On the Feasblty of Receve Collaboraton n Wreless Sensor Networs B. Bantaleb, S. Sgg and M. Begl Computer Scence Department Insttute of Operatng System and Computer Networs (IBR) Braunschweg, Germany {behnam, sgg, begl}@br.cs.tu-bs.de Abstract In ths paper, a new type of collaboraton n wreless sensor networs (WSN) s suggested that explots array processng algorthms for better recepton of a sgnal. For receve collaboraton, the transmsson power durng ntra-cluster transmssons decreases at the expense of ncreasng the ntercluster communcatons. It s shown that, as a result of usng receve collaboraton, the destnaton node s power consumpton and the networ nterference level decrease whch consderably mprove the data transmsson performance and networ lfe tme. Ths method s applcable both for cluster based and noncluster based WSNs. In order to show the feasblty of receve collaboraton and also to evaluate ts performance, an LS-CMA based channel equalzaton scheme s also smulated whch s performed durng cooperaton between cluster nodes. The comparson of the output BER between random dstrbuted and unform lnear dstrbuted cases shows a good performance of receve collaboraton. Keywords-receve collaboraton; wreless sensor networ; channel equalzaton I. INTRODUCTION Lmted lfetme of WSNs due to relatvely small and nonrenewable batteres of ther nodes maes power consumpton a prmary objectve of networ desgn [1]. Wth transmt collaboraton t s possble to reduce the power requred for transmsson by a sngle node by, for nstance, supermposng transmt sgnals from varous nodes. As a result of usng transmt collaboraton [2, 3], a group of nodes cooperate together to transmt a sgnal wth lower power. The overall transmsson power requred s dvded among dstnct nodes by ths approach. Although the supermposton of cooperatng nodes ncrease the computatonal load, ths approach s suted to postvely affect the WSNs lfetme, snce communcatons of the nodes are generally more energy consumng than ther computatons [1]. There are varous methods to beneft from transmt collaboraton. In [1] and [3], transmt collaboraton s suggested as dstrbuted or collaboratve beamformng. There, after ntroducng the advantages of usng beamformng n WSN, challenges regardng the mplementaton of ths scheme are consdered. Accordng to ths technque, neghborng nodes form a vrtual array and cooperate to sense and transmt envronmental parameters of nterest. It s shown that, n the case of usng dstrbuted beamformng, the power consumpton per node decreases consderably. Of course, dfferences between vrtual arrays n WSNs and array sensors cause some challenges, especally durng synchronzaton, whch are dscussed n [4]. Despte transmt collaboraton, some tass such as the recepton of mpngng sgnals are performed neffcently n ths scheme. Also, the approach to dstrbuted transmt beamformng detaled n [1] and [4] suffers from a comparably long and therefore energy consumng teratve synchronzaton process n whch nodes are constantly transmttng to a remote recever. In ths paper, another verson of collaboraton s ntroduced. We consder receve collaboraton n whch cluster nodes cooperate as a vrtual array for better recepton of mpngng sgnals. In partcular, Informaton about a sgnal receved by dstrbuted nodes over dstnct channels s aggregated and combned for the recepton. Receve collaboraton can be used n dfferent forms such as channel equalzaton [5] or blnd beamformng [6]. The ey parameter to determne whch of these schemes can be mplemented as receve collaboraton depends on the type of receved sgnals as well as accessble nformaton about the destnaton and the vrtual array. In ths paper we show the feasblty of receve collaboraton n WSNs. The problem of receve collaboraton s analyzed for a straghtforward channel equalzaton problem. The dscusson s organzed as follows. In the next secton transmt collaboraton s revewed brefly. After that, the dea of receve collaboraton n WSNs s ntroduced n secton III. A mathematcal analyss of the receve collaboraton problem as well as smulaton results are presented n sectons IV and V, respectvely. Fnally, secton VI concludes ths paper. II. TRANSMIT COLLABORATION Transmt collaboraton n WSNs usually nvolves technques n whch some sensors cooperate to send ther common data. Accordng to ths general defnton, transmt collaboraton ncludes dfferent schemes such as dstrbuted beamformng [1] and [3] and vrtual mult-nput mult-output (MIMO) systems [7]. In vrtual MIMO schemes the transmt data s encoded wth a certan space-tme code (whch s selected accordng to the node and transmsson channel characterstcs) and transmtted va cooperatng nodes to a destnaton.
