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150 ECTI TRANSACTIONS ON COMPUTER AND INFORMATION TECHNOLOGY VOL.9, NO.2 November 2015

Time Domain Equalization Method forDFTS-OFDM Signal without GI under Highly

Mobile Environments

Pongsathorn Reangsuntea1 , Pisit Boonsrimuang2 ,

Kazuo Mori3 , and Hideo Kobayashi4 , Non-members

ABSTRACT

In highly time-varying fading channel, the DiscreteFourier Transform Spreading Orthogonal FrequencyDivision Multiplexing (DFTS-OFDM) signal wouldbe damaged significantly by the inter-channel inter-ference (ICI) due to the loss of orthogonality amongsubcarriers which leads a fatal degradation of bit er-ror rate (BER) performance. To solve this prob-lem, this paper proposes a time domain equalization(TDE) technique in conjunction with a time domainchannel impulse response (CIR) estimation methodfor the DFTS-OFDM signal without using a guardinterval (GI). The features of proposed method is toemploy a time domain training sequence (TS) bothfor the estimation of time domain CIR at every sam-pling time and for removing the inter-symbol interfer-ence (ISI) incurred in the multipath fading channel.The proposed method also employs the TDE with amaximum likelihood (ML) estimation method in thedemodulation of received time domain signal at everysymbol instead of using the conventional MinimumMean Square Error-Frequency Domain Equalization(MMSE-FDE) method. This paper presents vari-ous simulation results to demonstrate the effective-ness of proposed demodulation method for the DFTS-OFDM signal without GI as comparing with the con-ventional MMSE-FDE and TDE methods both of us-ing GI under highly mobile environments.

Keywords: DFTS-OFDM, Time Domain Equaliza-tion (TDE), Channel Impulse Response (CIR), TimeDomain Training Sequence (TS)

1. INTRODUCTION

Discrete Fourier Transform Spreading Orthogo-nal Frequency Division Multiplexing (DFTS-OFDM)technique has been received a lot of attentions asan attractive alternative to OFDM technique for itslower Peak to Averaged Power Ratio (PAPR) and

Manuscript revised on October 18,2015.1,3,4 The authors are with Electrical and Electronic Engi-

neering, Graduate School of Engineering, Mie University, Tsu-shi, 514-8507 Japan., Email:[email protected],[email protected] and [email protected] The author is with Telecommunication Engineering, Fac-

ulty of Engineering, King Mongkuts Institute of TechnologyLadkrabang, 10520 Thailand., Email:[email protected]

robustness to the multipath fading. The DFTS-OFDM can achieve better bit error rate (BER) per-formance than that for OFDM by using the Mini-mum Mean Square Error Frequency Domain Equal-ization (MMSE-FDE) method [1-5]. From the aboveadvantages, the DFTS-OFDM has been adopted asthe standard transmission technique for the uplinkfrom the user terminal to the base station in the 4thgeneration mobile communication system (LTE: LongTerm Evolution) [6-7].

The DFTS-OFDM signal experiences severe inter-channel interference (ICI) due to the Doppler fre-quency spreads in highly time-varying fading chan-nel where the time domain channel impulse response(CIR) would be no more constant even during oneDFTS-OFDM symbol period [8-9]. Accordingly thechannel frequency response (CFR) which be em-ployed in the MMSE-FDE at the receiver is alsochanged relatively during one DFTS-OFDM symbolperiod. From this fact, it is hard to compensate theICI due to the Doppler frequency spreads by using theconventional MMSE-FDE method which leads the fa-tal degradation of BER performance in highly time-varying fading channel.

To solve the above problem, a time domain equal-ization (TDE) method of using GI have been pro-posed for the DFTS-OFDM signal [10-11]. The pro-posed TDE method for the DFTS-OFDM signal withGI can achieve better BER performance than the con-ventional MMSE-FDE method in highly time varyingfading channel. Because the TDE method can trackthe variation of CIR at every sampling time basis.However, in the quasi-static condition, the proposedTDE method with GI shows the worse BER perfor-mance than the conventional MMSE-FDE methodwhich can achieve the frequency diversity gain. Thisis the reason that the demodulation of conventionalTDE method with GI is operated in the time domainwhich is the different from the MMSE-FDE methodwhich is operated in the frequency domain.

