research article pilot-less time synchronization for ofdm systems: application...

Research ArticlePilot-Less Time Synchronization for OFDM SystemsApplication to Power Line Receivers

Aris S Lalos1 Athanasios Vgenis2 Fotios Gioulekas3 and Michael Birbas12

1Department of Electrical and Computer Engineering University of Patras Rio 26500 Patras Greece2Analogies SA Patras Science Park 26504 Patras Greece3Sub-Directorate of Informatics General University Hospital of Larissa 41110 Larissa Greece

Correspondence should be addressed to Aris S Lalos arislaloseceupatrasgr

Received 9 September 2015 Revised 12 November 2015 Accepted 9 December 2015

Academic Editor Manel Martınez-Ramon

Copyright copy 2016 Aris S Lalos et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Power line networks provide high-speed broadband communications without the need for new wirings However these networkspresent a hostile environment for high-speed data communications The most common modulation method used in such systemsis OFDM since it copes effectively with noise multipath fading selectivity and attenuation A potential drawback of OFDM is itssensitivity to receiver synchronization imperfections such as timing and sampling frequency offsets Although several approacheshave been proposed for estimating the time and frequency offset they are based on the use of pilot sequences that are notavailable in power line communication standards More importantly they focus on isolated algorithms for compensating eithertime or frequency offsets without providing a complete low complexity OFDM receiver architecture that mitigates jointly timeand frequency errors This paper focuses on providing an OFDM receiver architecture that can be compatible with many powerline standards Extensive simulation studies show under realistic channel and noise conditions that the proposed receiver providesenhanced robustness to synchronization imperfections as compared to conventional approaches

1 Introduction

Transmission of data through power line networks hasbecome the preferred connectivity solution to homes andoffices [1ndash3] Indoor power line networks can offer high-speed data without the need for new wires by using analready-existing infrastructure that is much more pervasivethan any other wired system However power line networkswere originally designed for the transmission and distri-bution of energy signals at 50 or 60Hz and as a resultthey present a hostile environment for high-speed datacommunications

A widely adopted method of encoding digital data priorto transmission in power line mediums is the OFDM tech-nique OFDM ability to cope with severe channel conditionsthat are present in such networks (eg high impulsive noise)has led to its adoption bymany industrial consortia for powerlines such as the High-Definition Power Line Communi-cation (HDPLC) Alliance [4] the HomePlug Power Line

Alliance (HPA) [5] the Universal Power Line Association(UPA) [6] and the ITU-T Gigabit Home Networking (Ghn)[7] Although it deals effectively with impulsive noise bydividing noise impulses among all the OFDM subcarriersdue to the discrete Fourier transform (DFT) operation inthe receiver a potential drawback of OFDM is its sensitivityto receiver synchronization imperfections (eg time andsampling frequency errors) Several approaches have beenproposed for estimating the time and frequency offset eitherjointly or individually [8ndash15]

Specifically the authors in [8] present a symbol-timingand carrier frequency synchronization method for OFDMsystems operating over multipath fading environmentsThe proposed method uses a specifically designed trainingsequence achieving a steep roll-off timing metric trajectoryThis type of training symbol achieves some improvementin timing estimation for time-varying multipath Rayleighfading channels Also the work in [9] exploits an interleaved

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2016 Article ID 8532941 12 pageshttpdxdoiorg10115520168532941

2 International Journal of Distributed Sensor Networks

subcarrier-allocation scheme that can be used to fully takeadvantage of the frequency domain diversity of OFDMAsystems Simulation results also show that the proposedscheme is robust to carrier frequency offset (CFO) estimationerrors However this approach targets wireless standardsand proposes the usage of some extra features that arenot employed by the PLC standards The authors in [10]proposed a solution that deals with CFO estimation bydesigningOFDMpilot sequences that are periodic in the timedomain The fractional CFO is estimated in closed form bymeasuring the phase rotations between the repetitive parts ofthe received preambles while the integer CFO is estimated ina joint fashion with the MIMO channel matrix by resortingto the Maximum Likelihood (ML) principleThis work is notapplicable to a standard that is pilot-less-like [7] Similarly thework in [11] incorporates periodic preambles as proposed inwireless standards while pilots are also inserted with a fixedspacing in order to assist the ML Carrier Frequency OffsetEstimation Algorithms

Despite the insights onto the design of isolated algorithmsfor efficient time and frequency offset estimation and cor-rection in OFDM systems the aforementioned works arebased on the use of pilot sequences that are not availablein power line communication standards The authors in[15] provide a solution for time synchronization that useintrablock phase rotations achieving significant performanceimprovements over conventional pilot-assisted estimatorsrelying on interblock phase rotations In this papermotivatedby the lack of pilot-less schemes for mitigating synchro-nization imperfection in base band OFDM systems wepropose a complete receiver architecture for broadband PLCsystems operating over low and medium voltage networksThe proposed scheme provides a coarse time estimation andmitigation in the time domain using a farrow filter interpo-lator followed by a fine estimation at the frequency domainthat is based on phase rotations estimated individually foreachOFDM symbol Extensive simulation studies carried outby using a frame format that is adopted in many power linecommunication standards [4ndash7] and realistic channel andnoise models have shown that the proposed scheme offersrobustness against the severe channel and noise conditionsthat are present in a power line medium outperformingrelevant pilot-less schemes

The remainder of this paper is organized as followsIn Section 2 we briefly review a baseband OFDM systemand the PHY frame structure adopted in PLC standards InSection 3 we present the different imperfections introduceddue to sampling clock errors and symbol-timing offset errorsIn Sections 4 and 5 we present the proposed samplingfrequency and time offset estimation andmitigation schemesIn Section 6 the performance of the proposedmethod is eval-uated through extensive simulation by selecting parametersin line with power line communication standards FinallySection 7 presents a discussion related to prospective diffi-culties for hardware implementation and Section 8 concludesthe paper

2 OFDM Signal Model and Preliminaries

Let us initially consider an OFDM system with119873 subcarriersas shown in Figure 2 Let

s119897 = [1199041119897 sdot sdot sdot 119904119873119897]119879 (1)

be a set of 119873 time domain symbols 119904119894119897 at the output of theConstellation Mapper which are forwarded at the input ofthe inverse discrete Fourier transform (IDFT) unit where119897 denotes the OFDM symbol time index and 119894 denotes thesubcarrier frequency index The output of the inverse DFTunit may be written as

u119897 = F119867119873s119897 (2)

whereF119873 is the normalized119873times119873 IDFTmatrixwith elements

[F119873]119896119897 =1

radic119873

119908(119896minus1)(119897minus1)

