Adaptation of Multiple Access Parameters in Time Hopping UWB Cluster Based Wireless Sensor Networks

Transcription

1 Adaptation o Multiple Acce Parameter in Time Hopping UWB Cluter Baed Wirele Senor Network İmail Güvenç andhüeyin Arlan Electrical Eng. Dept., Univ. o Sout Florida 422 E. Fowler Ave., ENB-8, Tampa, FL, iguvenc,arlang@eng.u.edu Sinan Gezici and Hiai Kobayai Department o Electrical Engineering Princeton Univerity, Princeton, NJ gezici,iaig@princeton.edu Abtract Ultrawideband (UWB) i an attractive pyical layer tecnology or wirele enor network due to it unique caracteritic. Flexibility in adjuting te proceing gain o UWB ytem make it poible to tune te data rate and tranmiion range to ulill te requirement o peciic application. Conventional ytem aign identical multiple acce parameter to all uer regardle o te ignal-to-intererence plu noie ratio o te received ignal. In ti paper an adaptive aignment ceme or multiple acce parameter in cluter baed wirele enor network i invetigated. Firt, an ortogonal time opping equence contruction i propoed or yncronou communication (downlink), were te number o pule per ymbol are adjuted to meet te bit error rate requirement o an application. Ten, adaptation o multiple acce parameter in ayncronou cenario (uplink) i evaluated 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. Finally, a matematical ramework i developed or approximating te intererence wen te number o pule per ymbol and te rame duration vary. Introduction Togeter wit recent advance in integrated circuit, te evolution o wirele enor network (WSN) toward inexpenive, low-power, and mall-ize implementation a gained incredible momentum. WSN can be implemented in a variety o area, uc a military, telemedicine, telemetry, robotic, ault detection, conumer electronic, and ecurity. Depending on te requirement o a peciic application, te number o node in a WSN may range rom a ew node to touand o node. In large WSN, it i eential to ave energy eicient communication to increae te network lietime. Ultrawideband impule radio (UWB-IR) i a igly promiing pyical layer tecnology or WSN due to it unique caracteritic uc a low power tranmiion, low cot and low complexity tranceiver circuitry, unlicened but maked pectrum availability, precie location capability, and ecure tranmiion due to employed multiple acce equence. Time-opping (TH) i a commonly ued multiple acce metod or UWB-IR ytem, beide te direct equence (DS), and requency opping (FH) metod. By appropriately deigning te TH code, it i poible to control multiple acce intererence in UWB ytem to a certain extent [4]. 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. Even i ome o te pule are corrupted, te ret o te pule will be uicient to extract te inormation. In addition, low complexity multiuer receiver, uc a cip dicriminator [8], can be ued to dicard te corrupted pule, and implement adaptive rate control algoritm baed on te intererence level. Adaptation o wirele communication ytem allow better exploitation o te ytem reource baed on te etimation o wirele link quality [2]. Te link quality i oten meaured by te ignal-to-intererence plu noie ratio (SINR) o te received ignal. For example, adaptive coding [6, 3] ceme can acieve iger trougput wen te cannel quality i good by decreaing te amount o redundancy tranmitted. On te oter and, wen te link quality i poor, reliable tranmiion can be inured by increaing te coding power (amount o redundancy). Similarly, adaptive modulation ceme can provide a range o modulation level tat can be implemented baed on te cannel quality [3]. For M-ary pule poition modulation (PPM), even toug te data rate i increaed by log 2 M, increaing te modulation order M increae te eective time panned by /4/$2. 24 IEEE 235

