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2 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC Performace aalysis ad eergy optimizatio of wake-up receiver schemes for wireless low-power applicatios Nafiseh Seyed Mazloum ad Ove Edfors epartmet of Electrical ad Iformatio Techology, Lud Uiversity, Lud, Swede {afiseh.seyed mazloum, ove.edfors}@eit.lth.se Astract The use of duty-cycled ultra-low power wake-up receivers WRxs) ca sigificatly exted a ode life time i low-power sesor etwork applicatios. I the WRx desig, oth low-power operatio of the WRx ad wake-up eaco WB) detectio performace are of importace. We preset a systemlevel aalysis of a duty-cycled WRx desig, icludig aalog frot-ed, digital ase-ad, WB structure, ad the resultig WB detectio ad false alarm proailities. We select a low-power WRx desig, with aout two orders of magitude lower power cosumptio tha the mai receiver. The associated cost is a icrease i raw it-error rate BER), as compared to the mai receiver, at the same received power level. To compesate, we use a WB structure that employs spreadig. The WB structure leads us to a architecture for the digital ase-ad with a high ess-space scalaility. We calculate closed form expressios for detectio ad false alarm proailities. Usig these we aalyze the impact of desig parameters. The aalytical framework is exemplified y miimizatio of WB trasmit eergy. For this particular optimizatio, we also show that the otaied results are valid for all trasmissio schemes with a expoetial relatioship etwee sigal-to-oise ratio ad it-error rate, e.g., the iary orthogoal schemes with o-coheret detectio used i may low-power applicatios. Idex Terms Medium access, wake-up receiver, sesor etwork, eergy optimizatio, low-power. I. INTROUCTION A log life-time etwork where the odes ca operate over a exteded time period is a mai requiremet i may sesor etwork applicatios. With limited source of eergy, oth due to ode sizes ad/or difficult attery replacemets, it ca e very challegig to fulfill demadig life-time requiremets. To optimize the etwork life-time it is crucial to desig a ultra low power commuicatio system [1] [7]. The use of ultralow power wake-up receivers WRxs) ca sigificatly reduce the overall power cosumptio of the system. Previous studies o WRx schemes maily ess scearios where delay is the mai desig requiremet ad therefore the WRxs moitor the chael cotiuously [8] [11]. The eergy cosumptio of the WRx due to cotiuous chael moitorig, however, ecomes domiat i scearios with rare data packets. Thus, to further lower the system power cosumptio, we comie the ultra-low power WRxs ad duty-cycled chael listeig [12], [13]. For this class of WRx schemes, periodic wakeup eacos WBs) are trasmitted ahead of data packets for sychroizatio of the commuicatig odes. The WRx is switched o periodically for a certai time iterval to TABLE I COMPARISON OF WAKE-UP RECEIVER ESIGNS Parameter [14] [15] [16] [17] [18] [19] Operatig frequecy [GHz] Modulatio OOK OOK PPM FSK OOK OOK Sesitivity BER ata rate [kps] Noise figure [db] Power cosumptio [µw] Techology [m] Supply voltage oserve the chael, listeig for the WB. The WB cosists of a preamle ad a ess part. The mai receiver is oly powered up whe the WRx detects a WB with the correct ess. We have show i [12] that y optimizig the sleep time of a duty-cycled WRx we ca miimize eergy cosumptio while meetig delay requiremets. It is therefore of iterests to further pursue this type of WRx schemes. Previous studies o low-power WRxs focus maily o the desig of the aalogue frot-ed for always-o WRx schemes, ut these frot-eds ca of course e used i duty-cycled schemes as well. We list the desig parameters of some of these pulished works i Tale I. The largest differece etwee always-o ad duty-cycled schemes is i the digital ase-ad processig performed to detect WBs. I the always o case the processig is cotiuous while for the duty cycled case it is doe i a lock wise periodic) fashio. I this paper we focus o the latter case ad the performace expressios are therefore ot directly applicale to always-o schemes. A WRx is desiged for low power operatio, typically two orders of magitude lower tha the power cosumptio of a mai trasceiver, e.g. i the order of 10µW uder realistic assumptios [11]. To meet strict power cosumptio requiremets, early attempts avoided power-hugry compoets such as mixers ad sythesizers ad simple modulatio schemes were ofte selected. Oe early such desig is give i [20], where a competitive power cosumptio of 65 µw is achieved, at the cost of a -50 dbm WRx sesitivity. Later desigs [14]

3 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC [19] 1 have refied the desig cocepts to improve sesitivity ad, i several cases, differet low-power mixig strategies have ee itroduced [15] [17]. Today we see power cosumptio levels at aroud 50 µw ad correspodig sesitivity levels at aout -70 dbm, i the 2.4GHz frequecy rage used i this paper. These sesitivity levels are typically related to raw it-error rates BERs) i the order of 10 3, cf. Tale I. While the improvemets are impressive, the sesitivity levels reached are sigificatly worse tha the oes for mai receiver desigs, where we allow orders of magitude higher power cosumptio. This also meas that orders of magitude higher trasmit power is eeded whe wakig up a ode, as compared to ormal data trasmissio. Usig a sigle trasmitter structure, such large variatios i trasmit power will make the desig more complicated ad also less power efficiet [21]. We therefore aim for a simple ad power efficiet solutio with a sigle trasmitter, usig the same trasmit power oth for data ad wake-up. With a low-power WRx frot-ed, ad the correspodig loss i sesitivity, the raw BER will e higher tha the 10 3 level ormally used for receiver echmarkig. We show that, y applyig proper WB structures ad digital ase-ad processig, the processig gai ca compesate for the high raw BER, eve for very aggressive power savigs i the WRx aalog frot-ed. The costs to pay are loger WBs ad loger wake-up delays, which may cause cogestio i situatios with high eough data traffic. However, i extreme low-power etworks with rare data trasmissio ad low demads o delay, these costs ca e quite tolerale. If our goal is to optimize a etire wake-up scheme, to achieve as low power cosumptio as possile, we eed to look eyod sesitivity levels ad i a more elaorate way take ito accout mechaisms that ifluece power cosumptio. A missed WB leads to additioal WB trasmissios y the source