119899 119896 119897 = 0 119873 minus 1 (3)

with 119908119899 = 119890minus119895(2120587119873) and 119896 119897 denoting the row and column

numbers The 119897th OFDM symbol u119897 is forwarded at the CPAdder where the time domain OFDM symbol u119897 of length119872 = 119873 + 119873CP and duration 119879119904 sec is formed by adding aCP of length119873CP at the beginning of vector s119897This operationmay be described in matrix form as follows

x119897 = ACPu119897 = [

0(119873minus119873CP)times119873 I119873CPI119873

] u119897 (4)

The119872times1OFDM symbol x119897 is windowed overlapped andadded with the two adjacent 119897 minus 1 119897 + 1 OFDM symbolsinterpolated and digitally upconverted by half the signalsspectrum so that all signal energy lies in the positive part ofthe spectrum We will use the term upshifting to address thisdigital IF upconversion from here on

In the receiver side under the assumption that there isno sampling frequency offset the baseband signal under-goes digital IF downconversion a procedure from hereon addressed as downshifting and then downsampled at arate 119879 = 119879119904119872 We assume that in discrete time modelthe channel is composed of 119871 + 1 independent multipathcomponents each of which has a gain ℎ119896 and delay 119896 times 119879119896 = 0 119871The channel taps are assumed to be constant overone OFDM symbol and the received 119897th OFDM time domainsymbol may be written in matrix form as

y119897 = H119897x119897 + w (5)

where H119897 is an 119872 times 119872 toeplitz matrix with ℎ0 on the maindiagonal and ℎ1 ℎ119871 on the subdiagonals andw is the noisevector Further details related to the power line channel andnoise models are provided in the section that follows

Assuming that we have perfect knowledge of the bound-aries of each OFDM symbol in the payload frame sectionthe 119897th block of time domain samples y119897 passes through theCP removal unit of the OFDM demodulator where the first119873CP samples are discarded This operation may be written inmatrix form as

z119897 = RCPy119897 = [0119873times119873CP I119873] y119897 (6)

International Journal of Distributed Sensor Networks 3

Power line medium

PMD

TX

PMD

RX

Narrow band

Coloured

Periodic impulse asynchronous

Periodic impulse synchronous

Nonperiodic impulsive

+

+Coupling

circuitCoupling

circuitS(t) r(t)H(t 120591)

n(t)

Figure 1 Power line channel model

where z119897 = [1199111198971 119911119897119873] and 119911119897119894 correspond to samplesobtained by sampling at time indices 119905119897119894 = (119894 +119873CP + 119897 times119873)119879Then vector z119897 passes through the DFT unit whose outputreads as

r119897 = F119873z119897 = F119873RCPH119897ACPF119867

119873⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Hd 119897

s119897 + w = Hd119897s119897 + w (7)

where the entries of w = F119873w correspond to the frequencydomain (FD) representation of noise Unlikemost other com-munication channels noise in the power line channel cannotbe described by the classical approach of additive whiteGaussian noise (AWGN) The following section providesdetails related to the adopted models for simulating severaleffects caused by power line channel and noise characteristics[16 17]

The matrix Hd119897 is a diagonal matrix with the channelfrequency response in the main diagonal

Hd119897 = diag [1198670 119867119873minus1]

119867119894 =

119871

sum

119896=0

ℎ119896119890minus2120587radicminus1119896119894119873

(8)

The aforementioned diagonalization directly occurs from thefact that RCPH119897ACP has a circulant structure and thereforeequalization is possible with O(119873) operations

21 Power Line Channel and Noise Model

211 Channel Model The channel frequency (impulse)response models the (i) attenuation that is the loss of thepower of the signal during its propagation and it dependson the physical length of the channel and the transmissionfrequency band (ii) multipath and reflection effects that are

caused by the impedance mismatches and mostly dependenton both the physical characteristics and the physical topologyof the channel and (iii) crosstalk between adjacent wires dueto electromagnetic couplingThe statistical description of in-home power line channel is based on the work performed in[18] where channel measurements have been conducted inthe 0 to 100MHz range In particular it has been shown thatthe power delay profile has a statistical distribution that couldbe well described by Weibull and Gaussian distributions

212 Noise Model The additive noise in broadband powerline communication channels can be separated into fiveclasses according to Figure 1

(i) Colored noise that results mainly from the summa-tion of harmonics of mains cycle and different lowpower noise sources present in the system It has arelatively low power spectral density (PSD) varyingwith frequency and over time in terms of minutes oreven hours

(ii) Narrow-band noise that is mostly sinusoidal signalswith modulated amplitudes This type of noise ismainly caused by ingress of broadcast stations in thelong medium and short wave broadcast bands Thereceived level is generally varying during daytime

(iii) Impulsive noise that is generated mostly by electricalappliances plugged into the power line network and isclassified to (i) periodic impulsive noise synchronouswith the AC cycle and (ii) periodic impulsive noiseasynchronous with the AC cycle and nonperiodicimpulsive noise

The coloured narrow-band and periodic impulsive asyn-chronous with the AC cycle noise types usually remainstationary over periods of seconds andminutes or sometimes


ConstellationMapper IFFT Interpolator Digital

upshifterCP Adder Windower

Figure 2 Block diagram of an OFDM tarnsmitter

even for hours and may be summarized as backgroundnoise The periodic impulsive noise synchronous with theAC cycle and the nonperiodic impulsive noises are timevariant in terms of microseconds and milliseconds Duringthe occurrence of such impulses the PSD of the noise isperceptibly higher and may cause bit or burst errors in datatransmission

(i) Color Background Noise Model According to [18] it canbe described by the background power noise density 119860

(dBmHz) via the following equation

119860 (119891) = 119860infin + 1198600119890minus1198911198910 (9)

where 119860infin is the power density for 119891 rarr infin and 1198600 is thedifferences between 119860infin and 1198600 1198600 follows a normal distri-bution 119860infin follows uniform distribution and 1198910 is modeledby a shifted exponential distribution with parameters that aredefined in [19]

(ii) Narrow-BandNoiseModelThenarrow-band interferencenoise can be modeled as a sum of 119873 multiple sine noise withdifferent amplitudes (deterministic model)

119860 (119905) =

119873

sum

119894=1

119860 119894 (119905) sin (2120587119891119894119905 + 120601119894) (10)

where 119873 is a number of waves of different frequencies 119891119894amplitudes and phases The amplitude 119860 119894(119905) is a constant inthe simplest case but it can be considered as amplitude mod-ulated for better approximation of AM-broadcast signalsThephase 120601119894 is randomly selected from interval [0 2120587] and isnot depending on time The carrier may either be separatelysynthesized in the time domain or jointly in the frequencydomain with help of an IFFT Further details related to theselection of the aforementioned parameters based on thedistances of the radio stations may be found in [18]

