Communication and Compression in Dense Networks of Unreliable Nodes. Dragan Rade Petrović

Transcription

1 Communication and Compession in Dense Netwos of Uneliable Nodes by Dagan Rade Petović B.S. (Univesity of Illinois at Ubana-Champaign) 999 M. S. (Univesity of Califonia, Beeley) 00 A dissetation submitted in patial satisfaction of the equiements fo the degee of Docto of Philosophy in Engineeing - Electical Engineeing and Compute Sciences in the GRADUATE DIVISION Of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in chage: Pofesso Kannan Ramchandan, Chai Pofesso Jan Rabaey Pofesso Paul Wight Sping 005

2 The dissetation of Dagan Rade Petović is appoved: Chai Date Date Date Univesity of Califonia, Beeley Sping 005

3 Communication and Compession in Dense Netwos of Uneliable Nodes Copyight 005 by Dagan Rade Petović

4 Abstact Communication and Compession in Dense Netwos of Uneliable Nodes by Dagan Rade Petović Docto of Philosophy in Engineeing Electical Engineeing and Compute Sciences Univesity of Califonia, Beeley Pofesso Kannan Ramchandan, Chai The dive towad the implementation and massive deployment of wieless senso netwos calls fo ulta-low-cost, low-powe and eve smalle nodes. While the digital subsystems of the nodes ae still epeiencing eponential eduction of all of these metics as descibed by Mooe's Law, thee is no such tend egading the pefomance of analog components needed fo the adios that enable the nodes to communicate wielessly with one anothe. This dissetation pesents a two pat appoach to educing the enegy consumption of the adios. Fist, a new adio achitectue is pesented that geatly educes the powe equied to opeate a tansceive, as well as educing the cost and size of the nodes. Secondly, a novel distibuted compession scheme is intoduced that allows the senso nodes to compess thei data in ode to educe the amount of communication that the adios must pefom.

5 The dissetation pesents a fully integated achitectue of both digital and analog components (including local oscillato) that offes significant eduction in cost, size and powe consumption of the oveall node. Even though such a adical achitectue cannot offe the eliable tuning of standad designs, it is shown that by using andom netwo coding, a dense netwo of such nodes can achieve thoughput linea in the numbe of channels available fo communication. Moeove, the atio of the achievable thoughput of the untuned netwo to the thoughput of a tuned netwo with pefect coodination is shown to be close to / e. By contast, it is also shown that if coding is not used (i.e. if nodes ae only allowed to fowad pacets without pocessing them), the pefomance does not impove with inceased density and available spectum. To educe the amount of communication among nodes equied, a novel appoach to educing enegy consumption in senso netwos using a distibuted adaptive signal pocessing famewo and efficient algoithm is poposed. Specifically, the dissetation pesents a distibuted way of continuously eploiting eisting coelations in senso data based on adaptive signal pocessing and distibuted souce coding pinciples. This appoach enables senso nodes to blindly compess thei eadings with espect to one anothe without the need fo eplicit and enegy-epensive inte-senso communication to effect this compession. Futhemoe, the distibuted algoithm used by each senso node is etemely low in compleity and easy to implement (i.e., one modulo opeation), while an adaptive filteing famewo is used at the data-gatheing

6 unit to continuously lean the elevant coelation stuctues in the senso data. Applying the algoithm to testbed data esulted in enegy savings of 0%-65% fo a multitude of senso modalities. Both the netwo coding fo communication with untuned adios and the distibuted souce coding schemes equie minimal compleity fom the lowpowe senso nodes. Instead, the compleity of the system is pushed towad the edge of the netwo whee a gateway between the wieless netwo and the wied wold esides. 3

7 TABLE OF CONTENTS List of Figues... iv List of Tables... vi Acnowledgments... vii Chapte : Intoduction.... Tading-off Radio Powe Dissipation fo Tunability...5. Distibuted Compession of Senso Node Data Contibutions... Chapte : Reliable Communication Using Untuned Radios...4. Dawbacs of Untuned Radios...7. Multi-Hop Communication Method....3 Pactical Justification of the Model Analysis Tansition Pobabilities Robustness Gows Eponentially with Density Stability and Optimal Ratio of Density to Channelization System Level View Compaison to Schemes Using Untuned Radios with Wide Receive Filtes Compaison to Schemes Using Tuned Radios...43 Chapte 3: Thoughput of Netwos of Untuned Radios...46 i

8 3. Maimum thoughput ove One Hop Maimum thoughput ove Many Hops Achievable Thoughput ove Many Hops Random Gaph Repesentation of the Netwo Connectivity Ma-Flow of the Random Gaph Simulation Results...59 Chapte 4: Distibuted Compession Bacgound on Compession with Side Infomation Code Constuction fo Distibuted Compession Coelation Tacing Paamete Estimation Decoding Eo Queying and Data Repoting Algoithm Data-Gatheing Node Algoithm Senso Node Algoithm Simulation Results Coelation Tacing Enegy Savings Robustness to Eos Conclusion...97 Chapte 5: Futue Wo...00 ii

9 Appendi A: Maimizing the Numbe of Channels with Eactly one Tansmitte...0 Appendi B: Thoughput of Routing without Coding in a Netwo of Untuned Radios...04 Bibliogaphy...09 iii