In dstrbuted beamformng, several nodes cooperate to steer a drectve beam to a certan destnaton. The ey pont of dfferent beamformng schemes s havng synchronous nodes and applyng proper phase shfts accordng to the drecton of the destnaton. Transmt sgnals are combned constructvely at the destnaton. However, n WSNs, the use of ndvdual local oscllators causes devatons n the phase synchronzaton process. Moreover, random dstrbuton of nodes and unnown drecton of the destnaton node mae t mpossble for cluster nodes to estmate proper phase offsets on ther own. The synchronzaton and modfcaton of the phases of the transmt sgnals for beamformng s usually performed together. Dfferent closed- and open-loop synchronzaton schemes are presented n [4]. III. RECEIVE COLLABORATION Receve collaboraton ncludes technques n whch several nodes cooperate to mprove the recepton of a sgnal. Accordng to ths defnton, receve collaboraton contans a wde range of schemes to ncrease the array gan n a certan drecton [8], blnd beamformng to mprove the recepton of sgnals wth certan characterstcs (maxmum sgnal to nose rato [6], constant modulus [5] or cyclo-statonary [8] property), channel equalzaton to remove or at least decrease undesred transmsson channel effects [5] and MIMO data recepton [9]. Durng receve collaboraton the mpngng sgnal s receved by all cooperatng nodes. In order to eep the battery storage balanced among all recevers, one node s selected randomly to process the receved data. Dependent on the networ structure, dfferent methods may be appled to mplement ths random process. We propose that after recevng a sgnal, nodes radate a specal collaboraton sgnal after a random dle tme. These contan the node-id. The frst node whose sgnal s receved s selected as the processor node. In dense networs whose nter-node dstances are relatvely short, the tme delays of nter-cluster transmssons are neglectable, but n some stuatons the synchronzaton step s necessary due to networ densty. To synchronze the cooperatng nodes, the processor node broadcasts a message and receves feedbacs from cooperatng nodes. The acheved tme delays of the local communcatons from the feedbacs are used to synchronze the aggregated sgnals by the processor node. The processor node collects all receved data from other nodes and performs the partcular receve collaboraton scheme. In most array processng schemes, the processng load decreases when t converges to ts optmum weghtng coeffcents. After convergence, t just needs to update ts weghtng coeffcents due to the transmsson channel varaton. Therefore, receve collaboraton has a reasonably low computatonal load. More especally, for CDMA based networs, aggregaton of the entre receved sgnals by the cooperatng nodes ncreases the memory demand of the processor node. Partally aggregaton of the receved sgnals or dstrbuted sgnal Fgure 1. Geometrcal dstrbuton of the cluster and destnaton nodes combnaton, n whch sgnal aggregaton s performed n several steps, can decrease the memory need of the processor node. Generally, t can be sad that receve collaboraton s a way to reduce the power per symbol durng ntra-cluster transactons. Although receve beamformng causes an ncrease n the nter-cluster communcatons, t effcently reduces the power consumpton of the remote node and the nterference level for other nodes. Decreasng the nterference level s also a way to save energy n the networ. For a fxed detecton threshold, decreasng the nterference level has the same result on the receved SNR as ncreasng the sgnal power. Therefore, t s possble to save further energy by transmsson at reduced power. One lmtng parameter n the expanson of WSNs s ncreased transmsson power because of long dstances between some clusters and remote node. Receve collaboraton may be suggested as a soluton due to the ablty of array processng schemes to gan a certan performance wth lower SNRs, The queston whch arses s when receve collaboraton should be used. Durng the synchronzaton of beamformng schemes [4], there are dfferent transactons between destnaton and cluster nodes. As an example, n one of the synchronzaton schemes, referred to as full-feedbac closedloop, the destnaton broadcasts a sgnal. Cluster nodes receve t and transmt bac to the destnaton. The destnaton node fnally estmates proper phase shfts and sends t bac to each node. In the case of M nodes n a networ, consequently, the destnaton node receves M dfferent sgnals, modfes and returns them. Ths leads to a severe computatonal complexty and power consumpton for the destnaton node. The supermposton of transmtted sgnals constructvely combnes at the destnaton, when cluster nodes transmt wth phase shfts equal to the dfference between the phases of ther receved sgnals and that of a reference sgnal. Accordng to the recprocty theorem, when the transmsson channel does not affect the receved sgnal severely, proper phase shfts are calculated by selectng a cluster node as the reference and comparng the sgnal of the other nodes wth ths node s sgnal. The resultng constant offset n the phase shfts has no effect on the beamformng process. However, when the receved sgnal s dstorted such that the above method s mpossble, the reference sgnal may be acheved by the use of channel equalzaton schemes.
