Implementation and Testing of a Low-Overhead Network Synchronization Protocol

Transcription

1 Implementation and Teting of a Low-Overhead Network Synchronization Protocol Skye R. Kowalki, Timothy M. Chritman, Andrew G. Klein Department of Engineering and Deign, Wetern Wahington Univerity Bellingham, WA 985 {kowald, chri70, andy.klein}@wwu.edu Mitchell W.S. Overdick, Joeph E. Canfield PACCAR Technical Center Mt. Vernon, WA 9873 {mitchell.overdick, joe.canfield}@paccar.com D. Richard Brown III Department of ECE, Worceter Polytechnic Int. Worceter, MA drb@wpi.edu Abtract Thi paper decribe a radio frequency implementation of precie ynchronization between two oftware defined radio without the ue of timetamp. Contemporary ynchronization protocol motly rely on exchanging digital timetamp between node. The finite preciion of thee digital timetamp limit the degree of ynchronization achievable, and the additional overhead of ending timetamp reduce data throughput. Previou experimental work demontrate that ynchronization information can intead be conveyed at the phyical layer through pairwie meage exchange between node. By forgoing the ue of digital timetamp the problem of finite preciion error can be avoided and the accuracy of ynchronization i only limited by fundamental bound of delay etimation. Our implementation wa ucceful in ynchronizing two Ettu N10 Software Defined Radio to within a tandard deviation of 8.18 n. TABLE OF CONTENTS 1. INTRODUCTION TIMESTAMP-FREE SYNCHRONIZATION PROTOCOL 3. DELAY ESTIMATION FOR BANDPASS RF SIGNALS. 4. PASSBAND RADIO-FREQUENCY IMPLEMENTATION 3 5. EXPERIMENTAL RESULTS DISCUSSION CONCLUSION ACKNOWLEDGMENTS REFERENCES BIOGRAPHY INTRODUCTION Recently, there ha been great interet in technique uch a ditributed MIMO and beamforming [1]. Thee technique permit multiple device to coordinate their communication and pool their antenna reource, thereby forming a virtual antenna array. Such ditributed tranmiion technique require precie ynchronization between device to permit carrier phae alignment. The pat few decade have een the development of a number of ynchronization protocol uch a Network Time Protocol [], the Global Poitioning Sytem [3], and everal lightweight ynchronization protocol for ue in reource contrained enor network [4]. A common /18/$31.00 c 018 IEEE theme with exiting protocol i that they rely on exchanging digital timetamp between device. Finite preciion error reulting from digital time tamp inherently limit the accuracy of uch ynchronization protocol. Furthermore, precie ynchronization require frequent exchanging of timing information. Exchanging digital timetamp at thee peed can preent a prohibitive amount of overhead to network channel between device. To eliminate the ignificant iue of conventional ynchronization for thi application, a timetampfree ynchronization protocol wa propoed that perform ynchronization implicitly at the phyical layer through pairwie meage exchange [5]. Theoretical analyi ha hown that thi lead to precie, accurate ynchronization between two device, and reult in lighter load on a network when compared with conventional timetamp-baed ynchronization approache. In the pat, thi protocol ha been ued to ynchronize variou DSP platform with mean error well below the period of the carrier frequency. Previouly, an implementation of thi protocol at acoutic frequencie uing a Texa Intrument TMS30C6713 DSK [6], and a ubequent implementation at radio frequency (RF) uing an Ettu E310 oftware defined radio [7] were teted. While thee experiment were encouraging, the former did not operate at radio frequencie, while the latter Ettu E310 implementation wa only able to achieve 70 n ynchronization due to practical limitation in the architecture of the oftware defined radio (SDR). That i, the delay etimation had to be performed on the baeband ignal after downconverion. It i well known from the Cramer-Rao lower bound that the achievable accuracy of delay etimator on uch ignal are limited when compared to performing delay-etimation on ampled RF ignal [8]. Thi paper decribe a