2 a ingle pule by M. Te good new i tat te power eiciency i improved or iger order M-ary PPM ceme, i.e. le power i required to aure te ame bit error rate (BER). On te oter and, iger order M-ary pule amplitude modulation (PAM) level ave wore power eiciency (compared to lower order M-ary PAM ceme), but te data rate improve by log 2 M wit te pule panning te ame time duration. Tee caracteritic o bot iger order modulation ceme can be ued to adapt to te cange in te link quality. Aigning multiple code to te uer, canging te pule ape [22] and duration, and canging te tranmitted pule power [7] a in conventional ceme are oter orm o adaptation in UWB ytem to better exploit te ytem reource. Adaptation o multiple acce parameter in TH-UWB ytem in term o te number o pule per ymbol, and te rame duration i anoter lexible mean o exploiting ytem reource eiciently. 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 receive it. However, tee improvement come in te expene o decreae in te data rate. By meauring te link quality (wic i aected rom te cannel realization, multiuer intererence etc.), it i poible to improve te data rate by modiying bot parameter, wile till enuring a minimum BER wic i ixed by te quality o ervice (QoS) requirement. Alternatively, i te data rate i ixed by ytem requirement, wen te link quality i good, te tranmiion power can be reduced to improve te network lietime. Adaptive rate and power allocation a been well tudied or code diviion multiple acce (CDMA) ytem in te pat [9, 6, 2, 4]. 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 [8], were te Gauian approximation i ued to caracterize te link quality and ae data rate gain or ayncronou communication. In [2], 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 [] 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 [2] in te context o medium acce control (MAC) or UWB ad oc network, a matematical ramework or te MAI a not been developed. In [7, 23], radio reource allocation problem wa analyzed a a teoretical contraint optimization problem or ad oc network, were te ytem trougput i maximized conidering 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 bot in yncronou and ayncronou communication i invetigated or cluter baed WSN, and teoretical perormance analyi to caracterize te link quality i preented or dierent cenario. For yncronou communication (downlink), an ortogonal TH equence contruction approac i propoed, wic reemble ortogonal variable preading actor (OVSF) code in CDMA ytem. For ayncronou communication, multiuer intererence i modelled wit 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 be employed in tranmiion i evaluated (wic implie joint aignment o bot te number o pule per ymbol and te rame duration, a te ymbol duration i contant). Improvement in te data rate and power conumption or bot ceme are demontrated wit computer imulation or ixed and mobile cluter ead cae. 2 Sytem Model 2. UWB Signal 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 k (t) = q tp j= a (k) j b (k) bj= c! tx(t jt (k) c (k) j T c ); were T (k) i te rame duration o uer k, j i te rame index, T c i te cip duration, tp i te tranmitted pule energy o uer k, and! tx repreent te tranmitted pule ape wit unit energy. Te number o rame per inormation bit or uer k i denoted a = T (k) =T (k),were T (k) i te ymbol period or uer k, and number o cip per rame o uer k i denoted by. Te random polarity code a (k) j are binary random variable taking value () 236

3 PN- T- Deired Uer Receiver Cannel- PN-k T-k Signal Proceing Detected Symbol Cannel-k T=T c PN-N U T-N U Noie Correlator Template Cannel-N U Figure. Te received ignal rom multiple uer and te correlator receiver. ± wit equal probability, and a (k) j and a (l) i are independent or (k; j) 6= (l; i) [9]. Alo, c (k) j 2; ; :::; N c g wit equal probability, and c (k) j and c (l) i are independent or (k; j) 6= (l; i). Te tranmitted bit o uer k are denoted by b (k) 2 ; +g. bj= c Te received ignal i expreed a Nu q r(t) = E (k) a (k) j b (k) k= j= bj= c! rx(t jt (k) c (k) j T c i k )+ n n(t); (2) were E (k) i te received pule energy, i k i te