IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 12, DECEMBER 2006 2155

Transactions Papers

Frequency-Domain Channel Estimation forSC-FDE in UWB Communications

Yue Wang, Student Member, IEEE, and Xiaodai Dong, Member, IEEE

Abstract—Recently, single-carrier block transmission withfrequency-domain equalization (SC-FDE) has been shown to be apromising candidate for ultra-wideband (UWB) communications.In this paper, we address the channel estimation problem forSC-FDE transmission over UWB channels. A mean-square error(MSE) lower bound for the frequency-domain linear minimummean-squared error (LMMSE) channel estimator is derived,and the optimal pilot sequence that achieves this lower boundis obtained. Further simplification leads to a frequency-domainchannel estimator with reduced computational complexity. Theperformance of the simplified estimator for SC-FDE over UWBchannels is evaluated and compared with that with perfect channelstate information. The effects of nonoptimal and optimal pilotsymbols are also investigated. Our results show that the proposedfrequency-domain channel estimator performs well over UWBchannels with only small performance degradation, comparedwith that with perfect channel estimation.

Index Terms—Frequency-domain channel estimation, minimummean-square error (MMSE) estimation, pilot-sequence-assistedchannel estimation, single-carrier block transmission with fre-quency-domain equalization (SC-FDE), ultra-wideband (UWB)communications.

I. INTRODUCTION

ULTRA-WIDEBAND (UWB) technology has receivedenormous attention in recent years for its potential to

provide very-high-data-rate communication with low powerconsumption. Both multicarrier UWB (MC-UWB) employingorthogonal frequency-division multiplexing (OFDM) andimpulse-based single-carrier (SC) transmission have beenproposed to IEEE 802.15.3a as the potential physical layertechnology [1], [2]. SC block transmission with frequency-do-main equalization (SC-FDE), where data is transmitted on ablock-by-block basis in the time domain while equalization iscarried out in the frequency domain, has been shown to have anoverall performance advantage over OFDM-UWB and the im-pulse-based SC-UWB, especially when implementation issues

Paper approved by Y. Li, the Editor for Wireless Communications Theoryof the IEEE Communications Society. Manuscript received October 18, 2004;revised March 22, 2006. This paper was presented in part at IEEE GLOBECOM,St. Louis, MO, November 2005.

The authors are with the Department of Electrical and Computer Engineering,University of Victoria, Victoria, BC V8W 3P6, Canada (e-mail: yuewang@ece.uvic.ca; xdong@ece.uvic.ca).

Digital Object Identifier 10.1109/TCOMM.2006.885084

such as power consumption and system complexity are takeninto consideration [3]. The bit-error rate (BER) performance ofSC-FDE over UWB channels has been presented in [3], withthe assumption that perfect channel state information (CSI) isavailable at the receiver. However, this is not the case in prac-tical systems where channel estimation has to be carried out atthe receiver. In this paper, we address the channel estimationproblem for the SC-FDE system over UWB communications.The frequency-domain channel coefficients are estimated frompilot symbols and then used by the subsequent equalizer toperform frequency-domain channel equalization.

UWB channel estimation is a subject of plenty of research in-terest [4], [5]. In coherent impulse radio UWB, a large numberof multipath gains and delays in the time domain have to beestimated within a short data transmission time, thus makingit more difficult than in typical narrowband or wideband com-munications. The use of an SC-FDE system for UWB trans-mission, however, makes it possible for both the channel es-timation and equalization to be carried out in the frequencydomain. Time-domain and frequency-domain channel estima-tion for block transmission systems in frequency-selective mul-tipath channels were studied in plenty of literature. In [6], achannel impulse response (CIR) was estimated by performingleast-square (LS) channel estimation in the frequency domain,followed by inverse discrete Fourier transform (IDFT). Thismethod produced a low-complexity search strategy for optimalpilot sequences, but it was shown in [7] that it does not alwaysresult in lowest mean-squared estimation error (MSE) achiev-able by the time-domain LS estimation. In [8], an LS channelestimation scheme for multiple-input multiple-output (MIMO)OFDM systems based on pilot tones was developed, and the op-timal pilot sequences and optimal placement of pilot tones withrespect to the MSE of LS channel estimation were derived. Twoestimation schemes for OFDM, the maximum-likelihood esti-mator (MLE) and the Bayesian minimum mean-square error es-timator (MMSE) estimator of the CIR, were compared in [9].Both [8] and [9] performed channel estimation in the time do-main first and used the fast Fourier transform (FFT) to obtainchannel frequency response. In [10] and [11], frequency-do-main channel estimators for OFDM were presented. Further-more, a low-rank channel estimator was proposed to reducethe computational complexity, which inspired our frequency-domain channel estimation schemes in this paper due to the sim-ilarity between OFDM and SC-FDE.

