IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER

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1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 Deecion, Synchronizaion, and Doppler Scale Esimaion wih Mulicarrier Waveforms in Underwaer Acousic Communicaion Sean F. Mason, Chrisian R. Berger, Suden Member, IEEE, Shengli Zhou, Member, IEEE, and Peer Wille, Fellow, IEEE Absrac In his paper, we propose a novel mehod for deecion, synchronizaion and Doppler scale esimaion for underwaer acousic communicaion using orhogonal frequency division muliplex () waveforms. This new mehod involves ransmiing wo idenical symbols ogeher wih a cyclic prefix, while he receiver uses a bank of parallel self-correlaors. Each correlaor is mached o a differen Doppler scaling facor wih respec o he waveform dilaion or compression. We characerize he receiver operaing characerisic in erms of probabiliy of false alarm and probabiliy of deecion. We also analyze he impac of Doppler scale esimaion accuracy on he daa ransmission performance. These analyical resuls provide guidelines for he selecion of he deecion hreshold and Doppler scale resoluion. In addiion o compuer-based simulaions, we have esed he proposed mehod wih real daa from an experimen a Buzzards Bay, MA, Dec. 5, 26. Using only one preamble, he proposed mehod achieves similar performance on he Doppler scale esimaion and he bi error rae as an exising mehod ha uses wo linearly-frequencymodulaed (LFM) waveforms, one as a preamble and he oher as a posamble, around each daa burs ransmission. Compared wih he LFM based mehod, he proposed mehod works wih a consan deecion hreshold independen of he noise level and is suied o handle he presence of dense mulipah channels. More imporanly, he proposed approach does no need o buffer he whole daa packe before daa demodulaion, which faciliaes fuure developmen of online realime receiver for mulicarrier underwaer acousic communicaions. Index Terms Underwaer acousic communicaion,, wideband channel, deecion, synchronizaion and Doppler scale esimaion. I. INTRODUCTION VARIOUS daa ransmission schemes are being acively pursued for underwaer acousic (UWA) communicaions, including mulicarrier modulaion in he form of orhogonal frequency division muliplexing () [] [4], single carrier ransmission wih ime-domain sparse-channel equalizaion [5] or frequency-domain equalizaion [6], and muli-inpu muli-oupu (MIMO) echniques combined wih single carrier [7], [8] or mulicarrier [9] ransmissions. These Manuscrip received February 29, 28, revised July 3, 28. This work is suppored by he ONR YIP gran N , he NSF gran ECS , he NSF gran CNS 72834, and he ONR gran N This work was parially presened a he IEEE/MTS OCEANS conference, Kobe, Japan, April 28. The auhors are wih he Deparmen of Elecrical and Compuer Engineering, Universiy of Connecicu, 37 Fairfield Way U-257, Sorrs, Connecicu 6269, USA ( {seanm, crberger, shengli, wille}@engr.uconn.edu). Digial Objec Idenifier.9/JSAC.28.82xx /8/$25. c 28 IEEE ransmission schemes are ofen examined via offline daa processing based on recorded experimenal daa. Towards he developmen of an online underwaer acousic receiver, deecion and synchronizaion are imporan, ye ofen overlooked asks. Typically, synchronizaion enails a known preamble, which is easily deeced by he receiver, being ransmied prior o he daa. Exising preambles used in underwaer elemery are almos exclusively based on linearly frequency modulaed (LFM) signals, also known as Chirp signals []. This is due o he fac ha LFM signals have a desirable ambiguiy funcion in boh ime and frequency, which maches well o he underwaer channel, which is characerized by is large Doppler spread. However, he receiver algorihms are usually machedfiler based, which ry o synchronize a known emplae o he signal coming from one srong pah, while suppressing oher inerfering pahs. This approach suffers from he following wo deficiencies: firs, he noise level a he receiver has o be consanly esimaed o achieve a consan false alarm rae (CFAR), usually accomplished using order saisics; second, is performance will degrade in he presence of dense and unknown mulipah channels. Due o he slow propagaion speed of acousic waves, he compression or dilaion effec on he ime domain waveform needs o be considered explicily. Once a Doppler scale esimae is obained, a resampling procedure is usually applied before daa demodulaion []. One mehod o esimae he Doppler scale is o use an LFM preamble and an LFM posamble around each daa burs [], so ha he receiver can esimae he change of he waveform duraion. This mehod esimaes he average Doppler scale for he whole daa burs. As such i requires he whole daa burs o be buffered before daa demodulaion, which prevens online real-ime receiver processing. In his paper, we propose he use of mulicarrier waveforms as preamble for underwaer acousic communicaions. A preamble ha consiss of wo idenical symbols preceded by a cyclic prefix (CP) is used. This raining paern has been sudied exensively in wireless sysems for radio channels, see e.g., [2], [3], and has been included as par of he raining preamble in he IEEE 82.a/g sandards [4]. The receiver effecively correlaes he received signal wih a delayed version of iself, since, hanks o he CP srucure, he repeiion paern persiss even in he presence of

2 2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 unknown mulipah channels [2]. However, he synchronizaion algorihms ha work in wireless radio channels will no perform well in dynamic underwaer acousic channels due o he large waveform expansion or compression, which changes he repeiion period o some unknown value. We combine echniques used in underwaer elemery wih he elegan, non-parameric self-correlaor approach used in radio channels o perform deecion, synchronizaion and Doppler scale esimaion based on mulicarrier waveforms. We use a bank of parallel branches, wih each branch using a selfcorrelaor mached o a differen repeiion period. Deecion of a daa ransmission burs is declared when any of he branches leads o a correlaion meric larger han a hreshold value. The branch wih he larges meric also yields he Doppler scale esimae and coarse synchronizaion poin. We characerize he receiver operaing characerisic (ROC) by developing an analyical expression for he probabiliy of false alarm and a Gaussian approximaion for he probabiliy of deecion. We also analyze he impac of Doppler scale esimaion accuracy on he daa demodulaion performance. These analyical resuls provide guidelines for selecing he deecion hreshold and Doppler scale resoluion. Compared wih he LFM-preamble based approach, he