474 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 11, NO. 5, OCTOBER 2009

A Frequency Domain Equalization Algorithm for FastTime-Varying Fading Channels

Le-Nam Tran, Een-Kee Hong, and Huaping Liu

Abstract: Conventional frequency domain equalization (FDE) sche-mes were originally devised for quasi-static channels. Thus, suchequalization schemes could suffer from significant performancedegradation in fast-fading channels. This paper proposes a fre-quency domain equalization algorithm to mitigate the effect of fasttime-varying fading. First, a mathematical expression is derived toquantify the total interference resulting from the time variation ofthe channel. Then, the proposed approach attempts to eliminatethe effect of time-variations of the channel. This cancellation allowsefficient use of the classical FDE structures in fast time-varyingfading environments, although they are built upon the quasi-staticchannel model. Simulation results of bit-error-rate performanceare provided to demonstrate the effectiveness of the proposed al-gorithm.

Index Terms: Cancellation, direct sequence code division multipleaccess (DS-CDMA), fast time-varying fading channels, frequencydomain equalization (FDE).

I. INTRODUCTION

The next-generation mobile communication systems are ex-pected to support high data rates that usually require a band-width larger than the coherence bandwidth of the channel, re-sulting severe frequency-selective fading channels. In turn, theintersymbol interference (ISI) caused by severe frequency se-lectivity of the channel could limit the maximum transmissionrate. As the time dispersion of the radio channel spans over anumber of symbol durations, the design for high-speed reliablecommunications becomes challenging since the traditional anti-multipath approaches such as multipath-diversity combining be-come inefficient to recover the transmitted signals [1].

To cope with severe frequency selectivity, the entire signalbandwidth could be divided into multiple sub-bands, each ofwhich is narrow enough to assume a frequency-flat fading. Thisconcept leads to the multi-carrier techniques, in particular, theorthogonal frequency-division multiplexing (OFDM) technique

Manuscript received April 15, 2008; approved for publication by Kwang SoonKim, Division II Editor, February 24, 2009.

This work was partly supported by the IT R&D program of IITA [2008-F-005-02, Game Theoretic Approach for Cross-layer Design in Wireless Communica-tions] and the MKE (The Ministry of Knowledge Economy), Korea, under theITRC (Information Technology Research Center) support program supervisedby the IITA (Institute for Information Technology Advancement) (IITA-2009-C1090-0903-0011).

L.-N. Tran and E.-K. Hong are with the School of Electronics and Information,Kyung Hee University, South Korea, email: {nltran, ekhong}@khu.ac.kr.

H. Liu is with the School of Electronic Engineering and Computer Science,Oregon State University, U.S.A., email: hliu@eecs.oregonstate.edu.

The authors wish to thank Dr. Jack Holtzman and Peter Gaal from QUAL-COMM. INC. for helpful discussions on methods to evaluate the performanceof the proposed algorithm, especially for the valuable suggestion on the practicalchannel estimation methods.

[2]. However, OFDM also has many disadvantages such as ahigh sensitivity to frequency offset, and to nonlinear distortionwhich requires expensive linear amplifiers due to the high peak-to-average-power ratio (PAPR) of the transmitted signals.

An alternative solution to deal with frequency selectivity isto equalize the received signals. Equalization could be accom-plished in either the time domain or the frequency domain. Gen-erally, the classical time domain equalization (TDE) has a highcomputational complexity if the channel delay spread is large.The complexity of TDE can be lowered by transforming its op-eration in time domain to frequency domain. Although the con-cept of frequency domain equalization (FDE) appeared almostthree decades ago [3], single-carrier frequency domain equaliza-tion (SC-FDE) has been investigated only recently as a promis-ing approach for broadband wireless communications [4].