ode ad a falsely detected WB leads to a uecessary powerup of the mai trasceiver y the WRx. Hece, we should focus our attetio o the WB detectio performace, ad its coectio to WB trasmit power cosumptio. A few studies [22], [23] ess WB detectio performace ad digital asead processig, ad there are also studies essig the etire WRx chai, e.g. [24]. However, oe of these attempts to make a complete aalysis where system parameters ca e optimized. Our approach is to aalyze the complete system-level desig of a duty-cycled WRx, icludig the aalog frot-ed ad digital ase-ad architectures, the WB packet structure, ad the resultig WB detectio ad false alarm proailities. First we express the characteristics of the aalog frot-ed for the resultig BER i terms of sigal to oise ratio. We the select a WB packet structure that allows for high flexiility i the size of the ess-space ad makes the desig a attractive cadidate oth for small etworks as well as massive oes. The choice of the WB structure leads us to a architecture for the digital ase-ad, where we improve the desig as compared to [25]. We show that y adjustig the WB packet 1 The desig preseted i [16] is iteded for a duty-cycled WRx scheme, ut this is ot explicitly aalyzed. parameters we ca compesate for icreased raw BERs from the aalog frot-ed ad achieve adequate levels of WB detectio performace, at the same received power levels as the mai receiver sesitivity. Fially, give the raw BER characteristics of the aalog frot-ed, the WB structure, ad the digital ase-ad architecture, we perform aalytical calculatios of WB detectio ad false alarm proailities. These proailities are defied per listeig iterval which, without loss of geerality, simplifies calculatios ad make them idepedet of the legth of the sleep iterval. Havig this aalytical framework, we have the prerequisites for a complete aalysis of eergy/power cosumptio of the etire system, alog the lies of what is itroduced i [12], where the ifluece of the legth of the sleep iterval is icluded i the eergy models rather tha i the detectio ad false-alarm proailities. Performig such a complete eergy aalysis is however eyod the scope of this paper ad, as a example, we perform a simplified aalysis where we focus o the eergy required to trasmit the WBs. Usig this simplified eergy model we illustrate how to optimize WB desig parameters for differet ess-space sizes. This paper is orgaized as follows. I Sectio II we give a descriptio of the overall operatio of the essed system. We preset a desig choice for the WRx aalog frot-ed ad propose a asic structure for the WB packet i Sectio III. I Sectio IV we further detail a structure for the digital ase-ad of the WRx ad the preset aalytical expressios for the detectio performace of the proposed desig cofiguratio. I Sectio V simulatios are performed to validate the aalytical expressios ad to evaluate the performace of the proposed structure. These expressios are further used i Sectio VI to determie the optimal desig parameters of WRx schemes. Coclusios ad fial remarks are give i Sectio VII. II. UTY-CYCLE MEIUM ACCESS Whe targetig wireless sesor etwork applicatios with low traffic itesity, idle chael listeig ecomes a domiat source of power cosumptio. Oe of the solutios to this prolem is duty-cycled chael listeig, where the receiver oly periodically wakes-up. This ca e doe usig the mai receiver [1] [7], which is also used for data commuicatio, ut we ca reduce power cosumptio eve more if a dedicated low-power WRx is employed. This cocept, uty-cycled Wake-up receiver ased Medium ACcess CW- MAC), was outlied ad partly aalyzed i [12]. As the medium access is the ceter of the aalysis i this study, we descrie the CW-MAC scheme i some more detail elow. A. CW-MAC I the CW-MAC scheme, as show i Fig. 1a), a ode cosists of a trasmitter, a high performace mai receiver, ad a low-power/high-ber WRx. All these compoets are switched off whe they are ot i use, ad therey we ca save eergy at the receiver side. The trasmitter is used oth for data ad WB trasmissios. I data-trasmissio mode it may

4 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC a) Simplified ode architecture lock diagram, with cotrol sigalig show. The wake-up receiver is roke dow i slightly fier structure. WB ackowledgmet WACK). Betwee the trasmitted WBs the SN is listeig to the chael with its mai receiver ad, whe a WACK is received, data trasmissio is iitiated. Oe thig that we eed to guaratee is that the listeig iterval of the WRx ca cover a complete WB, despite lack of sychroizatio. I other words, the WRx eeds to liste to the chael log eough so that if it arely misses oe WB it still has a chace to capture the ext oe i the same liste iterval. This meas that the listeig iterval has to e loger tha twice the time-extet of the WB plus the time etwee the WBs. The time etwee the WBs is assumed to e log eough to cotai a WACK packet. Ideally o error is ivolved i the detectio of the WB, ut i reality the trasmitted WB is corrupted y oise ad possily iterferece. This leads to imperfectios i terms of detectio errors ad associated eergy costs. While we iclude the aove effects i our aalysis, we assume that the data packets are rare ad far etwee, so that effects of collisios ca e igored. ) Timig diagram of the CW-MAC scheme for oe packet arrival ad a etwork of N odes, with oe source ode SN), oe destiatio ode N), ad N 2 o-destiatio odes NNs). Fig. 1. Sesor ode architecture ad timig diagram used for the CW-MAC scheme. use ay suitale modulatio techique, while i WB trasmissio mode it resorts to OOK to allow simple low-power detectio at the destiatio ode. All odes i a etwork share the same radio resource ad trasmissios are time duplexed. Figure 1) shows the timig diagram of the CW-MAC for oe packet arrival ad a etwork of N odes. The ode that has data availale for trasmissio is called the source ode SN), while the iteded receivig ode is called the destiatio ode N). The remaiig N 2 odes are what we call o-destiatio odes NNs), which are the oes that suffer from the false alarms metioed i the itroductio. Periodic WBs are trasmitted y the SN ahead of the data packet to sychroize commuicatio etwee the SN ad the N. The WRxs of all odes are switched o periodically, i a asychroous way, ad liste to the chael for WBs. The WBs carry oth the SN ad N esses/idetities ad this way we ca avoid overhearig [1] y the NNs i the etwork. If the WRx listeig iterval coicides with a WB trasmissio with the correct ess ad the WB is detected, the receivig