaton that s located n the far-feld. Due to the general property of beamformng, a hgh sgnal to nose rato (SNR) gan that s proportonal to the number of antenna elements s produced [2]. Therefore, CB s able to transmt sgnal over a long dstance that s outsde the transmsson range of a sngle sensor node. Moreover, CB reduces the transmsson energy requred for each sensor node by spreadng the requred transmsson energy among sensor nodes. The advantages of CB have motvated many researchers to study the practcablty mplementaton of CB n WSNs [3]. Extended work s carred out to understand the fundamental of CB n the context of WSNs. The far-feld beampattern of CB s studed by usng the random antenna array theory [4]. The analyss for Gaussan nodes dstrbuton was further studed by [5]. Both studes show that the beampattern produced by CB has a narrow manlobe n the drecton of the desred destnaton and the sdelobe can be reduced by addng more sensor nodes to perform CB. Node selecton method s also proposed to optmse the beampattern of CB [6]. Several challenges are countenanced n realzng CB such as nformaton sharng among dstrbuted sensor nodes, frequency and phase synchronsaton at the recever. Among these problems, the most crucal problem n the mplementaton of CB s achevng phase synchronsaton among the dstrbuted sensor nodes. Mudumba et al. has proposed one-bt feedback algorthm where phase synchronsaton s acheved teratvely n closed loop form [7]. Ths algorthm requres each sensor node to adjust ts phase settng wth random phase perturbaton n each tme slot. If the adjustment has shown mprovement of beamformng gan, the phase settng s adopted. Otherwse, the phase settng s dscarded. The convergence behavour of the synchronsaton algorthm was analysed n [8]. Varous mprovement works on one-bt feedback phase synchronsaton algorthm have been proposed [9, 1, 11]. All enhance closed loop algorthm have the same am, whch s to reduce the number of tme slot to acheve phase synchronsaton. Ths s because the crtcal drawback of ths algorthm requres large number of teratons to acheve an acceptable level of phase synchronsaton. Ths wll ncrease the energy consumpton for tranng procedure. Moreover, most algorthms used same step sze of phase perturbaton across tme slots. The behavour of changng the sze of the phase perturbaton at each tme slot s stll unexplored. Evolutonary algorthms are wdely appled n varous applcatons because t s a sutable searchng strategy [12, 13]. The evolutonary algorthm s random searchng feature can potentally apply nto CB. In ths paper, (1+1)-evoluton strategy (ES) s selected to adaptvely change the sze of the phase perturbaton at each tme slot. s mplemented as a search soluton to search for the correspondng phase settng n each sensor node durng phase synchronsaton. s able to search through large soluton space for the maxmum output. The rest of the paper s organsed as follows: In secton II, the system model of CB n WSNs s descrbed. In secton III, the conventonal one-bt feedback phase synchronsaton algorthm presented n [7] s revewed. A novel phase synchronsaton algorthm usng evoluton strategy (ES) s /13 $ IEEE DOI 1.119/AMS

2 ntroduced n secton IV. The smulaton result and dscusson are presented n secton V. Lastly, the concluson s gven n secton VI. II. SYSTEM MODEL In ths paper, the wreless communcaton system s consttuted by N number of sensor nodes whch collaboratvely transmt a modulated narrowband message sgnal m(t) to the recever. The system model whch conssts of phase components of the receved sgnal at the recever s llustrated n Fg. 1. The system presumes carrer frequency synchronsaton s acheved by usng the master-slave archtecture [1]. Therefore, all sensor nodes are supposed to modulate ther transmssons usng a rado frequency wth the same carrer frequency, f c. The carrer sgnal transmtted by the th sensor node s explaned n (1). The goal of the phase synchronsaton process s to adjust the complex gan of the sensor node at each tme slot. Therefore, t s mportant to descrbe the phase components n a tme-slot fashon. The phase of the transmtted sgnals from sensor nodes at perceved at the recever at tme slot th s expressed n (3). Φ = ϕ [ + γ + ψ [ (3) Due to small tmng msmatches between sensor nodes, the appearance of the narrowband