10 LIST OF FIGURES Numbe Page. An eample senso netwo topology in which consideable gains can be achieved fom distibuted compession.... Signal bandwidth elative to pocess vaiation Poposed multi-hop communication method Pobability distibution of numbe of tansmittes while the pacet is still alive Robustness v. Channelization fo vaious values of α Pobability of failing to tansmit a pacet ove 0 hops v. Channelization fo vaious values of α Random gaph epesenting connectivity in the netwo of nodes with untuned adios Simulation esults: Thoughput vs. numbe of input adios Distibuted compession set-up Achievable ate egions in distibuted compession A tee based constuction fo compession with side infomation An eample of the tee based codeboo Adaptive filteing bloc used to fom the side infomation and decode the senso eading...8 iv

11 4. Toleable noise and pediction noise fo 8,000 samples of humidity data Toleable noise and pediction noise fo 8,000 samples of tempeatue data Toleable noise and pediction noise fo 8,000 samples of light data Random gaph epesenting connectivity when only outing is allowed...05 v

12 LIST OF TABLES Numbe Page. Enegy savings of LMS-based coelation tacing and distibuted compession scheme...pp. Epected thoughput of outing...pp vi

13 ACKNOWLEDGMENTS The autho vii

14 Chapte INTRODUCTION Advances in wieless communication as well as embedded micopocesso design and manufactuing have led to geat inteest in ecent yeas in the possibility of doing distibuted sensing and contol. As a esult, the emeging field of wieless senso netwos has become a vey active aea of both academic eseach []-[4] and industial development [5]-[9]. The goal is to design and poduce tiny siliconbased devices, usually efeed to as nodes, that have some sensing capability (e.g. light-senso, themomete, humidity-senso, baomete, acceleomete, magnetomete, etc.) along with some amount of memoy and pocessing capability, as well as the ability to communicate wielessly with each othe. These nodes could then be deployed in some envionment and used to obseve, though thei sensing capability, some aspects of that envionment. Deploying many such nodes would allow fine-gained infomation about the state of the envionment that could then be used to tae some action to contol cetain paametes. In ode to distibute the nodes densely, they must be made small. This size constaint also imposes a limit on the pocessing powe as well as the enegy available to the individual nodes. Theefoe, pefoming comple tass would equie the coodination and coopeation of many nodes.

15 The potential scenaios fo use of senso netwos ae fa anging. One of the many applications fo which senso netwos ae aleady being used is monitoing the stuctual integity of buildings and bidges [0], in which nodes with acceleometes ae placed at ey unctions of the stuctue to measue its movement as a esponse to stesses due to seismic, tidal, and taffic activity. Having this data allows fo timely maintenance of the building o bidge that is also moe cost-effective than the taditional appoach of pefoming maintenance and einfocement at cetain time intevals, whethe they ae needed o not [0]. Anothe impotant application of senso netwos that is eceiving a lot of attention is envionmental contol within living and woing spaces []. While fully a thid of all enegy consumed in the developed wold is spent on envionmental contol of living and woing spaces (the othe two thids ae spent on agicultue, manufactuing, and tanspotation), it is estimated that 80% of this enegy is wasted due to inadequate ability to measue the state of the envionment and a lac of fine-gained actuation to influence it []. Senso netwos ae also used fo habitat monitoing in animal sanctuaies []. Using senso netwos allows biologists to eep tac of cucial envionmental factos that affect the health of animal and plant populations in diffeent ecosystems. In moe uban aeas, senso netwos ae being deployed fo highway taffic contol [3]. Instead of teaing up asphalt to install inducto coils to measue the flow of taffic, senso nodes with magnetometes ae being used to monito the taffic and this data can be used in eal time to contol the taffic by updating the pattens of taffic and meteing lights as well as suggested outes to tip-planning and global positioning system (GPS)-

16 based guidance systems [3]. Waehouse inventoy tacing with senso netwos is also gaining a lot of attention in industy [4]. In ode to gain epeience and ealy eposue, most initial effots in the field of senso netwos have elied on available off the shelf components (sensos, pocessos, adios, and memoy) to assemble the fist senso netwo nodes. The main lesson of those ealy epeiences was that the netwos wee vey fagile. The nodes fequently failed because they an out of enegy o because they wee damaged due to eposue to the envionment (e.g. bumped o stepped on). The communication channels between the nodes wee also found to be unstable. Depending on the topology of the envionment, it is not uncommon to find nodes a few metes apat that cannot eliably communicate with one anothe, while othe pais of nodes that ae tens of metes apat can. Pehaps most impotantly, the netwos did not scale well because inceased density esulted in geate contention fo the wieless communication medium causing collisions among the tansmissions. As a esult of this, most commecial effots have focused on maing the nodes moe eliable and equipping them with bette, and moe comple and powe-consuming adios, in ode to mae the lins among the nodes moe eliable. These effots have been successful in giving eposue in the technical community to this emeging field though the deployment of wieless senso netwos in the applications aleady mentioned. Howeve, maing the nodes moe eliable equies them to be costly, powe-hungy, and lage. This dissetation agues that, in ode to mae wieless senso netwos tuly 3