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2156 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 12, DECEMBER 2006

In this paper, we investigate the frequency-domain channelestimation problem for the SC-FDE over UWB channels. Alower bound for the MSE of the linear minimum mean-squarederror (LMMSE) channel estimator is derived, which achievesits minimum value when a flat spectrum of the pilot sequenceis assumed. A frequency-domain estimator that satisfies thislower bound is proposed, and is further simplified to reducecomputational complexity. Our simulation results show thatthis reduced-complexity channel estimator, which uses thetime-domain statistics to perform frequency-domain channelestimation, yields good performance under the currently pro-posed UWB channel models [12].

The remainder of this paper is organized as follows. Section IIpresents a brief description of the SC-FDE system model. InSection III, a lower bound for the MSE of frequency-domainLMMSE estimation is derived. Based on this lower bound, thefrequency-domain channel estimator with reduced complexityis proposed in Section IV. Simulation results and discussionsare presented in Section V. Section VI concludes this paper.

II. SC-FDE SYSTEM MODEL

Notation: , , and denote matrix transpose, Her-mitian transpose, and matrix inverse, respectively. We usefor the set of by matrix and for an identity ma-trix. Moreover, denotes the th entry of a matrix,denotes the trace of an matrix, denotes the de-terminant of a matrix, and denotes the complex conjugate.Furthermore, denotes expectation, and is the algebraicsign function.

We consider the cyclic-prefixed SC-FDE over UWB chan-nels. A block of signals is transmitted withblock length . Each has average energy . A cyclic prefix(CP) is inserted between blocks to mitigate interblock interfer-ence (IBI). As long as the duration of CP is longer than that ofthe CIR, IBI effects can be ignored.

Suppose that the equivalent -spaced CIR is of order withtaps . Assuming timing is acquired,the received signal can then be expressed in a matrix form as[13]

(1)

where , and is the circulant Toeplitzmatrix with the first column being zero-padded to length[13]. Each element in the noise vector is a Gaussianrandom variable (RV) with variance , where isthe one-sided noise power spectral density.

The frequency-domain received signal can be expressed as[3]

(2)

where is the discrete Fourier transform (DFT) matrix and, , . More-

over, matrix is a diagonal matrix, with its th entry as ,

where is the th coefficient of channel frequency response,and

(3)

Or, in a matrix form

(4)

where . The purpose of frequency-domain equalization (FDE) is to eliminate intersymbol interfer-ence (ISI) within individual transmission blocks. Here we con-sider the commonly used frequency-domain MMSE equaliza-tion with the equalizer taps [14]

(5)

In order to perform frequency-domain channel equalizationproperly, the estimation of channel spectrum coefficients ,

, are required for the subsequent equalizer.After FDE and IDFT, the received signal becomes

(6)

where is an diagonal matrix with its th diag-onal element as the frequency-domain equalizer taps ,

. Signal detection is performed in the timedomain. For simplicity and without loss of generality, binaryphase-shift keying (BPSK) modulation is considered here andthe decision variable becomes

(7)

where is the signal vector after the FDE and IDFT. Fig. 1shows the block diagram of the investigated SC-FDE system.Our objective is to estimate the channel frequency response forthe SC-FDE system over UWB channels.

III. MSE LOWER BOUND OF THE FREQUENCY-DOMAIN

LMMSE CHANNEL ESTIMATOR

Suppose a block of pilot sequence ,where is transmitted for channel estimation purposes.By matrix manipulations, (2) can be rewritten as

(8)

where is a diagonal matrix with its th diagonal elementas the th coefficient of the frequency-domain spectrum of thepilot sequences , and .

WANG AND DONG: FREQUENCY-DOMAIN CHANNEL ESTIMATION FOR SC-FDE 2157

Fig. 1. SC-FDE system.

