Adaptation of Two Types of Processing Gains for UWB-IR Wireless Sensor Networks

Transcription

1 Adaptation o Two Type o Proceing Gain or UWB-IR Wirele Senor Network İmail Güvenç 1, Member, IEEE, Hüeyin Arlan 2, Senior Member, IEEE, Sinan Gezici 3, Member, IEEE, Hiai Kobayai 4, Lie Fellow, IEEE Abtract Ultrawideband impule radio (UWB-IR) ytem oer two kind o proceing gain tat can be adaptively canged baed on te intererence level in te ytem o tat quality o ervice (QoS) requirement are ulilled. In ti paper, an adaptive aignment ceme or two type o multiple acce parameter in cluter baed wirele enor network i invetigated. A matematical ramework i developed or ayncronou communication uing a Gauian approximation metod to model te multiple acce intererence in two cae: one wit ixed rame duration, were te goal i to increae te average trougput, and te oter wit ixed ymbol duration, were te goal i to increae te network lietime. Extenion o te analyi to multipat cannel i carried out, and te validity o te Gauian approximation i invetigated uing te Kullback-Leibler ditance. I. INTRODUCTION Ultrawideband impule radio (UWB-IR) i a igly promiing pyical layer tecnology or wirele enor network (WSN) due to it unique caracteritic uc a low power tranmiion, low cot and low complexity tranceiver circuitry, lexibility to tranmit witin a large unlicened pectrum (a long a complying wit regulatory power requirement), precie location capability, and ecure tranmiion due to employed multiple acce equence. In a UWB-IR ytem, time-opping (TH) code are employed a a multiple acce metod [1]. By appropriately deigning te TH code, it i poible to control multiple acce intererence in UWB ytem to a certain extent [2], [3]. Te TH multiple acce can provide intererence ree communication in yncronou ytem. Even in an ayncronou ytem, exceive intererence can be avoided due to low duty cycle and large proceing gain o UWB-IR pule tranmiion. Adaptation o wirele communication ytem allow better exploitation o te ytem reource baed on te etimation o wirele link quality [4]. Te link quality i oten meaured by te ignal-to-intererence plu noie ratio (SINR) o te received ignal. For example, adaptive coding [5], [6] ceme can acieve iger trougput wen te cannel quality i good by decreaing te amount o redundancy tranmitted (or, increaing te modulation 1 DoCoMo USA Lab, 3240 Hillview Avenue, Palo Alto, CA 94304, USA, iguvenc@docomolab-ua.com 2 Electrical Engineering Dept., Univ. o Sout Florida, 4202 E. Fowler Ave., ENB-118, Tampa, FL 33620, USA, arlan@eng.u.edu 3 Department o Electrical and Electronic Engineering Bilkent Univerity, Bilkent, Ankara 06800, gezici@ee.bilkent.edu.tr 4 Department o Electrical Engineering, Princeton Univerity, Princeton, NJ 08544, USA, iai@princeton.edu

2 2 order). On te oter and, wen te link quality i poor, reliable tranmiion can be inured by increaing te amount o redundancy and coding power (or, by decreaing te modulation order). Aigning multiple code to te uer, canging te pule ape [7] and duration, and canging te tranmitted pule power [8] a in conventional ceme are oter orm o adaptation in UWB ytem to better exploit te ytem reource. Adaptation o multiple acce parameter in UWB-IR ytem i anoter lexible mean o exploiting ytem reource eiciently. Dierent rom many oter tecnologie uc a direct-equence code diviion multiple acce (DS-CDMA) ytem, UWB-IR oer two dierent type o proceing gain: number o pule per ymbol, and te rame duration. Increaing te number o pule per ymbol increae te SINR, wic can be conidered a a power control approac in te time domain witout canging pule amplitude. Increaing te rame duration (wic i related wit te cardinality o te code) again improve te SINR in a multiuer environment, a it become le likely tat te pule will be corrupted. By meauring te link quality (wic depend on te cannel, multiuer intererence etc.), it i poible to improve te data rate by modiying tee two dierent multi-acce parameter, wile atiying a minimum BER requirement et by QoS requirement. Alternatively, i a certain data rate i required by te ytem, by adjuting tee two proceing gain, te tranmiion power can be reduced to improve te network lietime, wen te link quality i good. Adaptive rate and power allocation a been well tudied or CDMA ytem in te pat [9]-[12]. Optimal aignment o number o pule per ymbol and te rame duration or UWB ytem in range limited and multiuer intererence limited environment were analyzed in [13], were te Gauian approximation i ued to caracterize te link quality and ae data rate gain or ayncronou communication. In [14], ue o te tandard Gauian approximation (SGA) to capture te multiple acce intererence (MAI) in power unbalanced cenario wa invetigated, and it wa own to be applicable to denely deployed network. Anoter Gauian approximation o MAI or cip yncronou and cip ayncronou cenario wa derived in [15] or a ytem wit ixed number o pule per ymbol and ixed rame duration. Altoug adaptation o rame duration and number o pule per ymbol wa analyzed in [16] in te context o medium acce control (MAC) or UWB ad oc network, a matematical ramework or te MAI a not been developed. In [17] and [18], te radio reource allocation problem wa analyzed a a teoretical contraint optimization problem or ad oc network, were te ytem trougput i maximized conidering a UWB pyical layer, traic pattern, and ytem topology. Bot reerved bandwidt (QoS) and dynamic bandwidt (bet eort) cenario are conidered, and admiion policie o new uer to te ytem are preented. In ti paper, adaptation o multiple acce parameter i invetigated in ayncronou environment or cluter baed WSN. Multiuer intererence i modelled by a Gauian approximation approac or two communication cenario: ixed rame duration, were te goal i to maximize te overall data rate, and ixed ymbol duration, were te goal i to ave an identical data rate or all te uer, and improve te network lietime. For te ixed ymbol duration cae, te required ymbol energy to meet te BER requirement i calculated, and te number o pule to tranmit i evaluated; ti implie joint aignment o bot te number o pule per ymbol and te rame duration, a te ymbol duration i contant. Extenion o te analyi to multipat cannel i perormed