real-time implementation of the timetamp-free network ynchronization protocol implemented on an Ettu N10 oftware defined radio, in which the delay etimator operate directly on the ampled RF ignal. Thi lead to ynchronization performance that i ignificantly improved with repect to the previou RF implementation of thi protocol in Overdick et al. [7]. Experimental reult preented in thi paper how that the protocol can ynchronize two radio to within 8.18 n of preciion while accounting for the preence of propagation delay. Thi experimental tudy erve to demontrate the improved ynchronization performance of the timetamp-free protocol in a oftware radio architecture that employ RF paband ignal rather than baeband ignal in performing delay etimation. 1

2 lave node tick t (a) t (a) +t(d) lave node timebae ˆδ mater node timebae mater node tick t (b) The lave node can then etimate it tick offet with repect to the mater node by calculating ˆδ = ( t (a) ) + t (d) () T 0 where the notation (z) T0 correpond to wrapping z to the interval [ T 0 /, T 0 /). The offet etimate in () can be ued directly for immediate offet correction at the lave node or a an input to a filtering algorithm to correct both offet and drift. t (d) t = t+ [k] t t (c) Figure 1. Timetamp-free ynchronization bidirectional ignal exchange.. TIMESTAMP-FREE SYNCHRONIZATION PROTOCOL Figure 1 how the interaction between a lave node and the mater node uing the timetamp-free ynchronization protocol. The time-varying offet at the lave node with repect to the mater node i denoted a [k] and local time at the lave node i denoted a t = t + [k] where t i the reference time correponding to the local at the mater node. The timetamp-free ynchronization protocol begin with the lave node tranmitting a ignal to the mater node at arbitrary local time t (a). The ignal arrive at the mater node at local time t (b) = t (a) [k] + τ where [k] i the current offet of the lave node with repect to the mater node and τ i the propagation delay between the lave node and the mater node. The mater node then tranmit a ignal back to the lave node at time t (c) where t (c) i elected uch that t (b) + t (c) (mod T 0 ) = 0 (1) where T 0 i mater node tick period. Note that, unlike the uual ender/receiver ynchronization protocol, e.g. [9], no timetamp are exchanged between the node. Implicit timing information i embedded in the mater node repone to the lave node by electing t (c) o that a local tick the mater node i centered between t (b) and t (c). Auming a reciprocal channel and tranmitter/receiver chain, the lave node receive the reply ignal from the mater node at local time t (d) = t (c) + [k] + τ. 3. DELAY ESTIMATION FOR BANDPASS RF SIGNALS Thi ection provide an overview of the delay etimator ued in the timetamp-free ynchronization protocol. Previou experimental work that reported on the accuracy of the timetamp-free protocol on RF ignal ued an Ettu E310 embedded oftware radio [7]. Due to the front-end architecture of the E310 oftware radio, etimation on a baeband ignal wa required and made ue of an approach baed on quadratic interpolation. Becaue the Ettu N10 radio employed in thi paper permit direct ampling of an RF ignal, we aume the ynchronization i a bandpa ignal of the form (t) = co(ω 0 t)u(t) where u(t) i a bandlimited ignal uch that U(Ω) = 0 for all Ω Ω 0. The ynchronization in dicrete time can be expreed a [l] = [co(ω 0 t)u(t)] t=lt = co(ω 0 l)u[l] where ω 0 = Ω 0 T i the normalized carrier frequency in radian/ample. The dicrete-time obervation with unknown delay τ can be expreed a y[l] = [co(ω 0 (t τ))u(t τ)] t=lt = co(ω 0 (l τf ))u(lt τ) for l = 0,..., L 1 where L i the number of ample in the obervation. Standard cro-correlation technique with the template waveform [l] can be ued to generate a quantized delay etimate ˆl Z. The accuracy of thi quantized delay etimate i limited, however, by the ampling rate of the delay etimator. To refine the delay etimate, we define i [l, ˆl] = co(ω 0 (l ˆl))u[l ˆl] q [l, ˆl] = in(ω 0 (l ˆl))u[l ˆl] for l = 0,..., L 1 where ˆl i the quantized delay etimate.