Our objective is to estimate the frequency-domain channelcoefficients , based on the receivedfrequency-domain signal . It is known that the LMMSE esti-mator can be expressed as [15]

(9)

where

(10)

and

(11)

are the cross-correlation matrix between and and the au-tocorrelation matrix of , respectively. Moreover, is theautocorrelation matrix of channel frequency-domain response

, which is assumed to be known for LMMSE channel estima-tors. The LMMSE channel estimator in (9) can be obtained as

(12)

where and is the weighting matrix, given by

(13)

A good estimator should minimize the variance of the esti-mated error. To evaluate the performance of the LMMSE esti-mators, we calculate the respective average MSE [10]

MSE (14)

where . Therefore, the MSE for the LMMSEchannel estimator can be written as

MSE

(15)

and

(16)

Following (13) and (16), the MSE for the LMMSE channel es-timator can be obtained as

MSE (17)

To analyze the MSE, we assume that the autocorrelation matrixis positive definite (see Appendix A), and therefore invert-

ible. Following (13), there is

(18)

where is the diagonal matrix containing the eigenvaluesof on its diagonal, and is a

unitary matrix containing eigenvectors of as its columns.The second equality is a result of the singular value decompo-sition (SVD) of matrix [(31) in Appendix A], and the lastequality is due to the fact that when

is a unitary matrix and . We want to minimize the

2158 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 12, DECEMBER 2006

MSE in (17) through the design of , which is equivalent tomaximizing (18).

Denote the matrix as

(19)

It is shown in Appendix B that

(20)

where the equality holds when

(21)

Or equivalently

for (22)

That is, the MSE of LMMSE estimator can achieve its minimumvalue when the pilot sequence has a flat spectrum. This result isin agreement with the optimal training-sequence properties forthe LS frequency-domain channel estimator in [6].

When the optimal pilot sequence is used, the average MSE ofthe channel estimator can be obtained from (13), (17), (21), and(31) as

MSE

(23)

Also, we can obtain from (20) that

MSE

MSE (24)

where the equality holds when (21) is satisfied. Therefore,the average MSE of the LMMSE channel estimator is lowerbounded by MSE , with its minimum value achieved when theoptimal pilot symbols with a flat spectrum are used.

Note that a different method to estimate the channel fre-quency response is to perform MMSE estimation of the

channel taps in the time domain, followed by anFFT. However, it can be shown that the time-domain methoddoes not guarantee the lowest MSE in the frequency domain.That is, performing FFT on the time-domain taps obtained by

MMSE estimation does not guarantee an optimal estimation interms of MSE in the frequency domain.

IV. LMMSE ESTIMATOR WITH REDUCED COMPLEXITY

Under the condition when the optimal pilot symbols are used,the matrix inverse in (13) is independent of the pilot sequenceand needs to perform only once if and are known be-forehand [10]. Therefore, the LMMSE estimator has a reducedcomplexity and becomes

(25)

where is the time-domain autocorrelationfunction, and the second equality in (25) is due to (31) inAppendix A.

As the estimator is now using time-domain channel statis-tics, the computational complexity of the LMMSE channel es-timator can be further reduced as in [10], by knowing the factthat for typical UWB channels, time-domain channel taps onlydominate the first taps, where varies for different channelmodels and data rates in UWB channels. Therefore, matrixcan be reduced as , which is an autocorrelation ma-trix of the first time-domain channel taps. The simplified es-timator can be obtained as

(26)

where is the first columns of the DFT matrix , and theweighting matrix becomes

(27)

The number of complex multiplications of the matrix calcula-tion in (26) therefore becomes , which is muchsmaller than , required in (25). The reduction in com-putational complexity, however, is at the expense of the perfor-mance degradation in terms of MSE. That is, the simplified es-timator in (26) no longer yields the MMSE as (25), since notall of the nonzero channel taps are involved in calculating thechannel autocorrelation matrix. Nevertheless, as long as a rea-sonable number of time-domain channel taps are chosen, theperformance degradation is very small and the simplified esti-mator performs well under the evaluated UWB channels, as willbe shown in Section V.

We further notice that in estimator (26), the optimal pilotblock with flat spectrum is required, which can be obtained bythe employment of a search procedure [6]. Efforts on the searchof the optimal sequence exert additional computational com-plexity in channel estimation. To further reduce the complexityin channel estimation, we simplify the estimator in (26) by usingnonoptimal pilot sequences and dividing the channel estimationinto two steps.

1) Perform the coarse LS estimation of by , with no re-strictions on the pilot sequence. That is, the pilot sequencesare not obligated to be optimal and have a flat spectrum.