3 3 or bot cae. Alo, te validity o te Gauian approximation or dierent parameter i evaluated uing te Kullback-Leibler (KL) ditance metric, and it eect on te BER i analyzed or dierent parameter and SINR. Improvement in te data rate and power conumption or te adaptation ceme are demontrated wit computer imulation or ixed and mobile cluter ead cenario. Te main contribution o te paper can be ummarized a ollow: 1) Derivation o an aymptotic cloed orm expreion or te probability ditribution o MAI in an UWB-IR ytem wit variou rame duration or dierent uer, 2) Evaluation o te aymptotic tudy by a metric baed approac or variou proceing gain parameter, and 3) A proceing gain adaptation ramework or UWB-IR wirele enor network baed on te aymptotic analyi. Te paper i organized a ollow. Section II give te ytem model or te UWB ignaling and te enor network. Adaptation ceme or ayncronou communication ytem are analyzed in Section III and extenion to multipat cannel are provided in Section IV. Te validity o Gauian approximation i invetigated in Section V wic i ollowed by te imulation reult in Section VI. Finally, ome concluding remark are made. A. UWB Signal Model II. SYSTEM MODEL In ti ection, a generic UWB ignal model i introduced, were a variable number o pule per ymbol, a well a variable rame duration are allowed or dierent uer. Te tranmitted UWB ignal rom uer k in an N u uer ytem i given by were T k (t) = tp j= a j b j/n ω tx(t jt c j T c ), (1) i te rame duration o uer k, j i te rame index, T c i te cip duration, ω tx repreent te tranmitted UWB pule wit unit energy, and tp rame/pule per inormation bit or uer k i denoted a N i te tranmitted pule energy or uer k. Te number o = T uer k, and number o cip per rame o uer k i denoted by N random variable taking value ±1 wit equal probability, and a j Alo, c j {0, 1,..., N 1} wit equal probability, and c j tranmitted bit o uer k are denoted by b { 1, +1}. j/n Te received ignal over an AWGN cannel i given by were N u r(t) = E k=1 j= a j b j/n /T, were T i te ymbol period or. Te random polarity code a are binary and a (l) i are independent or (k, j) (l, i) [19]. and c (l) i ω rx(t jt are independent or (k, j) (l, i). Te c j T c τ k ) + σ n n(t), (2) i te received pule energy, τ k i te delay o uer k, ω rx denote te received UWB pule, and n(t) i a zero mean wite Gauian noie proce wit unit pectral denity. Conider a MF receiver, a own in Fig. 1, wit te ollowing template ignal or te zerot bit o uer ξ (b 0 ), j

4 4 witout lo o generality: 1 temp(t) = N N 1 j=0 a j ω rx (t jt c j T c τ ξ ). (3) Ten, te output o te MF i given by Y = b 0 E N + M + N, (4) were N N (0, σ 2 n) i te output noie and M i te total MAI, wic i te um o intererence term rom te interering uer: M = N u k=1,k ξ were M k i te MAI rom uer k. Te tatitic o M will be analyzed in Section III. M k, (5) B. Senor Network Model and BER Evaluation A cluter baed WSN i conidered, were te cluter ead a more complex circuitry, and tereore iger proceing capabilitie compared to te enor node 1. Te communication appen in round a in [20], were, ater eac round, te cluter ead may update te multiple acce parameter. Conider a cluter o N u enor, wit te kt node aving a tranmitted pule energy o tp to communicate wit te cluter ead, wic tranmit te inormation to a remote bae tation. Te received pule energy or uer k at te cluter ead i given by = α k tp d n k, (6) were n denote te pat lo exponent, d k i te ditance between te kt enor node and te cluter ead, and α k i te ading coeicient or uer k. Wen tere i no MAI, te probability o error or uer k wic employ binary pae it keying (BPSK) modulation i given by P b ( ) = Q SNRk were, energy per ymbol (bit) o uer k i given by r = Q N σ 2 n, (7) = N E, Q(x) i given by 1 2 erc( x 2 ), and SNR denote te ignal-to-noie ratio (intererence eect will be conidered later). Conventional UWB network ue te ame number o pule per ymbol, and te ame rame duration or eac uer, enuring reliable communication wit te uer tat a te wort link quality. I te minimum BER required by te ytem i given by P b, te 1 In general, te cluter-ead may alo be elected rom one o te enor node a in [20]. However, ti may increae te overall complexity o te network ince larger complexity o te cluter-ead will be required or eac individual enor node. On te oter and, te adaptation ceme to be introduced can be applied to oter enor network arcitecture wit centralized control.