(iii) Impulsive Noise Model To simulate the impulsive noisefor the PLC channel we used the Middleton Class A Noise(AWCN) model The probability density function (PDF) ofthe real and imaginary part of the complex noise accordingto this model are approximated by

119901119911 (119911) =

3

sum

119898=1

119890minus119860

119860119898

119898

119890|119911|2

21205902

119898

21205871205902119898

(11)

with

1205902

119898= 1205902(119898119860 + Γ

1 + Γ) (12)

where 119860 is the impulsive index which measures the averagenumber of impulses over the signal period and

Γ =

1205902

119892

1205902

119894

(13)

is theGaussian to impulsive power-ratio (GIR) withGaussiannoise variance 120590

2

119892 impulsive noise power 120590

2

119894 and total

variance 1205902= 1205902

119892+ 1205902

119894

22 PHY Frame Structure The format of the PHY frameis presented in Figure 3 The PHY frame usually includes apreamble a header and a payload The preamble is intendedto assist the receiver in detecting synchronizing to the frameboundaries and acquiring the physical layer parameters suchas channel estimation and OFDM symbol alignment Thepreamble consists of a small number of sections as shown inFigure 3 Each section comprises 119870119894 repetitions of an OFDMsymbol employing subcarrier spacing 119870119894 times 119891sc where 119891scdenotes the subcarrier spacing of the payload symbols and119870119894 is usually a small integer value The number of repetitions(119870119894) and the size of each OFDM symbol 119878119894 (119873119878119894 samples) inthe preamble may change from section to section

3 Synchronization Imperfections

In this work we focus only on baseband systems and thuswe assume that there is no RF modulatordemodulator Thetransmitter baseband part includes inverse discrete Fouriertransform (IDFT) CP windowing and frequency upshift(see Figure 1) The following considerations motivate us tostudy the functionalities at anOFDMreceiver in the presenceof sampling clock errors and symbol-timing offset errors(we ignore completely carrier frequency offsets since weassume that there is no RF modulator and demodulator atthe transceiver and receiver resp) which have to be estimatedand compensated More specifically we assume that (i) thesampling time at the receiver 119879

1015840 is not identical to thetransmitter sampling time 119879 and (ii) the frame boundaries(ie when each preamble section starts and as a result


PayloadPreamble Header

PHY preamble structure

PLDPcp

H

1st section 2nd section 3rd section Header Payload

bbb b bb

b windowing factor

Hcp

S1 S1 S1 S1

S2 S2

S3 S3

middot middot middot

Window overlap and add operation at TX

PHY frame structure

Figure 3 PHY frame structure in time domain

the start of the payload OFDM symbols) are unknown atthe receiver Therefore the part of the receiver controllingthe removal of the CP interval from each payload symbolwill usually be offset from its ideal setting by a time 120598119879 Thereceived samples at the output of the DFT unit at the receiverthat occur by sampling at time indices 1199051015840

119897119894= (119894+119873CP+119897times119873)119879

1015840

will be denoted by r119897To be able to demodulate efficiently the transmitted

signal we need (i) initially to estimate some flag indicatingthe first symbol of the frame the first symbol of eachpreamble section and the first symbol of the payload section(frame boundaries) and (ii) then estimate and mitigate thefrequency offset due to the inaccuracies of the transmitterand receiver oscillatorsThe incorporation of the error effectsto the time domain baseband model at the output of theframe detector will be the basis for optimizing the receivercomponents in the following section

31 Frame Boundaries Detection For the detection of framearrival at the receiver the received signal is correlated withitself with a delay of one short symbol given by

119903119909119909 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) r119897 (119895 + 119899 + 119873119878119894) (14)

where 119909 denotes the received signal in the time domain119903119909119909(119899) is the correlation output at the time index 119899 and 119873119878119894is the length of the short symbol To smooth the output curveof the autocorrelation process described above a movingaverage filter may be also used The incoming frame canbe detected by comparing the magnitude of autocorrelationresult at time index 119899 with a specific threshold In order to beable to detect the preamble section boundaries we make use

of a combination of the aforementioned autocorrelator andthe following cross-correlator

119903119909119904 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) 1198781 (119895) (15)

where 1198781 = [1199041 1199041198731198781] denotes a preamble short OFDM

symbol in time domain For the detection of the preambletransition we detect a cross-correlation peak combined witha change in the sign of the autocorrelator Figures 4 and 5provide the theoretical and practical output of the proceduredescribed above

32 Effects of Timing and Sampling Frequency Offset Thereceiver OFDM symbol window controlling the removal ofthe guard interval will usually deviate from its ideal settingintroducing a specific timing offset that needs to be estimatedand removed In addition a sampling frequency offset isalso introduced primarily because of the tolerances of quartzoscillators with respect to temperature variations In thepresence of a fixed sampling frequency error the effects thatarise after the DFT unit at the receiver are (i) an amplitudereduction (ii) a phase shift of each QAM symbol 1199041119894 and(iii) intercarrier interference (ICI) due to loss of orthogonalitybetween the subcarriers The transmitted baseband OFDMsignal can be described as

119909 (119905) =1

119873

119873minus1

sum

119894=0

119904119894119897 exp(1198952120587119894 (119905 minus (119873CP + 119897119872)119879)

119873119879) (16)

where 119897 is the OFDM symbol 119896 is the subcarrier index 119879 isthe sample duration 119873 is the FFT size and 119873CP and 119872 =

119873+119873CP are the guard interval length and the OFDM symbollength respectively With the relative sampling frequency


1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b

Correlation based frame boundary detector

HHcp2

b

1st section2nd section

3rd sectionHeader

Payload middot middot middot

NS1NS1

NS1NS1 NS2

NS2NS3

NS3 H + Hcp minus b ACE + ACEcp minus b

Figure 4 Execution example of frame boundaries detector

AutocorrelationCrosscorrelation

1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35

Figure 5 Illustration of 119903119909119909 versus 119899 and 119903119909119904 versus 119899

offset (SFO) 120598119904 = (1198791015840minus119879)119879

1015840 the received time domain signalmay be written as in [8]

y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)

where 119905119899 = (119897119872+119873CP)1198791015840+1198991198791015840 and119908119897(119899) is samples of noise

After FFT the frequency domain samples at the receiver sidebecomes

119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))

sdot exp(119895120587119898 + 119894 (120598119904 minus 1) (119873 minus 1)

119873) + 119897119894

119894 = 1 119873

(18)

where 119897119894 is the frequency domain samples of noise and119867119897119898

is the channel frequency response at the 119898th frequency binand sin(120587119894120598119904)119873 sin(120587119894120598119904119873) cong 1