To improve the BER performance for the DFTS-OFDM signal furthermore than the conventionalTDE method of using GI in highly time-varying fad-ing channel, this paper proposes a time domain equal-ization (TDE) technique without using GI. In theproposed method, a time domain training sequence

Time Domain Equalization Method for DFTS-OFDM Signal without GI under Highly Mobile Environments 151

(TS) is added at the both ends of data symbol in-stead of adding the GI at the transmitter to com-pensate the inter-symbol interference (ISI) occurreddue to the unemployment of GI [12]. In the proposedTDE method, the CIR is estimated at every samplingtime by using the TS in highly time-varying fadingchannel. This paper also proposes the TDE methodwith a maximum likelihood (ML) estimation methodfor the received time domain signal after removingthe ISI which can achieve better BER performancethan the conventional MMSE-FDE and TDE meth-ods both employing the GI in highly time-varying fad-ing channel.

The rest of this paper is organized as follows. Sec-tion 2 presents a problem of conventional MMSE-FDE method of using GI for the DFTS-OFDM sig-nal in highly time-varying fading channel. Section 3proposes a time domain CIR estimation method atevery sampling time by using the time domain TSwhich is also used in the mitigation of both ISI andICI in the proposed ML based TDE method. Section4 proposes the ML based TDE method in conjunc-tion with the proposed time domain CIR estimationmethod. Section 5 presents various computer simula-tion results to verify the effectiveness of proposed MLbased TDE demodulation method as comparing withthe conventional MMSE-FDE and TDE methods ofusing the GI, and Section 6 draws some conclusions.

2. PROBLEM OF MMSE-FDE METHODFOR DFTS-OFDM SIGNAL WITH GI

When assuming the quasi-static or slow time-varying fading channel, the time domain CIR can beconsidered as a constant during one DFTS-OFDMsymbol period. Fig. 1 shows a schematic diagramfor the relationships between the CIR in the time do-main and the CFR in the frequency domain wherethe CFR can be obtained by performing a DFT tothe CIR at a certain sampling time during one sym-bol period. Fig. 1 (a) shows the CIR and its cor-responding CFR in the quasi-static channel. Fromthe figure, it can be seen that the CIRs at the threesampling times are almost constant. Accordingly theCFRs converted from the CIRs at these three sam-pling times during one symbol period are also almostthe same responses as shown in Fig. 1 (a). From thisfact, the received DFTS-OFDM signal affected by theslow time-varying fading distortion can be equalizedprecisely by using the MMSE-FDE method with thefixed CFR converted from the CIR at any samplingtime during one symbol period.

When assuming the highly time-varying fadingchannel occurred in the data communications suchas high speed vehicle to vehicle (V2V) and highspeed trains communications [9], the time domainCIR would be no more constant even during oneDFTS-OFDM symbol period. Fig. 2 shows an ex-ample of computer simulation results of time domain

CIR for 1st to 3rd delay paths at every sampling timein the Rician multipath fading channel. In the simu-lation, the normalized Doppler frequency fdmax/∆fis taken by 5% where fdmax is the maximum Dopplerfrequency spread and ∆f is the subcarrier spacingof DFTS-OFDM signal. From the figure, it can beseen that the amplitude of time domain CIR is chang-ing relatively even during one DFTS-OFDM symbolperiod. Fig. 1 (b) shows the relationships betweenthe time domain CIR and its corresponding frequencydomain CFR in higher time-varying fading channel.The time domain CIRs are changing during one sym-bol period and the frequency domain CFRs convertedfrom the time domain CIRs at the different samplingtimes are much different as shown in Fig. 1 (b).

Fig.1: Relationships between CIR and CFR.

Fig.2: Amplitude of CIR at every sampling time inhigh time-varying channel.

From this fact, it is difficult to mitigate the time-varying fading distortion by the MMSE-FDE methodof using one fixed CFR over one symbol period whichleads the fatal degradation of BER performance.

To solve the above problem of MMSE-FDEmethod in highly time-varying fading channel, this


paper proposes the ML based TDE method for theDFTS-OFDM signal without GI in conjunction withthe time domain CIR estimation method. The salientfeature of the proposed ML based TDE method is toachieve much better BER performance than the con-ventional MMSE-FDE method.