5 5 proceing gain aigned to eac uer i given by N = [ Q 1 (P b ) ] 2 σ 2 n E min. (8) were E min denote te minimum received pule energy, wic i rom te urtet away uer in an ideal environment. Te raw data rate or eac uer i ten given by 1 N N T c. In order to better exploit te ytem reource, it i poible to cange te number o pule (N ), and number o cip per rame (N ), or eac uer baed on te cannel quality, te ditance o te uer rom te cluter ead, te long and ort term ading eect, and te intererence level in te ytem. In [3], a yncronou cenario i invetigated were te ortogonal contruction o TH equence allow intererence-ree communication, uc a in te downlink. However, yncronou ignaling i not very practical or WSN in general, and ence we ocu on te ayncronou cenario in ere. In te next ection, adaptation o N and N in ayncronou ytem i analyzed under a BER contraint and or two dierent cae: ixed rame duration (to maximize te data rate), and ixed ymbol duration (to maximize te network lietime). III. PARAMETER ADAPTATION FOR ASYNCHRONOUS COMMUNICATIONS In order to calculate te BER o te deired uer in te preence o multiple uer wit random time opping code, we employ a Gauian approximation approac or large number o pule per inormation ymbol. Ti i imilar to te Gauian approximation employed in [15] and [19]. However, we derive a more generic expreion, wic i valid or variable number o rame ize, and cover te reult in [15] and [19] a a pecial cae. For analytical puoe, we approximate an ayncronou UWB ytem by a cip-yncronou ytem, were te mialignment between te ymbol o te uer are integer multiple o te cip interval T c. Auming witout lo o generality tat te delay o te deired uer i zero (τ ξ = 0), we aume tat τ k = k T c or k ξ, were k {0, 1,..., N N 1} wit equal probability. A tudied in [15], te cip-yncronou aumption uually reult in over-etimating te error probability in random TH UWB-IR ytem, and ence te ytem deign baed on ti approximation i uually on te ae ide. A. Cae 1: Fixed Trougput (Variable Frame Duration) Conider te cae were a ixed trougput i to be aigned to all uer. Hence, we conider a common ymbol time and BER in ti cenario. In oter word, te total proceing gain, deined by N c = N N, i contant in ti cae ( ee Fig. 2b, were (N (1), N (1) (2) ) = (3, 4), (N, N (2) (3) ) = (4, 3), and (N, N (3) ) = (6, 2)). Tereore, te number o pule per ymbol and te rame duration can be canged a long a teir multiplication i ixed. In ti cae, te ollowing lemma i employed in order to approximate te MAI rom uer k: Lemma 1: In a cip-yncronou cenario, te ditribution o te MAI rom uer k converge to te ollowing Gauian random variable M k N ( ) 0, E N, (9)

6 6 a min{n, N }. Proo: See Appendix A. In oter word, or large value o N and N, te MAI rom uer k converge to a zero mean Gauian random variable. Note tat te expreion in (9) reduce to te reult in [15] or N From (9), te total MAI can be approximated a M N 0, Ten, te SINR o te ytem can be obtained a N u k=1,k ξ E N = N k.. (10) SINR = N E σ 2 n + N u k=1 k ξ N, (11) wic can be expreed a E r SINR = σn Nu N c k=1 k ξ r, (12) by te deining te received ymbol energy o te kt uer by r = N E or k = 1,..., N u. Wen te ame SINR value i aigned to all te uer, tey ave te ame BER, ence te ame trougput, a tey ave te ame ymbol time. Hence, rom (12), it i oberved tat te ame received ymbol energy can be ued to acieve te ame BER or all uer. Tat common energy, denoted by E r, can be obtained rom (12) a σn 2 SINR E r = ( ). (13) 1 Nu 1 N c SINR In oter word, or a deired SINR value, te required received ymbol energy o te uer can be calculated. Since te ymbol energy i te multiplication o te number o pule per ymbol and te pule energy, te received ymbol energy can be expreed a E r = α k t d n k = N α k tp d n k. (14) Tereore, te uer can ue dierent number o pule per ymbol and/or dierent pule energy depending on te cannel tate and teir location. In a practical etting, te cluter ead can calculate te SINR or eac o te uer and eedback tem ow to cale teir ymbol energy in order to acieve te deired SINR. Note tat wen a uer i very ar away rom te cluter ead or it cannel i in a deep ade, te tranmitted ymbol energy need to be increaed coniderably, wic migt violate te FCC regulation [21]. Tereore, multi-opping migt be neceary in ome cae. Te received ignal energy in (14) implie tat given te ading coeicient and ditance o uer k, te energy can be et by canging N and/or tp. In oter word, tere i a lexibility in adjuting te ymbol energy. Note tat ti i dierent rom te reerved bandwidt (RB) cae in [17], ince N and N are bot variable (teir