3 We can then compute z i [ˆl] = = 1 y[l] i [l, ˆl] ( co(ω 0 (l τf ˆl)) + co(ω 0 (τf ˆl)) ) u(lt τ)u[l ˆl] 1 co(ω 0(τf ˆl)) u(lt τ)u[l ˆl] where the approximation reult from the fact that co(ω 0(l τf ˆl))u(lT τ)u[l ˆl] 0. Similarly, we can calculate z q [ˆl] = y[l] q [l, ˆl] 1 in(ω 0(τf ˆl)) u(lt τ)u[l ˆl] We can then compute ( ) θ = tan 1 z q [ˆl] z i [ˆl] ( tan 1 in(ω 0 (τf ˆl)) ) co(ω 0 (τf ˆl)) = ω 0 (τf ˆl). The refined delay etimate can then be computed a ) ˆτ = (ˆl + θω0 T where θ i calculated according to (3). Note that ˆl repreent the integer, ample-level delay, which in the equel we term θ the coare etimate; meanwhile, ω 0 repreent the fractionalample delay, o we term it the fine etimate. Again, the coare etimate can be be computed with tandard crocorrelation technique. 4. PASSBAND RADIO-FREQUENCY IMPLEMENTATION To demontrate the uperiority of paband over baeband ignal with repect to delay etimation, the timetampfree ynchronization protocol wa implemented with radiofrequency ignal on Ettu N10 SDR with wired connection between device. Unlike the Ettu E310 SDR which perform analog downconverion before ampling, the Ettu N10 SDR are able to ample the incoming RF ignal directly, which, according to the Cramer-Rao lower bound [8], lead to increaed ynchronization accuracy. To allow ufficient time for computation, a relatively low ampling frequency of 50kHz wa elected for thi implementation. The USRP device operate in block fahion, where each time (3) a receive command i iued, a block of ample i returned to the calling routine. Similarly, tranmiion alo work in block fahion, where tranmiion are cheduled in advance by paing block of data with a tranmit command. In addition, the deired time of tranmiion i provided to the tranmit command, and need to be ufficiently far in the future to prevent ampling under-run. In thi implementation, we ued the default block ize of 1000 ample and a tranmiion delay of fifteen block. Two Ettu USRP N10 were ued to implement the protocol: one a the mater node, a econd a the lave node. In addition, a third N10 wa ued a a meaurement device to determine the reulting offet. Each of the node oftware wa implemented in C++ uing the USRP Hardware Driver (UHD) provided by Ettu, and the USRP were connected to hot computer with Core i7-6700k proceor. A the N10 are part of Ettu networked erie of SDR, the ignal proceing and logic needed to implement the ynchronization protocol were run in real-time on the hot computer, and not on the N10 SDR themelve. The reult of thi i proceing latency that i ignificantly larger a compared to the previouly conidered tand-alone embedded E310 platform which perform all computation on the device itelf [7]. RX Daughter RX-A TX-A RX-B TX-B TX-A initiating from lave TX Daughter repone from mater RX-A Slave Node TX Daughter TX-B RX-B RX Daughter contant mater adjuted lave RX-A RX-B TX-A TX-B Meaurement Device RX Daughter TX Daughter Figure. Diagram of the connection between the N10 ued for the mater node, lave node, and meaurement device. Each N10 ha an independent local ocillator. A diagram of the timetamp-free ynchronization tet etup i hown in Fig.. Each of the three USRP utilized two Ettu LF daughterboard which provide acce to the 14-bit ADC and 16-bit DAC on the N10. One daughter-board wa et to receive incoming ignal while the other wa ued to tranmit. Each daughterboard contain two channel; for intance, the LFTX tranmitting daughterboard ha channel TX-A and TX-B, while the LFRX receiving daughterboard ha channel RX-A and RX-B. The baic operation i that the lave node tranmit an initial which i received by the mater node. Once the mater node detect that it 3

4 ha received a, it tranmit a time-revered copy of the received which i received by the lave node. In order to externally meaure the accuracy of ynchronization achieved, each node alo tranmit a ignal on it remaining TX channel. The mater node tranmit it ignal a driven by it internal ocillator while the lave node adjut it in attempt to tranmit imultaneouly with the mater node. In addition to ending the to the meaurement node, the are diplayed on the ocillocope for qualitative evaluation and debugging purpoe. implicity. Cro-correlation i ued to detect the preence of a. When the magnitude of the cro-correlation break a predefined threhold, the mater node chedule the time revered tranmiion of the received waveform to the lave node. The tranmiion at the mater node are cheduled 4 block in advance to accommodate the latency between the hot computer and the radio. Tranmit Chain Receive Chain ync channel (A) Signal ued in thi implementation were modulated inc a decribed in Section 3, with a carrier frequency equivalent to half of the Nyquit ampling rate of the mater and lave node, with baeband bandwidth choen to utilize a large proportion of the available pectrum while avoiding aliaing. For implicity the ame ignal were ued for exchange between the mater and lave node, and for ent to the meaurement device. Figure 3 how a 4 m recording of typical ynchronized tranmitted by the lave and mater node. get next received block ync channel (B) wait for ync earch for ync channel (A) end received? N Y 1600 Slave Mater 1400 found? 