message s gnored [3]. Moreover, the nose power s consdered farly small n comparson wth the sgnal power at the recever. Hence, the receved sgnal strength (RSS) n tme-slotted fashon s defned n (4). ( ) ( j ( 2π f c t +γ ) s t = R e ) (1) c RSS = N = 1 a h e Φ [ ) ( (4) where R s the real part operator and ndcate an unknown phase offset on th sensor node due to dstrbuted manner of the system. In order to make far comparson between the conventonal algorthm and the proposed algorthm, the same key assumptons n [7] are used. Sensor nodes are assumed to have equal transmt power a =1. All sensor nodes modulate the message sgnal m(t) wth the carrer sgnal s c (t). The channel response between th sensor node and recever s H(f)= h e ( ). It s assumed constant durng the phase synchronsaton process. For smplcty, channel coeffcent, h s assumed to be unty. s the channel phase response between the th sensor node wth the recever. Both and are also unformly dstrbuted wthn [,2 ) for each sensor node. Both phase components and are unknown to both sensor node and recever. An adaptve phase component s appled on th sensor node to acheve phase coherence n the drecton of the recever. The total receved sgnal s descrbed n (2). r( t) = R( m( t) e j(2πf N ct ) j( ϕ + γ + ψ ) = a h e 1 ) + n( t) Where n(t) s an addtve nose whch s model as a complex Gaussan random varable, wth zero mean and varance 2. Fgure 1. System model for feedback phase synchronsaton. (2) III. CONVENTIONAL ONE-BIT FEEDBACK PHASE SYNCHRONISATION ALGORITHM The conventonal one-bt feedback () phase synchronsaton algorthm was frst ntroduced n [7]. The algorthm can be expressed as follows: 1) A random perturbaton phase, n =± s added to each of the sensor node The best beamformng phase s recorded n memory. 2) The new adaptve phase component, [ s used to perform beamformng. 3) The new RSS, RSS[ s measure by the recever, the best RSS s updated nto the memory, RSS best [n+1]=max(rss [ ], RSS[ ]). 4) One-bt nformaton that ndcates the RSS ether has been mproved or not s feedback to all sensor node. 5) If RSS[ ]> RSS [ ], all sensor nodes update ther best known phases as n n [, otherwse, the new random pertubaton s dscarded and n n The procedure s repeated n the next teraton or tme slot. After many teratons, phase synchronsaton can be acheved. The detaled verson of the algorthm can be found n [7]. IV. PROPOSED PHASE SYNCHRONISATION ALGORITHM A. (1+1)-Evoluton Strategy s an optmsaton technque that was nspred by the deas of bologcal adaptaton an evoluton. utlses natural problem-dependent representatons such as mutaton, and recombnaton as search operators. However, recombnaton operator s not sutable for CB applcaton n WSNs due to ts costly energy requrement for the abundance of nformaton exchange among sensor nodes. Therefore, only mutaton operator wll be used as search operator for phase synchronsaton. The framework of (1+1)- ES s llustrated n Fg

3 Start Intalsaton Selecton operator Mutaton operator Termnaton condton? End Yes Fgure 2. Framework of (1+1)-evoluton strategy. The detals explanaton of the s summarsed as follows: a) Intalsaton: The phase synchronsaton process can be referred to as an optmsaton problem that search for the best phase settng of the sensor node to produce maxmum RSS. The populaton s ntalzed before the optmsaton s started. A populaton s referred to a set of soluton n the optmsaton problem. For the case of phase synchronsaton, the phase settng of all sensor nodes n a sngle tme slot s referred to as a sngle soluton for the populaton. For the purpose of provdng suffcent coverage on the search-space, the new offsprng soluton must be at least separated wth a certan dstance from ts parent soluton. b) Selecton operator: Selecton operator s mplemented to select the best soluton from a set canddate solutons n a populaton. Usually, ftness functon or objectve functon s requred to evaluate the soluton. As a populaton only conssts of a sngle soluton, selecton among ndvdual solutons n a populaton s mpossble. Therefore, the selecton operator s operatng between the parent soluton and the new offsprng soluton. If the new offsprng s better than the parent soluton, the new offsprng soluton s declared as the new parent soluton. Ths mean the new soluton s a better soluton