7 7 multiplication i contant) in our cae. In [17], te RB cae aume N te data rate i ixed), and tereore te adaptation i acquired by only caling tp. i ixed (implying tat N i ixed a Even toug tere i a lexibility in adjuting te received power, tere are a ew iue to conider wen etting te ymbol energy. Firt, te FCC implicit limitation on te peak-to-average ignal ratio can retrict te ue o very mall N value. Secondly, te inter-rame intererence (IFI) can be an iue in a multipat environment wen cooing te number o rame per ymbol, were cooing larger rame reduce te eect o te IFI. B. Cae 2: Fixed Frame Duration In ti cae, te rame duration o all te uer are te ame. Hence, N i common or all o tem ( ee or example Fig. 2a, were N (1) = 4, N (2) = 3, N (3) = 2, and N = 3 or all k ). Te aim i to meet te BER requirement or all uer in te ytem. In order to atiy a certain BER treold, te number o pule per ymbol i adapted in order to maximize te overall data rate o te ytem [13]. Te Gauian approximation approac in te previou cae can directly be applied to te ixed rame duration cae 2 in wic N = N k. Ten, te MAI rom uer k can be approximated by te ollowing Gauian random variable, wen te number o pule per inormation ymbol or uer ξ, N, i large: ( ) M k N 0, E, (15) N were i te energy o a received pule rom uer k. From (15), (4) and (5), te SINR o te ytem or uer ξ can be expreed a SINR N E σn Nu N k=1 k ξ, (16) rom wic te value o N i obtained a N = SINR E σn N N u k=1 k ξ. (17) In oter word, by etting te value o N according to (17), we tranmit jut enoug number o pule per ymbol to meet te BER requirement. Ti i contrary to conventional ytem, were te wort cae parameter are ued or all uer, ence a lower overall data rate i obtained. Note tat all te uer tranmit wit te ame power over a block, owever, or a given tranmit power, te bit rate will depend on te link quality. IV. EXTENSIONS TO MULTIPATH CHANNELS Due to extremely ort duration pule employed, it i likely to oberve individual multipat component (altoug not very diperive) even in low-power and very ort-range communication in denely deployed enor 2 Ti pecial cae i alo invetigated in [15].

8 8 network. Longer-range communication may yield muc evere and diperive cannel impule repone, were te maximum exce delay o te cannel may be on te order o undred o nanoecond. Tereore, it become very crucial to conider te eect o multipat, ince it can ave igniicant eect on te perormance. Conider tranmiion over requency elective cannel, were te cannel or uer k i modeled a were α l (t) = L l=1 α l δ(t (l 1)T c τ k ), (18) and τ k are te ading coeicient o te lt pat and te delay o uer k, repectively, and L i te total number o received tap. Aume tat τ 1 = 0 and L l=1 α l From (1) and (18), te received ignal can be expreed a were N u r(t) = E k=1 j= u (t) = 2 = 1, witout lo o generality. ) a j b j/n u( t jt c j T c τ k + σ n n(t), (19) L l=1 α l ω rx (t (l 1)T c ). (20) Conider a RAKE receiver or te ξt uer, wic a te ollowing template ignal or te 0t inormation bit: were 1 temp(t) = N v(t) = N 1 j=0 a j v(t jt c j T c ), (21) L β l ω rx (t (l 1)T c ), (22) l=1 wit β = [β 1,..., β L ] being te RAKE combining weigt. A conidered in [22], te template ignal given by (21) and (22) can repreent dierent multipat diverity combining ceme by appropriate coice o te weigting vector β. From (19)-(22), te output o te Rake receiver can be expreed a ollow: Y = r(t) temp(t)dt = b 0 N E L l=1 α l β l + M + N, (23) were te irt term i te deired ignal part, M i te MAI rom oter uer and N i te output noie, wic i ( approximately ditributed a N N 0, σn 2 ) L l=1 β2 l or large N [22]. Aume N (L 1) o tat te IFI and te inter-ymbol intererence (ISI) are negligible [23]. Te MAI term in (23) can be expreed a in (5); tat i, a te um o MAI term rom oter uer. For te ixed trougput cae, te ollowing reult can be obtained. Lemma 2: In a cip-yncronou cenario, te ditribution o te MAI rom uer k converge to te ollowing