17 ubiquitous, the nodes must be made cheap, thei powe dissipation must be compaable to the amount powe that can be scavenged fom the envionment, and they must be made small so that they can be deployed with high density. Also, a new class of potocols must be developed specifically fo wieless senso netwos that can benefit fom, athe than suffe fom density. The benefit of such an appoach will only incease in the futue with eve moe demanding applications. The potential applications of senso netwos that ae being consideed in the long-tem include such science-fiction-lie concepts as smat sufaces that can espond to contact o seve as a communication bacplane. Anothe possible application in the long tem is sin fo aiplanes that can povide eal-time monitoing of and alets egading the state of evey squae centimete of the aicaft s suface. It may even be possible to eventually poduce senso nodes small enough to be inseted into the blood-steam to povide eal-time diagnostics of factos such as blood pessue, blood flow, glucose and insulin levels, etc. To mae such deployments economically and technologically feasible, it is necessay to dastically educe the cost, size and enegy consumption of the nodes available today. Mooe s Law still povides fo eponential eduction of these metics ove time when it comes to the digital components that compise the memoy, computation and coding in the nodes. Howeve, thee is no equivalent tend to Mooe s Law that applies to the analog components needed fo the adios 4

18 that enable the nodes to communicate with one othe. This wo intoduces ) a new achitectue fo the analog adios and ) a distibuted souce coding scheme that allows the nodes to compess thei eadings in ode to educe the numbe of bits that have to be tansmitted by the adio, theeby educing the enegy consumed.. TRADING-OFF RADIO POWER DISSIPATION FOR TUNABILITY The poposed adio achitectue can geatly educe the cost, size (5 eduction) and enegy consumption (0 eduction) of the nodes. In fact it is epected that the poposed achitectue will allow the enegy consumption of the nodes to be so low that they could be fully poweed by enegy scavenged fom the envionment [5]. The penalty fo using such a adical achitectue is that the adios become untuned and it is no longe possible to guaantee that any abitay pai of nodes will be able to communicate with each othe. Instead, it becomes necessay to ely on the density of nodes to mae the oveall netwo capable of poviding eliable communication. Naowband adios have shown to be the achitectue of choice fo low-powe applications [6], [7], [6], as they ae low in compleity and consume less powe than spead spectum o othe wide-band techniques. One fundamental equiement of naowband adios is that the tansmitte s caie fequency and the eceive s detection fequency must be well-matched. This is taditionally 5

19 accomplished by employing a cystal at both the tansmitte and eceive to povide the same low fequency efeence. This efeence fequency is multiplied via a phase-loced loop (PLL) to geneate the caie wave. Howeve, the off-chip cystal contibutes significantly to the cost, size, and powe consumption of such tansceives. The cost is due to the etenal quatz cystals being moe epensive than the silicon used fo the baseband signal pocessing as well as the need to bond sepaate components. This poblem is especially acute in the design of highly integated tansceives fo wieless senso netwos. The size of taditional low powe tansceives is lagely due to the etenal cystal efeence and the inteface between the cystal and the silicon integated cicuit (IC). Additionally, the powe consumption of low powe adios is dominated by the cystal efeenced PLL. Theefoe, geat savings in all thee of these aeas could be obtained by eliminating the off-chip cystal and PLL. Even when cae is taen to ensue that all adios ae tuned and ae attempting to communicate on the same fequency, eliable communication is not guaanteed. Pactical implementations of senso netwos ae notoious fo having unstable lins because naowband communication is susceptible to deep fades between nodes [7], [8]. Since it is not feasible to ovecome these fades by tansmitting with moe powe (due to powe-constaints), it has been poposed that andomized algoithms be used to ensue eliable communication [9], [0]. Such algoithms popose to povide eliable multi-hop communication by eploiting the boadcast natue of wieless tansmissions. The ey idea is fo a tansmitting node to send a 6

20 beacon to many potential fowading nodes and then select one node to be the net hop fo the pacet among those that espond to the beacon. Howeve, collisions among the esponses to the beacon as well as the time-vaying quality of the communication channels (a channel may be good duing the beaconing, but become bad duing the esponse and/o data tansmission) contibute significant ovehead to such schemes. This dissetation poposes a fundamentally diffeent way of designing and opeating a tansceive. The quatz cystal is eliminated and eplaced by an onchip esonato such as an inducto-capacito (LC)-cicuit o a nanoelectomechanical esonant stuctue. This maes it possible to economically poduce millions of nodes and densely deploy them by, fo eample, weaving them into fabics o miing them with paint. The poposed achitectue allows a senso node to be developed entiely out of thin-film technologies (adio, digital components, battey, enegy scavenging, and sensing). Howeve, the dawbac of such achitectues is that the vaiations in the manufactuing pocess ae lage, esulting in un-tuned adios. Theefoe, two naowband adios poduced by such a pocess ae not liely to be able to communicate with each othe. To addess this poblem, a low-compleity communication potocol is poposed that maes use of the high density of nodes to ensue eliable communication using such untuned adios even without the need fo handshaing potocols o e-tansmission. By eliminating the need fo this ind of coodination, the potocol is also made 7

21 moe obust to lin failues, while the density that is made possible by such low cost designs maes the netwo obust to the failue of individual nodes.. DISTRIBUTED COMPRESSION OF SENSOR NODE DATA Motivated by the enegy constaint in senso netwos, thee has been consideable ecent inteest in the aea of enegy-awae outing fo ad hoc and senso netwos [8]-[30] and efficient infomation pocessing [3], [3] to educe the enegy usage of senso nodes. Fo eample, one method of conseving enegy in a senso node is to aggegate pacets along the senso paths to educe heade ovehead. This dissetation poposes a fundamentally new method of conseving enegy in senso netwos that is mutually eclusive and complementay to those appoaches, and can be used in combination with them to incease enegy-consumption eduction. The appoach is based on udiciously eploiting eisting senso data coelations in a distibuted manne. Coelations in senso data ae bought about by the spatiotempoal chaacteistics of the physical medium being sensed. Dense senso netwos ae paticulaly ich in coelations, whee spatially dense nodes ae typically needed to acquie fine spatial esolution in the data being sensed, and fo fault-toleance fom individual node failues. Eamples of coelated sensos include tempeatue and humidity sensos in a simila geogaphic egion, o magneto-metic sensos tacing a moving vehicle. Anothe inteesting eample of 8