n comparson wth the prevous soluton. Otherwse, the old parent soluton s set as the new parent soluton due to the newly produced offsprng s strctly worse than the prevous soluton. Ths selecton process s smlar to the procedure of for step 3 to step 5 where RSS s used as the objectve functon for the selecton. c) Mutaton operator: The selected ndvdual soluton s declared as new parent for the purpose of creatng new No offsprng for next generaton. Mutaton operator s ncorporated n the phase perturbaton step sze durng the phase synchronsaton process. The ntegraton of the mutaton operator n the phase perturbaton step sze can be mathematcally expressed as n (5). δ [ δ ~ N(, σ ) = (5) o where n denotes the phase perturbaton step sze for the th sensor node n tme slot of n. represents the ntal phase perturbaton step sze for all sensor nodes. ~N(, ) denotes a random number that s generated followng the Gaussan dstrbuted random functon wth standard devaton,. The mutaton operator used here s also called the Gaussan operator [14]. Typcally, the mutaton operator functons as a search operator that allows the fndng of the search-pont n the search-space regon that are not yet populated. The value of the standard devaton,, s also the mutaton value of the mutaton operator. Large mutaton value can cause large changes n the soluton space. It acts as exploraton mechansm and explores n the soluton space. However, small mutaton value acts as explotaton mechansm and explots n the soluton space. Hence, t s an arbtrary approxmaton of the optmum soluton. d) Termnaton condton: The common termnaton condtons s when the set teraton number s reached, the set tme of the optmsaton process s reach, a soluton has not mprove after a set of teratons operator s run and also the mnmum acceptable threshold s acheve. B. Algorthm Descrpton Smlar to conventonal one-bt feedback phase synchronsaton algorthm, the proposed phase synchronsaton algorthm also requred one-bt feedback from the recever. The pseudo code of s summarzed n Table I and exploraton and explotaton mechansm s shown n Table II. The detals of the pseudo code are expressed as follow: 1) Intalse a counter, success rule probablty value P r, explotaton rule probablty P e, constant value, c wth condton <c<1, and tral number m. 2) A random perturbaton phase, n = ~N(, ) s added to each of the sensor node The best beamformng phase s recorded n the memory. 3) The new adaptve phase component, [ s used to perform beamformng. 4) The new RSS, RSS[ s measure by the recever, and the best RSS s updated nto the memory, where RSS best [n+1]=max(rss [ ], RSS[ ]). 5) One-bt nformaton that ndcates whether the RSS ether has been mproved or not s feedback to all sensor node. 6) If RSS[ ]>RSS [ ], all sensor nodes update ther best known phases as = n n [ and the counter wll be ncrease by one. 291

4 7) If RSS[ ]< RSS [ ], all sensor nodes nverse back to prevous best known phases n A revert drecton of the ntal phase s used to generate a new random perturbaton phase [n+1] for the next tme slot. 8) For every m teraton, successful mutaton p s =counter/m s generated. Based on p s, ether exploraton or explotaton mechansm s appled. 9) The process s repeat steps 2 to 8 untl termnaton crtera s acheved. TABLE I. PSEUDO CODE FOR (1+1)-EVOLUTION STRATEGY ALGORITHM Intalsaton: counter = ; RSS best [ ] = Set: P r; P e; c and m Iterate: At sensor node sde 1. δ[ = δo ~ N(, σ ) 2. ϕ [ = φ[ + δ[ (Adaptve phase for beamformng) At recever sde: N ( Φ ) 3. Calculate RSS[ = e [ = 1 4. If RSS[ > RSSbest[ 5. RSS best [ n + 1] = RSS[ One-bt feedback to sensor node (feedback bt = 1) 6. Else 7. RSSbest [ n + 1] = RSSbest[ One-bt feedback to sensor node (feedback bt = ) 8. End f At sensor nodes sde: 9. If feedback bt =1 1. ϕ [ = φ[ + δ[ 11. counter = counter φ, best = ϕ[ n + 1] = φ[ + δ[ 13. Else 14. ϕ [ n + 1] = φ, best 15. δo = δo 16. End f 17. Check ether exploraton or explotaton mechansm shoud apply. (Table II.) 18. End Iterate TABLE II. PSEUDO CODE FOR EXPLORATION AND EXPLOITATION MECHANISM Exploraton and Explotaton Mechansm 1. If (n mod m)= 2. If counter m > Pr 3. σ = σ / c 4. Else f counter m < Pr 5. σ = σ c 6. End f 7. counter = 8. End f V. SIMULATION RESULT AND DISCUSSION The algorthm n Secton IV s smulated for the purpose of verfyng