3. PROPOSAL OF TIME DOMAIN CIR ES-TIMATION METHOD

Fig. 3 shows the frame format employed in theproposed TDE method. In the proposed frame for-mat, the time domain training sequence (TS) is addedat the both ends of every data symbol which be usedin the estimation of CIR at every sampling time. Thetime domain TS can be also used as the role of GIwhich is usually employed in the conventional DFTS-OFDM signal to avoid the ISI. Here it should be notedthat the ISI occurred in the received DFTS-OFDMsignal without GI can be removed by using the TS1and TS2 of which data patterns are known at thereceiver.

Fig. 4 shows the structure of transceiver for theproposed TDE method of using the proposed CIRestimation method. At the transmission side, the in-put information data is encoded by a forward errorcorrection (FEC) code [13]. The encoded M dataare modulated by the quadrature-amplitude modu-lation (QAM) method. Then the modulated signalxD(m,n) at the n−th sampling time ofm−th symbolis converted to the frequency domain signal XD(m, k)at the k− th subcarrier by the M −point DFT whichis given by the following equation.

XD(m, k)=

M−1∑n=0

xD(m,n)· e−j 2πknM , 0≤k≤M−1 (1)

The M subcarriers of XD(m, k) given in (1) aremapped into the certain frequency band within thefrequency bandwidth with N subcarriers continu-ously from the subcarrier number NZ1 to NZ2 (NZ2−NZ1+1 = M) and the null subcarriers (zero padding)are added at the both ends of M data subcarriers.After the subcarrier mapping, the frequency domainsignal X(m, k1) over N subcarriers can be given by,

X(m, k1)=

0(zero padding), 0≤k1≤NZ1−1X0(m, k1)−NZ1, Nz1≤k1≤NZ2

0(zero padding), NZ2+1≤k1≤N−1(2)

where (N −M) is the number of zero padding (NZ)added at the both ends of M data subcarriers inthe frequency domain. The frequency domain signalX(m, k1) including the zero padding given in (2) isconverted to the time domain signal as similar to theconventional OFDM signal by the N − point IFFTwhich can be given by,

x(m,n1)=1

N

Nz2∑k1=NZ1

x(m, k1) · e−j2πn1k1

N , 0≤n1≤N−1

(3)where x(m,n1) is the transmitted DFTS-OFDM sig-nal in the time domain.

The time domain training sequences TS1 and TS2with the length of NTS samples are added at the bothends of every data symbol as shown in Fig. 3 whichbe used in the estimation of CIR. The time domainTS added at the both ends of data symbol can bealso used as the role of GI in the conventional DFTS-OFDM signal to avoid the ISI. The transmitted timedomain signal xT (m,n2) at the n2−th sampling timeof m− th symbol including both TS1 and TS2 can beexpressed by,

xT (m,n2)

=

d(m,n2), 0≤n2≤NTS−1x(m,n2−NTS), NTS≤n2≤N+NTS − 1d2(m,n2−N−NTS), N+NTS≤n2≤N+2NTS−1

(4)

Fig.3: Proposed frame format in the time domain.

Fig.4: Structure of transceiver for proposed DFTS-OFDM system.

where d1(m,n) and d2(m,n) are the time domain TS1and TS2 with the length of NTS samples of whichdata patterns are known at the receiver. For sim-plicity, this paper assumes the data patterns both forTS1 and TS2 are the same as d(m,n). The length ofNTS should be taken longer than the length of delaypaths (L) which is the same condition of the conven-tional GI. Assuming that the timing synchronizationfor the received signal is perfect at the receiver, thereceived time domain TS signal after passing through


the multipath fading channel can be expressed by,

yTS(m,n2) =

L−1∑l=0

hl(m) ·d(m,m2 − 1)+w(m,m2),

= (0 ≤ n2 ≤ NTS − 1)

(5)

where L is the number of delay paths, hl(m) is thetime domain CIR for the l − th delay path at them − th symbol in the time-varying fading channeland w(m,n2) is an additive white Gaussian noise(AWGN) in the time domain. Here it should be notedthat the CIR is assumed to be constant during theshort time period of TS1 and TS2 even in highly time-varying fading channel. Assuming the time domainCIR hl(m) as the unknown parameters, the expectedreceived time domain TS signal yTS(m,n2) can beexpressed by,

yTS(m,n2)=

NTS−1∑i=0

hl(m)·d(m,n2−1), 0≤n2≤N−TS−1

(6)The unknown parameters for the time domain CIRhl(m) at the m−th symbol can be estimated by solv-ing the following maximum likelihood (ML) equation[14] under the constraint condition with minimizingthe difference between the actual received TS signalyTS(m,n2) in (5) and the expected received TS signalyTS(m,n2) in (6).