22 coelated senso data involves audio field sensos (micophones) that sense a common event such as a concet o whale cies. Audio data is paticulaly inteesting in that it is ich in spatial coelation stuctue due to the pesence of echoes, causing multiple sensos to pic up attenuated and delayed vesions of a common sound oigin. This dissetation poposes to emove the edundancy caused by these inheent coelations in the senso data though a distibuted compession algoithm which obviates the need fo the sensos to echange thei data among each othe in ode to stip thei common edundancy. Rathe supisingly, it will be shown that compession can be effected in a fully blind manne without the senso nodes eve nowing what the othe coelated senso nodes have measued. This enables a simple and inepensive achitectue fo each senso node and is in fact pefeable to an achitectue based on each senso nowing the othe sensos' measuements. The poposed paadigm is paticulaly effective fo senso netwo achitectues having two types of nodes: sensing nodes and datagatheing nodes. The sensing nodes gathe data of a specific type and tansmit this data upon being queied. The data-gatheing node queies specific sensos in ode to gathe infomation in which it is inteested (see Figue ). We will assume the above achitectue of Figue and show that fo such an achitectue, we can devise compession algoithms that have vey lightweight encodes, yet can achieve significant savings. Note, that this wo tagets vey lightweight encodes because we assume that the sensos have limited pocessing powe, but the 9

23 constuctions intoduced hee can be easily stengthened given geate computational powe at the sensos. The savings ae achieved by having the data-gatheing node tac the coelation stuctue among nodes and then use this infomation to effect distibuted senso data compession. The coelation stuctue is detemined by using an adaptive pediction algoithm. The sensos, howeve, do not need to now the coelation stuctue; they need to now only the numbe of bits that they should use fo encoding thei measuements. As a esult, each senso node is equied to pefom vey few opeations in ode to encode its data. The decode, howeve, is consideably moe comple, but it esides on the data-gatheing node, which is not assumed to be enegy-constained. Peliminay esults based on ou distibuted compession and adaptive pediction algoithms pefom well in ealistic scenaios, achieving 0-65% enegy savings fo each senso in typical cases. In addition, ou distibuted compession achitectue can be combined with othe enegy saving methods such as pacet/data aggegation to achieve futhe gains [33]. 0

24 senso node senso node senso node senso node senso node senso node senso node quey data senso node quey data Data Gatheing Node Figue. An eample senso netwo topology in which consideable gains can be achieved fom distibuted compession. A compute acts as the data-gatheing node and queies vaious sensos to collect data.

25 .3 CONTRIBUTIONS This dissetation focuses on educing the enegy spent by the adios of wieless senso netwo nodes. The fist pat poposes a new achitectue fo the adios that eliminates the tuning elements (off-chip cystal and the efeence phase loc loop (PLL)). Such a adio equies consideably less powe to opeate than taditional designs and is also much cheape and smalle than taditional adios, but it sacifices the ability to tune the tansceives. The second pat of the dissetation pesents a code constuction and coelation tacing algoithm that allow the senso nodes to compess thei eadings in ode to educe the amount of communication equied among the nodes. The contibutions of the dissetation ae: It is shown that the eliability of a netwo of untuned adios gows eponentially with node density and available bandwidth. It is shown that by using andom linea netwo coding (which is computationally vey simple), achievable thoughput of a netwo of untuned adios is linea in the density of nodes and the amount of spectum available fo communication, same as in a fully-coodinated netwo of tuned adios. The atio of the achievable thoughput of the untuned netwo to the achievable thoughput of a tuned netwo is shown to be close to / e.

26 It is also shown that if a netwo of untuned adios does not utilize any coding in the netwo (i.e. the intemediate nodes only fowad pacets without pocessing them), the thoughput of the netwo does not gow with node density and the amount of spectum available fo communication. A computationally inepensive encode is poposed that can suppot multiple compession ates, allowing senso nodes to compess thei data without having to do heavy pocessing. An adaptive coelation-tacing algoithm based on Least-Mean-Squae (LMS) filteing is pesented. The algoithm can continuously tac and eploit both spatial and tempoal coelation in the sensos' data. 3

27 Chapte RELIABLE COMMUNICATION USING UNTUNED RADIOS With the emegence of ubiquitous wieless communication netwos (such as senso netwos) and ambient intelligence, the design of low data-ate shot distance wieless tansceives has gained pominence. Naowband adios have shown to be the achitectue of choice fo such applications [6],[7],[6], as they ae low in compleity and consume less powe than spead spectum o othe wideband techniques. One fundamental equiement of naowband adios is that the tansmitte s caie fequency and the eceive s detection fequency must be wellmatched. This is taditionally accomplished by employing a cystal at both the tansmitte and eceive that povide the same efeence fequency fo the caie wave. Howeve, geat savings in both manufactuing cost and powe consumption could be obtained by eliminating the off-chip cystal. In [6] a mechanical esonato is used to povide the caie fequency at lowe cost and powe consumption elative to cystal-based designs. The State-of-the at-quatz cystalbased adios, such as the Chipcon CC40, typically equie 50mW of powe in both tansmit (T) and eceive (R) mode [6] fo communication ove 0 metes. The mico-electomechanical (MEMS) based adio shown in [6] povides substantial powe and integation savings ove taditional designs, opeating at 3.6mW in R mode and 5.9mW in T mode fo communication ove 30 metes. 4