ode switches o its trasmitter to reply with a B. Evet proailities ad eergy costs As a preparatio for the comig aalysis of detectio errors, let us discuss them i geeral terms ad itroduce some of the otatio we will use. Whe we have oise ad iterferece, there is a certai proaility that the trasmitted WB is missed y the WRx or the WRx accidetally detects a WB that is ot there. The latter ca happe oth whe oly oise is received or, more likely, whe a WB essed to aother ode is preset o the chael. We will call these evets a miss M) ad a false alarm ), respectively. The miss ad geerates extra eergy cosumptio i the SN, sice additioal WBs eed to e trasmitted efore the N WRx listeig time ad the SN WB trasmissio coicide agai. The false alarm evet evet occurs with some proaility M happes with a proaility ad geerates additioal eergy cosumptio o the receiver side, sice the mai trasceiver is switched o y the WRx without receivig ay data. The choice of the WB structure as well as the desig of the WRx, ad the resultig raw BER, highly ifluece the miss ad false alarm proailities, ad cosequetly the total power cosumptio of the etire etwork. For istace, trasmissio of a log WB may, o the oe had, reduce the miss ad false alarm proailities, ad cosequetly lowers the total eergy cost due to WB re-trasmissios. A log WB, o the other had, may also icrease the cosumed power at oth SN ad WRx N. The SN eeds to trasmit loger WBs ad the WRx has to oth liste for loger periods ad e ale to process loger sequeces. While this type of mechaisms lead to a complex eergy aalysis, it also allows us to optimize the total eergy cosumptio i a structured way. Our focus i this paper is o derivig the performace of our wake-up scheme, i terms of PM WB WB ad P, while we illustrate the priciple of eergy optimizatio usig a simplified eergy model. To e ale to aalyze the performace of the wake-up scheme we eed to fid characterizatios of the differet parts of the WRx, as show i Fig. 1a), ad provide a more detailed descriptio of the chose WB structure.

5 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC Fig. 2. Simplified lock diagram of the low-power/low-complexity WRx aalog frot-ed AFE) ad O-Off Keyig OOK) detector. III. FRONT-EN AN WAKE-UP BEACON STRUCTURE As we saw i Tale I, differet structures are availale for desig of the aalog frot-ed AFE) with differet characteristics i terms of operatig frequecy ad receiver sesitivity. I these works, differet modulatio techiques such as OOK, Pulse Positio Modulatio PPM), ad Frequecy Shift Keyig FSK) are used to keep the power cosumptio of the WRx at a low level. For the aalysis i this paper, details like the source of the oise or the choice of the modulatio techique is ot of prime iterest. From a coceptual poit of view, as log as the relatioship etwee BER ad SNR is kow for a certai cofiguratio, the aalysis framework of this paper ca e applied. Nevertheless, we will use a WRx referece desig ad characterize its BER vs. S/N performace usig simulatios. We have chose a simple o-coheret OOK modulatio for the WB trasmissio ad therey avoid the use of powerhugry compoets such as frequecy-sythesizer ad mixer at the AFE. Figure 2 presets a simplified lock diagram of the AFE ad OOK detector of the WRx. The RF sigal is dowcoverted to the ase-ad y a evelope detector. A direct curret C) locker ad a low-pass filter follow the evelope detector to filter out the C compoet ad compoets at the multiples of carrier frequecy, geerated y the oliear characteristics of the evelope detector. The OOK detector measures the eergy cotet of the icomig sigal durig oe symol iterval ad coverts the ase-ad sigals to a it-sequece. As metioed, the drawack of such a desig is a geerally poor receiver sesitivity. However, our etire WRx desig is ased o relaxig the requiremets o raw BER ad therey allowig it to operate at the same received power level as the mai receiver, i our case -90 dbm [13], thus allowig the same trasmit power for WB trasmissio ad data. I the followig we aalyze, y simulatio, the performace of the OOK detector ad adopt a fitted expoetial expressio for the BER that later allows us to aalytically optimize eergy cosumptio. A. OOK detector performace simulatio Figure 3 shows the simulated BER performace for a AFE ad OOK detector cosistig of the aove compoets ad i a Additive White Gaussia Noise AWGN) chael. The desig is tailored to the 80MHz wide 2.4GHz ISM ad Fig. 3. BER performace of the WRx aalog frot-ed ad OOK detector show i Fig. 2, for a Additive White Gaussia Noise AWGN) chael. The S/N is measured directly after the 80 MHz wide ad-pass filter, at the iput of the evelope detector. As referece, we show the BER performace of a optimal OOK detector, operatig o the same sigal. This shows that our low-power desig has aout 11 db implemetatio loss. [13] ad, to allow for o-chip itegratio ad ultra-low power cosumptio, the adwidth of the first filter adpass filter) is chose as the full 80MHz. We further model the evelope detector y a compoet that outputs the squared iput sigal. The adwidth of the low-pass filter is 250kHz to fit the 250kps data rate [13]. With the iary trasmissio, the umer of iformatio its per symol is oe where each it is sampled oce. After simulatio we fid a aalytical expressio for the raw BER p, y curve fittig, p = 0.5 e 12 S/N, 1) where S/N is the SNR at the iput of the evelope detector. At this poit it is worth otig that the BER resultig from our AFE ad OOK detector follows that of other o-coheret detectio schemes i that it is a expoetial fuctio of the S/N, while the low SNRs are a result of the 80 MHz wide ad-pass filter o the iput. Comparig to a optimal OOK detector, operatig o the same sigal, the implemetatio loss is aout 11 db. This is the price we pay to reduce the power cosumptio of the WRx i the rage of 20 db compared to the mai receiver [11]. Further, the expoetial relatioship etwee BER ad S/N i 1) will carry through to our eergy aalysis ad optimizatio i Sectio VI, makig the results more geeral ad valid for all o-coheret detectio schemes with the same type of BER relatioship. Sice we have delierately chose to operate our WRx at the same received power level as the mai receiver sesitivity, we will have to operate at very low SNRs o the iput. I our umerical examples we use a omial raw BER of p = 0.15, operatig at S/N = 10 db. To compesate for these high raw BERs, it is essetial to fid a WB structure that allows for low-complex/low-power compesatio i a digital ase-ad BB) processig.