Basically, FDE was developed based on the correspondencebetween the circular convolution of two sequences in the timedomain and the point-wise product of their DFT outputs in thefrequency domain [5]. If the transmitted data are designed to beperiodic, the received signals are the circular convolution be-tween the transmitted signal and the channel impulse response(CIR). To maintain circular convolution, in addition to the cyclicdata transmission format, the channel must be quasi-static, thatis, the path gains are constant over a block interval. Most ofpresent FDE structures are based on the quasi-static fading chan-nel. The problem of FDE in time varying channels has beentreated sparsely in different directions. For example, using thebasis extension model (BEM), the authors in [6] presented itera-tive FDE with widely linear filtering. In [7], the windowing tech-nique was utilized to transform the channel matrix into a bandedform. Based on this simplified model, the iterative equalizationwas applied. However, the optimal window design is compli-cated.

In this paper, rather than simplifying the channel matrix forefficient matrix inversion, we propose an equalization algorithmto mitigate the effect of time variations in fast time-varying fad-ing channels. First, we derive a mathematical model to charac-terize the interference caused by time-variations of the channel.As shown later, this interference depends on both the transmit-ted data and CIR. Thus, the suppression of this interference isonly possible if the transmitted data and CIR are available at thereceiver. In practice, the channel can be estimated, typically byusing the transmitted pilot signals, but the transmitted data can-not be known in advance. Hence, our equalization algorithm isperformed through several steps. In the first step, the tentativeestimates of the transmitted data are obtained by using the con-ventional FDE. From the second step, the interference causedby the time-variation of the channel is eliminated based on ten-tative estimates from the first step and the estimated CIR. Con-

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TRAN et al.: A FREQUENCY DOMAIN EQUALIZATION ALGORITHM FOR FAST TIME-VARYING · · · 475

ventional FDE is then applied again to the resulting signals. Theproposed method can be applied to any conventional communi-cation systems, but we will focus on direct sequence code divi-sion multiple access (DS-CDMA) systems in our analysis andnumerical examples as a study case.

The rest of this paper is organized as follows. Section IIbriefly reviews the background of FDE and their applications toDS-CDMA systems. The analysis of the effect of time-varyingmultipath fading channels on FDE and description of the pro-posed equalization algorithm are presented in Section III. Theperformances of our proposed approach are evaluated withcomputer simulations in Section IV, followed by conclusionsin Section V.

II. BACKGROUND OF FREQUENCY DOMAINEQUALIZATION

FDE has been investigated as one of the promising ap-proaches for the CDMA-based 3G systems and beyond [8], [9]since the RAKE combining technique [1] exhibits poor perfor-mance in severe frequency selective fading channels. Before an-alyzing FDE in time-varying channels, we first briefly reviewthe conventional FDE for quasi-static channels. For simplic-ity and convenient illustration purpose, we are interested in thefrequency domain liner equalization for DS-CDMA systems asan example. It means that the proposed equalization algorithmwhich will be described in the next section is applicable to allwireless communications systems, including other equalizationstructures (e.g., hybrid decision feedback equalization (HDFE)[5], [10], [11]) and non-spread spectrum systems.

A. Frequency Domain Linear Equalization (FD-LE) for DS-CDMA Systems

The general FD-LE for DS-CDMA applications is illustratedin Fig. 1. At the transmitter, a block of M data modulated sym-bols {dn} is spread by a spreading sequence cm with a process-ing gain SF to produce the spread signals sn. Then, a knownsequence of L chips is added to the spread signals to form atransmitted data block of size P = M × SF + L chips. Thisdata extension known as unique word (UW) extension [5] is tomake the transmitted data periodic, and thus the channel ma-trix become circulant. Another type of data extension that canplay the same role is cyclic prefix extension [10]. However, inthis paper, we employ UW extension because it is beneficial forchannel estimation. The received signals are written as

rn =ρ−1∑

l=0

hlsn−l + ηn, n = 0, 1, · · ·, P − 1 (1)

where hl, l = 0, 1, · · ·ρ− 1 denotes the fading coefficient of the(l+1)th path, ηn is the zero-mean complex white Gaussian noisewith variance σ2

n. In (1), the channel is assumed to be quasi-static (block fading model). Under the condition that L ≥ ρ, wecan express the frequency domain equivalence of (1) as

Rk = HkSk + Nk, k = 0, 1, · · ·, P − 1 (2)

Fig. 1. FD-LE for DS-CDMA systems.