28 The cost and powe consumption of the tansceive could be futhe educed by two odes of magnitude if a fully integated adio could be built that uses an onchip esonato to povide the efeence fequency. The dawbac of using an integated on-chip esonato (such as an LC cicuit o nano-electomechanical weight) is that the vaiations in the manufactuing pocess ae lage. Theefoe, two naowband adios poduced by such a pocess ae not guaanteed to be able to communicate with each othe. To mitigate this poblem, this dissetation poposes to eploit the high density of nodes in the netwo that would be made economically feasible by using such a low-cost design. The idea is to eploit the boadcast natue of wieless communications. At high node density, this ensues that when a node attempts to communicate, with high pobability at least one of its neighbos can eceive the message even though not all the nodes ae capable of communicating with each othe. Thee is a potential poblem with using this appoach fo multi-hop communication, howeve. If nodes ust boadcast thei pacets and have any of a numbe of candidate neighbos that hea the tansmission fowad the pacet, it is liely that multiple neighbos will eceive and fowad the pacet. This would esult in an eplosion in the numbe of copies of a pacet as it popagates though the netwo. To pevent this eplosion in the numbe of pacets, collisions - usually consideed a bane of wieless communications - could be eploited to ensue that the numbe of eceived copies of a pacet at each step does not gow unboundedly. If too many nodes ae tansmitting a copy of the pacet, they will 5

29 collide, esulting in a educed numbe of eceives that successfully eceive the pacet. If few tansmittes ae sending the pacet, the numbe of collisions will be low, inceasing the numbe of successful eceptions of the pacet. It will be shown analytically that these opposing foces cause the system to each a balanced equilibium allowing fo eliable communication though the netwo. Inceasing the density along with poviding fo channelization esults in eliability of the communication method that gows eponentially with density. An additional benefit of distibuting the esponsibility fo communication among many nodes is that it maes the netwo much moe obust to the inevitable failue o death of individual nodes. The adio achitectues enabled by such an appoach mae it possible to envision fully-integated, single-chip nodes that would be small enough (0 mm 3 ), cheap enough (<$0.0), and low powe enough (0 µw) that they could be woven into fabics o mied in with wall-paint. This would enable the ealization of tulydisappeaing electonics, that is ubiquitous computing and communication devices that can be effectively integated into the envionment, and disappea fom view. The availability of these integated meso-scale compute nodes would open the doo fo new concepts such as smat fabics, intelligent sufaces and ambient intelligence. The est of this chapte is oganized as follows: Section. descibes the issues involved in using such low-cost, low-powe, but uneliable adio achitectues. 6

30 Section. poposes a communication method that eploits the high density of nodes made feasible by using such low-cost and small-fom-facto nodes to ovecome the inheent uneliability of the adios. Section.3 discusses the pactical consideations that lead to the modeling assumptions made in Section.. Section.4 analyzes the eliability of the poposed scheme. Finally, Section.5 compaes the pefomance of the poposed scheme to two benchma schemes.. DRAWBACKS OF UNTUNED RADIOS The main dawbac of using an on-chip esonato is that the vaiations in the manufactuing pocess ae lage. To achieve fequency toleance appoaching a quatz cystal, pohibitively epensive timming would have to tae place. In addition, dift ove time and tempeatue would quicly ende the timming inaccuate. The othe option is to leave the tansmittes and eceives un-tuned, which means that two naowband adios poduced by such a pocess ae not guaanteed to be able to communicate with each othe. Figue pesents a qualitative illustation of the challenges pesented by this appoach. In a taditional naow-band achitectue using a quatz cystal efeence, the signal bandwidth is typically odes of magnitude lage than the cente fequency toleance. When using un-tuned eceives, the situation is evesed and the caie fequency vaiation is odes of magnitude geate than the signal bandwidth. This means that if two adios obtained fom such a pocess attempt to communicate, and the 7

31 eceive is sensitive only to a naow potion of the spectum (as would be done when using taditional, tuned adios), the pobability that the tansmitte is sending a signal in this naow potion of the spectum is vey low. The most staightfowad way of ensuing that adios poduced by such an impecise pocess can communicate with each othe is to allow the font-end filte of each eceive to admit all the fequencies in the ange of caie fequencies that could esult fom the manufactuing pocess. Such wide-band eceives would be able to hea any of the adios poduced by the pocess, but they would also admit all the noise and intefees in the band-pass ange of the font-end filte. This, in tun, would eithe foce the tansmitte to output moe powe to povide the same signal to noise atio (SNR) at the eceive, o it would geatly educe the communication ange of the nodes. 8

32 P(f caie ) Signal BW 3 σ vaiation f caie Figue. Signal bandwidth elative to pocess vaiation when using on-chip LC esonatos to povide the caie fequency fo naowband adios. When using an LC esonato without a cystal efeence, it is not possible fo a adio to now eactly at what fequency it is opeating. Howeve, thee is an altenative to using the bute-foce method of having a wideband font-end filte at the eceive that admits all the possible fequencies that might contain the tansmitted caie fequency. The eceive could employ filteing with the same bandwidth it would use in classical naowband communication when the tansmitte s caie fequency is nown with high accuacy. Of couse, in this case thee is no guaantee that a paticula tansmitte would be able to communicate with a paticula eceive. If the input fequency ange of a paticula eceive did admit the tansmitte s caie fequency, the pai would be able to communicate. Othewise, the esult would be the same as if the tansmitte wee communicating on a channel othogonal to the one that the eceive is monitoing. 9