Receve collaboraton can also be used to ncrease the drectvty of a vrtual array to mprove the recepton qualty of an mpngng sgnal. Based on the recprocty theorem, t s possble to use the phase shfts whch are estmated durng transmt beamformng [4] to steer a drectve beam to the destnaton. These are two possble examples of receve collaboraton applcatons but alternatve mplementatons are also possble. Each WSN whose nodes are able to cooperate together can beneft from receve collaboraton. Snce the neghborng nodes do not need a manager node, receve collaboraton s applcable n both cluster-based and non cluster-based networs. It s scalable and consderng ths feature for WSNs does not ncrease the sensor nodes complexty. IV. COLLABORATIVE CHANNEL EQUALIZATION In ths secton the receve collaboraton problem s presented as a channel equalzaton scheme. A. Sgnal and Channel Model The assembly of nodes s schematcally llustrated n Fg. 1. In ths model, M nodes are dstrbuted unformly at random on a ds of radus R. Provded that all nodes receve lne of sght (LOS) rays of the destnaton node, there s no lmtaton regardng the poston of the sensor nodes. It s also assumed that nodes do not possess any nformaton about ther postons or the destnaton node s drecton. A mult-path Raylegh fadng channel [10] wth addtve whte Gaussan nose (AWGN) s consdered. Although n ths model mpngng sgnals are receved by the nodes after scatterng, reflecton or dffracton from the objects of the transmsson channel, for ease of presentaton some transmsson channel effects such as angular spreadng or Doppler frequency shft are neglected. These phenomena happen due to the hgh densty of scatterng objects n urban envronments and the moblty of the transmsson channel elements, transmtter or receve, respectvely. To model the transmt sgnal, we assume a data sequence b wth rate R b spreaded by a spreadng code c (here we use the Walsh-Hadamard code) wth length L. The spreaded c sequence wth bt rate R c = Lc R s mapped nto a symbol b constellaton and s up converted n the modulaton bloc. Dfferent modulaton schemes can be used n ths bloc. Although the channel equalzaton scheme whch s used n ths paper was orgnally suggested for constant envelope sgnals, t can be used also for lmted-value varable-envelope modulatons such as ASK or hgher orders of QAM. The destnaton node s antenna radates the transmt sgnal s n. Assumng a rather flat envronment wthout consderable scatterers and consequently neglgble mult-path effect, receved sgnals by cluster nodes at tme can be wrtten as 1 2 M [ x x x ] x (1) = here, x, the baseband equvalent of the revved sgnal of the -th node at tme, s x = A s e jϕ + n (2) In ths formula, φ s the phase shft because of the dstance between destnaton node and -th cluster node, A s the Raylegh fadng coeffcent, and n s the addtve nose for the -th node. As mentoned before, after recevng the sgnal, a node s selected as the processor node that gathers all receved sgnals from the other nodes after synchronzaton (f s necessary) and then apples the channel equalzaton scheme. Fnally, ths node generates a 1 M weght vector w, to form the output as H y = w. x for each tme nstance such that the channel effects are partally removed from ths sgnal. B. Channel Equalzaton Algorthm The major goal of channel equalzaton algorthms s to remove or at least decrease the undesred effects of the transmsson channel (fadng and nose). Most channel equalzaton schemes n dgtal communcaton beneft from the constant envelope property of dgtal modulated sgnals. Least squares Constant Modulus Algorthm (LS-CMA) [5] s one of the algorthms we use to equalze the transmsson channel durng cooperaton between cluster nodes to exhbt the effcency of receve collaboraton. Accordng to ths algorthm, the weght vector w s generated durng mnmzaton of the LS-CMA cost functon J w wth respect to w. The cost functon s of the form ( ) ( ) = E 2 [( 1) ] 2 J w y (3) here, E[.] denotes the expected value. Accordng to the stochastc gradent method, the weght vector n each tme nstant s updated based on ts prevous value and the gradent of the cost functon. In practce, the weght vector s updated