WANG AND DONG: FREQUENCY-DOMAIN CHANNEL ESTIMATION FOR SC-FDE 2159

Fig. 2. MSE comparison of the proposed low-complexity estimator, frequency-domain LMMSE estimator, and MSE lower bound for the UWB channel CM1.

Fig. 3. MSE comparison of the proposed low-complexity estimator, frequency-domain LMMSE estimator, and MSE lower bound for the UWB channel CM2.

2) Get the fine estimation value by weighting within (27).

Simulation results employing the nonoptimal pilot symbols arealso presented in Section V, where randomly generated BPSKsymbols are used as pilots. Our results show that the perfor-mance degradation due to nonoptimal pilot symbols can be com-pensated by sending multiple blocks of pilot symbols.

V. SIMULATION RESULTS AND DISCUSSIONS

The performance of the proposed low-complexity fre-quency-domain channel estimator under UWB propagationenvironments is presented in this section, compared with thatof the perfect CSI. The UWB channels used are CM1-CM4channel models proposed by the IEEE 802.15.3a study group[12]. The investigated SC-FDE system follows that in [3],where a data-block length is used, with CP lengthof 64 and the bit duration of 2 ns, indicating an informationdata rate of approximately 400 Mb/s. The root raised cosine(RRC) pulse with rolloff factor is employed as the

Fig. 4. MSE comparison of the proposed low-complexity estimator, frequency-domain LMMSE estimator, and MSE lower bound for the UWB channel CM3.

Fig. 5. MSE comparison of the proposed low-complexity estimator, frequency-domain LMMSE estimator, and MSE lower bound for the UWB channel CM4.

pulse-shaping filter. In both numerical evaluation and simula-tions, the transmitted pulse-shaping filter, the receiver matchedfilter, and one of the 100 channel realizations for a particularUWB channel model are convolved to form 100 different equiv-alent channel realizations over which the BERs are averaged.The second-order channel statistics are obtained using MonteCarlo simulation, where is calculated and averaged over100 channel realizations. The length is chosen by simulationto gather up to 99% of the channel energy (30 for CM1, 40 forCM2, 70 for CM3 and 100 for CM4). Fewer time-domain tapscan be selected, at the cost of a performance degradation, aswill be shown in Fig. 10.

The lower bound of the MSE value and the MSE of the pro-posed channel estimator (26) for UWB channels CM1-CM4are shown in Figs. 2–5, compared with the MSE for LMMSEchannel estimator in (12). As can be observed, for each eval-uated UWB channel model, the MSE of the proposed channelestimator achieves its lower bound at low signal-to-noise ratios(SNRs). Reducing the dimension of the autocorrelation matrix

2160 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 12, DECEMBER 2006

Fig. 6. Performance comparison between the proposed low-complexity esti-mator with that of the perfect CSI of the SC-FDE transmission over the UWBchannel CM1.

Fig. 7. Performance comparison between the proposed low-complexity esti-mator with that of the perfect CSI of the SC-FDE transmission over the UWBchannel CM2.

tends to have more effect on performance at high SNRs, wherethe value of MSE diverges from the lower bound and becomesslightly larger than that of the frequency-domain LMMSE es-timator (12). However, the MSE of the proposed channel es-timator can achieve its lower bound MSE at all the evaluatedSNRs when additional nonzero channel taps are included in thecalculation of .

For multiple blocks of pilot symbols, the estimation ofchannel spectrum coefficients are obtained from each pilotblock and then averaged over these blocks. The nonoptimalpilot blocks used in the simulation are randomly generatedBPSK symbols, while the optimal pilots are simply a delta pulsewith energy , based on the assumption that the transmitteris capable of providing two distinct power levels, one for pilotsand one for data transmission. In practice, however, perfect

Fig. 8. Performance comparison between the proposed low-complexity esti-mator with that of the perfect CSI of the SC-FDE transmission over the UWBchannel CM3.

Fig. 9. Performance comparison between the proposed low-complexity esti-mator with that of the perfect CSI of the SC-FDE transmission over the UWBchannel CM4.

flat spectrum of pilot symbols is usually hard to obtain andefforts on the search of optimal pilot sequences are required.Some low-complexity search strategies have been presented in[6] and [7]. Nevertheless, with an ideal flat spectrum for pilotsconstructed in our simulation, the results presented here are thebest achievable performance of the proposed estimator whenoptimal pilot symbols are used.