6 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC Fig. 5. Block diagram of a detector cosistig of a matched filter MF) ad a threshold uit. Fig. 4. Wake-up eaco structure cosistig of a legth M preamle, ad legth L destiatio/source esses. The ess its are, i tur, spread y a K it sequece. B. Wake-up eaco structure A asic WB, as depicted i Fig. 4, should cosist of a preamle, a destiatio ess, ad a source ess. The M-it preamle sequece, used to detect the presece of a WB ad for time sychroizatio, is selected to e the same for all WBs. The preamle is followed y the L-it destiatio ad source ode esses. The destiatio ess is eeded to prevet power-up of other odes, while the source ess is used i the destiatio ess field of the WACK message. As we metioed previously, the WB is received y a high BER frot-ed ad odes are ot sychroized. Therefore, to fid a accurate startig-poit of the WB ad to achieve low proailities of miss ad false alarm, the preamle eeds to provide oth a processig gai ad should e selected from sequeces with good auto-correlatio properties. We have chose to geerate the preamle usig maximum-legth shiftregister sequeces m-sequeces). A importat characteristic of a m-sequece is the high peak auto-correlatio fuctio while the off-peak values of the auto-correlatio fuctio relative to the peak value are small [26] [28]. For the ess its we do ot eed good auto-correlatio properties, ut still eed a processig gai to compesate for the high BER. Each it i oth the source ad destiatio ess fields is therefore spread y a aritrary K-it code 2. The total umer of its of oth source ad destiatio esses, whe spreadig is applied, is KL. I this work we select the same spreadig, K, for oth the destiatio ad source esses. I priciple, however, the spreadig ca e differet. Additioal fields ca e attached to the WB to carry iformatio such as maximum umer of WBs or the ext liste iterval of the SN WRx [23], [29]. To keep the aalysis tractale, we disregard ay such fields ad focus o how WRx performace is related to the WB parameters M, K, ad L. IV. IGITAL BASE-BAN urig the liste iterval, the frot-ed of the WRx delivers its received sigal i the form of a it sequece, with a high raw BER sice we operate at lower received power tha the sesitivity level. The task of the digital ase-ad BB) is to detect the presece of a WB i this it sequece. We 2 Eve if the choice of spreadig code is less critical for the ess its, some sort of pseudo-radom code would e used i a real system to avoid a C level. I our simulatios we use m-sequeces. propose a desig, ased o the WB structure give aove, ad develop aalytical expressios for the detectio performace i terms of the WB detectio ad false alarm proailities per liste iterval. 3 The aalytical expressios are later used to aalyze the WRx operatig characteristic for differet desig parameters. A. igital ase-ad desig We use matched filters MFs) as the mai uildig locks i our BB, a very commo approach to detect kow determiistic sequeces i oise. The overall operatio of a detector uit is illustrated i Fig. 5. The icomig sigal is correlated with the kow sequece ad wheever the output of the MF exceeds a certai threshold, the sequece is declared to e preset y the threshold device. Figure 6a) illustrates the proposed BB desig cosistig of two detector uits ad a ess decoder. The detector uits cotai a preamle matched filter PMF) of legth M ad a ess-spreadig matched filter AMF) of legth K, respectively. This particular BB structure with iaryiput matched filters ca e implemeted with very high eergy efficiecy, similar to [25]. Iitially the BB ca power up oly the PMF ad search for the preamle to otai sychroizatio, sice detectig ess its oly makes sese after sychroizatio is otaied. A WB/preamle may arrive at ay radom time i the listeig iterval, which is twice the time-extet of the WB M + 2 KL plus the time-extet of the WACK message δ. The PMF ca catch a complete WB oly if the WB arrives at a positio i [0 M + 2 KL + δ], as show i Fig. 6). Note that, sice the WACK is received y the mai receiver of the SN, o spreadig eeds to e applied ad therefore the WACK widow is short compared to the WB legth. To simplify the aalysis, we therefore set δ = 0 i the remaider of this paper. With the ukow arrival time i of the WB, the PMF may eed to correlate the icomig it-sequece with all the possile arrival times of the preamle, i [0 M + 2 KL]. The MF stops the correlatio wheever the PMF output exceeds the decisio threshold ad aouces that a preamle is detected. After the preamle detectio, the AMF ad the ess decoder are activated ad the remaider of the iput sequece is fed to the AMF, where the idividual ess its are detected y correlatig the itsequece with the ess-spreadig. Kowig the positio of the preamle, the positios of the ess its i the sequece are also kow. Therefore, the AMF correlatio oly eeds to e performed oce per ess it. Fially, the detected its are collected y a ess decoder ad compared agaist 3 Here we chage from usig the proaility of miss, PM WB, to usig the proaility of detectio, P WB = 1 M, sice it will simplify the comig mathematical expressios.