Fig. 2. Performance of FD-LE in quasi-static and time-varying fadingchannels.

where

Rk =P−1∑

l=0

rne−j2πkn/P ,

Hk =ρ−1∑

l=0

hle−j2πkl/P ,

Nk =P−1∑

n=0

ηne−j2πkn/P

are the results of applying a P -point DFT to the received sig-nals, CIR and additive noise, respectively. It is important to men-tion that (2) holds only in quasi-static channels.

The P -point DFT outputs of the received signals {Rk} areweighted with linear equalizer coefficients {α

(LE)k }. The result-

ing signals are transformed back into the time domain by a P -point IDFT block. If the minimum mean-square error (MMSE)criterion is used, the FD-LE coefficients can be easily found as[8], [9]

α(LE)k =

H∗k

|Hk|2 + σ2n

, k = 0, 1, · · ·, P − 1. (3)

The equalized chips sn are passed through the despreader, fol-lowed by a threshold detector to detect the transmitted data.

476 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 11, NO. 5, OCTOBER 2009

B. Impact of Channel Variations on Performance of FDE

In this section, we provide the simulation results obtainedwith the FD-LE structure to demonstrate the impact of channeltime-variations on the BER performance when the user speedincreases. The detailed simulation parameters are given in Sec-tion IV.

Fig. 2 shows the BER of various anti-multipath approachesfor quasi-static and time-varying channels. For RAKE combin-ing, we consider RAKE combiner of 2 fingers. In quasi-staticfading channels, while RAKE combining technique is not re-liable due to the severe frequency selectivity of the channel,FD-LE achieves excellent performance. It is observed that theperformances of FD-LE in time-varying channels are signifi-cantly deteriorated as the user speed increases. When the userspeed v is 60 km/h, the maximum Doppler spread fD is 167 Hz,producing a normalized Doppler frequency change (defined asthe product of the block duration Tblock and Doppler frequencyfD) of 0.045. This degree of mobility represents a slowly time-varying channel. Thus, the traditional FDE is still efficient tocombat multipath distortion. However, the BER performanceexhibits an error floor as v reaches to 120 km/h. In this case,the maximum Doppler spread is doubled and the normalizedDoppler frequency becomes 0.09. This channel can be viewedas a fast time-varying channel [12], and the path gains are notconstant over a data block.

III. PROPOSED FDE ALGORITHM FORTIME-VARYING FADING CHANNELS

The FD-LE [8], [9] presented in Section II and many other tra-ditional FDE structures (e.g., HDFE in [5], [10], [11]) were de-veloped based on the assumption of quasi-static channel. Whenthe data block duration is longer than the channel coherencetime, the channel gain cannot be considered constant over oneblock. Consequently, FDE algorithms derived based on (2) willsuffer from significant performance degradation in fast time-varying channels.

For OFDM systems, time-varying fading causes a loss of sub-carrier orthogonality, which results in inter-carrier interference(ICI). While the impact of ICI caused by channel variations onthe performance of OFDM systems has been studied extensively[12]–[17], data transmission in time-varying channels with FDEhas received limited attention. In this section, we mathemati-cally analyze the effect of channel time-variations on the per-formance of FDE schemes. Based on such analysis, we developa equalization scheme to improve the performance of FDE intime-varying channels.