proposed mehod has he following advanages: () he deecion hreshold is beween and, and doesn depend on he channel or operaing SNR; (2) i has a very good deecion performance, which is based on he signal energy from all pahs raher han only a single pah; (3) i leads o accurae Doppler scale esimaion; (4) afer coarse iming and resampling, i allows he use of fine iming algorihms developed for radio channels, such as [5], [6]; (5) i has a low-complexiy implemenaion when he self-correlaion meric is compued recursively [7]. In addiion o compuer-based simulaions, we have esed he proposed mehod wih real daa from an experimen a Buzzards Bay, MA, Dec. 5, 26. Using only one preamble, he proposed mehod achieves similar performance on he Doppler scale esimaion accuracy and he bi error rae as hose mehods presened in [4], which are based on he LFM preamble and posamble. However, he proposed mehod needs neiher a posamble nor o buffer he whole daa burs before demodulaion. This faciliaes fuure developmen of an online realime receiver for mulicarrier underwaer acousic communicaions. Noe ha he proposed mehod provides a poin esimae of he Doppler scale a he beginning of a daa burs. Therefore, he proposed mehod is bes suied for applicaion scenarios where he Doppler scale says consan or varies slowly during he daa burs duraion. When he Doppler scale changes fas, he poin esimaes need o be frequenly updaed, e.g., by shorening of he daa burs, or, hrough he use of a racking algorihm based on poin esimaes available via insering muliple synchronizaion blocks ino a long daa burs a regular inervals. The res of his paper is as follows. The sysem model is described in Secion II, and he proposed receiver algorihm is presened in Secion III. Deecion performance is deermined in Secion IV, and analysis of he impac of Doppler scale mismach on he daa demodulaion performance is invesigaed in Secion V. Secion VI conains numerical resuls, preamble CP x x guard zeros ZP daa ransmission ZP Fig.. A preamble, consising of wo idenical symbols and a cyclic prefix (CP), precedes he daa ransmission which uses zero padding. boh from simulaion and from real daa. Secion VII conains he conclusion. II. SYSTEM MODEL To avoid power consumpion in he guard inerval beween symbols, zero-padded (ZP) is preferred for daa ransmission [3], [4]. For synchronizaion purposes, he preamble consiss of wo idenical symbols ogeher wih a cyclic prefix. The overall ransmission srucure is shown in Fig.. The parameers can be seleced independenly for he preamble and he daa ransmissions. Suppose ha K subcarriers have been used in he preamble, and one symbol is of duraion T. The subcarrier spacing is hen /T and he bandwidh is B = K /T. Le f c denoe he carrier frequency, and f k = f c + k/t denoe he frequency for he kh subcarrier in passband, where k S= { K /2,...,K /2 }. LeT cp denoe he lengh of he CP, and define a recangular window of lengh T cp +2T as { [ T cp, 2T ], q() = () oherwise. The preamble in baseband can be wrien as x() = s[k]e j2π k T q() (2) and he corresponding passband signal is { x() =Re e } j2πfc s[k]e j2π k T q() { } = Re s[k]e j2πfk q(), (3) where s[k] is he ransmied symbol on he kh subcarrier. The channel impulse response for a ime-varying mulipah underwaer acousic channel can be described by c(τ,) = A p ()δ (τ τ p ()), (4) p where A p () is he pah ampliude and τ p () is he imevarying pah delay. As in [4], we adop he following assumpions for algorihm developmen. A) All pahs have a similar Doppler scaling facor a such ha τ p () τ p a. (5) In shor, our algorihms are developed based on assumpions A) and A2). Hence, he applicaion of he proposed mehod shall be limied o underwaer environmens where A) and A2) hold rue approximaely. Mehods suied for applicaion scenarios where differen pahs have quie differen Doppler scales warran furher invesigaion.

3 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS 3 In general, differen pahs could have differen Doppler scaling facors, e.g., see field es resuls in [8], [9]. The mehod proposed in his paper is based on he assumpion ha all he pahs have approximaely he same Doppler scaling facor. When his is no he case, par of useful signals are reaed as addiive noise, which could increase he overall noise variance considerably [4]. However, we find ha as long as he dominan Doppler shif is caused by he direc ransmier/receiver moion, as i is he case in our experimen, his assumpion seems o be jusified. The value of a is usually less han. when he relaive speed beween he ransmier and he receiver is below m/s. A2) The pah delays τ p, he gains A p, and he Doppler scaling facor a are consan over he preamble duraion 2T + T cp. The preamble duraion is usually around 5 ms o 2 ms. Assumpion A2) is reasonable wihin such a duraion, as he channel coherence ime is usually on he order of seconds. When he passband signal in (3) goes hrough he channel described in (4) and (5), we receive: { ỹ() =Re s[k]e j2πf k(+a) A p q ( } ) ( + a) τ p e j2πf k τ p +ñ(), (6) p where ñ() is he addiive noise. Define τ max = max p τ p, which is usually less han he CP lengh T cp. Using he definiion of q() in (), we obain { } ỹ() =Re H k s[k]e j2πf k(+a) +ñ(), [ T cyclic = T cp τ max, +a ] 2T, (7) +a where we define he channel ransfer funcion C(f) = A p e j2πfτp (8) p and he frequency response on he kh subcarrier as H k = C(f k ). (9) Convering he passband signal ỹ() o baseband, such ha ỹ() =Re { y()e j2πfc},wehave: y() = H k s[k]e j2π k T +af k + n() = e j2πafc H k s[k]e j2π k T (+a) + n(), () for T cyclic and n() is he noise a baseband. As expeced for CP-, we observe a cyclic convoluion beween he signal and he channel in he specified inerval, where each subcarrier is only muliplied by he corresponding frequency response. Due o he wideband naure of he underwaer channel, he frequency of each subcarrier a baseband has been shifed differenly by an amoun of af k = af c + ak/t. conversion o baseband parallel self-correlaors window lengh N window lengh N l window lengh N L x x x max(x) Γ h Fig. 2. To accoun for he ime compression/dilaion, muliple parallel branches are used, each uned o a cerain period N l. III. THE PROPOSED ALGORITHM The ransmier sends a baseband waveform embedding a repeiion paern as x() =x( + T ), T cp T. () Such a repeiion paern persiss in he received signal y() even afer ime-varying mulipah propagaion as ( y() =e j2π a +a fct y + T ), +a T cp τ max +a T +a, (2) as can be verified from (). However, he receiver knows neiher he period nor he waveform due o he unknown mulipah channel. The problem is hen o deec a paern like (2) from he incoming signal, and