7 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC a) igital ase-ad BB) lock-diagram with a detector for the preamle, a detector for the ess its, ad a ess decoder. ) Illustratio of a wake-up eaco WB) arrivig at time istat i durig a WRx liste iterval. Fig. 6. Block diagram of the proposed WRx digital ase-ad ad a illustratio of the arrival of a wake-up eaco durig a WRx listeig iterval. the ode ess. If the detected ess its match the ode ess, the mai trasceiver is powered up. With the proposed architecture, the PMF ad AMF are idetical i all odes i the etwork. Oly the ess decoders eed to e programmed with the respective ode esses. This leads to a very flexile WRx desig, where the ode ess-space is easily scaled without ay major chage of the BB. For istace, to chage a etwork of 256 odes to a etwork of 8192 odes, oly the size of the ess decoder eeds to e icreased y 5 its, while the PMF ad AMF ca remai uchaged. B. etectio Performace Aalysis After discussig the overall operatio of the BB, we move o to characterizatio of the BB i terms of WB detectio ad false alarm proailities. More precisely, the detectio proaility P WB is defied as the proaility of successful WB detectio durig oe chael listeig iterval, whe a WB is ideed trasmitted to the N. The WB false alarm proaility P WB is the proaility of detectig either a WB with a icorrect ess or a o-existig WB, durig a WRx listeig iterval. The outlie of our aalysis is as follows. Our BB cosists of two MF-threshold uits with slightly differet parameters. Therefore, we first express the detectio performace of a geeric MF-threshold uit ad the use these geeric expressios to derive closed form expressios for the WB detectio ad false alarm proailities. Let us assume a iary symmetric chael, where the it errors at the OOK detector occur idepedetly ad with proaility p, for istace give y 1). Whe the kow sequece is preset o the chael, the proaility P, W ) that its i the sequece of legth W are detected correctly, is P, W ) = W ) 1 p ) p W. 2) Assumig that the arrival time of the sequece at the MF is kow, a MF detects the kow sequece correctly with proaility W W ) W ρ seq γ) = P, W ) = 1 p ) p W, 3) =γ =γ if the umer of correct its i the legth W sequece is aove the threshold γ [0, W 1]. Whe oly oise is preset o the chael, the OOK detector geerates radom its with equal proaility. Usig 3), the proaility that the MF erroeously detects a o-existig sequece therefore ecomes ν seq γ) = 1 W ) W 2 )W. 4) =γ Now, lets cotiue with the detectio performace of the BB, usig the aove geeric expressios. A WB is declared to e detected oly if oth the preamle ad the ode ess are correctly detected. The PMF ad AMF outputs used for detectio are calculated usig differet parts of the it sequece ad are therefore idepedet. Hece, the proaility of detectig a WB whe it is preset o the chael is equal to the product of the respective detectio proailities of the preamle ad the ess, = P pre P, 5) where P pre is the proaility that the PMF detects the preamle correctly ad P is the proaility that the ess decoder correctly detects the ode ess. The BB falsely detects a WB if i) oth the preamle ad the ess code are falsely detected or ii) the preamle is correctly detected, ut the ess decoder falsely detects a ess which elogs to aother ode. We defie the WB iterferece level, α, as the proaility that a WB with a icorrect ess is preset durig the WRx listeig. The proaility P WB that a WB is falsely detected ca therefore e calculated as = P pre P + α P pre P, 6) where P pre is the proaility that the PMF falsely detects a o-existig preamle, P is the proaility that a oexistig ess is erroeously detected as the correct oe y the ess decoder, ad P is the proaility that the ess decoder falsely detects a ess, which elogs to aother ode, as its ow. Below we first detail how to calculate the preamle detectio performace P pre pre ad P ad the tur our attetio

8 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC to the calculatio of the ode ess detectio performace i terms of P, P, ad P. Whe a WB is preset o the chael durig the WRx listeig iterval, the preamle detectio proaility P pre is determied y three factors: i) the proaility fi) that the WB arrives at time i, ii) the proaility ρ pre γ 1 ) of detectig the preamle at the correct arrival time i, ad iii) the proaility Ω pre γ 1, i) of o erroeous detectio of the preamle efore time i, where i [0 M + 2 KL] ad γ 1 [0 M 1] is the PMF threshold level. Cosiderig all the possile arrival times of the WB, we get M+2 P pre γ KL 1) = [fi) ρ pre γ 1 ) Ω pre γ 1, i)]. 7) i=1 Sice the odes are u-sychroized, the arrival time i of the WB is ukow ad it is reasoale to assume that all arrival times are equally likely, i.e., fi) = 1, 0 i M + 2 KL. 8) M + 2 K L To calculate ρ pre γ 1 ), we use 3) ad sustitute the preamle legth M ad the threshold γ 1 for W ad γ. Assumig ideal correlatio properties ad deotig the proaility of a preamle detectio at a icorrect time istat y ν pre γ 1 ), the proaility Ω pre γ 1, i) ecomes Ω pre γ 1, i) = 1 ν pre γ 1 )) i 1. 9) To calculate ν pre γ 1 ), we assume that detectig a preamle at icorrect timig is equivalet to detectig a preamle whe o data is availale o the chael, sice we assume ideal autocorrelatio properties. Usig 4), we sustitute the preamle legth M ad the threshold level γ 1 for W ad γ. Replacig 8) ad 9) ack i 7) the preamle detectio proaility ecomes M+2 P pre γ 1 KL 1) = M + 2 K L ρpre γ 1 ) 1 ν pre γ 1 )) i 1. i=1 10) The proaility P pre, that the PMF erroeously detects a preamle whe o data is availale i the listeig iterval, is equivalet to the proaility that the umer of radom its that matches the preamle sequece goes aove the threshold γ 1 at least oce i the oservatio iterval, i.e., P pre γ 1) = 1 1 ν pre γ 1 )) M+2 KL 1. 