33 The esult is that uneliable manufactuing pocesses can be used to povide channelization to the communication system. Even though a paticula tansmit-eceive pai may not be able to communicate because they would be effectively tuned to diffeent channels, a sufficiently high density of nodes ensues a high pobability that thee ae pais of tansmittes and eceives that can communicate with one anothe. The numbe of channels available in the system is detemined by the atio of the vaiations of the manufactuing pocess to the eceive bandwidth. Naowing the eceive input bandwidth esults in moe communication channels. This would decease the pobability that any given pai of nodes could communicate with each othe, but it would also decease the amount of noise admitted by the eceive, inceasing the eceive sensitivity and educing the necessay tansmitted powe level. It should be noted that the eceive bandwidth can be alteed by using digital contol to adust the eceive adio paametes. As long as the bandwidth admitted by the eceive filtes is geate than the signal bandwidth, thee will be a non-zeo pobability that two andomly selected nodes will be able to communicate with each othe. Thee is a potential poblem with using this appoach fo multi-hop communication, howeve. If nodes simply boadcast thei pacets and have any of a numbe of candidate neighbos that hea the tansmission fowad the pacet, it is liely that multiple neighbos will eceive and fowad the pacet. This would esult in an eplosion in the numbe of copies of a pacet as it popagates though the 0

34 netwo. This phenomenon is nown as boadcast stom. To pevent this eplosion in the numbe of pacets, collisions - usually consideed a bane of wieless communications - could be eploited to ensue that the numbe of eceived copies of a pacet at each step does not gow unboundedly. If too many nodes ae tansmitting a copy of the pacet, they will collide esulting in a educed numbe of eceives that successfully eceive the pacet. If few tansmittes ae sending the pacet, the numbe of collisions will be low inceasing the numbe of successful eceptions of the pacet. It will be shown in Section.4.3 that these opposing foces cause the system to each a balanced equilibium allowing fo eliable communication though the netwo. In the est of this chapte and the net, this abstaction of having multiple channels available fo communication is made. Note that it is not necessay fo the channels to be othogonal. What is impotant is the numbe of tansmitte caie fequencies that fall within the bandwidth being monitoed by a paticula eceive. The pobability that any given tansmitte falls within the eceive s ange is dependent only on the atio of the ange of possible caie fequencies to the eceive bandwidth. This atio is equivalent to the numbe of channels in the analysis pesented hee because it is equal to the maimum numbe of independent tansmissions that can be made simultaneously without intefeing with one anothe.

35 . MULTI-HOP COMMUNICATION METHOD In ode to convey the intuition of the poposed communication method, conside the scenaio shown in Figue 3. The souce node has a pacet to send to the destination node. If the souce and destination nodes ae fa enough apat, the souce node is not able to tansmit the pacet diectly to the destination node. Instead, it has to ely on nodes that lie between it and the destination to fowad the pacet in a multi-hop fashion. The egion between the souce and destination nodes can be divided into disoint blocs as shown in the Figue 3. This can be accomplished by including the coodinates of the cone points of bloc containing the net-hop nodes. If the size of the blocs is small enough elative to the tansmission ange of the nodes adios, it is possible fo any node to communicate with any othe node in a neighboing bloc. This maes it possible to have the pacet hop fom one bloc to the net until it eaches the destination. If the tansmitte selects a paticula node in the net bloc to be the net hop on the pacet s way to the destination, thee is a dange that the tansmitte and the selected eceive ae not communicating on the same channel. If the nodes ae allowed to duty cycle thei adios in ode to conseve thei enegy, it is also possible fo the selected eceive to be in the off state at the time when the communication is attempted. Also, selecting only one node to oute the pacet towad the destination does not mae use of the boadcasting natue of wieless communication. When a pacet is tansmitted, all of the nodes in the neighboing

36 blocs that ae listening to the tansmitte s channel will be able to eceive the pacet as long as they ae on. This aises the following question: Is it possible fo the tansmitte node to boadcast its pacet and safely assume that at least one of the nodes in the neighboing bloc have eceived it without any need fo acnowledging the eception? Souce Destination H Figue 3. Poposed multi-hop communication method. Nodes in each bloc listen to L andomly selected fequency bands. If a node detects tansmissions fom the pevious bloc in any of those bands, it combines the inputs using andom linea netwo coding and boadcasts the esult to the net bloc. The potential poblem is that, in ode to ensue that at least one neighbo will eceive the pacet with high pobability even in the pesence of uneliable channels o un-tuned adios, the numbe of potential net hop neighbos must be high. In this case, it is liely that many neighbos will eceive the pacet and fowad it onwad. As the pacet popagates towad the destination, thee is a dange that the numbe of copies of the pacet will gow unboundedly because at each step (bloc) thee will be moe and moe nodes tansmitting the pacet. To pevent this fom happening, it may be possible to mae use of collisions on the 3