Υ = argminhl(m)

[NTS−1∑n2=0

|yTS(m,n2)−yTS(m,n2)|2]

(7)

In this paper, we employ a simple solution for solv-ing ML equation in (7) by using the following simul-taneous equations.

yTS(m,n2) = yTS(m,n2) for 0≤n2≤NTS −1 (8)

By substituting yTS(m,n2) given in (6) into (8), (8)can be expressed by the following matrix operations.

[hl(m)]︸︷︷︸NTS×1

= [d(m,n2 − l)]−1︸︷︷︸NTS×NTS

· [yTS(m,n2)]︸︷︷︸NTS×1

(9)

By using (9), the time domain CIR hl(m) can beestimated at every symbol. The number of delaypaths to be estimated in (9) is assumed by NTS be-cause the actual number of delay paths occurred inthe real channel is unknown at the receiver. Here itshould be noted that since the data pattern of timedomain TS d(m,n2) is known at the receiver, the in-verse matrix of [d(m,n2 − l)]− 1 in (9) can be calcu-lated in advance. The calculated inverse matrix can

be used for every received data symbol which enablesthe considerable reduction of computation complex-ity in the estimation of CIR at every symbol by using(9).

By using the estimated [hl(m)] at every symbol,

the CIR at every sampling time [hl(m,n2)] can beestimated by using the cubic spline interpolationmethod over several estimated CIRs of [hl(m)]. Fig.5 shows a schematic diagram for the cubic spline in-terpolation method to estimate the time domain CIRat every sampling time. The estimation accuracy oftime domain CIR at every sampling time will be eval-uated in Section 5.

4. PROPOSAL OF TDE METHOD FORDFTS-OFDM SIGNAL WITHOUT GI

Assuming that the length of time domain TS(NTS) is longer than the maximum length of delaypaths (L) in the time-varying fading channel, the re-ceived time domain data signal yD(m,n2) at everysampling time during the observation period for thedata demodulation from NTS to N + 2NTS − 1 asshown in Fig. 3 can be expressed by,

yD(m,n2) =L−1∑l=0

hl(m,n2)·xT (m,n2 − l)+w(m,n2),

(NTS≤n2≤N+2NTS − 1)

(10)

where xT (m,n2) is the transmitted time domain sig-nal given in (4) and hl(m,n2) is the time domain CIRat every sampling time occurred in the actual time-varying fading channel. Fig. 6 shows the receivedtime domain signal in time-varying fading channel.From the figure, it can be seen that the receivedtime domain data signal yD(m,n2) in (10) includesthe ISI of TS which are added at the start and endof data symbol from the TS1 and TS2, respectively.As shown in Fig. 6, by using the estimated CIRhl(m,n2) at every sampling time and the data patternof d(m,n2) both for TS1 and TS2 which are known atthe receiver, the ISI added at the both ends of timedomain data signal can be removed by the followingequation.

Fig.5: Estimation of CIR at every sampling time byusing cubic spline interpolation method.


Fig.6: Time domain received signal in multipathfading channel.

yF (m,n2)

=

yD(m,n2)−NTS−1∑

l=n2−NTS+1

hl(m,n2) · d(m,n2−1),

(NTS≤n2≤2NTS−2)yD(m,n2), (2NTS−1≤n2≤N+NTS−1)

yD(m,n2)−n2−N−NTS−1∑

l=0

hl(m,n2)·d(m,n2−N−NTS−1),

(N+NTS≤n2≤N+2NTS−2)

(11)

In the derivation of (11), the following relationshipsare used.

n2−l ≤ NTS−1, xT (m,n2−l) = d(m,n2−l) (12)

n2−l≤N+NTS−1,xT (m,n2−1)=d(m,n2−N−NTS−l)

(13)

where yF (m,n2) in (11) is the received time domainsignal after removing the ISI of TS from the actualreceived time domain signal yD(m,n2) in (10). From(11) and Fig. 6, it can be observed that the superim-posed received time domain signal consists of trans-mitted data symbols with having the different delaytimes which corresponds to the original transmittedsignal given in (3). When employing the conventionalTDE method of using GI, the received time domainsignal in the time-varying fading channel includes thepartial signal within GI at the start of every de-lay path signal. From this fact, it can be expectedthat the proposed TDE method without GI showsthe better BER performance than the conventionalTDE method with GI in the ML based demodulationmethod.