11) As show i 6), to calculate the detectio performace of the ode ess, we cosider the operatio of the AMF together with the ess decoder. The proaility P of detectig a ess correctly i the ess decoder is equal to the proaility that the AMF detects all idividual ess its correctly. Sice the outputs of the AMF are ucorrelated, eig ased o differet parts of the it sequece, P γ 2 ) = ρ spcode γ 2 )) L, 12) where ρ spcode deotes the detectio proaility of a ess it ad is calculated y sustitutig the spreadig code legth K ad the AMF threshold level γ 2 [0 K 1] for W ad γ i 3). Whe there is o data availale o the chael, the AMF geerates radom ess its. Therefore the proaility P that the ess decoder falsely aouces that the correct ess is detected ecomes P = 1 2 )L. 13) Fially, it is likely that a WB which refers to aother ode is falsely detected. To derive the expressio for the proaility P, we itroduce q which refers to the umer of its that the odes ow ess differs from the ess that elogs to aother ode. Give q, the proaility P is expressed as P γ 2 ) = L [ ) L /2 L ρ spcode γ 2 ) ) L q q q=1 1 ρ spcode γ 2 ) ) ] q, 14) where L q) /2 L is the proaility that q its are differet i radomly chose L-it esses. The secod factor is the proaility that the AMF detects the L q matchig ess its correctly. The third factor represets the proaility that the q o-matchig ess its are erroeously detected. We approximate 14) usig the fact that errors caused y a sigle ess it error q = 1) are the most likely, P γ 2 ) L 2 L ρ spcode γ 2 ) ) L 1 1 ρ spcode γ 2 ) ). 15) The aalysis elow has ee performed usig oth the exact expressios 14) ad the approximatio 15), without oticeale differeces i the results. For the sake of revity, we oly preset expressios ased o the approximatio. Sustitutig 7) ad 12) i 5) ad 11), 13), 7), ad 15) i 6) we ca calculate the WB detectio ad false alarm proailities. The calculatio is a relatively straightforward, ut tedious, operatio that results i = P pre P = 1 M + 2KL ρpre γ 1 ) ρ spcode γ 2 ) ) L = M+2KL i=1 [ 1 M M + 2 KL =γ 1 M+2 KL 1 1 M 2 )M K i=1 =γ 2 1 ν pre γ 1 )) i 1 ) ) ) M 1 p ) p M =γ 1 M ) ) i 1 ) ) L K 1 p ) p K, 16)

9 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC ad = P pre P i=1 + αp pre =γ 1 P = 1 1 ν pre γ 1 )) M+2KL 1) 1 2 )L + ) M+2KL 1 α M + 2KL ρpre γ 1 ) 1 ν pre γ 1 )) i 1 i=1 L ρ spcode 2 L γ 2 ) ) L 1 1 ρ spcode γ 2 ) ) ) = M ) ) M+2KL 1 M 2 )M 1 2 )L + =γ 1 [ 1 M ) ) M α 1 p ) p M M + 2KL =γ 1 M+2KL M ) ) i 1 Fig. 7. Simulated ad calculated receiver operatig characteristics, ROCs, M 1 1 p ) p M for a wake-up eaco WB) with a preamle of legth M = 63, L = 8 it esses ad ess spreadig K = 15, for two differet levels of WB iterferece, α = 1 ad α = 0.1. L 2 L K 1 =γ 2 K =γ 2 ) L 1 ) K 1 p ) p K ) )] K 1 p ) p K With the aove derivatios, we have closed form expressios for the WB detectio performace. The rest of the paper will focus o verifyig the expressios ad illustratig how they ca e used to aalyze ad optimize wake-up receiver schemes. V. RECEIVER OPERATING CHARACTERISTICS The aalytical expressios for WRx detectio performace were derived for ideal correlatio properties, while realistic WBs will have a certai amout of auto-correlatio. By performig Mote Carlo simulatios i MATLAB, usig m- sequeces oth for WB preamle ad ess spreadig we otai realistic values o WRx performace. By comparig simulated ad calculated receiver operatig characteristics ROCs), we oth verify the correctess of the aalytical derivatios ad the validity of the ideal-correlatio assumptios made. To ehace uderstadig of the aalytical results, we also discuss the overall ifluece from parameters such as raw BER, preamle legth, ess spreadig legth, ad etwork size. We simulate the ehavior of the etire WRx sigal chai, detectig WBs, as specified i sectios III ad IV, for a Additive White Gaussia Noise AWGN) chael. I the simulatio we set the omial raw BER p to 0.15, ased o a frot-ed operatig at S/N = 10 db, cf. Fig. 3. The legth of the preamle M determies the sharpess of the peak at the PMF output ad therey the preamle detectio performace, while the ess spreadig K determies the performace of the ess decodig y the AMF. We chage the threshold level γ 1 [0, M 1] of the PMF, oth i the simulatios ad i the aalytical expressios, to evaluate the ehavior of the WRx for differet choices. As the outputs of the AMF are symmetric, the ess it threshold level is set to the midpoit of the rage of possile outcomes, γ 2 = K/2. Figure 7 shows two example ROCs for a WB with a preamle legth. 17) M = 63, ess spreadig legth K = 15, ad a etwork of 256 odes L = 8). The ROCs are for two levels of WB iterferece, α = 1 ad α = 0.1. The aalytical ROCs match the simulated oes well, ut there is a small differece that ca e see i the upper right part of the curve with full WB iterferece α = 1. The aalytical expressios over-estimate the false alarm proaility somewhat i this regio of low to medium threshold levels. The est detectio proaility P WB of 0.97 is achieved for oth cases at a decisio threshold γ 1 i the order of For lower or higher thresholds γ 1, the most sigificat effect o the ROC is the reduced detectio proaility. For low thresholds we fid the icorrect preamle positio ad for high thresholds we miss the preamle etirely. That the false alarm proaility stays elow a certai value, less tha 10 2 i this example, for all thresholds is a result of usig the destiatio ess to decrease overhearig. I Fig. 7 we ca see clear asymptotic ehavior of the aalytic ROC for small ad large threshold levels. By quatifyig these, we simplify the iterpretatio of how differet parameters ifluece the overall WRx detectio performace. of 0.76 with a resultig false alarm proaility For high thresholds γ 1, the relatioship etwee P WB ca e approximated as ρ spcode ad 1 α L1 ρ spcode ) 2L. 18) The ratioale ehid the approximatio is that at high thresholds γ 1, we may miss preamles o the chael, ut if they are detected it is most likely i the correct positio. Further, at high thresholds, it is also very ulikely that we make a falsealarm if there is o preamle o the chael. Therefore 10) collapses to P pre γ 1) ρ pre γ 1 ) ad 11) to P pre γ 1) 0, which through 5) ad 6) leads to 18). The scalig factor i 18) depeds idirectly o the raw BER ad the ess spreadig legth, through ρ spcode, while the size of the ode