delay o uer k,! rx denote te received UWB pule, n(t) i a zero mean wite Gauian noie proce wit unit pectral denity, and n denote te tandard deviation o te noie beore te matced ilter (MF). Conider a MF receiver (ee Fig. ) wit te ollowing template ignal or te zerot bit o uer ο (b (ο) ), witout lo o generality: (ο) temp (t) = j= a (ο) j! rx (t jt (ο) c (ο) j T c i ο ): (3) Ten, te output o te MF i given by q Y = E (ο) b (ο) N (ο) + M + N; (4) were N οn( ;N (ο) n 2 ) i te output noie and M i te total MAI, wic i te um o intererence term rom te interering uer Nu M = k=;k6=ο M k ; (5) were M k i te MAI rom uer k. Te tatitic o M will be analyzed in Section Senor Network Model and BER Evaluation In ti paper, a cluter baed WSN i analyzed, were te cluter ead a more complex circuitry, and tereore iger proceing capabilitie compared to te enor node. Note tat rom robutne, el conigurability, and an overall network lietime peective it i more appropriate tat eac node can ave te capability to be te cluter ead. However, ti increae te overall cot o te node, a being a cluter ead a coniderably larger complexity, and in particular or UWB ytem, require a eparate correlator or eac enor. Tereore, te ormer approac i taken or te ret o te paper. Te communication appen in round a in [5], were, ater eac round, te cluter ead may update te multiple acce parameter. Conider acluteron u enor, wit eac 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 k = E(k) tp d n k were n denote te pat lo exponent, d k i te ditance between te kt enor node and te cluter ead, and 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 (k) b = Q psnr k = E (k) 2 n (6) A ; (7) 237

4 Table. Code contruction algoritm or k =:N u c k = rand(s; ) S = S c k end were, energy per ymbol (bit) o uer k i given by r =, Q(x) i given by 2 erc( xp 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 urtet away uer. I te minimum BER required by te ytem i given by P b, te proceing gain aigned to eac uer i given by N = Q (Pb )Λ 2 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. NN Tc Te raw data rate or eac uer i ten given by. 3 Adaptation o Multiple Acce Parameter In order to better exploit te ytem reource, it i poible to cange te number o pule ( ), and number o cip per rame ( ), 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 ti ection, irt, yncronou communication will be conidered, were te ortogonal contruction o TH equence allow intererence-ree communication, uc a in te downlink. Ten, adaptation o and 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). 3. Syncronou Communication In yncronou communication, it i poible to deign te TH code ortogonally to avoid MAI. In ti mode o operation, te cluter ead may aign jut enoug number o pule to eac enor node k to enure te deired BER P b () c = [ 3 6 9] Symbol Duration (2) (3) c = [ 7] c = [ ] Figure 2. An example code contruction or tree uer wit dierent proceing gain. =& Q (Pb )Λ 2d ' n k 2 n ; (9) tp k were dxe i te mallet integer greater tan or equal to x. Te ortogonal contruction o te code wit dierent proceing gain i carried out a ollow. Let N c denote te number o cip poition witin te ymbol period. Ater eac round, eac enor can report te oberved SNR, and uing (9), cluter ead can evaluate N c prior to contructing new et o time opping code a ollow N c = Nu k= : () Note tat N c i a jut enoug number o cip per ymbol, and determine te data rate common to all enor node. In addition to cange in te cannel quality, due to movement/deat o te node or a movement o te cluter ead, te ditance may cange, wic may cange te value o N c ater eac round. Ater calculating N c,te cluter ead contruct te ortogonal code a given in Table, were S i te et o integer ranging rom to N c, rand(s; ) denote random integer coen rom et S, and te operator exclude te et o number on te rigt o te operator rom te et on te let o te operator. In Fig. 2, a imple example or te downlink TH equence o 