100 Y amplitude N play ipped received ip received Figure 5. Flow diagram of mater node operation. -00 A tate-diagram of the lave node i hown in Fig. 6. TXA and RX-B facilitate all communication of ync to and from the mater node and TX-B output the ynchronized output. Becaue the lave node adjut it baed on the mater timed repone, the implementation complexity of the lave node i ignificantly higher than the mater node. When earching, the lave node perform cro-correlation on every receive block in order to locate the ample at which the peak of the inc wa received. A with the mater node, the lave node compute the magnitude of the cro-correlation when earching for a to confirm that the threhold i urpaed. When the detection threhold i broken and a i detected the lave node et a flag for calculation, and ave both the poition of the peak in the mot recent block of received ample a well a the complex value reulting from the cro-correlation. The calculation tep ue the peak poition a the coare delay etimate, and the fine delay etimator in equation (3) ue the peak crocorrelation value to calculate the fractional delay time (m) Figure 3. Example recording of ent by mater and lave node. The reulting total delay (coare and fine) i ued at the lave node to calculate an etimate of the mater node offet and drift uing a moothing filter. The lave node maintain etimate of the mater node offet and drift that are updated every block, and are ubequently ued to generate a new delayed template which i tranmitted on channel TX-B of the lave node. When a new delay offet obervation i available at the lave node, the lave node prediction of the mater offet and drift i refined. The moothing Figure 4. Experimental tet etup. A tate-diagram of the mater node i hown in Fig. 5. The TX-B and RX-A ignal path at the mater node facilitate all communication of ync to and from the lave node while TX-B facilitate the output. Each ignal path on the mater node i controlled ynchronouly within the oftware, but i diplayed on the diagram aynchronouly for 4

5 Receive Chain ync channel (B) get next received block earch block for found? N ync channel (A) end ync Tranmit Chain channel (B) end predict mater new o et? N 5. EXPERIMENTAL RESULTS Thi ection ummarize our experimental reult in implementing the timetamp-free ynchronization protocol uing bandpa RF ignal. Firt, we invetigate the N10 ability to etimate offet between ignal by yntheizing ignal with known offet, and comparing thee known offet with the meaurement device etimate. Second, we tet the N10 when meauring two ignal from the ame ource, iolating the meaurement integrity from the tranmitter induced error. Third, we report on the proce of calibrating the peudo-kalman filter ued to refine the output of the delay etimator. Finally, we report on ynchronization data collected. The ent out by the mater and lave node were recorded by the meaurement device while the offet between thee ignal were calculated after runtime in MATLAB. Y calculate o et from mater Y update etimate Figure 6. Flow diagram of lave node operation. filter make ue of the tandard two-tate (offet and drift) model [10], and i implemented a a peudo-kalman filter with a tatic Kalman gain; thi reult in a performance penalty with repect to a true Kalman filter; however, the tatic gain alo yield a reduction in complexity by avoiding computation of the covariance matrix that update the gain to appropriate magnitude a the proce approache teadytate. Intead, an optimized et of gain are experimentally choen uing the approach decribed in [6] and ample time i given for the ytem to approach teady-tate. The lave node prediction of the offet and drift etimate at time k are denoted k k 1 and D k k 1, and are initially et to zero and one repectively. In each block, the peudo-kalman prediction i computed via [ ] k k 1 D = k k 1 [ ] [ ] 1 T k 1 k D k 1 k 1 where