A. Analysis of the Impact of Time-Varying Fading Channels onClassical FDE

For multipath time-varying channel model, the received sig-nal is written by

rn =ρ−1∑

l=0

hl(n)sn−l + ηn. (4)

An P -point DFT is applied to {rn} to transform the receivedsignals into the frequency domain. To simplify notation, we only

consider the mathematical expression for a certain kth frequencybin of the received signal in our analysis, which is given by

Rk =P−1∑

n=0

rne−j2πkn/P

=P−1∑

n=0

ρ−1∑

l=0

hl(n)sn−le−j2πkn/P +

P−1∑

n=0

ηne−j2πkn/P .(5)

For each block, we can decompose hl(n) into two components,a time-invariant part and a time-variant part, as

hl(n) = ωl + ψl(n) (6)

where• ωl denotes the average channel gain of the lth path within

one block. This term represents the constant (time-invariant)component of CIR in one data block. If P is the block size,ωl can be written by

ωl =

P∑n=1

hl(n)

P. (7)

• ψl(n) is the difference between channel coefficient at time nand the average value ωl of the lth path. This value measuresthe deviation of the channel coefficient at time n from the av-erage value ωl. In other words, ψl(n) measures the degree ofchange of the CIR. Note that, ψl(n) can be computed using(6) as ψl(n) = hl(n) − ωl if the estimates of hl(n) are avail-able.

From (5) and (6), the received signal in the frequency domaincan be written by

Rk =P−1∑

n=0

ρ−1∑

l=0

{ωlsn−l + ηn}e−j2πkn/P

︸ ︷︷ ︸Ωk

+P−1∑

n=0

ρ−1∑

l=0

ψl(n)sn−le−j2πkn/P

︸ ︷︷ ︸Δk

. (8)

The first term of the right-hand side of (8), Ωk, can be viewedas the frequency response of the received signal in quasi-staticchannels. According to (2), we can simplify Ωk as

Ωk = HkSk + Nk, k = 0, 1, · · ·, P − 1 (9)

where Hk =∑ρ−1

l=0 ωle−j2πkl/P and Nk =

∑P−1n=0 ηne−j2πkn/P

are the DFTs of the average value of CIR and additive noise, re-spectively. Let us define

Ψ(l)k =

P−1∑

n=0

ψl(n)sn−le−j2πkn/P (10)

which is the DFT of the product of the two sequences {ψl(n)}and {sn−l}. The second term Δk in (8) can be written by

Δk =ρ−1∑

l=0

P−1∑

n=0

ψl(n)sn−le−j2πkn/P =

ρ−1∑

l=0

Ψ(l)k (11)

TRAN et al.: A FREQUENCY DOMAIN EQUALIZATION ALGORITHM FOR FAST TIME-VARYING · · · 477

resulting in a more compact form of (5) which is expressed as

Rk = HkSk + Nk︸ ︷︷ ︸Ωk

+ρ−1∑

l=0

Ψ(l)k

︸ ︷︷ ︸Δk

, k = 0, 1, · · ·, P − 1. (12)

In (12), Δk is considered as the interference resulting fromthe channel variation. If the channel is assumed to be constantwithin one block period (i.e., ψl(n) = 0, ∀n), Δk will van-ish. For time-varying channels, Δk destroys the correspondingequivalency between circular convolution in the time domainand multiplication in the frequency domain, and thus degradesthe performance of FDE. The value of Δk is dependent on theseverity of the channel fluctuation; Δk increases as the mobilespeed increases.

Our goal is to eliminate this interference, but this requires apriori knowledge of the transmitted signals sn, as well as thechannel coefficients. In the following, we propose an equaliza-tion algorithm which is accomplished through several steps toreduce the effect of time variations of the channel.

B. The Proposed FDE Algorithm

For time-varying channels, FDE is not conceptually applica-ble due to the presence of Δk in (12), since the frequency re-sponse of the received signal is no longer equal to the point-wiseproduct of the frequency responses of the transmitted signal andthe CIR. It is desirable to cancel Δk so that FDE can be effi-ciently exploited. From (11), the computation of Δk requiresthe followings:• The values of ψl(n): These values can be obtained through

channel estimation which generates estimates hl(n). An esti-mate of ψl(n) is then given by

ψl(n) = hl(n) − ωl (13)

where the average channel gain ωl can be estimated using (7).• The values of the transmitted sequence sn−l: In practice,

these values are not known at the receiver in advance. How-ever, we can make use of the tentative signal estimates that areobtained by applying conventional FDE algorithms to the re-ceived signals over time-varying channel, ignoring the effectof time-variant components.Our proposed method is carried out through several steps as

follows:• Step 1: Apply FDE for time-varying channels to yield tenta-

tive symbol estimates.Any existing FDE structures (e.g., FD-LE in Fig. 1 or HDFEin [11]) can be employed.