infer he repeiion period o find he Doppler scale. Alhough he problem of esimaing an unknown delay (synchronizaion) and Doppler scale has been sudied in he lieraure, [2] [22], hese approaches assume a non-dispersive channel and are herefore based on mached filer processing and he ambiguiy funcion. Ref. [23] has reaed random echos, bu he suggesed approach relies on esimaing he unknown channel ransfer funcion joinly wih delay and Doppler scale, herefore leading o high-complexiy receiver processing, which is no suied for coninuous daa monioring and deecion. Our proposed approach is o use a bank of self-correlaors, see Fig 2, wih each one mached o a differen periodiciy. Deecion, synchronizaion, and Doppler scale esimaion are accomplished based on he correlaion merics from he bank of self-correlaors. We now presen he proposed receiver processing, based on he sampled baseband signal. The baseband signal is usually oversampled a a muliple of he sysem bandwidh s =/(λb): y[n] =y() =ns, (3) where he oversampling facor λ is an ineger. The receiver processing includes he following seps: ) Each of he L branches calculaes a correlaion meric wih one candidae value of he window size N l.the window size N l shall be close o λk, which is he number of samples of one symbol when no

4 4 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 Doppler scaling occurs. For each delay d, he correlaion meric corresponding o he window size N l is M(N l,d)= d+nl i=d y [i] y[i + N l ] d+nl, (4) i=d y[i] 2 d+n l i=d y[i + N l ] 2 for l =,...L. 2) A deecion is declared if he correlaion meric of any branch exceeds a prese hreshold Γ h : H if: max M(N l,d) > Γ h (5) l Since he norm of he meric in (4) is beween and, he hreshold Γ h akes a value from [,]. 3) The branch wih he larges correlaion meric is viewed as having he bes mach on he repeiion lengh. Since Doppler scaling changes he period T o T /( + a), he Doppler scale facor can be esimaed as â = λk ˆN, where ˆN ˆN =argmax M(N l,d) {N l } (6) The speed esimae follows as ˆv = câ, (7) where c is he speed of sound in waer. Addiional processing can be used o refine he Doppler scale esimae, as will be shown laer on in Secion VI. 4) Synchronizaion is performed on he branch ha yields he maximum correlaion meric. Afer he maximum is deermined, he sar of ransmission can be seleced as suggesed in [2]; saring from he peak he 8% shoulders are found (firs sample of his correlaor branch before and afer he peak ha is less han 8% of he peak) and he middle is chosen as synchronizaion poin. This is beneficial, since due o he CP srucure he correlaion meric has a plaeau around he peak [2]. Remark (Doppler scale resoluion): Since he window size N l is an ineger, he minimum sep size on he Doppler scale is /(λk ). To improve he Doppler scale resoluion, he receiver operaes on he oversampled baseband signal. The oversampling facor depends on he needed Doppler scale resoluion and he parameer K. The maximum value of λ is he raio of he passband sampling rae o he baseband signal bandwidh, which is ypically less han 5 in underwaer applicaions. Remark 2 (implemenaion complexiy): The hree sliding summaions in (4) can be compued recursively. For example, define ψ(n l,d) = d+n l i=d y [l]y[i + N l ]. Insead of summing over N l muliplicaions, one can use ψ(n l,d+) = ψ(n l,d)+y [d+n l ]y[d+2n l ] y [d]y[d+n l ], (8) which amouns o wo complex muliplicaions and wo complex addiions for each updae. Hence, for each delay d, he meric M(N l,d) in (4) can be compued by no more han seven complex muliplicaions, six complex addiions, one square roo operaion, and one division. Noe ha he complexiy does no depend on he window size. Such a lowcomplexiy approach was implemened in a DSP board for one self-correlaor branch [7]. Remark 3 (fine-iming): Wih he esimaed Doppler scale â, he receiver can resample he preamble. This way, he wideband channel effec of frequency-dependen Doppler shifs can be reduced o he narrowband channel effec of frequency-independen Doppler shifs [4]. The fine-iming algorihms developed for narrowband radio channels, such as hose in [5], [6] can be applied on he resampled preamble. This way, he firs pah can be synchronized [6], insead of he sronges pah in case of he LFM based mehod. Due o channel fading, he sronges pah can appear a random posiions wihin he delay spread, which is undesirable for he ask of daa block pariioning afer he synchronizaion. In conras, he posiion of he firs pah is more sable. So far, we have described he general procedure of he proposed deecion, synchronizaion, and Doppler scale esimaion algorihm, while some parameers are lef o be specified. Imporan quesions include: How o se he deecion hreshold? How many parallel branches are needed? Wha is he desired Doppler scale resoluion? We nex address hese quesions by analyzing he deecion performance in Secion IV, and he daa demodulaion performance under Doppler scale mismach in Secion V. IV. RECEIVER OPERATING CHARACTERISTICS The oupu of each correlaor is a random variable due o he addiive noise. The probabiliies of false alarm P fa and deecion P d are he probabiliies of he correlaor oupu exceeding a hreshold Γ h under he no signal and signal hypoheses, respecively. We now analyze he false alarm and deecion probabiliies of a single branch, as a funcion of he hreshold Γ h and he Doppler scale a. This will give us an undersanding of he necessary Doppler scale spacing in he parallel self-correlaor srucure for deecion purposes. Due o over-sampling, he summaions in he meric given in (4) of he lh branch can be well approximaed wih coninuous ime inegrals: ( ) + ˆT M ˆT, y(τ) y(τ + = ˆT ) dτ + ˆT y(τ) 2 dτ + ˆT y(τ + ˆT, ) 2 dτ (9) where ˆT = N l s = T +â, = d s. (2) A. Probabiliy of False Alarm When no signal is presen, y() =n(). SinceB ˆT K, we can find a se of orhonormal basis funcions {f i ()} K i=, such ha n(τ) = n(τ + ˆT )= K i= K n,i f i (τ), τ [, + ˆT ] (2) n + ˆT,i f i (τ), τ [, + ˆT ]. (22) i=