by the followng recursve relaton 2 ( y ) y w = 1 (4) + 1 w μx where μ s the step sze that controls the convergence rate of the algorthm. It can be seen n (3), (4) that LS-CMA does not need the relatve of the nodes. Due to ts smplcty, ths algorthm s well suted for wreless sensor networs. V. SIMULATION RESULTS In ths secton, the feasblty of receve collaboraton s nvestgated n smulatons by usng the LS-CMA based channel equalzaton scheme to mprove the qualty of a receved sgnal. A data sequence of 250 bts s spreaded wth a Walsh- Hadamard code wth length 64. Although spreadng the transmt sequence s not necessary, t s helpful n our
Fgure 2. Ponts of nterest to calculate BER n the recever structure smulatons. We use BPSK unless another modulaton scheme s mentoned. In most of the smulatons, t s assumed that M = 25 nodes cooperate for channel equalzaton (unless another value s mentoned). In order to smulate receved sgnals, assumng ndependent transmsson channels between destnaton and cluster nodes, M vectors contanng L (length of the sgnal after spreadng and modulaton) Raylegh random varables are generated as the channel coeffcents. These vectors are multpled by the modulated sgnal. The addtve nose whch s also a set of M vectors wth length L contanng zero mean Gaussan random varables wth varance equal to 1, add to the receved sgnal. Fnally, dependent on the dstance between destnaton and each ndvdual cluster node, proper phase shfts are calculated and appled. The bloc dagram n Fg. 2 llustrates the sgnal processng flow. The four sgnals of nterest are: S 1 : Before channel equalzaton and after despreadng, S 2 : After channel equalzaton and despreadng, S 3 : Before channel equalzaton and despreadng, S 4 : After channel equalzaton and before despreadng. In dgtal communcaton, BER s a parameter well suted for demonstraton and comparson. We utlzed t as the major parameter to evaluate our smulatons. Smulaton results represent medan values acheved n 500 smulatons. Frst, the ablty of LS-CMA to extract dfferent symbols and concentrate them around ther orgnal postons s nvestgated. Fg s 3 and 4 represent S 3 and S 4, respectvely. In order to develop a better understandng of the performance of a LS-CMA based equalzer, these sgnals are llustrated before detecton. As observed n these two fgures, LS-CMA can effcently mtgate the channel effects by concentratng the symbols around ther orgnal postons (+1, -1 n BPSK). For ths scenaro, the correspondng BER to Fg's 3 and 4 are 0.3176 and 0.0133, respectvely. To obtan a more comprehensve vew of the channel equalzaton performance, the BER of the sgnals S 1 to S 4 are calculated for dfferent SNR values n Fg 5. Correspondng bt error rates of the sgnals before and after despreadng are plotted separately n Fg's 5-a and 5-b, respectvely. Moreover, the BER curves for before and after channel equalzaton are mared wth crcles and dots, respectvely. Fgure 3. Poston of the symbols n the complex plan before channel equalzaton and despreadng; to better llustraton of the results, BER's are calculated before dspreadng. Fgure 4. Poston of the symbols n the complex plan after channel equalzaton and despreadng; to better llustraton of the results, BER's are calculated before dspreadng. Fg 5 shows that when the SNR s equal or less than -9 db, channel equalzaton fals and BER s equal to ts maxmum value. For hgher SNRs, the channel equalzer wors properly and the BER of the equalzer output (S 4 ) gets less than 0.2 whle the fnal BER (S 1 ) descends to zero. Comparng the BER curves before and after equalzaton (before despreadng) shows that the equalzer performance ncreases wth ncreasng SNR. In Fg 6 the effect of node densty on the output BER s llustrated. In ths fgure, the BER of the equalzer output (S 4 ) for dfferent SNR values versus the number of nodes per cluster (whch s consdered as a ds wth radus 50m) s depcted. Accordng to ths fgure, to gan lower values of the BER, the node densty should be ncreased. Moreover, as the SNR gets hgher, the slope of the curves ncreases and the BER decreases wth hgher rate. Ths means that ncreasng the node densty for hgher NR s more effcent.