When the transmitted time domain data x(m,n1)given in (3) is assumed as the unknown parame-ters, the expected received time domain data sig-

nal yE(m,n2) without including the ISI which cor-responds to the actual received time domain signalafter removing the ISI in (11) can be given by,

yE(m,n2)

=

n2−NTS∑l=0

hl(m,n2) · x(m,n2−NTS−l),

(NTS≤n2≤2NTS−2)NTS−1∑

l=0

hl(m,n2) · x(m,n2−NTS−l)

(2NTS−1≤n2≤N+NTS − 1)NTS−1∑

l=n2−N−NTS+1

hl(m,n2) · x(m,n2−NTS−l),

(N+NTS≤n2≤N+2NTS−2)

(14)

The unknown parameter of time domain data sig-nal x(m,n1) which corresponds to (3) can be esti-mated by solving the following maximum likelihood(ML) equation under the constraint with minimiz-ing the difference between the actual received timedomain signal yF (m,n2) in (13) and the expected re-ceived time domain signal yE(m,n2) in (14).

Υ = argminx(m,s)

[N+2NTS−2∑n2=NTS

|yF (m,n2)−yE(m,n2)|2](15)

The maximum likelihood (ML) equation in (15) canbe converted to the simultaneous equations by takingthe partial differentiation for the unknown parame-ters x∗(m, s) which can be expressed by the followingequation.

∂Υ

∂x∗(m, s)=

∂

(N+2NTS−2∑n2=NTS

|yF (m,n2)−yE(m,n2)|2)

∂x∗(m, s)= 0,

(0 ≤ s ≤ N − 1)

(16)

where ∗ represents the conjugate complex number.By using (16), the ML equation (15) can be expressedby the following simultaneous equations with N un-known time domain data information of x(m,n1).

[b(m, s)]︸︷︷︸N×1

= [Am(s, n1)]︸︷︷︸N×N

· [x(m,n1)]︸︷︷︸N×1

(17)

where b(m, s) and Am(s, n1) can be given by,


b(m, s) =

N+2NTS−2∑n2=NTS

yF (m,n2)∂y∗E(m,n2)

∂x∗(m, s)

=[hHl (m, s)]︸︷︷︸

N×(N+NTS−1)

·[yF (m,n2)]︸︷︷︸(N×NTS−1×N)

, 0≤s≤N−1(18)

Am(s, n1) =

N+2NTS−2∑n2=NTS

yE(m,n2)∂y∗E(m,n2)

∂x∗(m, s)

= [hHl (m, s)]︸︷︷︸

N×(N+NTS−1)

· [hl(m,n1)]︸︷︷︸(N×NTS−1×N)

, 0≤n1≤N−1(19)

where the parameter of s and n1 can be given by,

s = n2 − nTS − l in∂y∗E(m,n2)

∂x∗(m, s)(20)

n1 = n2 −NTS − l in yE(m,n2) (21)

From (17), the unknown parameters [x(m,n1)] canbe solved by using the inverse matrix of [Am(s, n1)]which can be given by,

[x(m,n1)]︸︷︷︸N×1

= [Am(s, n1)]−1︸︷︷︸

N×N

· [b(m, s)]︸︷︷︸N×1

(22)

where [·]−1 represents the inverse matrix opera-tion. Here it should be noted that the inverse ma-trix calculation in (22) would be the dominant factorin the computational complexity required for the re-ceiver. The computation complexity for the inversematrix calculation is estimated by the order of O(N3)when the matrix size is N × N . As one of solutionsto reduce the computation complexity for the inversematrix calculation, we proposed the iterative basedTDE method for OFDM signal in [14]. The featureof this method is to employ the iterative method forsolving the simultaneous equations instead of usingthe direct calculation of inverse matrix. From theevaluation results in [14], we concluded that the iter-ative method can achieve almost the same accuracywith smaller computation complexity than the directcalculation of inverse matrix. From the reason that,we are focusing on the feasibility study for the po-tential capability of proposed TDE method in thispaper. The investigation of iterative method for theDFTS-OFDM signal with the proposed TDE methodis subject to the future work.