4 Sampling Frequency Offset Estimation andMitigation at Time Domain

In this section we will give a brief description of themethods applied for estimating and mitigating the effects of


the difference between the sampling period 1198791015840 at the receiver

and 119879 at the transmitter leading to a relative samplingfrequency error 120598119904 = (119879

1015840minus119879)119879

1015840 so called sampling frequencyoffset

41 SFO Acquisition Initially the estimation of the samplingfrequency offset denoted by 120598119904 can be performed by exploitingthe structure of the preamble and comparing the phasesbetween successive repeated symbols on all the frequencybins at the FD The phase difference between the FFT valuesof the successive received preamble symbols has two maincauses [9] (i) either carrier frequency offset or (ii) samplingfrequency offset Since we have assumed that there is nocarrier frequency offset the phase difference is exclusivelyattributed to SFOAt this point it should be pointed out that inthe PLC case the accuracy of applying the conventional FFTand estimating the phase difference is significantly reduceddue to the presence of impulsive noise and the fact that thepower signal contains multiple harmonics

To overcome this limitation a special FFT algorithmso called all phase FFT (APFFT) [20] is often employedAccording to this algorithm a vector that consisted of tworepeated known symbols is initially formed

r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)

Then the ouput is computed as

R119897 = F119873 [C1 + C2 + sdot sdot sdot + C119873] (20)

whereC119894 denotes the 119894 column of the circulantmatrixCwithC1 = [119903119897+11 119903119897119873 1199032119873]

119879Similarly from symbols r119897+1|119897+2 we are able to calculate

R119897+1 and it can be easily shown that

R119897+1 (119894) = R119897 (119894) 119890minus2radicminus1120587120598119904119894 (21)

The SFO 120598119904 can then be estimated from the 119894th APFFToutput of consecutive symbols that are spaced 119873 samplesapart as follows

120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)

At this point it should be noted that in practice the repeatedsymbols of the 1st preamble section have length 119873119904 lt 119873In order to reduce the complexity of the aforementionedestimator an APFFT unit of length 119871 119904 lt 119873119904 could beemployed In that case (22) may be rewritten as

120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)

To efficiently exploit the estimation based on each output 119894

of the APFFT unit a least square estimator may be used (LSFit unit in Figure 6(c)) The output of this estimator can bewritten as

120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =

[1206010 120601119873119904minus1] 120601119894 = angR119897(119894)R119897+1(119894) and 120575 is a samll constant

(ie 120575 = 10minus4)

Similarly to the initial SFO estimation process trackingof the SFO variations can be performed in a similar way byautocorrelating the APFFT outputs of consecutive CPs thatare spaced 119871 samples apart The measured slope of the phasedifferences (including phase difference and time filtering)will provide the SFO estimation A block diagram of theoperations described above is given in Figure 6(c)

42 Farrow Sample Rate Converter (SRC) This unit evaluatesthe new sample values at arbitrary points between theexisting samples by utilizing a digital interpolation filter Theinput sequence 119909((1198991198972)119879

1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879

1015840) is formed of the uniformly spaced

samples with respect to the sampling interval 1198791015840 The newsample 119910(119897119879) also called the interpolant occurs betweenthe samples 119909(119899119897119879119909) and 119909((119899119897 + 1)119879119909) at the point 119897119879 =

1198991198971198791015840+ 120583119897119879

1015840 where 119899119897 is the basepoint index and 120583119897 is thefractional interval The fractional interval can take any valuein the range 0 le 120583119897 lt 1 An efficient implementation of alagrange polynomial interpolation filter can be realized byusing a farrow structure [21] as the one shown in Figure 6(d)

5 Time Offest Estimation and Mitigation atFrequency Domain

Sampling timing offset (STO) significantly downgrades thesystem performance and is attributed to the fact that theequalizer (EQ) coefficients estimated by the probe frame areoutdated To be compatible with the power line standardswe choose to estimate the equalizer coefficients by exploitingthe presence of a probe frame (PROBE CE EQcoeffs) whichare transmitted between the data frames Ideally if channelestimation and equalization were performed at each framethen we would not suffer from any STO issues Howeverin a real life scenario we need to compensate the STO byappropriately adjusting the phase of the equalizer coefficientsthat are going to be applied in each frame The referencedcoefficients for STO estimation are the EQ coefficients esti-mated from the preamble section (Preamble CE EQ) To bemore specific we initially estimate the phase shift betweenthe corresponding coefficients of the Preamble CE EQ and thePROBE CE EQcoeffs Motivated by the fact that the resultingshifts correspond to a series of values that can be fitted by aline we choose to estimate the line parameters (eg slopeand offset) by using a least square (LSfit) procedure similarto that presented in (24) The estimated slope correspondsto the STO while the offset value is caused mainly by themismatch between the phase shifts of the RX downshifterand the TX upshifter due to their free-running natureAfter deriving these parameters we compensate the phaseof each PROBE CE EQ coefficient by performing a simplefixed point multiplication of the stored EQ coefficient witha value that corresponds to the phase mismatch between thepreamble and probe coefficients In hardware this operationis efficiently implemented by using a cordic rotation [22] At


Output to VGA

OFDM baseband receiver

Farrow SRC Downsampler Downshifter

SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker

Equalizer Demodulator

Stored TD preambles 1st section PRMBL

2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT

Input 1 modes 1 (initialization) and 2 (tracking)

(1) 32 samples from i short symbol from section 1

(2) 32 samples from front CP section of k payload symbol

LPF for smoothing SFO LS fit SFO drift to SRC

Sampling frequency offset estimation

Phase calculationFeedback to farrow

SRC filter

SP

SP


(1) 32 samples from (i + D) short symbol from section 1

D 1 or 2 it should be defined

(2) 32 samples from back CP section of k OFDM symbol

Input 1

Input 2

X1

X2

(b)

Short equalizer Phase calculation

Integer STOLPF LS fit

Initial integer timing offset and downshifter

Short channel from DSP

Feedback to CPremoval

symbol from section 1

Equalized preamble

from i stored shortShort FFT of N samples

Feed forwardto FD rotator

DNS

(c)

+

times

+

times

+

times

times times times times

+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216

Compute need 19 multiplications and 12 additions for I and the same for Q

x((k + 1)T1)Zminus1 Zminus1 Zminus1

minus16

minus16

minus12

minus12

minus1

minus13

For computing each TD sample we

y(mT2)

dt = 1 minus T2T1120583u = mod(1 (m minus 1) lowast 1) if (T1 gt T2)minus dt

SFO correctormdashfarrow SRC

(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)

Figure 6 Block diagram of an OFDM receiver robust to timing and sampling frequency errors