37 channel to pevent the numbe of copies of the pacet eceived in any bloc fom gowing unboundedly. Conside the scenaio in which thee ae multiple channels available fo communication among the nodes (as is the case when using un-tuned adio achitectues), and each of the nodes can dynamically select a channel to tansmit on o listen to. If moe than one tansmitte is opeating on a paticula channel concuently, a collision will occu and any node listening to that channel will be unable to decode any tansmissions on that channel duing that time. Note that the assumption that nodes dynamically select a channel to communicate on can be satisfied by eithe vaying the eactance of an LC-esonato (o selecting one of seveal available esonatos) on a single node, o by duty-cycling the nodes theeby maing a andom subset of them active in communication at any point in time. Conside the case when the netwo is divided into a vitual gid as shown in Figue 3 and the numbe of nodes in each bloc is equal. Let us define the following vaiables: K Numbe of channels N Numbe of nodes/bloc T Numbe of tansmittes in bloc b b The poposed communication method opeates as follows: 4

38 . All nodes that ae awae and do not have a pacet to send ae in eceive mode. They andomly and independently select, with unifom pobability, one of the K channels to monito.. The souce node andomly selects, with unifom pobability, one of the K channels to tansmit on. 3. Any of the N nodes in Bloc that ae monitoing the channel on which the souce node is tansmitting, will eceive a copy of the pacet and fowad it at the net time step. Let us call the numbe of nodes in Bloc that eceived the pacet T. T 4. At the net time step, all of the nodes in Bloc that eceived a copy of the pacet fom the souce node fowad it towad the destination. They andomly and independently select, with unifom pobability, one of the K channels to tansmit on and boadcast the pacet on that channel. 5. If moe than one tansmitte boadcasts on a paticula channel, the esult is a collision, and any eceives monitoing that channel ae unable to eceive the pacet. Thus, only those eceives in Bloc that ae listening to a channel on which eactly one tansmitte is sending will eceive a copy of the pacet. We denote the numbe of nodes in Bloc that eceive a copy of the pacet as T same manne as descibed in Step These nodes then poceed to fowad the pacet in the

39 The andom pocess specified by the numbe of nodes, T, in Bloc b that eceive a copy of the pacet foms a discete time Maov chain with the state space { 0,,..., N }, whee the zeo-state is absobing and all othes ae tansient. This implies that the chain will eventually be absobed in the zeo-state with pobability one. What is of inteest to us is how long it will tae until the chain is absobed in the zeo-state. This povides a measue of the obustness of the scheme because it indicates how many hops the pacet can tavese befoe it is lost. As long as this numbe is geate than the distance between the souce and the destination, it is possible to use this method of communication. Section.4 consides the b obustness of the scheme as a function of K and N as well as the enegy equied to povide this level of obustness..3 PRACTICAL JUSTIFICATION OF THE MODEL The poposed communication method maes seveal assumptions that ae necessay to simplify the analysis. This section gives pactical ustification fo those assumptions showing that they can be met in pactice. The analysis maes the simplifying assumption that the communication channels ae othogonal to each othe, even though this is clealy not the case in pactice. Channelization is obtained by having each of the eceives listen to a potion of spectum that is much smalle than that coveed by the vaiations in the manufactuing pocess of the adios. Since the tansmitte caie fequencies and 6

40 the cente fequencies of the eceive filtes ae continuous andom vaiables, potions of spectum monitoed by diffeent eceives can patially ovelap. Howeve, the pobability of channel collisions is the same whethe the channels ae othogonal o not. A channel collision at a paticula eceive occus when moe than one tansmitte boadcasts a signal within the fequency ange monitoed by the eceive. The pobability of this occuing is independent of the fequency anges monitoed by othe eceives. It only depends on the atio of the vaiations of the manufactuing pocess to the fequency ange monitoed by each eceive. That atio is taen to be the numbe of channels in this analysis. The analysis also assumes that the tansmitting and eceiving nodes andomly select a channel to tansmit on and monito. In pactice, this can be achieved by having a high density of nodes in the netwo and allowing most of them to sleep much of the time and have only a andom subset of them on at any time. Having a andom subset of nodes on has the same effect as allowing the nodes to andomly choose thei eceive cente fequencies. As long as the nodes have two diffeent on-chip esonatos povide thei eceive cente fequency and thei tansmit caie fequency, the effect will be the same as if the eceiving nodes andomly choose a channel on which to fowad the pacet they have eceived. Altenatively, the andom channel selection could be accomplished by having the nodes andomly adust the capacitances of thei efeence fequency geneatos. This would allow the nodes to andomly select, with nea-unifom pobability, a fequency in the 7

41 ange of inteest, although the node would not be awae of the eact fequency it is selecting. The system is modeled as being discete time. I.e. it is assumed that the nodes in each bloc will mae thei tansmissions concuently. This can be achieved in pactice by having each node that successfully eceives the pacet fowad it as soon as the node fom which they head it stops its tansmission. Since the poposed potocol does not equie any handshaing and acnowledgements thee is no vaiable pat in the latency, maing it possible to maintain the discete time model. To initiate the pocess, it is possible fo the node that oiginally poduced the pacet to tansmit the pacet seveal times in succession so that any nodes that wae up duing this time and ae tuned to its fequency will have an oppotunity to hea the pacet and fowad it. This can be used to educe the pobability that the pacet is lost at the fist hop because thee is only one tansmitte and no nodes may be listening to its channel. The vitual gid used to divide the netwo into blocs is not eally necessay in pactice. It is used to simplify the analysis by ensuing that all tansmittes could be head by all eceives in the net hop; howeve, in pactice this is not necessay. (If equied, the gid could be achieved by sending the coodinates of the endpoints of the eceiving bloc sent in the pacet heade. This would indicate that only nodes that fall within those coodinates should fowad the pacet towads the destination if they hea it.) Lie all geogaphical outing methods, this 8