the functonalty and valdty of the proposed phase synchronsaton algorthm usng. Before dscussng on the performance evaluaton of the phase synchronsaton algorthm, ths secton prefaces wth the dscusson on the proper selecton of the tral number and success rule probablty selecton that are used to control the exploraton and explotaton mechansm. Smulaton results of dfferent values of tral number and success rule probablty are used to analyse the convergence behavour. The ntal phase perturbaton used n the smulaton s set as δ o = π 1. The constant value, c s set to.85 as suggested n [15]. The number of trals m should be set to be as small as possble. A large number of trals wll cause delay n applyng the exploraton and explotaton mechansm nto phase perturbaton. Moreover, the number of trals must be larger than the denomnator of the success rule probablty, P r. Ths s to avod the lost of balance between exploraton and explotaton features. The probablty of applyng exploraton wll sgnfcantly reduce as the denomnator of the success rule probablty s much larger than the tral number. Therefore, the parameter range of the smulaton s from three to eleven for the tral number, and from one to ten for the denomnator of the success rule probablty. The detals of the smulaton results are summarzed n Table III. The smulaton results show that there s a wde range of parameter settngs that s capable of achevng the requred RSS wth for a small range of total tme slot. Ths reveals the robustness of algorthm, as t has small msmatches wth dfferent parameter settngs. The results also show that the algorthm usng 8 as tral number and a success rule probablty of P r = 1 3 requre a mnmum average of tme slot to acheve phase synchronsaton. Therefore, ths combnaton of parameters s the most sutable combnaton value for. TABLE III. AVERAGE TIME SLOTS REQUIRED TO ACHIEVE 9 % RSS FOR DIFFERENT SUCCESS RULE PROBABILITY AND TRIAL NUMBER P r Average tme slots usng dfferent tral number m

5 Next, the effect of choosng dfferent ntal phase perturbaton step szes for and s studed. Smulaton s generated usng sensor nodes that are randomly deployed. All sensor nodes are assumed to be transmttng sgnal wth unty ampltude. The smulaton results of both algorthms usng dfferent ntal phase perturbaton step sze s shown n Fg. 3. The x-axs of the smulaton result n Fg. 3 s the ntal phase perturbaton step sze and the y axs s the average number of tme slots requred to acheve RSS of at least 9 %. Monte Carlo smulaton s conducted to generate ths statstcal result. Based on the results, t s shown that has an optmum ntal phase perturbaton step sze that wll acheve the correspondng RSS. However, s nsenstve to the ntal phase perturbaton step sze. Moreover, algorthm shows a better result n convergence speed as the mnmum requred tme slots s 594 whle requred a mnmum of 798 tme slots. To further demonstrate the performance of the both algorthms, average performance of and s compared. The average performance s generated usng Monte Carlo wth 1 runs of smulaton. In order to compare the results farly, optmum phase perturbaton step sze for each algorthm s selected. By referrng to Fg. 3, optmum ntal phase perturbaton step sze to acheve 9 % RSS for s δ o = 3.2π 1. For, the optmum ntal phase perturbaton step sze s δ o = π 1. The total number of sensor nodes used n the smulaton s N=1. The smulaton results of the average performance for both algorthms are shown n Fg. 4. The results show that has a faster convergence property compared to CB1F. Receved Sgnal Strength (RSS) Tme Slots Fgure 4. Smulaton results of the average performance for dfferent algorthm. Usng N=1 of sensor node, the smulaton for mnmum number of tme slots that s needed to acheve varous values of RSS s smulated. The smulaton results are plotted as n Fg. 5. The correspondng values of the ntal phase perturbaton step sze that result n Fg. 5 s shown n Fg. 6. Monte Carlo smulaton s conducted to generate the both statstcal results. Based on Fg. 5, t shows that approach s able to acheve the correspondng RSS wth mnmum number of requred tme slots that s less than the mnmum number requred for the approach. 2 Average Number of Tme Slots Phase Perturbaton Step Sze, δ x(π/1) Fgure 3. Smulaton results of dfferent algorthm under dfferent ntal phase perturbaton step sze. Average Number of Tme Slots Receved Sgnal Strength (RSS) % Fgure 5. Smulaton results of mnmum number of tme slots at dfferent RSS. 293