10 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC ess-space L ad the WB iterferece level α have direct ifluece. For low thresholds γ 1, the false alarm proaility is, as we metioed, upper limited y the use of a destiatio ess i the WB. At very low thresholds the proaility of erroeously detectig a preamle is close to oe ad the proaility of detectig a preamle at its correct positio is very low. This essetially leads to etirely radom detectio of ess its ad the proaility that the otaied ess matches the ode ess depeds oly o the size of the ess-space the more ess its, the smaller the proaility. I more detail, at low thresholds, 11) collapses P pre to P pre γ 1) 1 ad the WB false alarm proaility P WB i 6) ca e approximated 1 2 )L. 19) I Fig. 8 we illustrate the pricipal detectio ehavior, usig the asymptotes 18) ad 19), together with correspodig theoretical ROCs. For performace reasos the primary regio of iterest is where we have high detectio proailities, as idicated i the figure. The omial desig, with full WB iterferece α = 1, is show as a solid lue lie. If, o the oe had, the WB iterferece level is decreased, α < 1, the umer of false alarms for high thresholds reduces ad the left asymptote is shifted accordigly. As a result, the dotted red ROC curve is otaied ad the regio of iterest icreases. If, o the other had, the detectio proaility of ess its ρ spcode decreases, we ca see i 18) that the false alarm proaility for high thresholds icreases. As a result, the left asymptote is shifted to the right ad the regio of iterest ecomes smaller. Note that a lower ρ spcode is otaied through shorter ess spreadig K ad/or higher raw BER p, accordig to 3) with W = K. Reducig the umer of its L i the ess-space results i higher umer of false alarms for oth low thresholds ad high thresholds ad therefore oth asymptotes are shifted accordigly. The regio of iterest, however, icreases as compared to the omial desig. If we reduce the preamle legth M the asymptotes stay i place, ut the detectio proaility decreases i the regio of iterest ad the dashed gree curve is otaied. The detectio proaility i the regio of iterest is also decreased if the raw BER icreases 4. Aove we provided a qualitative ad quatitative uderstadig of how differet parameters ifluece the detectio performace of the proposed WRx. We have doe it y discussig oth the full ROC as well as the locatios of highad low-threshold asymptotes. VI. OPTIMAL ESIGN PARAMETERS By comiig our detailed uderstadig of how detectio performace of the proposed WRx depeds o differet system parameters with a cost fuctio we ca make optimal system desigs. Such a cost fuctio will, for sesor etworks, typically reflect eergy cosumptio of idividual odes or of the 4 Note: A chage i BER also affects the locatio of the left asymptote, as descried aove. Fig. 8. Illustratio of the geeral properties of the receiver operatig characteristic, ROC, for differet desig parameters, together with the asymptotes i 18) ad 19). etire etwork. Assumig that the cost fuctio Jθ) depeds o a umer of parameters collected i θ ad the permissile rage of parameters is, the optimal system desig is give y θ opt = argmijθ). 20) θ Most relevat cost fuctios related to eergy will idirectly deped o the ROC of the WRx, as derived aove, sice detectio performace has a fudametal impact o eergy cosumptio. Some of these mechaisms were riefly discussed i Sectio II. A comprehesive optimizatio for a etire etwork is a very complex task ad therefore a topic that eeds to e covered separately. Therefore, to illustrate how the ROC expressios ca e used for WRx system optimizatio, we have chose a simplified case where we are oly iterested i miimizig the eergy used y the source ode, SN, to wake up the destiatio ode, N. Whe doig this, we also assume that the total eergy required at the SN to trasmit a WB is proportioal to the received WB eergy at the N. The proportioality factor icludes trasmitter efficiecy, propagatio losses, etc. These assumptios result i a tractale optimizatio where we fid the optimal WB parameters, preamle legth M ad ess spreadig K, for differet umer of ess its L ad raw BERs p. Our cost fuctio ca e expressed i terms of the eergy required to trasmit a sigle WB, E WB, ad the average umer of WBs, η, eeded to activate the N, accordig to Jθ) = E WB θ) ηθ), 21) where θ cotais WB parameters we optimize, M ad K. I the sequel we will suppress θ i our expressios. With the frot-ed characteristic from 1) the trasmitted/received eergy per it is proportioal to l2 p ). As we already idicated i Sectio III, this expressio will e the same for all o-coheret schemes where the raw BER is a expoetial fuctio of the S/N at the receiver iput ad the followig optimizatio is therefore valid for all schemes i

11 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC that class. With this proportioality, the total eergy eeded to trasmit a sigle WB with a legth M preamle ad two L it esses spread y a factor K is E WB l2 p ) M + 2 KL). 22) We will ot optimize the sleep time of the WRx, as was doe i [12], ad simply assume a costat activity factor where the liste period is a costat fractio of the etire sleep-liste cycle. Through this, there will always e a fixed umer of WBs per sleep-liste cycle, idepedet of WB legth. Therefore, the average umer of WBs trasmitted efore a successful wake-up, η, is proportioal to the average umer of sleep-liste cycles, i.e. η k=0 k 1 P WB ) k = 1 P WB 0.5, 23) which is a result of radom startig times, due to asychroous commuicatio, ad a proaility P WB of detectig the WB durig the liste iterval. The proportioality factor is the, i our case fixed, umer of WBs per sleep-liste cycle. Replacig 22) ad 23) ack i 21), the total eergy cost ecomes ) 1 J l2 p ) M + 2 KL) P WB ) The optimizatio parameters M ad K ifluece the total eergy through two cotradictig mechaisms. Icreasig M ad K will icrease the eergy required per trasmitted WB, while, at the same time, it decreases the umer of WBs required to activate the N. The alace etwee these two mechaisms is what our aalytical framework provides, i this case, through 16). Let us move o to umerical optimizatio of the preamle legth M ad ess spreadig K to miimize the eergy cost 24) for differet raw BERs p, for three differet sizes of the ess-space, amely 4, 8 ad 16 ess its. To cover oth the reported BERs of the WRx desigs i Tale I ad our choice to use low-power/low-performace frot-eds, we perform the optimizatio for BERs from to 0.3. For these parameter rages, with discrete parameter values, we resort to a quite tractale exhaustive search for 30 values o BER etwee ad 0.3. Figure 9 shows the optimal WB legth, resultig from the optimal choices of M ad K. At low BERs, there is o ess spreadig K = 