The time domain signal x(m,n1) estimated in (22)

is converted to the frequency domain signal X(m, k1)by N-point FFT. After subcarrier de-mapping inthe frequency domain data, the data informationxD(m,n) can be obtained from the frequency domain

signal XD(m, k) by M − point IDFT as shown inFig. 4. The proposed TDE method with the es-timated CIR at every sampling time can mitigate

both for the ISI and ICI at the sampling time ba-sis during one DFTS-OFDM symbol period. Fromthis fact, it can be expected that the proposed TDEmethod without GI can achieve better BER perfor-mance than the conventional MMSE-FDE and con-ventional TDE method of using GI under highly mo-bile environments.

In this section we derive the mathematical form forthe ML based CIR estimation method of using theTS and the ML based TDE demodulation method inhigh time-varying fading channel as given in (7) and(15), respectively. From these ML equations, we de-rive the simultaneous equations theoretically whichcan obtain the solutions by using the Moore Penroseinverse matrix calculation for the non-square matrixand the inverse matrix calculation for the square ma-trix as given in (9) and (22), respectively.

Here it should be noted that the proposed methodis required to store the received time domain signal atevery symbol basis at the receiver. The data demod-ulation is conducted at every symbol for the storedsignal of which store and processing technique is alsoemployed in the conventional DFTS-OFDM receiver.However the proposed method is required for the ad-ditional processing’s in the estimation of CIR at everysampling time, the removing of ISI and the calcula-tion of inverse matrix at every symbol. From theseprocessing, the additional delay would be occurred inthe proposed method as compared with the conven-tional method. The hardware size of transceiver forthe proposed method may not be increased so muchas compared with that for the conventional methodby using the state-of-the-art digital signal processing(DSP) device.

5. PERFORMANCE EVALUATIONS

Although it should be desirable if the CIR esti-mation accuracy and BER performance of proposedmethod can be evaluated theoretically by using themathematical closed form. However it is very hardto derive the mathematical model for the proposedTDE method of using the CIR estimation methodespecially in high time-varying fading channel. Themain purpose of this section is to demonstrate the ef-fectiveness of proposed method in high time-varyingfading channel. This section evaluates the perfor-mance of proposed method by using the computersimulation results which is usually employed in thebasic design of new transmission technique. In thissection, various computer simulations are conductedto evaluate the performance of proposed TDEmethodas comparing with the conventional MMSE-FDE andTDE methods of using GI in highly time-varying fad-ing channel. The simulation parameters to be usedin the following evaluations are listed in Table 1.The proposed channel estimation method of using thetime domain training sequence (TS) is employed inthe estimation of time domain CIR for the conven-


tional TDE of using GI and proposed TDE withoutusing GI methods. The proposed channel estima-tion method is also used in the estimation of chan-nel frequency response (CFR) for the conventionalMMSE-FDE method in order to compare the BERperformances with the proposed TDE method fairly.The communication channel is modelled by the Ri-cian multipath fading which is usually experienced inthe communications by the user on the highly mov-ing vehicle or train [9]. In the following evaluations,the normalized Doppler frequency RD = fdmax/∆f isemployed as the measure of mobile conditions wherefdmax is the maximum Doppler frequency spread and∆f is the DFTS-OFDM subcarrier spacing.

The estimation accuracy for the time domain CIRat every sampling time is evaluated by the normalizedmean square error (NMSE) which is given by,

Table 1: Accuracy Comparison of Two Service Ar-eas.