9 9 Gauian random variable M k N ( [ 0, E L N j=1 j=1 ( j l=1 l=1 β l α l+l j) 2 + ( L 1 j j=1 l=1 α l β l+l j ) 2 ]), (24) a min{n, N }. Proo: See Appendix B. Note tat te reult reduce to te reult in [22] or N = N = N k. Tat pecial cae can be ued or te ixed rame duration cae to obtain te aymptotic MAI ditribution a ( [ L ( M k N 0, E j 2 ( L 1 j ) 2 ]) β l α N l+l j) + α l β l+l j (25) or large N. From (24) and (25), it i oberved tat te MAI rom an interering uer converge, a N j=1 l=1 and N ininity, to Gauian random variable wit zero mean, imilar to te one in (9) and (15), repectively, wit te only dierence being te caling actor to te variance term, wic purely depend on te multipat cannel o te interering uer and te inger aignment o te RAKE receiver. In oter word, te ame dependence on te received pule energy and te proceing gain parameter (N and N ) i preerved a in te AWGN cae. go to V. VALIDITY OF GAUSSIAN APPROXIMATION In te previou ection, Gauian approximation were ued to model te multiuer intererence in an ayncronou environment. In ti ection, te dependence o te accuracy o Gauian approximation on te two type o proceing gain i analyzed uing te KL ditance [24]. Moreover, te accuracy o te Gauian approximation i evaluated or dierent multiple acce parameter and SNR value. A. KL Ditance Between te Approximate and Actual MAI Ditribution Conider te equation (9) and (15) or cae 1 and cae 2, repectively, were te intererence rom a econd uer wa approximated uing a Gauian ditribution wit it variance depending on te parameter N, N, and (N i contant or cae 2). In order to ee ow well te approximation capture te actual intererence probability denity unction (PDF), te teoretical Gauian PDF and te MAI PDF obtained rom imulation can be compared or dierent range o multiple acce parameter. Te KL ditance (or relative entropy) i commonly,n teo,n im ued to caracterize te imilarity between two ditribution. Let N correponding to a et o parameter N, N ; and let N denote te PDF o te intererence denote te PDF o te intererence generated uing imulation and correponding to te ame et o parameter. Ten, te KL ditance between two ditribution i given by ( K N teo,n N im,n ) = N,N teo i= (i) ln N,N teo N,N im (i). (26) (i)

10 10 Te larger te KL ditance, te le would be te imilarity between te two PDF. A te KL ditance metric i not ymmetric, te average o te two KL ditance ( i.e. K( teo im ) and K( im teo ) ) i ued in ti paper to evaluate te imilarity between te two ditribution. Note tat wile te intererence ditribution lie between ( E N, E N ), te upport o te teoretical Gauian ditribution i (, ). Analyzing (26) under ti act implie tat KL ditance may converge to ininity i not properly treated. Tereore, a an approximation, we truncate te teoretical Gauian ditribution to lie witin te upport o te intererence ditribution, and te area under te omitted tail o te Gauian ditribution are included a delta unction at te edge o te truncated Gauian ditribution. In Fig. 3, imulation reult or cae 2 are preented or variou value o rame duration and proceing gain. Two uer wit equal power level are conidered, and te KL ditance are computed or dierent value o N and N value o N are oberved.. It i oberved tat te MAI converge to a Gauian ditribution or larger value o N, and or maller ( bit are ued in imulation). Similar imulation are repeated or cae 1, were imilar reult B. BER Perormance Uing te GA and te Actual MAI Ditribution Even toug te KL ditance caracterize te accuracy o Gauian approximation or dierent et o parameter (relative to anoter et o parameter), ow muc ti will aect te BER i alo dependent on SNR. For example, i te noie variance i large, inaccuracy o te Gauian approximation may not yield igniicant deviation rom te actual BER. On te oter and, BER o te ytem operating at ig SNR environment may be very enitive againt inaccuracie in te Gauian approximation. In Fig. 4, te BER v. SNR curve or cae 2 and or dierent multiple acce parameter are preented, wic are obtained uing te imulation and te Gauian approximation. It i oberved tat te larger value o N increae te accuracy o Gauian approximation. It i alo een tat a te SNR increae, te deviation between te BER obtained uing te Gauian approximation and te imulation increae. Te teoretical and imulation BER reult or our uer were alo preented or comparion puoe, were it can be oberved tat Gauian approximation provide a tigter bound. VI. SIMULATION RESULTS Computer imulation are perormed to demontrate te improvement in te data rate and reduction in power conumption. Only a ingle cluter o a WSN i conidered in te imulation, and 100 enor node are randomly ditributed over a meter ield. Te reult can alo be generalized or multiple cluter, were enor node in eac cluter communicate adaptively wit te cluter ead, and te cluter ead (wic orm anoter upper-level cluter witin temelve) communicate adaptively wit te ink. Correponding to a BER o 10 4 or BPSK modulation, SNR = 8.39dB i targeted. Te pat lo exponent i taken to be n = 2.4, te pule widt i et to T c = 0.3n, and te cip yncronou cae i conidered in all cenario. It i aumed tat te tranmitted pule occupie te wole 7.5GHz o bandwidt in between 3.1GHz 10.6GHz. Since te FCC mak allow a maximum