The performance of the frequency-domain low-complexitychannel estimator (26) for SC-FDE under UWB channelsCM1-CM4 are plotted in Figs. 6–9, where both the optimaland nonoptimal pilot sequences are employed. The BER per-formance with perfect CSI is also shown for comparison. It isobserved that the proposed low-complexity estimator performswell for the SC-FDE system under a UWB propagation environ-ment. Compared with the performance with perfect CSI, when

WANG AND DONG: FREQUENCY-DOMAIN CHANNEL ESTIMATION FOR SC-FDE 2161

Fig. 10. BER performance of the proposed channel estimator using differentnumbers of time-domain channel taps for the autocorrelation matrix in CM4.

three blocks of nonoptimal pilot symbols are used, only a slightperformance degradation of about 0.5 dB is incurred for CM1and CM2, while approximately a 2 dB performance degradationrelative to the performance with perfect CSI is observed forCM3 and CM4. Furthermore, increasing the length of the pilotsymbols only slightly improves the BER performance for CM1and CM2, where the performance with two or three blocks pilotsymbols are already very close. However, this is not the casefor channel models CM3 and CM4, where a performance gainof about 1 dB can be obtained when the length of pilot symbolsincreases from one to three blocks. When the optimal pilotsymbols are used, a slight performance improvement of 0.5 dBcan be obtained for CM3 and CM4 by increasing the length ofpilot symbols from one to two blocks. It can also be observedthat for each evaluated UWB channel model, the performancewith three blocks of nonoptimal pilot symbols is very close tothat with one block of optimal pilot symbols. Therefore, thedegradation due to nonoptimal pilots can be compensated bysending multiple pilot blocks at the transmitter, at the cost ofreduced throughput.

In order to illustrate the effect of selection for the pro-posed low-complexity frequency-domain channel estimator, weplotted in Fig. 10 the averaged BER performance over 100 UWBchannel realizations of CM4 using the proposed low-complexityfrequency-domain channel estimator with different numbers ofchannel taps. The percentile of the gathered energy averagedover 100 UWB channel realizations is shown in Table I. It canbe observed that at low-to-medium SNRs, there is minor per-formance degradation using fewer time-domain channel taps(such as 60, 70, or 80). However, at high SNRs, although thechannel energy gathered by fewer time-domain channel tapsonly slightly decreases, obvious performance degradation canbe observed by using 60, 70, or 80 time-domain channel taps.Therefore, gathering enough channel energy does not guaranteea reasonable performance for the low-complexity frequency-do-main channel estimator at high SNRs, and a sufficient number

TABLE INUMBER OF TAPS VERSUS GATHERED CHANNEL ENERGY IN CM4

of channel taps has to be used. Note that even when 100 tapsare used for the time-domain autocorrelation matrix, the dimen-sionality is still much lower than the -by- frequency-domainautocorrelation matrix.

VI. CONCLUSION

Based on a derived lower bound for the MSE of thefrequency-domain LMMSE estimator, a low-complexityfrequency-domain channel estimator using second-ordertime-domain channel statistics for SC-FDE transmission overUWB IEEE 802.15.3a channels has been proposed, and itsperformance has been evaluated. The effects of employingoptimal and nonoptimal pilot symbols in the proposed channelestimator have been compared and discussed. It has been shownthat the proposed channel estimator works reasonably well forthe SC-FDE system under UWB channels, and the performancedegradation due to nonoptimal pilots can be compensated bysending multiple blocks of pilot symbols.

APPENDIX A

In this Appendix, we show the rationality of the assumptionthat is positive definite. Denote the autocorrelation ma-trix of the time-domain channel taps as , that is,

, which is a real symmetric matrix, and therefore, canbe diagonalized as [16]

(28)

where is a unitary matrix and is a diagonal ma-trix with eigenvalues , of on itsdiagonal. Furthermore, is also positive semidefinite, sinceit is an autocorrelation matrix [17]. We assume that some of theeigenvalues in , equal zero. Denoteas the diagonal matrix with its th diagonal entry substituted by

for . That is

forfor (29)

where is chosen to be a small positive value that can be as closeto zero as possible. Therefore, the positive definite counterpartof the positive semidefinite matrix can be obtained as

(30)

2162 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 12, DECEMBER 2006

with its th element as . Since is theunitary matrix, we have . Therefore, the difference be-tween each element in and due to the substitution ofzero eigenvalues by will be no more than , where isthe number of zero eigenvalues of . As long as is chosensmall enough, the difference between and is negli-gible. Therefore, for analysis purpose, it is reasonable to assumethe time-domain channel autocorrelation matrix as positivedefinite, with positive eigenvalues for .Following (4) and (28), we have

(31)

where and is a unitary matrix. Moreover,is a diagonal matrix with the eigenvalues of as

for . Therefore, is alsopositive definite.