Parameters ValueNo. of FFT/IFFT points (N) 128No. of DFT/IDFT points (M) 96No. of zero padding (NZ) 32Modulation for data subcarrier 16QAMNo. of data symbols per one frame (NS) 33Allocated bandwidth 1 MHzRadio frequency 5.9 GHz

Forward Error Correction (FEC) Code [13]Encoding ConvolutionFEC rate 1/2Constraint length 7

DecodingViterbi withhard decision

InterleaverMatrix withone frame

Conventional Modulation for TS 16QAMMMSE-FDE Length of TS (NTS) 16

and Length of GI 16TDE method Symbol duration (TD) 132µs

ProposedTDE

Modulation for TS 16QAMLength of TS (NTS)) 16Symbol duration (TD) 120µs

Rician multipath fading channel modelRice factor (K) 6dBDelay profile ExponentialDecay constant -1dBNo. of delay paths (L) 14No. of scattered rays 20

NMSE=

L−1∑l=0

Ns−1∑m=0

N+2NTS−1∑n2=0

|hl(m,n2)−hl(m,n2)|2

L−1∑l=0

Ns−1∑m=0

N+2NTS−1∑n2=0

|hl(m,n2)|2

(23)

where NS is the number of DFTS-OFDM symbolsper one frame.

Fig. 7 shows the time domain CIR estimation ac-curacy at every sampling time which is evaluated bythe normalized mean square error (NMSE) for theproposed CIR estimation method of using the time

domain TS when changing the normalized Dopplerfrequency RD and operation C/N. Here it should benoted that the CIR estimation accuracy at every sam-pling time is evaluated taking into account both theestimation accuracy for the estimated CIR at everysymbol by using time domain TS and the estimatedCIR at every sampling time by using the cubic inter-polation method. From the figure, it can be observedthat the proposed method can keep higher estimationaccuracy when RD is up to 20% which corresponds tothe vehicle speed of 381km/hr even at lower operationC/N.

Fig.7: CIR estimation accuracy (NMSE) for pro-posed method when changing the normalized Dopplerfrequency RD and operation C/N.

From these results, it can be confirmed that the pro-posed CIR estimation method of using the time do-main TS can be used in the proposed TDE method tomitigate the inter-symbol interference (ISI) and inter-channel interference (ICI) precisely when RD is up to20%.

Fig. 8 shows the BER performances for the pro-posed TDE method as comparing with conventionalMMSE-FDE and TDE methods of using GI whenchanging the normalized Doppler frequency RD atthe operation C/N=20dB. In the figure, the BER per-formance for the proposed TDE method of using theideal CIR at every sampling time is also shown forthe purpose of comparison with the proposed TDEmethod of using the estimated CIR. From the figure,it can be observed that the proposed TDE methodwith the estimated CIR shows better BER perfor-mance than the conventional TDE method with theestimated CIR. The proposed method can keep betterperformance until the normalized Doppler frequencyRD =20% with a little degradation of BER perfor-mance as compared with that in the static condition(RD =0%). On the contrary the BER performance ofconventional MMSE-FDE method is degraded dras-


tically when the normalized Doppler frequency RDis larger than 5% (vehicle speed ≈ 95km/hr.). Theconventional TDE method shows better BER per-formance than the conventional MMSE-FDE methodwhen the normalized Doppler frequency RD is largerthan 6%. However, the conventional TDE methodshows worse BER performance than the MMSE-FDE method in the slow time-varying fading chan-nel (RD < 5%). This is the reason that the conven-tional TDE method of using GI cannot obtain the fre-quency diversity gain like the MMSE-FDE method.On the contrary the proposed TDE method withoutGI which can compensate the ISI by using the esti-mated CIR and the known TS at the receiver showsthe better BER performance than the MMSE-FDEmethod even in the slow time-varying fading chan-nel. From these results, it can be concluded that theproposed TDE method without GI can achieve betterBER performance than the conventional MMSE-FDEand TDE methods especially in highly time-varyingfading channel. From the above results, it can be ex-pected that the proposed method can be employed inthe high speed vehicle to vehicle (V2V) communica-tions even when both cars are running in the oppositedirection. For instance, when both cars are runningat the speed of 150km/hr in the opposite direction,the relative speed becomes 300km/hr. The proposedmethod can be also employed in the data communi-cations for the users in the high speed train runningat higher than the speed of 300km/hr.

Figs. 9 and 10 show the BER performances for theproposed TDE method as comparing with conven-tional MMSE-FDE and TDE methods when changingC/N at the normalized Doppler frequency RD =10%(vehicle speed ≈ 190km/hr.) and RD =15% (vehi-cle speed ≈ 286km/hr.), respectively. From the fig-ures, it can be observed that the BER performance forthe proposed TDE method shows much better BERperformance than the conventional MMSE-FDE andTDE methods.