3 uer employing dierent proceing gain i preented. In a ene, te propoed contruction i imilar to OVSF code in CDMA ytem, owever, our contruction i more lexible, a te lengt o a particular code doe not need to be a multiple o te lengt o any o te orter lengt code. For te ake o implicity, te code are contructed in a random manner, wic work well or ingle tap (lat ading) cannel. For diperive cannel, more opiticated code deign can be ued [4], were a Note tat conventional rame-baed code and ignal notation in (2) i not ued ere, were te equence c k or uer k point to te location o te pule witin te ymbol, rater tan witin te rame (i.e. tere are no rame, and te common ymbol duration i NcTc). 238

5 Symbol duration (Cae II: Fixed Trougput) (a) Symbol duration (Cae I: Fixed Frame Duration) (b) Figure 3. Example tranmitted ignal or a) Fixed trougput, and b) Fixed rame duration. larger pule duration may be preumed to companate or te cannel eect. Te average data rate wit te propoed ceme will improve ince te average number o pule per ymbol decreae, and i given by. On te oter and, te to- NcT tal tranmitted power or any round i ixed or all cae, and individual uer power are adapted indirectly troug canging number o pule per ymbol. Te propoed metod alo improve te energy conumption (per ymbol), a le aggregate energy will be ued per ymbol. 3.2 Ayncronou Communication In te previou ection, it i aumed tat te UWB ytem i completely yncronized. Ti require compenation o delay in variou multipat arrival, wic i not generally eaible in te uplink, but may be conidered or downlink communication. Tereore, uplink tranmiion i uually aumed to be ayncronou, and multiple acce intererence degrade te ytem perormance. 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 (i d = ), we aume tat i k = kt c or k 6= d, were k 2; ;::: ; g wit equal probability. A tudied in [], te cip-yncronou aumption uually reult in over-etimating te error probability, and ence te ytem deign baed on ti approximation will be on teaeide. In order to calculate te BER o te deired uer in te preence o multiple uer wit random time opping code, we will employ Gauian approximation or large number o pule per inormation ymbol. Ti i imilar to te Gauian approximation employed in [9] and []. However, we derive a more general ormula in te cae o dierent number o pule per ymbol in te ixed trougput cae below. Later in ti ection, ixed rame duration and ixed ymbol duration cae are analyzed eperately Cae : 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. 3b, were N () =4, N (2) =3, N (3) =2,and =3or all k. Te aim i to meet te BER requirement or all uer in te ytem. In order to atiy a certain BER treold, we adapt te number o pule per ymbol o tat we can maximize te overall data rate o te ytem [8]. Similar to te approac in [], we can approximate te MAI rom uer k by te ollowing Gauian random variable, wen te number o pule per inormation ymbol or uer ο,,ilarge: M k οn ψ ; N ; ()! were i te energy o a received pule rom uer k. Ten, we can expre, uing (4) and (5), te SINR o te ytem or uer ο a SINR = ( ) 2 E (ο) n 2 + N(ο) N P Nu k= k6=ο ; (2) 239

6 rom wic te value o = 2 6 SINR E (ο) 2 n + N can be obtained a Nu k= k6=ο 3 A C 7 7 : (3) Cluter ead Senor node In oter word, by etting te value o according to (3), 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 tranmitted power, te bit rate will depend on te link quality Cae 2: Fixed Trougput Now 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 = i contant in ti cae ee Fig. 3a, were (N () ;N () ) = (3; 4), (N (2) ;N (2) (3) )=(4; 3), and(n ;N (3) )=(6; 2). Tereore, we can cange te number o pule per ymbol and te rame duration a long a teir multiplication i ixed. In ti cae, we employ te ollowing lemma to approximate te MAI rom uer k: Lemma : In a cip-yncronou cenario, te ditribution o te MAI rom uer k converge to te ollowing Gauian random variable M k οn ψ ; a min ; g!. Proo: See