T i the time-tep, equal to 1000-ample in our cae. We denote z[k] a the new offet obervation. When new obervation arrive, we compute the innovation ỹ[k] which correpond to the difference between the predicted offet from the Kalman filter and the new offet obervation at the time of the new offet obervation, or ỹ[k] = z[k] k k 1. Thi innovation proce i ubequently multiplied by the tatic Kalman filter gain K 1 and K, and ued to adjut the lave node prediction of the mater node offet and drift via the update equation [ ] k k D k k = (4) [ ] [ ] k k 1 K1 D + k k 1 K ỹ[k]. (5) Due to contraint mentioned in the dicuion ection below, the mater and lave node were not able to operate at a rate higher than 50 kilo-ample per econd without running out of time to complete each operation before the next block. The meaurement device wa able to operate at 5 mega-ample per econd becaue proceing of the data recorded by the meaurement device wa not done in real-time, but intead wa conducted in MATLAB after recording each eion. Clock were ent from each node to the meaurement device in 1000 ample block (equivalent to 4 m in duration) back-to-back. Synchronization ignal exchanged between node were ent at a period of 15 block (60 m) to allow enough time to compute cro-correlation, and to allow for tranmiion delay between node. Characterizing the Preciion of the Tranmiion and Meaurement Device In order to validate the reult derived from ampled data it i imperative to know the preciion and accuracy between the tranmiion and meaurement device. To accomplih thi a ingle N10 wa configured to end on both of it TX channel, but with an adjutable, intentional offet between the ignal. The meaurement device recorded thee ignal and offet between were calculated in MATLAB. Thee calculated offet were compared to the true offet a decribed by the tet. Signal were tranmitted with delay offet ranging from ± µ in increment of 400 n, correponding to ±0.5 ample period at an increment of 0.1 ample. Signal were tranmitted at each offet 50 time each eion, and reult were averaged over 5 eion. Figure 7 how a plot of the error tatitic of a run of thi tet. The tandard deviation of the error over all offet from ±0.5 fractional ample wa found to be 5.97 n. Thi wa a limiting factor in our experimentation a the coarene of thi meaurement determined the minimum delay offet the receiver node wa able to accurately detect. Characterizing the Preciion of Received Pule with a T- Junction Following a imilar model of the preciion tet, a radio wa configured to end imultaneou to the device under tet (DUT) along a T-Junction connector. Thi way, the tranmiion i duplicated along two wire, effectively tranmitting two ynchronized and eliminating potential error introduced by the tranmiion device. The error from 5

6 etimation error (n) true offet (fractional ample) Figure 7. Statitic howing meaurement device accuracy each meaurement device (labeled A,B, and C) i iolated and quantified for each radio with thi proce. The reult of thi experiment are reported in Table 1. DUT mean[ỹ[k]] td[ỹ[k]] A n 8.54 n B 0.55 n 7.16 n C -0.8 n 6.77 n Table 1. Summary of T-Junction preciion reult Selection of Peudo-Kalman Filter Gain A decribed earlier in Section 4, and by equation (4) and (5), we implemented a implified, peudo-kalman filter to mooth and correct for meaurement error in delay offet etimate. Due to the ue of a reduced-complexity peudo- Kalman filter without an adaptive Kalman filter gain, it wa neceary to determine tatic filter gain which provided the bet moothing performance and minimized prediction error. The tatitic of prediction error calculated by the lave node during runtime can erve a an indicator of performance in abence of ground truth. To take advantage of thi we configured the lave node to record delay between ent and received ignal calculated during runtime. We then ued MATLAB pot-proceing to apply peudo-kalman filter with different gain and imulate the reulting prediction error tatitic a if the data had been filtered in real time. By doing thi we were able to determine which filtering coefficient minimized the reulting prediction error. Filtering coefficient were choen to minimize error over the lat minute of a 5 minute recording, allowing the filter to take advantage of prediction error memory accrued during the beginning of the eion. Synchronization Accuracy Tet To evaluate the effectivene of the timetamp-free ynchronization protocol we implemented the procedure decribed in the implementation ection above. To control for