42 equies that the nodes have nowledge of thei own locations elative to each othe. Fotunately, the pefomance of most position estimation algoithms fo senso netwos impoves with inceasing density []..4 ANALYSIS As stated in Section., the numbe of copies of a pacet being tansmitted in each bloc, T b, using this communication method foms a Maov chain on the } state space { 0,,..., N whee the zeo-state is absobing and all the othe states ae tansient. Theefoe, the chain is guaanteed to eventually be absobed in the zeo-state. This implies that if the distance (numbe of blocs) that the pacet attempts to tavese is unbounded, the pacet will eventually be lost. Thee ae two ways in which this can happen. Conside the tansmission of the pacet fom Bloc b to Bloc b +. Thee ae T tansmittes in Bloc b and b N eceives in Bloc b +. One possibility is that all of the T tansmittes ae intefeing with each othe. In othe wods, thee is no channel that is being used by eactly one tansmitte. The othe possibility is that thee ae channels on which eactly one b among the T b tansmittes is sending, but none of those channels ae being monitoed by any of the N eceives. What is of inteest to us is how long it taes fo the chain descibed by T b to be absobed in the zeo-state. This indicates how fa (how many blocs) the pacet 9

43 can tavese befoe being lost. Also impotant is the aveage numbe of tansmittes pe bloc that ae tansmitting the pacet. This is equal to the aveage value of T b befoe the chain is absobed in the zeo-state. This is impotant because it povides a metic of how much enegy is spent on tansmitting the pacet fo one bloc. It is possible to detemine both the aveage numbe of steps until the chain is absobed in the zeo-state and the aveage value taen on by the chain befoe absoption fom the tansition pobability mati of the Maov chain. The challenge then becomes finding this tansition pobability mati, K N P,, as a function of K and N..4. Tansition Pobabilities K N P, The pobability, l, l', that the Maov chain tansitions fom state l to state l' is the pobability that l tansmittes boadcast the pacet and l' eceives get a copy of the pacet. Let us denote with p,, l K the pobability that thee ae eactly good channels (i.e. channels with eactly one tansmitte) given that thee ae l tansmittes and K channels fo {,..., min( l, K) }. We now that the pobability of having l' successful eceptions given N eceives and good channels out of a total of K channels is 30

44 N l' K l' K K N l' () fo {,..., min( l, K) } and l ' {,..., N}. Thus, the pobability of having l tansmittes boadcast the pacet and { N} l ',...,, is l' eceives get a copy of the pacet, fo K, N P l, l ' l' N l' min( l, K ) N K = p, l, K () = l' K K The value p,, l K can be computed by counting the ways in which out of l tansmittes can each select a unique channel out of K total channels, while the othe K channels each have no tansmittes o moe than one tansmitte and dividing this total numbe of combinations by the total numbe of ways in which l tansmittes can select one of K channels. Thee ae a total of l K ways to distibute K l l tansmittes among K channels and! ways to place each of out of l tansmittes in a unique channel out of K total channels. The numbe of ways of assigning l tansmittes among K channels such that no channel has eactly one tansmitte can be shown to be equal to the coefficient of l the /(l )! tem in the epession ( e ) [6]. This tem is given by K 3

45 K K m l m ( l )! ( ) ( K m) (3) m= 0 m ( l m)! Combining this with () gives us the tansition pobability mati K N P,. Once K N P, is computed, the epected time until the Maov chain is absobed in the zeo state (i.e. the obustness of the scheme), given that it stats in state i, is given by the th i enty of the column vecto ( I N Q) N v (4) whee I N is the N N identity mati, v N is a column vecto of N ones, and Q is the N N mati containing the tansition pobabilities among the ecuing states (non-zeo states) of the Maov chain [7]. ( ) I N Q is an N N mati whose l,l' enty is the epected numbe of visits to state l' given that the chain stated in state l. Fom this, it is possible to compute the pobability distibution of Tb befoe the chain is absobed in the zeo-state given that it stats in state l. The aveage value of T b befoe the chain is absobed in the zeo-state given that it stats in state l is equal to the l ow of the column vecto [7]: th ( I Q) [,,..., N ] T N (5) This gives us the tools necessay to evaluate the obustness and enegy equiements of the communication scheme fo any given values of K and N. 3

46 .4. Robustness Gows Eponentially with Density The ey paamete in this communication scheme is the atio of the node density to the numbe of channels. Let us define the following notation α N / K to specify the atio of node density (numbe of nodes/bloc) to the total numbe of channels. This value is impotant because if α is too small, thee will be few tansmittes and eceives compaed to the numbe of channels, maing it unliely that any pai of tansmit and eceive nodes will be attempting to communicate on the same channel. On the othe hand, if α is too lage, thee is a high pobability that the numbe of tansmittes is so lage that all of the channels will epeience collisions. Howeve, fo a easonable choice of α, the poposed communication scheme possesses a nice self-egulating popety in that the numbe of tansmittes pe bloc, specified by the pocess T b, esists gowing eithe too lage o too small. This is because, if the numbe of tansmittes in one bloc T b is small, thee will be few collisions esulting in moe good eceptions and T will be geate than T. Convesely, if the numbe of tansmittes in a bloc is too lage, the esult will be many collisions and T will be less than T. Indeed, this intuition is confimed by b+ Figue 4, which shows the pobability distibution of the numbe of tansmittes in a given bloc povided that the pacet eaches that bloc. This paticula pobability b b+ b distibution coesponds to the case when K = 30, N = 96, and α = N / K =