Table 1 System parameters

Parameter ValueOFDM Payload Symbol Length (119873) 2048Cyclic Prefix Length (119873CP) 512Window Value 120573 256Interpolation factor 10Sampling frequency offset values 40 ppmTiming offset values minus13 samplesConstellation QAM 64OFDM Preamble Symbol Length (1198731198781 ) 256Number of preamble sections 7 + 2Bandplan 50MHzPayload Subcarrier Spacing 244140625 kHzPreamble Subcarrier Spacing 1953205 kHz

this point it should be also mentioned that during the LSfitprocedure we need to take also into account the subcarriermasking (SM) values defined by the corresponding standard

6 Performance Evaluation

We have developed a MATLAB simulator that incorporatesboth the transmitter and receiver blocks presented in Figures2 and 6 while the channel and noise have been modeledaccordingly In order to introduce a sampling frequencyoffset we have used the farrow structure described aboveInteger STO is caused by frame boundary detection errorsthat is the start of the frame flag raised some samplesearlier or later Finally to introduce fractional STO we tookadvantage of the interpolation unit at the transmitter Bystarting our sample collection at the receiver from any of theavailable interpolation factor samples that correspond to anoninterpolated sample we can simulate fractional STO witha step quantized to 1interpolation factorWe have consideredthe channel and noise models presented in Section 2 For theAWCN noise the GIR ratio was set to 005

In the following subsection we present the results ofour experiments The PHY layer parameters are presented inTable 1 A sampling frequency offset equal to 40 ppm and atiming offset of 13 samples were introduced

In Figure 7we plot theConstellation diagrams for the fifthpayload OFDM symbol at (a) the output of the equalizer (b)the output of the phase corrector with the decision directedphase tracker deactivated where it is clearly shown that phasedistortion due to residual SFO is evident and (c) the output ofthe phase corrector with the decision directed phase trackeractivated where residual SFO has been compensated Anyphase corruption is mitigated when both SFO corrector andphase tracker are enabled

In Figure 8 we provide the phase shift between thereceived and the original OFDM symbols measured at eachsubcarrier at the output of the receiver DSP blocks Morespecifically we plot the phase shifts (a) at the output of theequalizer before the phase corrector (b) at the output ofthe phase corrector with the decision directed phase trackerdeactivated and (c) at the output of the phase corrector with

the decision directed phase tracker activatedWhen the phasetracker is deactivated (case b) the effect of residual SFO isdemonstrated with the phase slope increasing with the countof OFDM symbols At this point it should also be notedthat the phase tracker measurement period is two OFDMsymbols hence OFDM symbols 3 and 5 have the best phaseerror compensation

Finally we performed an extensive evaluation by enablingand disabling the farrow filter We assumed 16 QAM symbolThe STO was set to 0124 samples and the SFO at 200 ppmwhile we transmitted in total 10

6 symbols In Figure 9 weprovide the measured mean square error at the output of theQAM demapper for different measured SNR values at thereceiver

At this point it should be noted that the Gaussian toimpulsive noise ratio was set to 005 By inspecting Figure 9it can be shown that the use of the sample rate converter atthe time domain significantly increases the robustness of thesystem in a PLC environment Motivated by this remark weexpect that the use of a farrow interpolator at the TD could bebeneficial for other similar methods that consider both SFOand STO and perform only phase rotation after the FFT unitat the demodulator side (eg [15])

7 Discussions

71 Impulsive Noise Modeling In most cases the structure ofthe impulses induced in PLC channels consist of dampedsinusoids while themost powerful contents of these impulsesare located in low frequencies and are represented as the sumof damped sinusoids

119899119894 (119905) =

119873119889

sum

119896=1

119860119896

sdot sin (2120587119891119896 (119905 minus 119905119901) + 120601119896) 119890(minus119905minus119905119901)119905119896120578(

119905 minus 119905119901

119905119899

)

(25)

where 119873119889 is the number of damped sinusoids that formthe impulse 119860119896 119891119896 and 120601119896 represent the amplitude thefrequency and the phase of the 119896th sinusoid 119905119901 is the arrivaltime of the impulses 119896 is the damping factor and 120578(119905) denotesa square pulse with a duration of 119905119899 The amplitude of eachdamped sinusoid 119860119896 is selected to be sim 119873(0 119866119896120590

2

119899) where

119866119896 denotes the increment of the impulse over the backgroundnoise with a variance of 1205902

119899 Values of 119866119896 can range between

20 and 30 dBAlternatively to the aforementioned model the AWCN

model can be employed as described in Section 2 Withthe AWCN model various classes of impulsive noise areexpressed by a simple function with a small number ofparameters However the disadvantage of this model is thefact that it does not define time domain features The PDFdoes not describe whether the noise waveform is peaky(impulsive) or smooth in the time domain This is becausethe noise of the proposed model has different variancesat different phases of the AC voltage In other words theMiddleton PDF in PLC channel is the description of powerline noise without the consideration of time depending


Scatterplot for equalized symbol 5

minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)

Scatterplot for rotated symbol 5

minus1

minus05

0

05

1

Qua

drat

ure

minus05 0 05 1minus1In-phase

(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)

Figure 7 Scatterplot of equalized symbols with (a) farrow SRC and phase corrector disabled (b) farrow SRC enabled and phase correctordisabled and (c) farrow SRC enabled and phase corrector enabled

(periodic) features Thus with the stationary model we candefine the time arrival and duration of impulses while withthe Middleton model we can simulate random spikes thatarrive at random time intervals

72 Prospective Difficulties forHardware Implementation Thedigital implementation of a power line OFDM basebandmodem is in itself a difficult procedure Due to the resourceslimitations and the demand for low power of the hardware

platforms used in sensor network infrastructures the designteam should proceed with a systematic trade-off analysisbetween OFDM performance and the usage of specific fixedpoint arithmetic during the hardware development Thistrade-off analysis will also have an impact to the cost ofthe sensor network fabrication The difficulty of approachingthe best performance of the OFDM systems stems fromthe fact that the design team (most of the time) shouldcompromise with an affordable performance degradationwhich will not affect the specified link-budget Consequently


Port 1 phase shift for all symbols

Symbol 1Symbol 2Symbol 3

Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)

Figure 8 These plots are taken from probe symbols in the frequency domain only that is (a) equalizer output (b) rotator output (phasetracker off) and (c) rotator output (phase tracker on) Farrow SRC is always on

each parameter used in theOFDMbaseband receiver requiresretuning taking into account both the power line channelimpairments and the specified performance The algorithmspresented in this paper are selected accordingly in order tolead to a straightforward hardware implementation takinginto account the potential limitations

8 Conclusion

OFDM is the most commonly adopted scheme from manypower line communication standards However its sensi-tivity to receiver synchronization imperfections motivatedresearchers to provide isolated solutions for estimating either

the time or the sampling frequency offset individually Thispaper focuses on providing a complete architecture thatcan be adopted by low complexity power line receivers forcompensating any kind of synchronization errors in powerline networks The proposed solution provides a robust esti-mation and mitigation of time and frequency imperfectionswithout making use of pilot symbols that are not present inmany existing power line standards