• Step 2: Compute Δk from the tentative symbol estimates ob-tained in step 1.

Ψ(l)k =

P−1∑

n=0

ψl(n)sn−le−j2πkn/P , l = 0, 1, · · ·, ρ − 1

Δk =ρ−1∑

l=0

Ψ(l)k . (14)

Fig. 3. Signal processing flow of proposed FDE for time-varying chan-nels.

• Step 3: Subtract Δk from Rk in (12), which yields

Rk = Rk − Δk. (15)

If the estimate of Δk is perfect, Rk is equal to Ωk. Sinceperfect data detection in step 2 is impossible, only part of thetotal interference will be removed.

• Step 4: Apply FDE to Rk computed in step 3 to obtain symbolestimates again.This step is very similar to step 1. Because the impact of Δk

is partially reduced, better symbol estimates can be achieved.Therefore, the overall performance of FDE is improved. Thesignal processing flow of steps from 1 to 4 is depicted inFig. 3.

We also notice that the number of phases in the proposed al-gorithm can be increased by applying the turbo principle [18].Namely, steps 2 to 4 can be repeatedly carried out to further en-hance the performance. The method used in [19] can be helpfulto account for the improved reliability of signal detection aftereach phase of the proposed algorithm. However, such a methodrequires high computational complexity, and thus is not consid-ered in this paper.

478 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 11, NO. 5, OCTOBER 2009

Table 1. Taped-delay-line parameters for vehicular environment.

Tap Delay (ns) Average power Doppler spectrum1 0 −2.5 Classic2 271 0 Classic3 8943 −12.8 Classic4 13008 −10.0 Classic5 17073 −25.2 Classic6 20054 −16.0 Classic

Table 2. Simulation parameters.

Parameters Selected valuesFFT size 1024

Spreading factor 16Modulation QPSK

Carrier frequency 3 GHz

IV. PERFORMANCE COMPARISON

In this section, we evaluate the performance of the proposedalgorithm for FDE in time-varying channels to demonstrate theeffectiveness of the proposed algorithm to mitigate the effect offast time-varying fading. We also examine the robustness of theproposed algorithm with practical channel estimation. Althoughwe focus on DS-CDMA applications as a case study, the pro-posed algorithm can be applied to most wireless communicationsystems.

A. System Parameters

The channel B of the vehicular environment as described inRecommendation ITU-R M.1225 [20] is considered. The chiprate is selected to be 3.6864 Mbps as in CDMA2000. The de-lay between multipaths is assumed to be an integer multiple of achip interval (1/3.6864 Mcps ≈ 271 ns ), so a modified versionof the channel model is used. The power delay profile for the sixindependent paths of the modified channel B is listed in Table 1.

We consider the performance of an uncoded DS-CDMA sys-tem using QPSK modulation. A 16-ary Walsh code is used forspreading. The FFT size is 1024; thus the number of symbols(including unique word extension) in one transmission block is1024/16 = 64 symbols. Consequently, the block duration isTblock = 0.28 ms. The maximum Doppler shift is calculated as-suming a carrier frequency of 3 GHz. Simulation parameters aresummarized in Table 2. The channel simulator is built based onthe JTC channel model in [21].

B. Simulation Results with Ideal Channel Estimation

The UW length for FDE is required to be longer than thelength of the CIR. The modified channel model in Table 1 hasan excess delay spanning 20054/271 = 74 chips. The UW of80 chips selected from a PN sequence is inserted into each datablock. The performances of FD-LE combined with the proposedequalization algorithm and the conventional FD-LE (i.e., FD-LEwithout canceling the effect of channel variation) are comparedin Fig. 4.