5 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS 5 Assume ha n() is a Gaussian noise process, hen n,i and n + ˆT,i are independen and idenically disribued Gaussian random variables. Define 2 n = [n,,...,n,k ] T and n + ˆT = [n + ˆT,,...,n + ˆT,K ]T, and heir normalized versions ñ = n / n and ñ + ˆT = n + ˆT / n + ˆT. The correlaor oupu (9) can be simplified o he inner produc beween wo uni lengh vecors as ( ) M ˆT, = ñ H ñ+ ˆT. (23) Finding he probabiliy of false alarm can now be linked o he Grassmannian line packing problem in [24]. Specifically, ñ can be viewed as coordinaes of a poin on he surface of a hypersphere wih uni radius, cenered around he origin. This poin dicaes a sraigh line in a complex space C K ha passes hrough he origin. The wo lines generaed by ñ and ñ + ˆT have a disance defined as: d(ñ, ñ + ˆT ):=sin(θ )= ñ H ñ+ ˆT 2, (24) where θ denoes he angle beween hese wo lines. The disance d(ñ, ñ + ˆT ) is known as chordal disance [24]. Since n() is addiive whie and Gaussian, ñ and ñ + ˆT are uniformly disribued on he surface of he hypersphere. Wihou loss of generaliy, we can assume ha ñ + ˆT is fixed a priori and ñ is uniformly disribued, o evaluae he disribuion of he chordal disance. Based on [25, eq. (34)] (which was derived based on he geomerical framework in [26]), we infer Pr { d 2 (ñ, ñ + ˆT ) <z } = z K, <z<. (25) Hence, he probabiliy of false alarm is P fa =Pr { M( ˆT,) } > Γ h (26a) { } =Pr d 2 (ñ, ñ + ˆT ) < Γ 2 h (26b) =( Γ 2 h) K. (26c) Noe ha P fa does no depend on he power of he addiive noise. Once he hreshold Γ h is chosen, a consan false alarm rae (CFAR) is achieved independen of he noise level. B. Probabiliy of Deecion Assume ha he signal is presen, we rewrie () as where he signal is y() =x c ()+n(), (27) x c () =e j2πafc H k s[k]e j2π k T (+a), T cyclic. (28) Treaing he signal as deerminisic unknown, we define he auocorrelaion funcion of x c () as +T φ xx (T,ΔT)= x c (τ)x c (τ +ΔT )dτ. (29) T The noise is viewed as wide sense saionary, and we define is auocorrelaion funcion as φ nn (τ). Assuming ha he 2 Bold upper case and lower case leers denoe marices and column vecors, respecively; ( ) T, ( ),and( ) H denoe ranspose, conjugae, and Hermiian ranspose, respecively. and sand for for he absolue value of a complex number and he norm of a vecor, respecively. inegraion is done in a proper window where x c () is well defined as in (28), we can easily obain: { } + ˆT E y(τ) y(τ + ˆT ) dτ = ˆTφ xx ( ˆT, ˆT ), [ T plaeau := T cp τ max, T ] ( + 2â a) (3) +a ( + a)( + â) { } { + ˆT } + ˆT E y(τ) 2 dτ = E y(τ + ˆT ) 2 dτ = ˆT [φ xx ( ˆT,) + φ nn ()], T plaeau. (3) In [2], he absolue value of he correlaion meric has been approximaed as a Gaussian random variable o derive some approximae resuls. We would like o follow he same principle here. To his end, we propose o approximae he mean of he correlaor oupu as: { ( ) } M ˆT φ xx ( E ˆT, ˆT, ˆT ) ˆTφ xx ( ˆT,) + ˆTφ nn () = αγ γ +, T plaeau, (32) where γ = φ xx ( ˆT,)/φ nn () is he signal-o-noise-raio (SNR) a he receiver, and α is he correlaion coefficien α = φ xx( ˆT, ˆT ). (33) φ xx ( ˆT,) The variance can be approximaed as { ( ) } M Var ˆT, 2γ3 +5γ 2 +3γ + 2K (γ +) 4, T plaeau. (34) The variance in (34) was derived in he radio channel case wihou Doppler scaling where α =. We argue ha i can sill be used in he case wih Doppler scaling, since he variaion of he correlaion oupu is mainly due o addiive noise. We now specify he correlaion coefficien α. Based on (28), we have for T plaeau φ xx ( ˆT, ˆT )= ˆT + ˆT [ x c (τ)x c(τ + ˆT ] ) dτ (35a) = e j2πafc ˆT H k s[k]hl s [l] l S + ˆT h e j2π(+a) k T τ l T (τ + ˆT i ) ˆT dτ, (35b) which lead o φ xx ( ˆT, ˆT ) = H k s[k]hl s [l]e j2π(+ɛ)l l S e jπ(+ɛ)(k l) sinc [( + ɛ)(k l)], (36) where sinc(x) =sin(πx)/(πx) and ( + ɛ) =(+a)/( + â) wih â = T / ˆT from (2). Therefore, ɛ a â. Assume ha ɛ is iny, we approximae sinc[( + ɛ)(k l)] δ[k l]. For consan ampliude modulaion s[i] 2 = σs,wehave 2 φ xx ( ˆT, ˆT ) σs 2 H k 2 e j2πk(a â). (37)

6 6 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER γ = db approx.: μ approx.: μ ±2σ sim.: μ sim: μ ±2σ noise: μ noise: μ +2σ γ = db approx.: μ approx.: μ ±2σ sim.: μ sim: μ ±2σ noise: μ noise: μ +2σ M(ε).5 M(ε) γ = db.3.2 γ = db c ε: speed mismach in m/s (a) non-dispersive c ε: speed mismach in m/s (b) dispersive Fig. 3. Saisics of he correlaor oupu, including he mean μ and sandard deviaion σ as a funcion of he unknown speed for wo differen levels of SNR γ; (a) non-dispersive channel wih a single pah, (b) dispersive channel wih an exponenial decay profile. Similar approximaion can be done for φ xx ( ˆT,). We hus have α H k 2 e j2πk(a â) H k 2. (38) In summary, wih α approximaed in (38), he mean μ α approximaed in (32), and he variance σ α approximaed in (34), an approximae expression for he probabiliy of deecion in T plaeau is { ( ) } ( ) M Γh μ α P d =Pr ˆT, Γh Q, (39) where Q(x) =(/ 2π) /2 d. x e 2 C. Numerical Validaion To confirm he heoreical analysis, we use numerical simulaion using he following seps: ) Generae he baseband signal via () and sample i as in (3). 2) Compare he saisics of he correlaor oupu a signal sar =on a branch wih N l = λk. For he non-dispersive channel wih a single pah, he mean of he correlaor (32) can be simplified o { ( ) } M E ˆT, = αγ γ = sinc [K(a â)] γ + γ +. (4) The simulaion resuls for he non-dispersive channel are shown in Fig. 3(a); we observe ha he loss of correlaion due o he unknown speed is modelled well by he sinc funcion, while he approximaion of he sandard deviaion is fairly exac for he low SNR case bu only of he righ magniude for he high SNR case. For dispersive channels we average over differen channel realizaions, where we choose an exponenially decaying channel profile ha loses abou 2 db wihin ms. For each channel realizaion, we evaluae he mean and variance of he σ α Gaussian approximaion, hen average hese by approximaing hem via a single Gaussian disribuion wih mached momens. Since his is basically a Gaussian mixure disribuion, he resuling mean is he average mean, while he variance is increased: i consiss of he average variance and he addiional spread of he means. The resuls are in Fig. 3(b); we see an idenical behavior for K(a â) (inside he main lobe of he sinc funcion). This is because for ɛ a â =, α is fixed as uniy (c.f. (38)), while for ɛ, α is a random variable depending on he specific channel realizaion. Accordingly he addiional variaion in α leads o an increased variance for larger ɛ and he sinc shape is disored depending on he channel saisics. Sill, for a small speed mismach he behavior can be well approximaed by he non-dispersive channel. To assess he effec of Doppler scale mismach, i.e., unknown speed, on he deecion performance, we plo he receiver operaing characerisic (ROC) in Fig. 4. The exac probabiliy of false alarm (26c) is ploed agains he Gaussian approximaion as well as Mone-Carlo simulaion resuls for boh AWGN and dispersive channels. For he non-dispersive case we see ha he simulaion resuls mach he Gaussian approximaion reasonably for he chosen speeds and SNR. Comparing o Fig. 3, he deecion performance is superb as long as he mean, μ α, of he correlaor oupu under he signal hypohesis and he mean under he noise hypohesis are separaed by more han six imes he sandard deviaion, σ α. In case of he dispersive channel, we had seen in Fig. 3 ha he mean μ α of he correlaor was always higher for large Doppler scales, bu a he cos of an increased variance. This resuls in he ROC s having less seep slopes, inersecing he curves for he AWGN channel accordingly performing beer for deecion probabiliies around one half, bu worse owards one (ha are he regions of ineres). This derimenal effec is negligible when he Doppler scale mismach is less han, e.g., c(a â).5 m/s, which are also he regions of