6. CONCLUSION

This paper proposed the ML based TDE methodin conjunction with the time domain CIR estimationmethod for the DFTS-OFDM signal without GI. Thesalient feature of proposed method is to employ a timedomain training sequence (TS) both for the estima-tion of CIR at every sampling time and for removingthe inter-symbol interference (ISI). The proposed MLbased TDE method can track the time-varying CIRat every sampling time basis for the received time do-main signal after removing the ISI. From the variouscomputer simulation results, it can be concluded thatthe proposed ML based TDE method with the CIRestimation method by using the time domain trainingsequence (TS) can achieve much better BER perfor-mance than the conventional MMSE-FDE and TDEmethods of using GI in highly time-varying fading

Fig.8: BER performance for proposed TDE methodwhen changing RD at C/N=20dB.

Fig.9: BER performance for proposed TDE methodwhen changing C/N at RD =10% (vehicle speed ≈190km/hr.).

channel.

ACKNOWLEDGMENT

The authors would like to thank to the JapaneseGovernment (Monbukagakusho: MEXT) Scholar-ships who supported this research.

References

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Fig.10: BER performance for proposed TDEmethod when changing C/N at RD =15% (vehiclespeed ≈ 286km/hr.).

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[6] 3GPP TS 36.211, Evolved Universal TerrestrialRadio Access (EUTRA); Physical Channels andModulation, 3GPP Standard, Rev. 10.0.0, 2011.

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Pongsathorn Reangsuntea receivedthe B. Eng and M. Eng degrees inTelecommunications Engineering fromKing Mongkuts Institute of Technol-ogy Ladkrabang (KMITL), Thailand in2010, and 2012, respectively. He is cur-rently working toward the Ph.D. de-gree at Mie University, Japan. His re-search interests include high-speed mo-bile communications and wireless LANsystems. He received IEEE VTS Japan

2015 Young Researcher’s Encouragement Award in VTC2015-Spring, Glasgow, UK, May 2015.

Pisit Boonsrimuang received the B.Eng, M. Eng, and Doctor degreesin Telecommunications Engineering, in1997, 2000, and 2007, respectively. Heis currently an associate professor at theKing Mongkuts Institute of TechnologyLadkrabang (KMITL), Thailand. Hisresearch interests include transmissiontechniques for future multimedia wire-less LAN systems and next generation ofmobile communication systems. He re-

ceived the Student Award of Young Research’s EncouragementAward from IEICE Tokai branch and Doctor Thesis Award forinformation technology from Nation Research Council of Thai-land (NRCT) in 2005 and 2008, respectively.


Kazuo Mori received the B.E. degreein computer engineering from NagoyaInstitute of Technology, Japan, in 1986and received the Ph.D. degree in in-formation electronics engineering fromNagoya University, Japan in 2000. In1986, He joined the Hyper-media Re-search Center, SANYO Electric Co.,Ltd. and was engaged in research anddevelopment on telecommunication sys-tems. From 1995 to 2000, he was a re-

search engineer at YRP Mobile Telecommunications Key Tech-nology Research Laboratories Co., Ltd., where he was engagedin research on mobile communication systems. Since August2000 he has been with Mie University, Japan, where he is cur-rently a Professor in the division of Electrical and ElectronicEngineering, Graduate School of Engineering. During 2005–2006, he was a Visiting Research Fellow at King’s College Lon-don, UK. His research interests include mobile communicationsystems, wireless sensor networks, radio resource management,and teletraffic evaluation. He received the Excellent PaperAward from IEICE, Japan in 2002. Dr. Mori is a memberof IEEE.

Hideo Kobayashi received the B.E.,M.E., and Ph.D in 1975, 1977 and 1989,respectively from Tohoku University inJapan. He joined KDD in 1977, andengaged in the research and develop-ment of digital fixed satellite and mo-bile satellite communications systems.From 1988 to 1990, he was with Interna-tional Maritime Satellite Organization(INMARSAT) at its London Headquar-ters as the Technical Assignee and in-

volved in the design and development of Inmarsat-M commu-nications system. From 1997 to 1998, he was with the NECICO project office as the technical consultant at its Londonoffice and involved in the development of the ICO personalsatellite communications system. Since 1998 he has been theProfessor of Graduate School of Engineering, Mie Universityin Japan. His current research interests include mobile com-munications and wireless LAN systems. Dr. Kobayashi is amember of IEEE.

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