In Fig. 4, the legend ‘no cancellation’ denotes the systemperformance when the conventional FD-LE is applied to time-varying channels, and ‘practical cancellation’ represents the

Fig. 4. Performance of the proposed algorithm applied to FD-LE withideal channel estimation, UW = 80 chips.

performance of the proposed algorithm scheme where the can-cellation is performed with practical data detection (detecteddata from the first step). For comparison purpose, we alsoconsider the ideal case labeled by ‘perfect cancellation,’ inwhich the channel coefficients and the transmitted data areknown a priori at the receiver. In this ideal case, the inter-ference term can be reconstructed accurately and cancelledperfectly. Accordingly, we can infer from Fig. 4 that the per-formance of the proposed FDE in this ideal case is independentof Doppler frequency, and is equal to that of traditional FDE ap-plied to quasi-static channel. It is also noted that a higher perfor-mance gain of the proposed equalization over the conventionalFD-LE can be achieved as the user mobility increases and theproposed algorithm can eliminate the error floor. When the nor-malized Doppler frequency is 0.09, a performance gain of about2.2 dB is observed between between ‘no cancellation’ and ‘prac-tical cancellation’ at the BER = 7 × 10−4.

C. Simulation Results with Practical Channel Estimation

C.1 Channel Estimation

In the proposed algorithm, the channel gain (fading coeffi-cient) at every data symbols within one block must be known.An additional benefit of UW is that it can be used as pilot signalsto estimate the channel. The time-varying channel estimationin our work is performed through two steps. First, the channelgains at UW positions are estimated using the multi-stage serialinterference cancellation approach (M-SIC) as described in [22].Second, the channel gains at the data field are obtained by inter-polating the estimated channel coefficients at the UW positions.To ensure an accurate estimation using the M-SIC approach, theUW length is increased to 160 chips (a little more than twice ofthe channel length) at the cost of a lower bandwidth efficiency.A comprehensive study of interpolation method for channel es-

TRAN et al.: A FREQUENCY DOMAIN EQUALIZATION ALGORITHM FOR FAST TIME-VARYING · · · 479

Fig. 5. Performance of the proposed algorithm applied to FD-LE withpractical channel estimation (UW = 160 chips), and different degreesof mobility.

timation can be found in [23]. When computing the channel esti-mates at the data field of each block, we use the estimated chan-nel gains at the UW position of the previous and current blocks.The estimated channel gains at the data fields are given by usinga simplified sinc interpolation as below

h(l, n) =2∑

i=1

h(l, ni)sin(2πfDTc(ni − n))

2πfDTc(ni − n)(16)

where Tc is the chip duration, and fD is the maximum Dopplerfrequency. For the mobile speed estimation, the simple methodin [24] can be employed. In this paper, the value of mobile speedis assumed to be known at the receiver. In (16), h(l, ni) is theestimated channel gain of the lth path at the UW portion, ni

indicates the center position of the ith UW, and n is the positionof each chip in the block.

C.2 Performance of the Proposed Algorithm with PracticalChannel Estimation in Time Varying Channel

Fig. 5 plots the BER performances of the proposed equaliza-tion algorithm with practical channel estimation in time varyingchannels. Several degrees of mobility are considered where thenormalized Doppler frequency is up to 0.18 (v = 240 km/h). Itis observed that the proposed algorithm provides a remarkablegain over the traditional method with practical channel estima-tion in high mobility scenarios.