proce parameter variation acro device, the accuracy of ynchronization wa teted with each SDR configured to operate a each role in the protocol. A total of 6 tet were conducted with each of the three different SDR erving alternately a the meaurement device, mater node, or lave node. During each tet the mater and lave node ran the protocol for 3 minute prior to recording to allow the node to ynchronize. The meaurement device then recorded two minute of ignal (about 30,000 ) ent from each node, and thi recording wa ued to evaluate the accuracy of ynchronization between the node. Prediction error tatitic and mater/lave were recorded in each tet. The reult of thee tet are ummarized in Table. The mean tandard deviation acro all configuration wa 13. n. In the next ection, we will dicu the implication and limitation of thee reult. M/S mean[ỹ[k]] td[ỹ[k]] A/B 4.66 n 8.18 n B/A n 8.41 n C/A.7 n 16.3 n A/C 1.77 n 13.4 n B/C n 15.9 n C/B n 16.7 n Table. Summary of ynchronization reult 6. DISCUSSION Thi work repreent a ignificant improvement with repect to the previou RF implementation of the protocol on Ettu E310 SDR [7]. Reult indicate a wort-cae ynchronization error with a tandard-deviation of 16.7 n, correponding to about 0.1% of the period of the carrier frequency. It i worth mentioning that the inaccuracy of our meaurement device ha been hown to be comparable to the degree of ynchronization achieved. Without the ability to meaure delay offet between ignal to a finer reolution, our reported reult will continue to be dominated by the meaurement error in our etimation device. There were everal other key factor that limited the degree of ynchronization, including network latency, computational complexity, and error compounded from finite-preciion effect, all of which we now explore in more detail. In our implementation the data rate of the receiver i limited by the proceing delay between the radio and the computer. In addition to thi, due to the nature of the USRP, all tranmiion mut be cheduled in advance. Accounting for the drift that occur from the time when the tranmiion i cheduled to the time when it actually tranmit i imple, but the need to accommodate thi additional latency doe add potential error to the ytem. Additionally, the complexity of the computation, and requirement to operate in real-time limit the poible ampling rate of the USRP N10. By far the mot computationally intenive operation in the protocol i the repeated crocorrelation (i.e. receive filtering) that i performed at both the mater and lave node. If cro-correlation doe not finih executing before the next block of ample i ready, then ample are lot and the device report underrun. Thi limit the degree of ynchronization achievable a lower ampling frequencie require lower bandwidth ignal which limit the degree of delay etimation accuracy a given by the Cramer- Rao Lower Bound [8]. 6

7 One more item that negatively impacted ynchronization performance wa the enitivity of the arctangent-baed fine delay etimator in (3) when fractional delay approached a half ample. Specifically, we oberved that mall error from finite preciion effect ourced from the ADC created mall error in the cro-correlation, which ubequently accumulated to larger error in the fine delay etimator. 7. CONCLUSION Thi work demontrate the ynchronization accuracy and implementation challenge of implementing timetamp-free ynchronization protocol at RF uing ampled paband ignal intead of modulated baeband ignal. An implementation of the protocol uing uch ignal i preented along with with experimental reult and analyi. Experimental reult how that the protocol i able to achieve ynchronization to within a tenth of a percent of the period of the carrier frequency over 4 m prediction interval. Future work could improve the accuracy of the timetampfree ynchronization protocol by addreing iue mentioned in Section 6. Specifically, the ampling rate of our device i currently bottlenecked by the time it take the CPU to compute cro-correlation between template and received waveform. Thi latency could be reduced by offloading computation from the CPU of the hot computer to the GPU uing NVIDIA CUDA API. Alternatively, when the development of Ettu RFNoC technology i ufficiently mature, much of the computation (i.e. the cro-correlation) can be offloaded to the FPGA on the Ettu radio. Future work could alo extend thi implementation to operate in a wirele etting with multipath and additional noie, or to work with more than two ynchronizing node. In a fully