11 11 tranmiion power o 41dBm/MHz witin ti requency range, te maximum tranmit energy per econd can be calculated to be 0.562mW. Ti i te maximum power tat any enor can tranmit witin te limit o FCC regulation, wic migt retrict te election o optimum N and N even i SINR i appropriate. Simulation reult or ayncronou cenario o cae 1 are preented in Fig. 5 and 6, were te data rate are identical or all te uer: (N c T c ) 1 = ( ) 1 = 33kbp, wit N c = N N = For imulation puoe, continuou tranmiion o all te enor and very low initial battery energy aignment (1mJ) or eac node are aumed. Te parameter are updated ater eac round o 300µec to adapt to te Rayleig ading cannel and poibly canged ditance, and te energy conumption in round i analyzed. Simulation reult indicate ubtantial gain in network lietime wen uing adaptive aignment o proceing gain (PG). Alo, te eect o mobility o te cluter ead (CH) i analyzed. Ti may be conidered, or example, or recue-robot application were te robot act a a cluter ead to communicate wit variou enor, and altoug te power conumption o te robot i not tat crucial, we would like to maximize te network lietime o te enor. It i oberved in Fig. 5 and 6 tat i te cluter ead randomly move in te network, te network lietime orten eriouly. On te oter and, te movement o te cluter ead ater eac round to an optimal location (i.e., te expected value o te location o te alive enor node) ligtly increae te network lietime compared to te cae wen te cluter ead i motionle and located at te center o te network. In Fig. 7, we alo compare (averaged over 10 4 enor realization) te metric T 0.95 = T (adapt) 0.95 /T (ixed) 0.95 or dierent parameter, were T (adapt) 0.95 and T (ixed) 0.95 are te time duration were te total network energy all to 95% o te initial network energy or adaptive PG and ixed PG cae, repectively. We oberve tat a te number o enor node increae or te network dimenion decreae (i.e., te enor intenity increae), te gain obtained rom te adaptive PG approac diminie. In particular, or te 15 15m 2 cenario, tere i almot no gain. Ti implie tat te propoed tecnique i le appropriate or ort-range communication were te pat-lo i le evere. Nevertele, a implied by Fig. 5, adaptive PG approac will till ave merit or longer obervation window. VII. CONCLUSION In ti paper, adaptation o multiple acce parameter in cluter baed UWB-IR WSN a been analyzed. A Gauian approximation metod a been employed to adapt te tranmiion power and te proceing gain o te enor, and a matematical ramework a been developed or te analyi o MAI wen te uer employ dierent number o pule per ymbol and dierent rame duration. Te main contribution o te paper i on te analyi o variable rame duration cae, bot in AWGN and in multipat cannel. Alo, te accuracy o te Gauian approximation a been invetigated and quantiied uing te KL ditance baed on te parameter (N, N ) in a way not addreed in te literature beore. It a been own to be accurate or populated network wit large N, mall N, and low SNR value. Simulation reult outline te potential improvement in energy aving uing te adaptive ytem deign baed on te two parameter. Many o te analyi dicued in te paper can alo be extended to oter centralized enor arcitecture (not necearily cluter-baed) tat employ UWB ignal, were a central node control te aignment o TH code to

12 12 te oter node. On te oter and, te Gauian approximation ramework can be applied to any ayncronou network. Te autor believe tat te propoed adaptation ceme can be ued or cognitive communication or extending te capabilitie o uture wirele network. REFERENCES [1] M. Z. Win and R. A. Scoltz, Impule radio: How it work, IEEE Commun. Letter, vol. 2, no. 2, pp , Feb [2] I. Guvenc and H. Arlan, Deign and perormance analyi o time opping equence or UWB-IR ytem, in Proc. IEEE Wirele Commun. Networking Con. (WCNC), vol. 2, Atlanta, GA, Mar. 2004, pp [3] I. Guvenc, H. Arlan, S. Gezici, and H. Kobayai, Adaptation o multiple acce parameter in time opping UWB cluter baed wirele enor network, in Proc. IEEE Mobile Ad-oc and Senor Sytem Con. (MASS), Ft. Lauderdale, FL, Oct. 2004, pp [4] H. Arlan, Adaptation Tecnique and te Enabling Parameter Etimation Algoritm or Wirele Communication Sytem. Book Capter, Signal Proceing Communication Handbook, CRC Pre, [5] J. Y. L. Boudec, R. Merz, B. Radunovic, and J. Widmer, A MAC protocol or UWB very low power mobile ad-oc network baed on dynamic cannel coding wit intererence mitigation, EPFL Tecnical Report ID: IC/2004/02, Lauanne, Switzerland, Tec. Rep., Jan [6] G. Giancola, L. D. Nardi, M. G. D. Benedetto, and E. Dubui, Dynamic reource allocation in time varying ultra wideband cannel, in Proc. IEEE Int. Con. Commun. (ICC), vol. 6, Pari, France, June 2004, pp [7] H. Zang and R. Kono, Sot-pectrum adaptation in UWB impule radio, in Proc. IEEE Peronal Indoor Mobile Radio Commun. (PIMRC), vol. 1, Beijing, Cina, Sep. 2003, pp [8] S. S. Kolencery, J. K. Townend, J. A. Freeberyer, and G. Bilbro, Perormance o local power control in peer-to-peer impule radio network wit burty traic, in Proc. IEEE Global Telecommun. Con., vol. 2, Poenix, AR, Nov. 1997, pp [9] S. J. O and K. M. Waerman, Adaptive reource allocation in power contrained cdma mobile network, in Proc. IEEE Wirele Commun. Networking Con. (WCNC), vol. 1, New Orlean, LA, Sept. 1999, pp [10] D. Kim, Rate-regulated power control or upporting lexible tranmiion in uture CDMA mobile network, IEEE J. Select. Area Commun., vol. 17, no. 5, pp , May [11] L. C. Yun and D. G. Meercmitt, Variable quality o ervice in CDMA ytem by tatitical power control, in Proc. IEEE Int. Con. Commun., vol. 2, Seattle, WA, June 1995, pp [12] F. Berggren and S. L. Kim, Energy-eicient control o rate and power in DS-CDMA ytem, IEEE Tran. Wirele Commun., vol. 3, no. 3, pp , May [13] J. Diaz and Y. Bar-ne, Adaptive tranmiion or UWB impule radio communication, in Proc. Con. on Inormation Science Syt. (CISS), Baltimore, MD, Mar [14] G. Giancola, L. D. Nardi, and M. G. D. Benedetto, Multi uer intererence in power-unbalanced ultra wide band ytem: Analyi and veriication, in Proc. IEEE Ultrawideband Syt. Tecnol. Con. UWBST, Reton, VA, Nov. 2003, pp [15] S. Gezici, H. Kobayai, H. V. Poor, and A. F. Molic, Perormance evaluation o impule radio UWB ytem wit pule-baed polarity randomization in ayncronou multiuer environment, in Proc. IEEE Wirele Commun. Networking Con. (WCNC), Atlanta, GA, Mar [16] H. Yomo, P. Popovki, C. Wijting, I. Z. Kovac, N. Deblauwe, A. F. Baena, and R. Praad, Medium acce tecnique in ultra-wideband ad oc network, in Proc. 6t National Con. o Society or Electronic, Telecommun., Automatic, and Inormatic (ETAI), Orid, Macedonia, Sep [17] F. Cuomo, C. Martello, A. Baiocci, and F. Capriotti, Radio reource aring or ad oc networking wit UWB, IEEE J. Select. Area Commun., vol. 20, no. 9, pp , Dec [18] H. Zu and A. Ganz, A radio reource control metod in UWB MAC protocol deign, in Proc. IEEE Military Commun. Con. (MILCOM), vol. 2, Boton, MA, Oct. 2003, pp [19] E. Filer and H. V. Poor, On te tradeo between two type o proceing gain, in Proc. 40t Annual Allerton Con. on Commun. Control Computing, Monticello, IL, Oct