APPENDIX B

It is well known that the inverse of an matrix is, where is the matrix with its th ele-

ment given by the th cofactor of . Accordingly, we have

(32)

where is the principal submatrix of obtainedby deleting the th row and column of matrix , which is de-fined in (19).

Bergstrom’s inequality states that [16]

(33)is valid for any positive definite matrix , , where

denotes the principal submatrix of obtainedby deleting the th row and column of , and similarly for .Furthermore, the equality holds when and are diagonal.

Following (19), we denote matrix as

(34)

where , are

(35)

and

(36)

respectively. Matrix is real and positive definite, since ispositive and real as in Appendix A. Also, matrix is positivedefinite, since for all nonzero column vectors , we have

(37)

where , . The inequality in(37) is due to the fact that is positive definite with the theigenvalue being .

Furthermore, it is straightforward to see that

for (38)

We also show in Appendix C that

for (39)

Therefore

for (40)

Applying Bergstrom’s inequality to (34) and inequality (40), wehave

(41)

with the maximum achieved when is diagonal. This condi-tion satisfies when , where is a constant for

. Applying Parseval’s theorem to and ,we have that

(42)

Therefore, constant should be chosen as for the max-imum value in (41) to be achieved, or equivalently, .

Under the condition when the equality holds, we have

for (43)

and

for (44)

WANG AND DONG: FREQUENCY-DOMAIN CHANNEL ESTIMATION FOR SC-FDE 2163

Following (41), (43), and (44), we have

for (45)

where the equality holds when . It follows from (32)that

(46)

where the equality holds when .

APPENDIX C

In this Appendix, we show that Itis known that the is the th diagonal entry ofmatrix (see Appendix B). Also, from (36), we have that theth diagonal entry of is .

Therefore

(47)

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[6] C. Tellambura, M. G. Parker, Y. J. Guo, S. J. Shepherd, and S. K.Barton, “Optimal sequences for channel estimation using discreteFourier transform techniques,” IEEE Trans. Commun., vol. 47, no. 2,pp. 230–238, Feb. 1999.

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[15] S. M. Kay, Fundamentals of Statistical Signal Processing-EstimationTheory. Englewood Cliffs, NJ: Prentice-Hall, 1993.

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Yue Wang (S’05) received both the B.Sc. and M.Sc.degrees in electrical and computer engineering fromXi’an Jiaotong University, Xi’an, China, in 1995and 2002, respectively. She was working towardthe Ph.D. degree at the Electrical and ComputerEngineering Department, University of Alberta,Edmonton, AB, Canada, from 2003 to 2004. Sheis currently working toward the Ph.D. degree at theDepartment of Electrical and Computer Engineering,University of Victoria, Victoria, BC, Canada.

Her research focuses on ultra-wideband communi-cations.

Xiaodai Dong (S’97–M’00) received the B.Sc.degree in information and control engineering fromXi’an Jiaotong University, Xi’an, China, in 1992,the M.Sc. degree in electrical engineering fromthe National University of Singapore, Singapore,in 1995, and the Ph.D. degree in electrical andcomputer engineering from Queen’s University,Kingston, ON, Canada, in 2000.

She was with Nortel Networks, Ottawa, ON,Canada, from 1999 to 2002, and involved in the basetransceiver design of third-generation (3G) mobile

communication systems. From 2002 to 2004, she was an Assistant Professorwith the Department of Electrical and Computer Engineering, University ofAlberta, Edmonton, AB, Canada. She is presently an Assistant Professor andCanada Research Chair (Tier II) in ultra-wideband communications with theDepartment of Electrical and Computer Engineering, University of Victoria,Victoria, BC, Canada. Her research interests include communication theory,modulation and coding, and ultra-wideband radio.

Dr. Dong is an Associate Editor for the IEEE TRANSACTIONS ON

COMMUNICATIONS and an Editor for the Journal of Communications andNetworks.