wirele, multiplenode cenario, one could invetigate ue of the timetampfree network ynchronization protocol in combination with conenu-baed technique [11] for operation in a ditributed etting without the need for a centralized mater/lave approach. All ource code for thi experiment i available at tfreeync-n10 ACKNOWLEDGMENTS Thi work wa upported by a Reearch Experience for Undergraduate (REU) Supplement to National Science Foundation award CCF REFERENCES [1] R. D. Preu and D. R. B. III, Two-way ynchronization for coordinated multicell retrodirective downlink beamforming, IEEE Tranaction on Signal Proceing, vol. 59, no. 11, pp , Nov 011. [] D. Mill, Internet time ynchronization: the network time protocol, IEEE Tran. Commun., vol. 39, no. 10, pp , Oct [3] W. Lewandowki, J. Azoubib, and W. Klepczynki, GPS: primary tool for time tranfer, Proceeding of the IEEE, vol. 87, no. 1, pp , Jan [4] F. Sivrikaya and B. Yener, Time ynchronization in enor network: a urvey, IEEE Netw., vol. 18, no. 4, pp , Jul. Aug [5] D. R. Brown and A. G. Klein, Precie timetampfree network ynchronization, in Information Science and Sytem (CISS), th Annual Conference on. IEEE, 013, pp [6] M. Li, S. Gvozdenovic, A. Ryan, R. David, D. R. Brown, and A. G. Klein, A real-time implementation of precie timetamp-free network ynchronization, in th Ailomar Conference on Signal, Sytem and Computer, Nov 015, pp [7] M. Overdick, J. Canfield, A. G. Klein, and D. R. Brown, A oftware-define radio implementation of timetampfree netwrok ynchronization, in IEEE Intl. Conf. on Acoutic, Speech and Signal Proceing (ICASSP), Mar. 017, pp [8] A. Wei and E. Weintein, Fundamental limitation in paive time delay etimation Part I: Narrow-band ytem, Acoutic, Speech and Signal Proceing, IEEE Tranaction on, vol. 31, no., pp , April [9] S. Ganeriwal, R. Kumar, and M. Srivatava, Timingync protocol for enor network, in Proceeding ACM SenSy 003. ACM New York, NY, USA, Nov. 003, pp [10] L. Galleani, A tutorial on the two-tate model of the atomic noie, Metrologia, vol. 45, no. 6, p. S175, 008. [11] D. R. Brown, A. G. Klein, and R. Wang, Monotonic mean-quared convergence condition for random pairwie conenu ynchronization in wirele network, IEEE Tranaction on Signal Proceing, vol. 63, no. 4, pp , Feb

8 B IOGRAPHY [ Joeph E. Canfield work a an electrical hardware validation engineer at the PACCAR Technical Center in Mount Vernon, WA. Hi reearch interet include radio communication and analog audio technology. Skye R. Kowalki i currently puruing a B.S. in electrical engineering from WWU and expect to graduate in June 018. Her current reearch activitie include working with oftware-defined radio, and ynchronization. She wihe to continue her tudie in Embedded and Cyberphyical ytem in application of IoT enor network. D. Richard Brown III received the B.S. and M.S. degree from the Univerity of Connecticut in 199 and 1996, repectively, and the Ph.D. degree from Cornell Univerity in 000, all in electrical engineering. From 199 to 1997, he wa with General Electric Electrical Ditribution and Control. He wa a Faculty Member with the Worceter Polytechnic Intitute, Worceter, MA, USA, in 000. He wa a Viiting Aociate Profeor with Princeton Univerity from 007 to 008. Since 016, he ha been with the Computing and Communication Foundation Diviion, National Science Foundation, a a Program Director. Timothy M. Chritman i currently puruing a B.S. in electrical engineering from WWU and expect to graduate in June 018. Hi current reearch activitie include oftware-defined radio, ynchronization, and fault line detection in power ytem. He hope to tudy or work with application in machine learning in the future. Andrew G. Klein received the B.S. degree from Cornell Univerity, Ithaca, NY, USA, the M.S. degree from the Univerity of California, Berkeley, CA, USA, and the Ph.D. degree from Cornell Univerity, all in electrical engineering. Previouly, he wa an Aitant Profeor with the Worceter Polytechnic Intitute, Worceter, MA, USA, from 007 to 014, and he wa a Pot-Doctoral Reearcher with Suplec/LSS, Pari, France, from 006 to 007. He joined the Department of Engineering and Deign, Wetern Wahington Univerity, Bellingham, WA, USA, in 014, where he i currently an Aociate Profeor. Mitchell W.S. Overdick received hi B.S. degree in Electrical Engineering at WWU in 017, and wa a member of the ASPECT Lab. Currently, he work a an embedded ytem validation engineer at PACCAR in Mount Vernon, WA. Hi reearch interet include Embedded Sytem, Signal Proceing, Machine Learning, and Automotive. 8