13 13 [20] W. R. Heinzelman, A. Candrakaan, and H. Balakrinan, Energy eicient communication protocol or wirele microenor network, in Proc. Annual Hawaii International Conerance on Sytem Science, Hawaii, Jan. 2000, pp [21] Federal Communication Commiion: Reviion o part 15 o te commiion rule regarding ultra-wideband tranmiion ytem, Firt Report and Order, ET Docket , FCC 02-48, April [22] S. Gezici, H. Kobayai, H. V. Poor, and A. F. Molic, Perormance evaluation o impule radio UWB ytem wit pule-baed polarity randomization, IEEE Tran. Sig. Proceing, vol. 53, no. 7, pp. 1 13, July [23] N. He and C. Tepedelenlioglu, Adaptive yncronization or non-coerent uwb receiver, in Proc. IEEE International Conerence on Acoutic, Speec, and Signal Proceing (ICASSP 04), vol. 4, Montreal, Quebec, Canada, May 2004, pp [24] S. Kullback, Inormation teory and tatitic. Wiley, New York, [25] P. Billingley, Probability and Meaure. Jon Wiley & Son, New York, 2nd edition, A. Proo o Lemma 1 APPENDIX From (2) and (3), te MAI rom uer k, M k in (5), can be expreed a ollow were M k,l = a l j= a j b M k = j/n N N 1 l=0 R(jT lt M k,l, (27) + c j T c c l T c k T c ), (28) wit k = (τ k τ ξ )/T c being te amount o ayncronim between te deired uer and uer k in term o te cip interval, and R(x) = w rx(t + x)w rx (t)dt. Firt, conider te cae in wic N N. It can be own tat {M k,l } N (1) 1 l=0 orm a 1-dependent equence [25], wic mean tat M k,l1 and M k,l2 are independent or l 1 l 2 > 1. Ti i due to te act tat te intererence to rame l 1 and l 2 o te deired uer alway come rom dierent rame o uer k or l 1 l 2 > 1, and tat te random polarity code are independent and identically ditributed a binary random variable ( 1, +1). Te random polarity code alo reult in a zero mean ditribution or eac term o te equence {M k,l } N (1) 1 l=0 ; i.e., E{M k,l } = 0 or l = 0, 1,..., N (1) 1. For a 1-dependent zero mean equence, te central limit teorem or dependent equence can be applied to obtain ( ) 1 te aymptotic ditribution o N 1 N l=0 M k,l, a N, a N 0, E{Mk,l 2 } + 2E{M k,lm k,l+1 } [25]. It can be own tat te correlation term are zero due to te act tat random polarity code are zero mean and independent or dierent indice. Alo ater ome manipulation, it can be own tat E{M 2 k,l it i obtained tat a N For N N N 1 l=0 M k,l N ( ) 0, E N. Tereore, or large N, M k in (27) can be approximated a in (9). } = 1/N. Hence,, (29) > N, te MAI rom uer k can be expreed a te ummation o rame intererence term a