(a) Before despreadng (b) After despreadng Fgure 5. BER of the receved data before and after channel equalzaton and before despreadng; WSN scenaro In order to evaluate the effcency loss due to the random dstrbuton of nodes, the same scenaro as for Fg 5 s consdered based on unform lnear arrays. By comparng both cases we observed that approxmately the same results are obtaned. Ths means that a random dstrbuton of nodes n a WSN does not have negatve effect on the LS-CMA based equalzer performance. Ths was also mentoned by Chen and et al. n [11]. VI. CONCLUSION We presented an approach of applyng receve channel equalzaton n wreless sensor networs. The general problem structure was defned analytcally. For ths scenaro, we dscussed smulaton results obtaned n a Matlab-based smulaton envronment. Usng collaboraton by receve nodes affects transmsson and energy effcency postvely when compared to conventonal wreless sensor networs. The followng effects have been derved: Increase of the destnaton node s lfetme due to decreasng transmsson power durng ntra-cluster transactons, Decrease of the nterference level n the networ due to decreasng ntra-cluster transactons, Power effcency due to mplementaton of array processng schemes n the clusters, Ablty to expand the networ dmensons due to ncreasng senstvty of nodes. The aforementoned advantages are acheved at the expense of Increasng the nter-cluster communcatons, Increasng the computatonal complexty for nodes. Fgure 6. Effect of node densty on output BER; to better llustraton of the results, BER s are calculated before despreadng Fnally, t can be concluded that, wth respect to the type of accessble nformaton about the cluster nodes, destnaton and transmt sgnal, there are varous methods to explot receve collaboraton. Smulaton results regardng collaboraton of the cluster nodes for channel equalzaton, approve the effcency of ths approach. REFERENCES [1] I. Ayldaz, W. Su, Y. Sanarasubramanan and E. Cayrc, A survey on sensor networs, IEEE Communcatons Magazne, August 2002. [2] R. Mudumba, G. Barrac, U. Madhow, On the feasblty of dstrbuted beamformng n wreless networ, IEEE Transactons on Wreless Communcatons, vol. 6, no. 5, May 2007, pp. 1754-1763. [3] H. Ocha, P. Mtran, H. V. Poor, V. Taroh, Collaboratve beamformng for dstrbuted wreless Ad Hoc sensor networs, IEEE
Transacton on Sgnal Proceedng, vol. 53, no. 11, November. 2005, pp. 4110-4124. [4] Mudumba, et. al., Dstrbuted Transmt Beamformng: Challenges and Recent Progress, IEEE Communcaton Magazne, Feb 2009, pp. 102-110. [5] B. G. Agee, The least squares CMA: a new technque for rapd correcton of constant modulus sgnals, Proceedngs IEEE ICASSP 1986, pp. 953-956. [6] K. Yao, R. E. Hudson, C. W. Reed, D. Chen, and F. Lorenzell, Blnd beamformng on a randomly dstrbuted sensor array system, IEEE Journal of Selected Area n Communcatons, vol. 16, no. 8, October 1998, pp. 1555-1567. [7] S. K. Jayaweera, Vrtual MIMO-based cooperatve communcaton for energy-constraned wreless sensor networs, IEEE Transactons Wreless Communcatons, vol. 5, no. 5, May 2006,pp. 984-989. [8] H. L. Van Trees, Optmum Array Processng. John Wley & Sons Inc., 2002. [9] H. Jafarhan, Space-Tme Codng; theory and practce. Cambrdge Unversty Press, 2005. [10] R. B. Ertel, P. Carder, K. W. Sowerby, T. S. Rappaport, and J. H. Reed, Overvew of spatal channel models for antenna array communcaton systems, IEEE Personal Communcatons Magazne, February 1998. [11] Y. Chen, T. Le-Ngoc, B. Champagne, and C. Xu, Recursve least squares constant modulus algorthm for blnd adaptve array, IEEE Transacton on Sgnal Processng, vol. 52, no. 5, May 2004.