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Farrow enabled STO enabledFarrow disabled STO enabled

12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)

Figure 9MSE versus SNRwith andwithout the farrow interpolator

References

[1] L T Berger A Schwager and J J Escudero-Garzas ldquoPowerline communications for smart grid applicationsrdquo Journal ofElectrical and Computer Engineering vol 2013 Article ID712376 16 pages 2013

[2] M Yigit V C Gungor G Tuna M Rangoussi and EFadel ldquoPower line communication technologies for smart gridapplications a review of advances and challengesrdquo ComputerNetworks vol 70 pp 366ndash383 2014

[3] N Ginot M A Mannah C Batard and M MachmoumldquoApplication of power line communication for data transmis-sion over PWMnetworkrdquo IEEETransactions on Smart Grid vol1 no 2 pp 178ndash185 2010

[4] ldquoThe HD-PLC Alliancerdquo httpwwwhd-plcorg[5] ldquoThe HomePlug Powerline Alliancerdquo httpwwwhomeplug

org[6] The Universal Powerline Association httpwwwupaplcorg[7] ldquoUnified high-speed wireline-based home networking tran-

sceivers-system architecture and physical layer specificationrdquoTech Rep ITU-T Std G9960 2011 httpswwwituintrecT-REC-G9960en

[8] M Sliskovic ldquoSampling frequency offset estimation and cor-rection in OFDM systemsrdquo in Proceedings of the 8th IEEEInternational Conference on Electronics Circuits and Systems(ICECS rsquo01) vol 1 pp 437ndash440 IEEE September 2001

[9] H Minn V K Bhargava and K B Letaief ldquoA robust timingand frequency synchronization for OFDM systemsrdquo IEEETransactions onWireless Communications vol 2 no 4 pp 822ndash839 2003

[10] D Huang and K B Letaief ldquoAn interference-cancellationscheme for carrier frequency offsets correction in OFDMAsystemsrdquo IEEE Transactions on Communications vol 53 no 7pp 1155ndash1165 2005

[11] M Moretti M Morelli and G Imbarlina ldquoA practical schemefor frequency offset estimation in MIMO-OFDM systemsrdquoEurasip Journal on Wireless Communications and Networkingvol 2009 Article ID 821819 2009

[12] Y-H Kim and J-H Lee ldquoJoint maximum likelihood estimationof carrier and sampling frequency offsets for OFDM systemsrdquoIEEE Transactions on Broadcasting vol 57 no 2 pp 277ndash2832011

[13] J Sun F Li C-X Wang X Hong and D Yuan ldquoFrequencysynchronization algorithms for MIMO-OFDM systems withperiodic preamblesrdquo International Journal of Distributed SensorNetworks vol 2014 Article ID 740906 12 pages 2014

[14] R Mo S W Oh and Y Zeng ldquoTime and frequency syn-chronization for power line OFDM systems with colorednoiserdquo in Proceedings of the IEEE International Conference onCommunications (ICC rsquo09) pp 1ndash5 Dresden Germany June2009

[15] C Chen Y Chen N Ding et al ldquoAccurate sampling timingacquisition for baseband OFDM power-line communicationin non-gaussian noiserdquo IEEE Transactions on Communicationsvol 61 no 4 pp 1608ndash1620 2013

[16] M Nassar J Lin Y Mortazavi A Dabak I H Kim andB L Evans ldquoLocal utility power line communications in the3ndash500 kHz band channel impairments noise and standardsrdquoIEEE Signal ProcessingMagazine vol 29 no 5 pp 116ndash127 2012

[17] H Meng Y L Guan and S Chen ldquoModeling and analysis ofnoise effects on broadband power-line communicationsrdquo IEEETransactions on PowerDelivery vol 20 no 2 pp 630ndash637 2005

[18] H B Celebi Noise and multipath characteristics of power linecommunication channels [PhD thesis] University of SouthFlorida Tampa Fla USA 2010

[19] D Benyoucef ldquoA new statistical model of the noise powerdensity spectrum for powerline communicationrdquo inProceedingsof the 7th International Symposium on Power-Line Communica-tions and its Applications pp 136ndash141 Kyoto Japan 2003

[20] D F Elliott Handbook of Digital Signal Processing EngineeringApplications Academic Press New York NY USA 2013

[21] Y-M Chen ldquoOn the design of Farrow interpolator for OFDMreceivers with asynchronous IF samplingrdquo in Proceedings of the4th International Conference on Communications and Network-ing in China (ChinaCOM rsquo09) pp 407ndash412 IEEE Xirsquoan ChinaAugust 2009

[22] P K Meher J Valls T-B Juang K Sridharan and KMaharatna ldquo50 Years of CORDIC algorithms architecturesand applicationsrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 56 no 9 pp 1893ndash1907 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



subcarrier-allocation scheme that can be used to fully takeadvantage of the frequency domain diversity of OFDMAsystems Simulation results also show that the proposedscheme is robust to carrier frequency offset (CFO) estimationerrors However this approach targets wireless standardsand proposes the usage of some extra features that arenot employed by the PLC standards The authors in [10]proposed a solution that deals with CFO estimation bydesigningOFDMpilot sequences that are periodic in the timedomain The fractional CFO is estimated in closed form bymeasuring the phase rotations between the repetitive parts ofthe received preambles while the integer CFO is estimated ina joint fashion with the MIMO channel matrix by resortingto the Maximum Likelihood (ML) principleThis work is notapplicable to a standard that is pilot-less-like [7] Similarly thework in [11] incorporates periodic preambles as proposed inwireless standards while pilots are also inserted with a fixedspacing in order to assist the ML Carrier Frequency OffsetEstimation Algorithms

Despite the insights onto the design of isolated algorithmsfor efficient time and frequency offset estimation and cor-rection in OFDM systems the aforementioned works arebased on the use of pilot sequences that are not availablein power line communication standards The authors in[15] provide a solution for time synchronization that useintrablock phase rotations achieving significant performanceimprovements over conventional pilot-assisted estimatorsrelying on interblock phase rotations In this papermotivatedby the lack of pilot-less schemes for mitigating synchro-nization imperfection in base band OFDM systems wepropose a complete receiver architecture for broadband PLCsystems operating over low and medium voltage networksThe proposed scheme provides a coarse time estimation andmitigation in the time domain using a farrow filter interpo-lator followed by a fine estimation at the frequency domainthat is based on phase rotations estimated individually foreachOFDM symbol Extensive simulation studies carried outby using a frame format that is adopted in many power linecommunication standards [4ndash7] and realistic channel andnoise models have shown that the proposed scheme offersrobustness against the severe channel and noise conditionsthat are present in a power line medium outperformingrelevant pilot-less schemes