7 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS 7 probabiliy of deecion Δ v =.5 m/s Δ v = 2. m/s AWGN.5 approx. dispersive approx probabiliy of false alarm Δ v = 2.5 m/s Fig. 4. Receiver operaing characerisic (ROC) of he deecion scheme for K = 52 carriers, γ =db and varying speeds; ploed are he Gaussian approximaion of he probabiliy of deecion and he Mone-Carlo simulaed probabiliy of deecion (doed lines) for differen channels agains he exac analyic probabiliy of false alarm. generally good performance. Therefore for a limied Doppler scale mismach, he deecion performance is no changed much by he dispersive naure of he channel. D. Comparison o LFM Based Deecion We now compare he deecion performance of our approach wih he deecion performance based on an LFM preamble wih mached filer processing a he receiver followed by a hreshold es. Alhough in pracice his hreshold has o be esimaed online, for his comparison we assume he noise level o be known for he LFM based approach. We use a dispersive channel wih L pahs, wih a uniform power profile and a oal channel lengh of abou 2 ms. Boh approaches use a bandwidh of 2 khz and a preamble lengh of abou ms. The based approach has K = 52 subcarriers and herefore a deecion SNR of approximaely K γ,whereγ is he SNR per subcarrier. The LFM uses an upsweep wih he same oal energy, giving effecively a 3 db advanage since he full preamble is used for correlaion. Fig. 5 shows he ROCs for varying channel condiions and available oversampling. We noe he following: The LFM based approach is less favorable when he number of pahs increases, loosing abou 3 db when he number of pahs riples; c.f. Fig. 5(a), he ROC for γ = 3 db, L = 5 is almos idenical wih he ROC for γ = db, L = 45. This loss can be linked o a comparison beween selecion combining (SC) and maximum raio combining (MRC) [27], as he LFM based approach only uilizes he energy from he sronges pah. Compared o he LFM based approach, he muli-carrier approach degrades faser wih SNR, see Fig. 5(a), since we use a noisy emplae for correlaion. This effec depends on he per carrier SNR γ. Onceγ is larger han db his effec is negligible. The LFM based approach degrades when no oversampling is used, see Fig. 5(b), as he widh of he ambiguiy funcion is small along he ime axis. Noe ha for communicaion sysems, boh mehods will work well in he pracical SNR range, as daa demodulaion requires a decen SNR (much higher han he deecion hreshold). Furher, he proposed mehod has a low-complexiy implemenaion as discussed in Remark 2, which is no available for he LFM based approach. Due o is non-parameric naure and low-cos implemenaion, he proposed approach is an appealing choice for he preamble design in underwaer mulicarrier communicaion sysems. V. IMPACT OF DOPPLER SCALE ESTIMATION ACCURACY In his secion, we analyze he performance degradaion on daa ransmission due o Doppler scale mismach. This will help o specify he needed Doppler scale resoluion from a daa communicaion perspecive. For daa ransmission, we use ZP-. Since block by block processing is used, le us focus on one ZP- block. Le T denoe he symbol duraion and T g he guard inerval. The oal block duraion is T = T + T g and he subcarrier spacing is /T.Thekh subcarrier is a frequency f k = f c + k/t, k = K/2,...,K/2, (4) where f c is he carrier frequency and K subcarriers are used so ha he bandwidh is B = K/T. Les[k] denoe he informaion symbol o be ransmied on he kh subcarrier. The non-overlapping ses of acive subcarriers S A and null subcarriers S N saisfy S A S N = { K/2,...,K/2 }; he null subcarriers are used o faciliae Doppler compensaion a he receiver [4]. The ransmied signal in passband is hen given by ] } e j2πfc {[ x() =Re A s[k]e j2π k T g(), [,T+T g ], (42) where g() describes he zero-padding operaion, i.e., g() =, [,T] and g() = oherwise. Due o he adoped channel model, he received passband signal is { [ ] ỹ() =Re s[k]e j2π k T (+a τp) g( + a τ p ) p A A p e j2πfc(+a τp) } +ñ(), (43) where ñ() is he addiive noise. A wo-sep approach o miigaing he channel Doppler effec was proposed in [4]. The firssepisoresampleỹ() in he passband wih a resampling facor b, which represens our esimae of a, leading o ( ) z() =ỹ. (44) +b

8 8 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 P D γ = db.2 LFM, L = 5 LFM, L = 3. LFM, L = P FA (a) muli-pah γ = 3 db P D P FA (b) oversampling LFM, λ = LFM, λ = 2 LFM, λ = 4 LFM, λ = 8 Fig. 5. Comparison of ROC beween an approach based on an LFM preamble/mached filer processing and our muli-carrier based approach; (a) as he number of pahs L increases, he LFM performance decreases, λ =; (b) he LFM based approach is also more sensiive o available oversampling, L =45, γ =db; lines for varying L or λ are have same formaing as LFM case. Convering o baseband, we obain z() a b j2π z() =e +b fc s[k]e j2π [ A A p e j2πf kτ p g p +a k +b T ( ) ] +a +b τ p + n(), (45) The second sep is o perform fine Doppler shif compensaion on z() o obain z()e j2πɛ,whereɛis he esimaed residual Doppler shif. Performing ZP- demodulaion, he oupu z m on he mh subchannel is T +Tg z m = T z()e j2πɛ e j2π m T d. (46) Plugging in z() and carrying ou he inegraion, we simplify z m o ( ) +b z m = C +a (f m+ ɛ) s[k]ϱ m,k + v m, (47) where v m is he addiive noise, C(f) is defined in (8), and ϱ m,k = +b +a sin(πβ m,kt ) e jπβm,kt, πβ m,k T (48) β m,k =(k m) T + (a b)f m ( + b)ɛ. +a (49) Defining he symbol energy as σs 2 = E [ s[k] 2] and he noise variance as σv 2,wefind he effecive SNR on he mh subcarrier o be: ϱ m,m 2 σs 2 γ m = σv ( 2 ) +. (5) ϱ m,k 2 σ 2 +b C +a (f m + ɛ) 2 s k m The firs erm in he denominaor is due o addiive noise, while he second erm is due o he self-inerference aroused by he Doppler scale mismach. Even when he addiive noise diminishes, he effecive SNR is bounded by γ m γ m := ϱ m,m 2 k m ϱ m,k 2 (5) due o self-inerference induced by Doppler scale mismach. We now evaluae he SNR upperbound for wo cases: Case : No Doppler shif compensaion by seing ɛ =. Case 2: Ideal Doppler shif compensaion where ɛ op = a b +b f c, (52) such ha β m,k =(k m) T + a