C.3 Impact of Spreading Factor

In Fig. 6, we evaluate the proposed equalization algorithmwith different values of spreading factor (SF) to investigate theeffect of SF on the proposed algorithm. The normalized Dopplerfrequency is set to be 0.09 (v = 120 km/h). Although our ap-proach always outperforms the traditional FDE scheme, its per-

Fig. 6. Performance of the proposed algorithm applied to FD-LE withpractical channel estimation (fDTs = 0.09, UW = 160 chips), anddifferent values of spreading factor (SF).

formance is degraged as the spreading factor becomes small.This is understandable and can be explained as follows. ForFDE, the equalization is performed in frequency domain and de-tection is performed in time domain. The interference expressedin (11) depends on time-varying coefficients and detected chips.The accuracy of detected chips in time domain detection relieson the spreading factor. Namely, a small value of SF resultsin less accuracy of detected chip, and thus the interference isnot correctly recovered. This eventually causes a performancedegradation on the performance of the proposed method.

V. CONCLUSIONS

We have proposed an effective algorithm to cancel the time-variant component of the received signals for robust operationof SC-FDE over fast time-varying fading channels. We first de-rived the mathematical expressions to model the effect of chan-nel time-variations on the performance of FDE and then pro-vided the multi-step equalization scheme. The proposed schemeimproves the performance of conventional FDE by cancelingthe effect of fast time-varying fading channel. In the proposedscheme, the tentative data estimates are obtained with the con-ventional FDE and then the interference term caused by thetime-variation of the channel is quantified and canceled, fol-lowed by further equalization on the signal after interferencecancellation.

To demonstrate the robustness of our proposed algorithm, wehave evaluated the performance of the proposed interferencecancellation scheme combined with the existing FD-LE schemein different time-varying fading channels by computer simula-tions, where the performance with perfect interference cancel-lation is used as the baseline performance. For relatively highDoppler spreads, the interference cancellation method can pro-

480 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 11, NO. 5, OCTOBER 2009

vide about 2.2 dB gain over the traditional FD-LE algorithmswithout the cancellation of time variation components at a BERof 7× 10−4. The multi-step FDE algorithm proposed in this pa-per is a promising solution to achieve robust performance in timevarying fading environments since it can reduce the irreducibleerror floor that appears in traditional FDE schemes.

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Le-Nam Tran received the B.S. degree in Electri-cal Engineering from Ho Chi Minh National Univer-sity of Technology, Vietnam in 2003. Since 2004,he has been supported by “Korean Government ITScholarship Program” to follow the M.S. degree inKyung Hee University, Kyunggi, Korea, and receivedhis M.S. Electrical Engineering in 2006. He is work-ing toward the Ph.D. degree in electrical engineeringat the same university. He received the Best PaperAward from IITA in August 2005. His current interestsinclude mobile communication systems, equalization

techniques, spread spectrum and CDMA schemes, multiuser MIMO systems.

Een-Kee Hong received the B.S., M.S., and Ph.D. de-grees, all in electrical engineering, from Yonsei Uni-versity, in 1989, 1991, and 1995, respectively. He wassenior research engineer at SK Telecom from Septem-ber 1995 to February 1999 and visiting senior en-gineer at NTT DoCoMo from October 1997 to De-cember 1998. He is currently Associate Professor atKyung Hee University, South Korea. His research in-terests are in physical layer in wireless communica-tion, spectrum engineering, and cross-layer optimiza-tion. He was awarded the Best Paper Award, Institute

of Information Technology Assessment, and Haedong Best Paper Award, KICSin 2005.

Huaping Liu received his B.S. and M.S. degreesfrom Nanjing University of Posts and Telecommu-nications, Nanjing, P. R. China, in 1987 and 1990,respectively, and his Ph.D. degree from New JerseyInstitute of Technology, Newark, NJ, in 1997, allin electrical engineering. From July 1997 to August2001, he was with Lucent Technologies, New Jer-sey. He joined the School of Electrical Engineeringand Computer Science at Oregon State University inSeptember 2001, and is currently an Associate Pro-fessor. His research interests include ultra-wideband

schemes, MIMO OFDM systems, communication techniques for multiusertime-varying environments with applications to cellular and indoor wirelesscommunications. He currently serves as an Associate Editor for the IEEE Trans-actions on Vehicular Technology and IEEE Communications Letters.