The remainder of this paper is organized as followsIn Section 2 we briefly review a baseband OFDM systemand the PHY frame structure adopted in PLC standards InSection 3 we present the different imperfections introduceddue to sampling clock errors and symbol-timing offset errorsIn Sections 4 and 5 we present the proposed samplingfrequency and time offset estimation andmitigation schemesIn Section 6 the performance of the proposedmethod is eval-uated through extensive simulation by selecting parametersin line with power line communication standards FinallySection 7 presents a discussion related to prospective diffi-culties for hardware implementation and Section 8 concludesthe paper

2 OFDM Signal Model and Preliminaries

Let us initially consider an OFDM system with119873 subcarriersas shown in Figure 2 Let

s119897 = [1199041119897 sdot sdot sdot 119904119873119897]119879 (1)

be a set of 119873 time domain symbols 119904119894119897 at the output of theConstellation Mapper which are forwarded at the input ofthe inverse discrete Fourier transform (IDFT) unit where119897 denotes the OFDM symbol time index and 119894 denotes thesubcarrier frequency index The output of the inverse DFTunit may be written as

u119897 = F119867119873s119897 (2)

whereF119873 is the normalized119873times119873 IDFTmatrixwith elements

[F119873]119896119897 =1

radic119873

119908(119896minus1)(119897minus1)

119899 119896 119897 = 0 119873 minus 1 (3)

with 119908119899 = 119890minus119895(2120587119873) and 119896 119897 denoting the row and column

numbers The 119897th OFDM symbol u119897 is forwarded at the CPAdder where the time domain OFDM symbol u119897 of length119872 = 119873 + 119873CP and duration 119879119904 sec is formed by adding aCP of length119873CP at the beginning of vector s119897This operationmay be described in matrix form as follows

x119897 = ACPu119897 = [

0(119873minus119873CP)times119873 I119873CPI119873

] u119897 (4)

The119872times1OFDM symbol x119897 is windowed overlapped andadded with the two adjacent 119897 minus 1 119897 + 1 OFDM symbolsinterpolated and digitally upconverted by half the signalsspectrum so that all signal energy lies in the positive part ofthe spectrum We will use the term upshifting to address thisdigital IF upconversion from here on

In the receiver side under the assumption that there isno sampling frequency offset the baseband signal under-goes digital IF downconversion a procedure from hereon addressed as downshifting and then downsampled at arate 119879 = 119879119904119872 We assume that in discrete time modelthe channel is composed of 119871 + 1 independent multipathcomponents each of which has a gain ℎ119896 and delay 119896 times 119879119896 = 0 119871The channel taps are assumed to be constant overone OFDM symbol and the received 119897th OFDM time domainsymbol may be written in matrix form as

y119897 = H119897x119897 + w (5)

where H119897 is an 119872 times 119872 toeplitz matrix with ℎ0 on the maindiagonal and ℎ1 ℎ119871 on the subdiagonals andw is the noisevector Further details related to the power line channel andnoise models are provided in the section that follows

Assuming that we have perfect knowledge of the bound-aries of each OFDM symbol in the payload frame sectionthe 119897th block of time domain samples y119897 passes through theCP removal unit of the OFDM demodulator where the first119873CP samples are discarded This operation may be written inmatrix form as

z119897 = RCPy119897 = [0119873times119873CP I119873] y119897 (6)


Power line medium

PMD

TX

PMD

RX

Narrow band

Coloured




+

+Coupling

circuitCoupling


n(t)



r119897 = F119873z119897 = F119873RCPH119897ACPF119867

119873⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Hd 119897

s119897 + w = Hd119897s119897 + w (7)



Hd119897 = diag [1198670 119867119873minus1]

119867119894 =

119871

sum

119896=0


(8)

















119860 (119891) = 119860infin + 1198600119890minus1198911198910 (9)



119860 (119905) =

119873

sum

119894=1

119860 119894 (119905) sin (2120587119891119894119905 + 120601119894) (10)



119901119911 (119911) =

3

sum

119898=1

119890minus119860

119860119898

119898

119890|119911|2

21205902

119898

21205871205902119898

(11)

with

1205902

119898= 1205902(119898119860 + Γ

1 + Γ) (12)


Γ =

1205902

119892

1205902

119894

(13)


2


2

119894 and total

variance 1205902= 1205902

119892+ 1205902

119894








PLDPcp

H


bbb b bb

b windowing factor

Hcp

S1 S1 S1 S1

S2 S2

S3 S3



PHY frame structure



119897119894= (119894+119873CP+119897times119873)119879

1015840




119903119909119909 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) r119897 (119895 + 119899 + 119873119878119894) (14)



119903119909119904 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) 1198781 (119895) (15)




119909 (119905) =1

119873

119873minus1

sum

119894=0

119904119894119897 exp(1198952120587119894 (119905 minus (119873CP + 119897119872)119879)

119873119879) (16)




1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b


HHcp2

b


3rd sectionHeader


NS1NS1

NS1NS1 NS2

NS2NS3




1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35


offset (SFO) 120598119904 = (1198791015840minus119879)119879


y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)



119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))


119873) + 119897119894

119894 = 1 119873

(18)








1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Power line medium

PMD

TX

PMD

RX

Narrow band

Coloured




+

+Coupling

circuitCoupling


n(t)



r119897 = F119873z119897 = F119873RCPH119897ACPF119867

119873⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Hd 119897

s119897 + w = Hd119897s119897 + w (7)



Hd119897 = diag [1198670 119867119873minus1]

119867119894 =

119871

sum

119896=0


(8)

















119860 (119891) = 119860infin + 1198600119890minus1198911198910 (9)



119860 (119905) =

119873

sum

119894=1

119860 119894 (119905) sin (2120587119891119894119905 + 120601119894) (10)



119901119911 (119911) =

3

sum

119898=1

119890minus119860

119860119898

119898

119890|119911|2

21205902

119898

21205871205902119898

(11)

with

1205902

119898= 1205902(119898119860 + Γ

1 + Γ) (12)


Γ =

1205902

119892

1205902

119894

(13)


2


2

119894 and total

variance 1205902= 1205902

119892+ 1205902

119894








PLDPcp

H


bbb b bb

b windowing factor

Hcp

S1 S1 S1 S1

S2 S2

S3 S3



PHY frame structure



119897119894= (119894+119873CP+119897times119873)119879

1015840




119903119909119909 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) r119897 (119895 + 119899 + 119873119878119894) (14)



119903119909119904 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) 1198781 (119895) (15)