Appendix A.. Hence, te total MAI can be approximated a M ;N (ο) Nu k=;k6=ο! ; (4) Ten, te SINR o te ytem can be obtained a SINR = wic can be expreed a ( ) 2 E (ο) P n 2 + Nu k= k6=ο E (ο) r SINR = P n 2 + Nu Nc k= k6=ο A : (5) ; (6) ; (7) r 25 meter 25 meter Figure 4. A realization o enor ditribution over te geograpical area. by te deining te received ymbol energy o te kt uer by r = or k =;::: ;N u. Wen we aign te ame SINR value to all te uer, tey ave te ame BER, ence te ame trougput ince tey ave te ame ymbol time. Hence, rom (7), we ee tat we can cooe te ame received ymbol energy to acieve te ame BER or all uer. Denoting tat common energy by E r, we obtain rom (7) tat n 2 E r = SINR : (8) Nu SINR In oter word, or a deired SINR value, we can calculate te required received ymbol energy o te uer. Note tat te received ymbol energy can be expreed a Nc E r = k t d n : (9) k Since te ymbol energy i te multiplication o te number o pule per ymbol and te pule energy, we get E r = tp k d n k : (2) Note tat 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 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 24

7 Average data rate (bp) Average data rate (bp) 4 x Conventional (yncronou) Propoed (yncronou) Number o enor x 8 Conventional (ayncronou) Propoed (ayncronou) Number o enor Figure 5. Data rate improvement uing te adaptive approac in yncronou and ayncronou cenario. Sum o enor energie (Joule) Adaptive PG (Fixed CH) Fixed PG Adaptive PG (Randomly Mobile CH) Adaptive PG (Optimally Mobile CH) 5 5 Time (ec) Figure 6. Remaining aggregate energy in te network. violate te FCC regulation []. Tereore, multi-opping migt be neceary in ome cae. Finally, it i oberved tat given te ading coeicient and ditance o uer k, te energy can be et by canging and/or. In oter word, tere i a lexibility in tp adjuting te ymbol energy. However, tere are a ew iue to conider wen etting te ymbol energy. Firt, te FCC retriction on te peak-to-average ignal ratio can retrict te ue o very mall value. Secondly, altoug we conider lat ading cannel in ti paper, 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. 3.3 Extenion to Multipat Cannel Altoug te previou analyi aume AWGN cannel, extention to multipat cannel i alo poible. In tat cae, we conider RAKE receiver ince a MF would not gater uicient ignal energy due to large delay pread o UWB cannel. By imilar approace to te one in [], it can be own tat te MAI rom an interering uer converge to zero mean Gauian random variable imilar to te one in () and (4), wit te only dierence being a caling actor to te variance term. Tat caling actor 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 )ipre- erved. Due to pace limitation, extenive analyi o te MAI in adaptive IR-UWB ytem over requency-elective cannel i not included in ti tudy. 4 Simulation Reult Computer imulation are perormed to demontrate te improvement in te data rate and power conumption. Single cluter o a WSN i conidered, and enor node are randomly ditributed over te ield (25 25 meter a in Fig. 4). An SNR o 8:39dB i targeted, wic correpond to a BER o 4 or BPSK modulation, pat lo exponent i taken a n =2:4, pule widt i et to T c =:3n, and cip yncronou cae i taken in all cenario. It i aumed tat te tranmitted pule occupie te wole 7:5GHz o bandwidt in between 3:GHz :6GHz,and knowing tat te FCC mak allow a maximum tranmiion power o 4dBm/MHz witin ti requency range, maximum tranmitted energy per econd can be calculated a :562mW. Ti i te maximum power tat any enor can tranmit to comply wit FCC regulation, and may retrict cooing optimum N and N even i SINR i appropriate. For yncronou communication, data rate improvement wit repect to number o uer i evaluated wen optimum are ued to contruct ortogonal equence or eac uer (equation (8) and (9)), and averaged over realization o te enor ditribution. Noie variance i taken to be 2dB weaker tan te energy per tranmitted pule. Two ceme are analyzed: conventional approac, were te wort cae proceing gain are ued or all te 24