6 δ for Mnmum Tme Slots x(π/1) Receved Sgnal Strength (RSS) % Fgure 6. Optmum ntal phase perturbaton step sze that acheves dfferent RSS percentage wth mnmum tme slots. VI. CONCULSIONS A new phase synchronsaton algorthm usng s proposed to acheve phase coherence at the recever. The new proposed algorthm utlses exploraton and explotaton mechansm of to search for the optmum phase settng among sensor nodes. The algorthm has faster convergence speed of phase synchronsaton n comparson to the algorthm n the lterature. Smlar to, algorthm only requres one-bt feedback from the recever n each tme slot. Therefore, mantans the advantage of. Importantly, no addtonal hardware s requred for the mplementaton of ths algorthm. For future work, nvestgaton and the desgn of an algorthm wth the ablty to track n tme-varyng channel should be consdered. ACKNOWLEDGMENT The authors would lke to acknowledge the fnancal assstance of the Research Acculturaton Grant Scheme (RAGS), grant no. RAG5-TK-1/212, and the Unverst Malaysa Sabah Postgraduate Scholarshp Scheme. REFERENCES [1] G. Barrac, R. Mudumba, and U. Madhow, Dstrbuted Beamformng for Informaton Transfer n Sensor Networks, Proc. of Thrd Internatonal Symp. on Informaton Processng n Sensor Networks, 24, pp , do: 1.119/IPSN [2] J. Uher, A.Wysock, and B. J. Wysock, Revew of Dstrbuted Beamformng, Journal of Telecommuncatons and Informaton Technology, vol 1, no. 1, 211, pp [3] R. Mudumba, G. Barrac, and U. Madhow, On the Feasblty of Dstrbuted Beamformng n Wreless Sensor Networks, IEEE Trans. Wreless Communcatons, vol. 6, no. 4, pp , 27, do: 1.119/TWC [4] H. Ocha, P. Mtran, H. V. Poor, and V. Tarokh, Collaboratve Beamformng for Dstrbuted Wreless Ad Hoc Sensor Networks, IEEE Trans on Sgnal Processng, vol. 53, no. 11, 25, pp , do: 1.119/TSP [5] M.F.A. Ahmed, and S.A.Vorobyov, Collaboratve beamformng for Wreless Sensor Networks wth Gaussan Dstrbuted Sensor Nodes. IEEE Trans on wreless communcaton, vol. 8, no. 2, 29, pp , do: 1.119/TWC [6] C. H. Wong, Z.W. Sew, M.K. Tan, R.K.Y. Chn, K.T.K. Teo, Optmzaton of dstrbuted and collaboratve beamformng n wreless sensor networks, Proc. 4th Internatonal Conference on Computatonal Intellgence, Communcaton Systems and Networks, pp , 212, do: 1.119/CICSyN [7] R. Mudumba, J. Hespanha, U. Madhow, and G. Barrac, Scalable Feedback Control for Dstrbuted Beamformng n Sensor Networks. Proc. of Internatonal Symp. on Informaton Theory. 25, pp , do: 1.119/ISIT [8] C. Ln, V. V. Veeravall, and S. P. Meyn, A Random Search Framework for Convergence Analyss of Dstrbuted Beamformng wth Feedback. IEEE Trans on Informaton Theory, vol. 56, no. 12, 21, pp , 1.119/TIT [9] S. Song, J. Thompson, P. J. Chung, and P. M. Grant, Improvng the One-bt Feedback Algorthm for Dstrbuted Beamformng, IEEE Wreless Communcatons and Networkng Conference, 21, pp. 1-6, do: 1.119/WCNC [1] I. Thbault, G. E. Corazza, and L. Deambrogo, Random, Determnstc, and Hybrd Algorthms for Dstrbuted Beamformng, 5th Advanced satellte multmeda systems conference and the 11th sgnal processng for space communcatons workshop. 21, pp , do: 1.119/ASMS-SPSC [11] I. Thbault, G. E. Corazza, and L. Deambrogo, Phase Synchronzaton Algorthms for Dstrbuted Beamformng wth Tme Varyng Channels n Wreless Sensor Networks. 7th Internatonal Wreless Communcatons and Moble Computng Conference, 211, pp , do: 1.119/IWCMC [12] K. T. K. Teo, W. Y. Kow, Y. K. Chn, Optmzaton of Traffc Flow wthn an Urban Traffc Lght Intersecton wth Genetc Algorthm, Proc. 2nd Internatonal Conference on Computatonal Intellgence, Modellng and Smulaton, 21, pp , do: 1.119/CIMSM [13] Z. W. Sew, C. H. Wong, C. S. Chn, A. Krng, K. T. K. Teo. Cluster Heads Dstrbuton of Wreless Sensor Networks va Adaptve Partcle Swarm Optmzaton, Proc. 4th Internatonal Conference on Computatonal Intellgence, Communcaton Systems and Networks, 212, pp , do: 1.119/CICSyN [14] Y. Lu, Evaluatons of Mutatons n Evolutonary Programmng, 2nd Internatonal Symp. on Aware Computng, 21, pp , do: 1.119/ISAC [15] H. G. Beyer, and H. P. Schwefel, Evoluton Strateges: A Comprehensve Introducton, Journal Natural Computng, vol 1, no. 1, 22, pp