119909 (119905) =1

119873

119873minus1

sum

119894=0

119904119894119897 exp(1198952120587119894 (119905 minus (119873CP + 119897119872)119879)

119873119879) (16)




1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b


HHcp2

b


3rd sectionHeader


NS1NS1

NS1NS1 NS2

NS2NS3




1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35


offset (SFO) 120598119904 = (1198791015840minus119879)119879


y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)



119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))


119873) + 119897119894

119894 = 1 119873

(18)








1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119860 (119891) = 119860infin + 1198600119890minus1198911198910 (9)



119860 (119905) =

119873

sum

119894=1

119860 119894 (119905) sin (2120587119891119894119905 + 120601119894) (10)



119901119911 (119911) =

3

sum

119898=1

119890minus119860

119860119898

119898

119890|119911|2

21205902

119898

21205871205902119898

(11)

with

1205902

119898= 1205902(119898119860 + Γ

1 + Γ) (12)


Γ =

1205902

119892

1205902

119894

(13)


2


2

119894 and total

variance 1205902= 1205902

119892+ 1205902

119894








PLDPcp

H


bbb b bb

b windowing factor

Hcp

S1 S1 S1 S1

S2 S2

S3 S3



PHY frame structure



119897119894= (119894+119873CP+119897times119873)119879

1015840




119903119909119909 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) r119897 (119895 + 119899 + 119873119878119894) (14)



119903119909119904 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) 1198781 (119895) (15)




119909 (119905) =1

119873

119873minus1

sum

119894=0

119904119894119897 exp(1198952120587119894 (119905 minus (119873CP + 119897119872)119879)

119873119879) (16)




1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b


HHcp2

b


3rd sectionHeader


NS1NS1

NS1NS1 NS2

NS2NS3




1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35


offset (SFO) 120598119904 = (1198791015840minus119879)119879


y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)



119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))


119873) + 119897119894

119894 = 1 119873

(18)








1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












PLDPcp

H


bbb b bb

b windowing factor

Hcp

S1 S1 S1 S1

S2 S2

S3 S3



PHY frame structure



119897119894= (119894+119873CP+119897times119873)119879

1015840




119903119909119909 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) r119897 (119895 + 119899 + 119873119878119894) (14)



119903119909119904 (119899) =

119873119878119894

sum

119895=1

r119897 (119895 + 119899) 1198781 (119895) (15)




119909 (119905) =1

119873

119873minus1

sum

119894=0

119904119894119897 exp(1198952120587119894 (119905 minus (119873CP + 119897119872)119879)

119873119879) (16)




1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b


HHcp2

b


3rd sectionHeader


NS1NS1

NS1NS1 NS2

NS2NS3




1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35


offset (SFO) 120598119904 = (1198791015840minus119879)119879


y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)



119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))


119873) + 119897119894

119894 = 1 119873

(18)








1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 1 1 3 3 PLD1

b b b

Pcp

PRcrosscorrelation

(abs)

PRautocorrelation

b

2

b


HHcp2

b


3rd sectionHeader


NS1NS1

NS1NS1 NS2

NS2NS3




1000 2000 3000 4000 5000 6000 700000

05

1

15

2

25

3

35


offset (SFO) 120598119904 = (1198791015840minus119879)119879


y119897 (119899) =1

119873ℎ119897 (119899)

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894 (119905119899 minus (119897119872 + 119873CP) 119879)

119873119879) + 119908119897 (119899) =

1

119873

sdot ℎ119897

119873minus1

sum

119894=0

119904119894119897

sdot exp(1198952120587119894119899 (1 + 120598119904)

119873+

1198952120587 (119897119872 + 119873CP) 120598119904119899

)

+ 119908119897 (119899)

(17)



119897119894 =sin (120587120598119904119894)

119873 sin (120587120598119904119894119873)exp(minus1198952120587119894

119897119872 + 119873CP119873

120598119904)119867119897119894119904119897119894

+1

119873

sdot sum

119898=0119898 =119894

119867119897119898119904119897119898

sin120587 (119898 + 119894 (120598119904 minus 1))

119873 sin (120587 ([119898 + 119894 (120598119904 minus 1)] 119873))


119873) + 119897119894

119894 = 1 119873

(18)








1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1015840minus119879)119879




r119897|119897+1 = [1199031198971 119903119897119873 | 119903119897+11 119903119897+1119873] (19)








120598119904119894=

1

2120587119894ang

R119897 (119894)

R119897+1 (119894) (22)


120598119904119894=

119873119904

2120587119894119871 119904

angR119897 (119894)

R119897+1 (119894) (23)



120598119904 = (f119879f + 120575)minus1

f119879120601 (24)

where f = [0 2120587119871 119904119873119904 2120587119871 119904(119873119904 minus 1)119873119904]119879 120601 =


(ie 120575 = 10minus4)



1015840) 119909((1198991198971)119879

1015840) 119909(119899119897119879

1015840) 119909((119899119897 +

1)1198791015840) 119909((119899119897 + 2)119879



1198991198971198791015840+ 120583119897119879





Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Output to VGA



SFO estimate

Packet DET

DAGC(normalize)

FFTCP removal

Stored equalizer

STO estimator

phase tracker



2nd section PRMBL

ADC inputPhase

corrector

FD PRMBL

(SFO correct)

(a)

32-point APFFT

32-point APFFT







SRC filter

SP

SP





Input 1

Input 2

X1

X2

(b)







Equalized preamble



DNS

(c)

+

times

+

times

+

times


+ + +

0 10 0


+ + +

1


+ + +

12120


+ + +

1216



minus16

minus16

minus12

minus12

minus1

minus13


y(mT2)



(d)

Phase corrector

Cordic

Cordic

Cordic

X1_Re

X1_Im

1206011

X2_ReX2_Im

1206012

120601N

Y1_Re

Y1_Im

Y2_Re

Y2_Im

XN_Re

XN_ImYN_ReYN_Im

(e)















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















7 Discussions


119899119894 (119905) =

119873119889

sum

119896=1

119860119896


119905 minus 119905119901

119905119899

)

(25)


2

119899) where







minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus15

minus1

minus05

0

05

1

15

Qua

drat

ure

0 1minus1In-phase

(a)


minus1

minus05

0

05

1

Qua

drat

ure


(b)



minus1

minus08

minus06

minus04

minus02

0

02

04

06

08

1

Qua

drat

ure

(c)








Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Symbol 4Symbol 5

minus4

minus3

minus2

minus1

0

1

2

3

4

50 100 150 200 2500

(a)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(b)



Symbol 4Symbol 5

minus005

0

005

01

015

02

50 100 150 200 2500

(c)



8 Conclusion







12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











12 14 16 18 20 22 24 26 28 3010SNR (dB)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MSE

(dB)


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article pilot-less time synchronization for ofdm systems: application...

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