1) ad oly a short preamle is used to otai sychroizatio. Whe the BER icreases eyod a certai poit, the WB legth icreases sharply, sice additioal WB trasmissios due to misses are more costly tha icreasig the WB legth. Both preamle legth ad ess spreadig are icreasig rapidly, ut the ifluece from icreases i ess spreadig chages are more visile, sice its ifluece o the WB legth is magified y the umer of ess its. It is quite atural that icreasig BERs lead to loger WBs, i geeral terms, sice detectio of them ecomes icreasigly difficult. However, the relatioship etwee BER ad optimal Fig. 9. Optimal wake-up eaco WB) legth vs. OOK raw BER, for essspaces of size 4, 8 ad 16 its. WB legth is more itricate tha that. Perhaps somewhat couter-ituitively, there are also examples of icreasig BERs leadig to shorter optimal WB-legth. Several examples of this ca e see i Fig. 9, especially for the 4-it ess case where the shorter WB legths make them more visile. I these cases, eve if shorter WBs mea lower detectio proaility ad a higher average umer of WBs eed to e trasmitted, the total cost ecomes smaller for a shorter WB sice it requires less trasmissio eergy. The cost fuctio we are usig i this paper measures the required trasmit eergy ad, as such, it oly depeds o the detectio proaility part of the ROC. The detectio proailities resultig from the optimizatio are show i Fig. 10a). The detectio proaility has a tedecy to decrease with icreasig BERs, ut adjustmets of WB legth i the optimizatio rigs it ack up agai whe this is favorale from a trasmissio eergy poit of view. The largest variatios ca e see i the trasitio regios of BERs where the WB legth starts to icrease rapidly, as we oserved i Fig. 9. The geerally shorter WBs for smaller ess spaces also lead to the fact that trasmissio of additioal WB due to a miss i the WRx is less costly. Hece, we see that lower detectio proailities ca e optimal, from a trasmit eergy poit of view, for smaller ess spaces. False alarm proailities do ot ifluece our cost fuctio, ut the ROC relatio implicitly gives us certai false alarm values. These are related to other eergy costs i the etwork, due to uecessary wake-ups. It is therefore of iterest to study these proailities as well. The false alarm proailities resultig from the optimizatio are show i Fig. 10). We ca see that they are aout 5-10 times lower tha the upper asymptote 19) we derived for the ROC solid lie aove each curve). For reasoaly large ess-spaces, the false alarm rates are at very low levels ad uecessary wake-ups should ot have a large impact o the total eergy cosumptio of the etwork. A detailed aalysis of these iflueces is oth otrivial ad requires more detailed ad complete iformatio aout how eergy cosumptio relates to the optimizatio parameters. While importat, this aalysis is eyod the scope

12 FINAL MANUSCRIPT: PUBLISHE IN IEEE TRANS. WIRELESS COMMUN., EC a) Proaility of detectio P WB ) vs. OOK raw BER. Fig. 11. Optimal wake-up eaco WB) trasmit eergies, per wake-up, for differet raw BERs ad ess-spaces of size 4, 8 ad 16 its. Eergies are ormalized to the miimal eergy for the smallest 4-it ess space. quite small. Sice we aim at usig the same trasmitter ad the same trasmit power oth for data ad wake-up, our lowcomplexity/low-power WRx will operate at high raw BERs, ad i this cotext the most iterestig part of the eergy curves is at high BERs. The omial BER i our WRx desig is therefore set to 0.15, as discussed i Sectio III, ad the additioal Tx eergy cost as show i Fig. 11 is oly aroud 2-3 db. This relatively small additioal cost i trasmit eergy for the SN should e compared to the roughly two orders of magitude power savigs estimated o the WRx side for all odes i the etwork. ) Proaility of false alarm P WB ) vs. OOK raw BER. The solid lie aove each curve is the correspodig upper asymptote 19). Fig. 10. Optimal proaility of detectio ad the correspodig proaility of false alarm, resultig from the optimizatio, vs. OOK raw BER, for essspaces of size 4, 8 ad 16 its. of this paper. Fially, let us study the optimal trasmissio eergy cost, per wake-up, as a fuctio of raw BER. Sice we oly kow the eergy cost up to proportioality, as detailed i 24), we preset the ormalized optimal WB trasmit eergies i Fig. 11, for the three ivestigated ess-space sizes. The ormalizatio is with respect to the miimal eergy cost for the smallest, 4-it, ess space. For all three ess-spaces, we ca see that the 10 3 BER used as a referece level i previous studies, cf. Tale I, is ot the optimal poit of operatio whe usig the duty-cycled wake-up scheme studied i this paper. The optimal BER is closer to 10 2 for all three essspaces ad larger ess-spaces ted to have a slightly lower optimal BER. Whe raw BER is lower tha the optimal oe, the icreased trasmit power required to lower the BER is larger tha the correspodig shorteig of the WB, resultig i a higher total eergy cost. The differeces are, however, VII. CONCLUSIONS AN REMARKS The goal of this paper has ee to provide a aalysis framework for duty-cycled low-complexity/low-power wakeup receiver schemes, which ca e used for desig optimizatio. We perform a complete system-level aalysis ased o a proposed wake-up eaco structure ad the correspodig WRx architecture. The aalysis first leads to closed form expressios for detectio ad false alarm proailities, as well as qualitative ad quatitative uderstadig of how detectio performace relates to chages i desig parameters. This uderstadig of detectio performace is fudametal to system-level aalysis ad optimizatio of eergy cosumptio. Such a optimizatio ca e doe i may differet ways, depedig o what the ultimate goal is. For istace, it is quite possile to miimize the total power cosumptio of a etire etwork, give that we have access to detailed eough iformatio aout how eergy cosumptio is related to differet desig parameters. With limited space we chose to focus o how the detectio performace expressios ca e used for a optimizatio of wake-up eaco trasmit eergy. This meas that the preseted optimizatios are oly related to the trasmit eergy of the source ode. While somewhat limited i its scope, the optimizatio led to several importat oservatios regardig the trasmit eergy required to successfully activate a destiatio ode. The trade-off etwee icreasig trasmit