b +a m T. (53) For he firs case, he leading erm (k m)/t in β m,k is he frequency disance beween he kh and he mh subcarriers, while he second erm a b +a f m is he exra frequency shif. For he second case, he leading erm (k m)/t in β m,k is he frequency disance beween he kh and he mh subcarriers, while he second erm a b +a m T is he exra frequency shif. Since f m is much larger han m T, we can see ha Doppler shif compensaion will improve he performance. Consider an example of f c =27kHz and B/2 =6kHz, we have f m m [2, 33] khz and max m T =6kHz. Hence, he accuracy of (a b) can be relaxed a leas by four imes o reach similar performance. Doppler shif compensaion is one crucial sep in he receiver design, which was he key in he success of he receivers in [4]. We now numerically evaluae he upperbound γ m for ɛ = and ɛ op.wesef c =27kHz, B =2kHz, and K = 24. Fig. 6 shows he bounds for hese wo cases respecively. Suppose ha we wan o limi he self noise o be a leas 2 db below he signal power. In case of ɛ =, we need Δv o

9 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS Δ v =.6 m/s Δ v =.2 m/s Δ v =.5 m/s.7.6 coarse muli grid inerpolaion 5.5 SNR (db) 4 3 RMSE(v) Subcarrier Index speed in m/s Fig. 6. The SNR upperbound γ m for ɛ = ɛ op (hick, full lines) and ɛ = (hin, dashed lines) as a funcion of Δv, wherea b =Δv/c. Fig. 7. Average velociy esimaion error using varying amouns of correlaors and a simple inerpolaion beween he measured poins; hin, dashed lines are γ =db and hick full lines are γ =db. be less han.6 m/s. While in case of ɛ op,heδv can be as large as.3 m/s. Fig. 6 provides guidelines on he selecion of he Doppler scale spacing of he parallel correlaors. For example, assuming ha he correlaor branch closes o he rue speed will yield he maximum meric, hen wih fine Doppler shif compensaion ɛ = ɛ op we can se he Doppler scale spacing o be.4 m/s (where we need Δv o be less han.2 m/s) o achieve an SNR upperbound of a leas 25 db. On he oher hand, if an SNR upperbound of 5 db is sufficien, he Doppler scale spacing could be as large as. m/s. VI. IMPLEMENTATION AND PERFORMANCE TESTING In Secion IV, i was shown ha for K = 52 carriers in he preamble, a speed mismach of up o.5 m/s will no degrade he deecion performance considerably. On he oher hand, he SNR analysis for daa recepion using K = 24 subcarriers in Secion V indicaed ha he speed mismach should no exceed.3-.5 m/s o limi ICI. This suggess a muli-grid approach for he implemenaion: ) Coarse-grid search for deecion. Only a few parallel self-correlaors are used o monior he incoming daa. This helps o reduce he receiver complexiy. 2) Fine-grid search for daa demodulaion. Afer a deecion is declared, a se of parallel self-correlaors wih beer Doppler scale resoluion are used only on he capured preamble. Fine-grid search is cenered around he Doppler scale esimae from he coarse-grid search. Insead of muli-grid search, one may also use an inerpolaion based approach o improve he esimaion accuracy beyond he limi se by he sep size. We borrow a echnique from [28], which is usually used in specral peak locaion esimaion based on a limied amoun of DFT samples. Afer coarse or fine-grid search, le X k denoe he ampliude from he branch wih he larges correlaion oupu, and X k and X k+ are he ampliudes from he lef and righ neighbors. Le Δa denoe he grid spacing. The formula X k+ X k δ = Δa (54) 4 X k 2 X k 2 X k+ can be used o esimae an offse δ of he Doppler scale deviaing from he sronges branch owards he second sronges branch. A. Simulaions for Velociy Esimaion We use K = 52 subcarriers and an oversampling facor of λ =8and se he coarse grid spacing as Δa =Δv/c, where Δv is.46 m/s. Fig. 7 depics he roo mean square error of he speed esimaes ˆv = câ, a wo SNRs of db and db. We observe a saw-ooh shape for he coarse esimaes, and he SNR decrease has lile impac on his shape. This suggess ha he probabiliy of no finding he closes branch is negligible and he dominaing error is he quanizaion o he coarse grid. Afer deecion of he coarse-grid search, we use anoher six self-correlaors wih spacing of Δv =.366 m/s o search around he esimaed Doppler scale from he previous sage. Much improved esimaes are obained, as shown in Fig. 7. The achieved accuracy exceeds he mismach specificaion we se earlier of.3-.5 m/s. We can see more degradaion of he saw-ooh shape for low SNR. This is reasonable. As he separaion in enaive Doppler scales beween correlaors diminishes, neighboring correlaors will have very similar oupus. Also, Fig. 7 shows he RMSE for velociy esimaion wih inerpolaion applied afer he coarse grid search wih Δv =.46 m/s. We observe ha he inerpolaion approach is very effecive. B. Resuls wih Experimenal Daa When he ransmier and he receiver are saionary, Doppler scale esimaion is no needed, and only one self-correlaion

10 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 LFM preamble preamble # #2 #Nb LFM posamble posamble preamble daa posamble Fig. 8. The srucure of he daa packe used in he Buzzards Bay experimen, Dec. 5, LFM Resul Ampliude ρ ms (a) LFM mached filer ms (b) self-correlaor Fig. 9. Comparison of he mached filer oupu for one LFM preamble and he plaeau oupu of he proposed synchronizaion meric. branch is necessary a he receiver. The deecion and coarse synchronizaion algorihms based on one branch have been used in he PC- and DSP-based mulicarrier modem prooypes [7], [29]. We now work on he daa from an experimen performed a Buzzards Bay, Dec. 5, 26 wih a fas-moving ransmier. The same daa se was used previously in [4] o demonsrae he capabiliy of recepion in a dynamic seup. The used packe srucure is shown in Fig. 8, where each packe conains muliple blocks. A oal of 2 packe ransmissions were conduced when he ransmier was moving owards he receiver and passing by he receiver a he end. See [4] for he deailed descripions. Doppler scale esimaion is done in [4] based on he measured ime difference beween he LFM pre- and posamble. This scheme showed good performance, as afer Doppler scale compensaion via resampling he daa could be decoded wih reasonable BER. The drawback is ha he whole packe needs o be buffered before daa processing. For example, one packe conains 32 blocks wih K = 24 subcarriers where he packe duraion is abou 3.8 s [4]. Buffering 3.8 seconds of daa before acual decoding inroduces excessive processing delays. Firs we plo a comparison of he iming merics for a mached filer using he LFM waveform wih our proposed scheme in Fig. 9. We observe ha he channel energy is fairly consrained wihin he firs 2-3 ms accordingly he plaeau observed a he self-correlaor oupu is almos of lengh