8 Number o alive node Adaptive PG (Fixed CH) Fixed PG Adaptive PG (Randomly Mobile CH) Adaptive PG (Optimally Mobile CH) 5 5 Time (ec) Figure 7. Number o alive node in te network. node are aumed or imulation puoe. Te parameter are updated ater eac round o 3μec to adapt to Rayleig ading cannel and poibly canged ditance, and energy conumption in 5 4 round i analyzed. Simulation reult ow 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, wic may be conidered or example or recuerobot 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 important, we would like to maximize te network lietime o te enor. It i oberved in Fig. 6 and 7 tat i te cluter ead randomly move in te network, te network lietime orten erioult. On te oter and, movement o te cluter ead ater eac round to an optimal location (wic i te expected value o te location o te alive enor node, i.e. E[x ;y ],were(x ;y ) are te coordinate o eac 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. uer; and te adaptive approac, were jut enoug proceing gain i aigned to eac uer. Reult in irt part o Fig. 5 ow tat te average data rate or yncronou communication wit te propoed metod i at leat twice te conventional approac. Note tat Fig. 5 doe not demontrate te gain obtained due to deat and mobilitie o te enor, wic are exploited periodically to update te code and increae te data rate. Furtermore, a trivial analyi can be repeated to demontrate te additional aving in power conumption due to te decreae in te average proceing gain ued per ymbol. For ayncronou communication, cae and cae 2 are analyzed eparately. For cae, Gauian approximation i ued to evaluate te data rate or conventional and propoed metod in an intererence limited environment. Simulation reult in econd part o Fig. 5 imply tat increaing te number o enor doe not eect te data rate igniicantly a it aect te yncronou communication. Ti i becaue a ixed rame duration i ued or dierent number o uer, and te number o pule per ymbol i te only term tat determine te data rate. In te conventional metod, te data rate i lower-bounded by te data rate o te urtet away uer, wic doe not cange igniicantly wit te number o uer. For adaptive implementation, ince ewer pule are ued or cloer enor, iger aggregate data rate are acieved. Simulation reult or cae 2 are preented in Fig. 6 and 7, were te data rate are identical or all te uer and i et to (N c T c ) = ( 4 :3 9 ) = 33kbp. Continuou tranmiion o all te enor, and very low initial battery energy aignment (mj) or eac 5 Concluion In ti paper, adaptation o multiple acce parameter in cluter baed UWB-IR WSN a been analyzed or bot yncronou and ayncronou communication cenario. For yncronou communication, an ortogonal equence contruction a been preented, wic aign variable proceing gain to te enor, and acquire te deired BER requirement at eac enor. For ayncronou communication ytem, Gauian approximation metod ave been ued to adapt te tranmiion power and proceing gain o te enor, and a matematical ramework a been developed or te analyi o MAI wen te number o pule per ymbol and rame duration o eac uer are dierent. Data rate and power aving improvement ave been demontrated uing computer imulation. Reerence [] Federal Communication Commiion: Reviion o part 5 o te commiion rule regarding ultra-wideband tranmiion ytem, April 22. [2] H. Arlan. Adaptation Tecnique and te Enabling Parameter Etimation Algoritm or Wirele Communication Sytem. Book Capter, Signal Proceing Communication Handbook, CRC Pre, 24. [3] N. J. Augut, R. Tirugnanam, and D. S. Ha. An adaptive UWB modulation ceme or optimization o energy, BER, and data rate. In Proc. IEEE Ultrawideband Sytem Tecnol. (UWBST), Kyoto, Japan, May