14 14 ollow: M k = E N N l=0 ˆM k,l, (30) were ˆM k,l i te intererence related to te lt rame o uer k: ˆM k,l = a l b l/n N 1 j=0 a j R(jT lt + c j T c c l T c k T c ). (31) It can be own tat { ˆM k,l } N 1 l=1 orm a 1-dependent equence 3. Ten, a N, 1 N N 1 l=1 For large N, M k i approximately ditributed a N contant or all uer; tat i, N N All in all, or large value o min{n by (9). = N N ˆM k,l N ( 0, ( 0, N 1 N N ) N, te variance i te ame a tat in (9).. (32) ). However, ince te total gain N c i, N }, te ditribution o te MAI rom uer k i approximately given B. Proo o Lemma 2 Te proo i imilar to te proo in Appendix A. Firt, conider te cae in wic N uer k can be expreed, rom (19)-(23), a M k = N ξ N 1 j=0 < N. Te MAI rom M k,j, (33) were M k,j = a (1) j m= a m b m/n φ uv ( ) mt jt (1) + (c m c (1) j )T c + k T c, (34) wit φ uv (x) being deined a Note tat {M k,j } N j=0 φ uv (x) = u (t x)v(t)dt. (35) orm a 1-dependent equence [25] ince it i aumed tat te delay pread o te cannel are maller tan te rame interval, wic reult in dierent intererence term or eac pair o intererence term M k,j1 and M k,j2 or j 1 j 2 > 1. Due to te ditribution o te polarity code, te mean and correlation term can be own to be zero; i.e., E{M k,j k } = 0, and E{M k,j M k,l k } = 0 or l j. In order to calculate te variance, te act tat te polarity 3 A N, te edge value, ˆMk,0 and ˆM k,n can be omitted or implicity.

15 15 code are independent or dierent uer and rame indice, and tat te TH equence are uniormly ditributed are employed. Ten, it can be own tat E{M 2 k,j k } = 1 N N N 1 N 1 i=0 wic reduce, ater ome manipulation, to l=0 m= E{M 2 k,j k } = 1 N From (35), (20) and (22), (37) can be expreed a E{M 2 k,j k } = 1 N [ L ( j j=1 i=1 { ( )} 2 φ uv mt jt + (i l)t c + k T c, (36) L 1 j= (L 1) β i α i j+l) [ φ uv (jt c )]. (37) ( L 1 j j=1 i=1 α i β i j+l ) 2 ]. (38) Note tat te reult i independent o te oet k. Tereore, E{Mk,j 2 } i given by (38), a well. Since {M k,j } N 1 j=0 i a 1-dependent equence wit zero mean and correlation term, te ditribution o ( ) converge to te Gauian ditribution given by N 0, E E{Mk,j 2 }, a N rom (38) or te N For N < N cae. N, te MAI rom uer k can be expreed a M k = N N j=0 intererence related to te jt rame o uer k. Ten, by imilar argument, (24) can be derived. Tereore, te reult in Lemma 2 i obtained a min{n, N }. N [25]. Ten, (24) ollow ˆM k,j, were ˆM k,j denote te N 1 j=0 M k,j

16 16 Lit o Table and Figure Caption: Fig. 1: Te received ignal rom multiple uer and te correlator receiver. Fig. 2: Example tranmitted ignal or a) Fixed rame duration, and b) Fixed trougput. Fig. 3: KL ditance or cae 2 wit repect to N and N. Only two uer wit equal power are conidered. Fig. 4: Comparion o teoretical and imulation BER or cae 1. Only two uer wit equal power are conidered (N = 10). Fig. 5: Remaining aggregate energy in te network wit repect to time. Fig. 6: Number o alive node in te network wit repect to time. Fig. 7: Te ratio o te time period or te propoed and conventional tecnique were te total network energy all to 95% o te initial network energy.

17 17 PN-1 TX-1 Deired Uer Receiver Cannel-1 PN-k TX-k Signal Proceing Detected Symbol Cannel-k T=T c PN-N U TX-N U Noie Correlator Template Cannel-N U Fig. 1.

18 Fig

19 KL Ditance N=4 N=8 N=16 N=32 N= log 2 (N ) Fig. 3.

20 Bit Error Rate N=2 (im) N=2 (teo) N=5 (im) N=5 (teo) N=10 (im) N=10 (teo) N=30 (im) N=30 (teo) N=2, Nu=4 (im) N=2, Nu=4 (teo) SNR (db) Fig. 4.

21 Adaptive PG (Fixed CH) Fixed PG Adaptive PG (Randomly Mobile CH) Adaptive PG (Optimally Mobile CH) 0.08 Sum o enor energie (Joule) Time (ec) Fig. 5.

22 Adaptive PG (Fixed CH) Fixed PG Adaptive PG (Randomly Mobile CH) Adaptive PG (Optimally Mobile CH) Number o alive node Time (ec) Fig. 6.

23 x 25 m 2 20 x 20 m 2 15 x 15 m 2 4 T Number o enor Fig. 7.