T cp, which in his case is 25.6 ms. We compare he Doppler scale/relaive speed esimaion accuracy beween he wo schemes. In Fig. (a) we plo he relaive velociy esimaes beween he sender and receiver; as also an preamble and posamble were available we include boh esimaes. Even hough he posamble would no be used for decoding purposes as real-ime operaion is he goal, i gives inuiion abou he resuls, since no ground ruh is available. Fig. (b) zooms in on he ransmissions where he Doppler scale changes dynamically. This was caused by he ransmier passing by closely a he receiver s locaion around ransmission 9. As he Doppler scale is assumed consan during each ransmission, his will also be he mos challenging ransmissions o decode. Generally he speed esimaes are close, when looking a he deails (see zoom), i is ineresing o consider ha he previous mehod uses he duraion of a complee ransmission while our new approach is a poin esimae. Since he experimen used a large number of blocks per ransmission (32 blocks for he case of 24 subcarriers resuling a packe duraion of 3.8 s), he ime-varying naure of he acual Doppler speed is refleced differenly in he wo approaches. Inspecing he esimaes for ransmission 4, 6 or 2, he LFM-based resul is no he average beween he pre- and posamble poin esimaes. We observe ha his new proposed mehod differs from he previous mehod by no more han kno (.5 m/s) for any ransmission. We nex carry ou a comparison on he BER performance using he daa se from [4], where a 6-sae rae 2/3 convoluional code is used and each subcarrier is QPSK modulaed. Demodulaion and decoding were done wice for each packe ransmission; once using he Doppler scale

11 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS speed esimaes [m/s] 2 2 speed esimaes [m/s] LFM pre & pos ambles preamble posamble Transmission LFM pre & pos ambles preamble posamble Transmission (a) full ransmission (b) zoom Fig.. Comparison of velociy esimaion echniques; he previous mehod calculaed he ime difference beween LFM pre- and pos-ambles, while he new approach is solely based on eiher preamble or posamble a one paricular ime. LFM pre & pos ambles, uncoded preamble, uncoded LFM pre & pos ambles, coded preamble, coded Doppler scale changes rapidly, he packe duraion can be decreased, or muliple synchronizaion blocks are insered ino he ransmission, o allow for more frequen updaes of he Doppler scale esimaes. BER Transmission Fig.. Comparison of he uncoded and coded bi error raes; decoding afer resampling wih eiher he offline speed esimaes based on he LFM pre- and pos-ambles or based on he new speed esimae for online processing. VII. CONCLUSION In his paper we proposed a new mehod for deecion, synchronizaion, and Doppler scale esimaion for underwaer communicaion based on mulicarrier waveforms. We characerized he receiver operaing characerisic and analyzed he impac of Doppler scale mismach on he sysem performance. Compared o exising LFM-based approaches, he proposed mehod works wih a consan deecion hreshold independen of he noise level and is suied o handle he presence of dense mulipah channels. More imporanly, he proposed approach does no need o buffer he whole daa packe before daa demodulaion, which is very appealing for he developmen of online realime receivers for mulicarrier underwaer acousic communicaion. esimae obained from he LFM mehod and once using he esimae based on he preamble only. Fig.shows ha similar uncoded and coded BER resuls are obained. The proposed mehod, however, does no need o buffer he whole packe and can sar decoding when each new block comes in. The insances where differences in BERs are observed are wih ransmissions 9 and 8. There are several environmenal facors which could have conribued o his anomaly, including ship noise and a rapid rae of change in velociy, as discussed in [4]. Perhaps since he original mehod for velociy esimaion uses he average compression/dilaion over he enire ransmission, his new mehod, which only relies on one preamble sequence, is more suscepible o rapid changes in velociy during a ransmission. For scenarios where he REFERENCES [] M. Chire, S. H. Ong, and J. Poer, Performance of coded in very shallow waer channels and snapping shrimp noise, in Proc. MTS/IEEE OCEANS, vol. 2, 25, pp [2] P. J. Gendron, Orhogonal frequency division muliplexing wih on-offkeying: Noncoheren performance bounds, receiver design and experimenal resuls, U.S. Navy Journal of Underwaer Acousics, vol. 56, no. 2, pp , Apr. 26. [3] M. Sojanovic, Low complexiy deecor for underwaer channels, in Proc. MTS/IEEE OCEANS conference, Boson, MA, Sep. 8-2, 26. [4] B. Li, S. Zhou, M. Sojanovic, L. Freiag, and P. Wille, Mulicarrier communicaion over underwaer acousic channels wih nonuniform Doppler shifs, IEEE J. Ocean. Eng., vol. 33, no. 2, Apr. 28. [5] W. Li and J. C. Preisig, Esimaion of rapidly ime-varying sparse channels, IEEE J. Ocean. Eng., vol. 32, no. 4, pp , Oc. 27. [6] Y. R. Zheng, C. Xiao, T. C. Yang, and W.-B. Yang, Frequencydomain channel esimaion and equalizaion for single carrier underwaer acousic communicaions, in Proc. of MTS/IEEE OCEANS conference, Vancouver, BC, Canada, Sep Oc. 4, 27.

12 2 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 28 [7] D. B. Kilfoyle, J. C. Preisig, and A. B. Baggeroer, Spaial modulaion experimens in he underwaer acousic channel, IEEE J. Ocean. Eng., vol. 3, no. 2, pp , Apr. 25. [8] S. Roy, T. M. Duman, V. McDonald, and J. G. Proakis, High rae communicaion for underwaer acousic channels using muliple ransmiers and space-ime coding: Receiver srucures and experimenal resuls, IEEE J. Ocean. Eng., vol. 32, no. 3, p , Jul. 27. [9] B. Li, S. Zhou, M. Sojanovic, L. Freiag, J. Huang, and P. Wille, MIMO- over an underwaer acousic channel, in Proc. MTS/IEEE OCEANS conference, Vancouver, BC, Canada, Sep Oc. 4, 27. [] D. B. Kilfoyle and A. B. Baggeroer, The sae of he ar in underwaer acousic elemery, IEEE J. Ocean. Eng., vol. 25, no., pp. 4 27, Jan. 2. [] B. S. Sharif, J. Neasham, O. R. Hinon, and A. E. Adams, A compuaionally efficien Doppler compensaion sysem for underwaer acousic communicaions, IEEE J. Ocean. Eng., vol. 25, no., pp. 52 6, Jan. 2. [2] T. M. Schmidl and D. C. Cox, Robus frequency and iming synchronizaion for, IEEE Trans. Commun., vol. 45, no. 2, pp , Dec [3] H. Minn, V. Bhargava, and K. Leaief, A robus iming and frequency synchronizaion for sysems, IEEE Trans. Wireless Commun., vol. 2, no. 4, pp , Jul. 23. [4] R. D. J. van Nee, G. A. Awaer, M. Morikura, H. Takanashi, M. A. Webser, and K. W. Halford, New high-rae wireless LAN sandards, IEEE Commun. Mag., vol. 37, no. 2, pp , Dec [5] E. G. Larsson, G. Liu, J. Li, and G. B. Giannakis, Join symbol iming and channel esimaion for based WLANs, IEEE Commun. Le., vol. 5, no. 8, pp , Aug. 2. [6] C. R. Berger, S. Zhou, Z. Tian, and P. Wille, Performance analysis on an MAP fine iming algorihm in UWB muliband, IEEE Trans. Commun., 28 (o appear); downloadable a hp:// shengli/bztw8.pdf. [7] H. Yan, S. Zhou, Z. Shi, and B. Li, A DSP implemenaion of acousic modem, in Proc. of he ACM Inernaional Workshop on UnderWaer Neworks (WUWNe), Monréal, Québec, Canada, Sep. 27. [8] J. C. Preisig and G. B. Deane, Surface wave focusing and acousic communicaions in he surf zone, The J. Acousical Sociey of America, vol. 6, no. 4, pp , Oc. 24. [9] M. Siderius, M. B. Porer, P. Hursky, and V. McDonald, Modeling Doppler effecs for acousic communicaions (A), The J. Acousical Sociey of America, vol. 9, no. 5, p. 3397, May 26. [2] L. Weiss, Waveles and wideband correlaion processing, IEEE Signal Processing Mag., vol., no., pp. 3 32, Jan [2] G. Giuna, Fas esimaors of ime delay and Doppler srech based on discree-ime mehods, IEEE Trans. Signal Processing, vol. 46, no. 7, pp , Jul [22] X. X. Niu, P. C. Ching, and Y. T. Chan, Wavele based approach for join ime delay and Doppler srech measuremens, IEEE Trans. Aerosp. Elecron. Sys., vol. 35, no. 3, pp. 9, Jul [23] L. H. Sibul and L. G. Weiss, A wideband wavele based esimaor correlaor and is properies, Mulidimensional Sysems and Signal Processing, vol. 3, no. 2, pp , Apr. 22. [24] J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, ec.: Packings in Grassmannian space, Experimenal Mah., vol. 5, no. 2, pp , 996. [25] S. Zhou, Z. Wang, and G. B. Giannakis, Quanifying he power-loss when ransmi-beamforming relies on finie rae feedback, IEEE Trans. Wireless Commun., vol. 4, no. 4, pp , Jul. 25. [26] K. Mukkavilli, A. Sabharwal, E. Erkip, and B. Aazhang, On beamforming wih finie rae feedback in muliple-anenna sysems, IEEE Trans. Inform. Theory, vol. 49, no., pp , Oc. 23. [27] M. K. Simon and M.-S. Alouini, Digial Communicaion over Fading Channels. New York: Wiley, 2. [28] E. Jacobsen and P. Koosookos, Fas, accurae frequency esimaors [DSP Tips & Tricks], IEEE Signal Processing Mag., vol. 24, no. 3, pp , May 27. [29] S. Mason, R. Anse, N. Anicee, and S. Zhou, A broadband underwaer acousic modem implemenaion using coheren, in Proc. Naional Conference for Undergraduae Research (NCUR), San Rafael, California, Apr. 27. Sean F. Mason was born in New Haven, Connecicu on Augus 2, 983. In 26 he received he B.S. degree in elecrical engineering and is currenly working oward he M.S. degree, boh in elecrical engineering, a he Universiy of Connecicu (UCONN), Sorrs. For he periods of June hrough Augus in 27 and 28, he was employed a he Naval Research Laboraory in Washingon D.C. Mr. Mason s research ineress lie in he field of signal processing and communicaions, specifically synchronizaion and wideband modulaion for underwaer acousic communicaion. He is an acive member of he honors sociey Ea Kappa Nu, has served as a reviewer for he IEEE Transacions on Vehicular Technology and was a session chair for he 28 Oceans conference in Quebec Ciy, Canada. Chrisian R. Berger (S 5) was born in Heidelberg, Germany, on Sepember 2, 979. He received he Dipl.-Ing. degree in elecrical engineering from he Universiä Karlsruhe (TH), Karlsruhe, Germany in 25. During his degree he also spen a semeser a he Naional Universiy of Singapore (NUS), Singapore, where he ook boh undergraduae and graduae courses in elecrical engineering. He is currenly working owards his Ph.D. degree in elecrical engineering a he Universiy of Connecicu (UCONN), Sorrs. In he summer of 26, he was as a visiing scienis a he Sensor Neworks and Daa Fusion Deparmen of he FGAN Research Insiue, Wachberg, Germany. His research ineress lie in he areas of communicaions and signal processing, including disribued esimaion in wireless sensor neworks, wireless posiioning and synchronizaion, underwaer acousic communicaions and neworking. Mr. Berger has served as a reviewer for he IEEE Transacions on Signal Processing, Wireless Communicaions, Vehicular Technology, and Aerospacespace and Elecronic Sysems. In 28 he was member of he echnical program commiee and session chair for he h Inernaional Conference on Informaion Fusion in Cologne, Germany. Shengli Zhou (M 3) received he B.S. degree in 995 and he M.Sc. degree in 998, from he Universiy of Science and Technology of China (USTC), Hefei, boh in elecrical engineering and informaion science. He received his Ph.D. degree in elecrical engineering from he Universiy of Minnesoa (UMN), Minneapolis, in 22. He has been an assisan professor wih he Deparmen of Elecrical and Compuer Engineering a he Universiy of Connecicu (UCONN), Sorrs, since 23. His general research ineress lie in he areas of wireless communicaions and signal processing. His recen focus is on underwaer acousic communicaions and neworking. Dr. Zhou has served as an Associae Edior for IEEE Transacions on Wireless Communicaions from Feb. 25 o Jan. 27. He received he ONR Young Invesigaor award in 27.

13 MASON e al.: DETECTION, SYNCHRONIZATION, AND DOPPLER SCALE ESTIMATION WITH MULTICARRIER WAVEFORMS 3 Peer Wille (F 3) received his BASc (Engineering Science) from he Universiy of Torono in 982, and his PhD degree from Princeon Universiy in 986. He has been a faculy member a he Universiy of Connecicu ever since, and since 998 has been a Professor. His primary areas of research have been saisical signal processing, deecion, machine learning, daa fusion and racking. He has ineress in and has published in he areas of change/abnormaliy deecion, opical paern recogniion, communicaions and indusrial/securiy condiion monioring. He is edior-in-chief for IEEE Transacions on Aerospace and Elecronic Sysems, and unil recenly was associae edior for hree acive journals: IEEE Transacions on Aerospace and Elecronic Sysems (for Daa Fusion and Targe Tracking) and IEEE Transacions on Sysems, Man, and Cyberneics, pars A and B. He is also associae edior for he IEEE AES Magazine, edior of he AES Magazines periodic Tuorial issues, associae edior for ISIFs elecronic Journal of Advances in Informaion Fusion, and is a member of he ediorial board of IEEEs Signal Processing Magazine. He has been a member of he IEEE AESS Board of Governors since 23. He was General Co- Chair (wih Sefano Coraluppi) for he 26 ISIF/IEEE Fusion Conference in Florence, Ialy, Program Co-Chair (wih Eugene Sanos) for he 23 IEEE Conference on Sysems, Man, and Cyberneics in Washingon DC, and Program Co-Chair (wih Pramod Varshney) for he 999 Fusion Conference in Sunnyvale.