9 [4] F. Berggren and S. L. Kim. Energy-eicient control o rate and power in DS-CDMA ytem. IEEE Tran. Wirele Commun., 3(3): , May 24. [5] P.Billingley. Probability and Meaure. Jon Wiley & Son, New York, 2nd edition, 986. [6] 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. Tecnical report, EPFL Tecnical Report ID: IC/24/2, Lauanne, Switzerland, Jan. 24. [7] F. Cuomo, C. Martello, A. Baiocci, and F. Capriotti. Radio reource aring or ad oc networking wit UWB. IEEE J. Select. Area Commun., 2(9): , Dec. 22. [8] J. Diaz and Y. Bar-ne. Adaptive tranmiion or UWB impule radio communication. In Proc. Con. on Inormation Science Syt. (CISS), Baltimore, MD, Mar. 23. [9] E. Filer and H. V. Poor. On te tradeo between two type o proceing gain. In Proc. 4t Annual Allerton Con. on Commun. Control Computing, Monticello, IL, Oct. 22. [] S. Gezici, H. Kobayai, H. V. Poor, and A. F. Molic. Perormance evaluation o impule radio UWB ytem wit pule-baed polarity randomization. Submitted to IEEE Tran. Sig. Proceing, Nov. 23; Revied May 24. [] 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. 24. [2] 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, page , Reton, VA, Nov. 23. [3] 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), Pari, France, June 24. [4] 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), volume 2, page 94 99, Atlanta, GA, Mar. 24. [5] W. R. Heinzelman, A. Candrakaan, and H. Balakrinan. Energy eicient communication protocol or wirele microenor network. In Proc. Annual Hawai International Conerance on Sytem Science, page 35 33, Hawai, Jan. 2. [6] D. Kim. Rate-regulated power control or upporting lexible tranmiion in uture CDMA mobile network. IEEE J. Select. Area Commun., 7(5): , May 999. [7] S. S. Kolencery, J. K. Townend, J. A. Freeberyer, and G. Bilbro. Perormance o local power control in peer-topeer impule radio network wit burty traic. In Proc. IEEE Global Telecommun. Con., volume 2, page 9 96, Poenix, AR, Nov [8] W. M. Lovelace and J. K. Townend. Adaptive rate control wit cip dicrimination in UWB network. In Proc. IEEE Ultrawideband Sytem Tecnol. (UWBST), page 95 99, Reton, VA, Nov. 23. [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), volume, page 5 54, New Orlean, LA, Sept [2] 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. 23. [2] L. C. Yun and D. G. Meercmitt. Variable quality o ervice in CDMA ytem by tatitical power control. In Proc. IEEE Int. Con. Commun., volume 2, page 73 79, June 995. [22] H. Zang and R. Kono. Sot-pectrum adaptation in UWB impule radio. In Proc. IEEE Peronal Indoor Mobile Radio Commun. (PIMRC), volume, page , Beijing, Cina, Sep. 23. [23] H. Zu and A. Ganz. A radio reource control metod in UWB MAC protocol deign. In Proc. IEEE Military Commun. Con. (MILCOM), volume 2, page , Boton, MA, Oct. 23. A Appendice A. Proo o Lemma Uing (2) and (3), te MAI rom uer k, M k in (5), can be expreed a ollow were M k;l = a (ο) l M k = j= q a (k) j b (k) l= bj=n (k) c M k;l ; (2) (k) R(jT lt (ο) + c (k) j T c c (ο) l T c kt c ); (22) wit k =(i k i ο )=T c being te amount o ayncronim between te deired uer and uer k in term o te cip interval. Aume tat N (ο)» N (k). In ti cae, it can be own tat M k;l g N () l= orm a -dependent equence [5], were eac term i zero mean due to te random polarity code (EM k;l g = ). Hence, a N (ο)! P, p N () N () l= M k;l converge to N ( ; EMk;l 2 g + 2EM k;l M k;l+ g) [5]. 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, 243

10 we obtain EM 2 (k) k;lg ==N. Hence, we get q l= M k;l οn ψ ;! ; (23) a!. Tereore, or large N (ο), we can approximate M k in (2) a in (4). For >, we can ollow a imilar approac and expre te MAI rom uer k a te ummation o term, wic orm a -dependent equence. Ten, a!, q N (k) l= ^M k;l οn ψ ;! ; (24) were ^M k;l i te intererence related to te lt rame o uer k. Ten, or large, M k i approximately ditributed a N ( ; ). However, ince te total gain N c = i contant or all uer, te variance i te ame a tat o equation (4). All in all, or large value o min ; g, te ditribution o te MAI rom uer k i approximately given by (4). Λ 244