Robust Channel Estimation For Ofdm Systems With Rapid...

902 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 7, JULY 1998

Robust Channel Estimation for OFDM Systemswith Rapid Dispersive Fading Channels

Ye (Geoffrey) Li, Senior Member, IEEE, Leonard J. Cimini, Jr.,Senior Member, IEEE,and Nelson R. Sollenberger,Fellow, IEEE

Abstract—Orthogonal frequency-division multiplexing (OFDM)modulation is a promising technique for achieving the highbit rates required for a wireless multimedia service. Withoutchannel estimation and tracking, OFDM systems have to usedifferential phase-shift keying (DPSK), which has a 3-dB signal-to-noise ratio (SNR) loss compared with coherent phase-shiftkeying (PSK). To improve the performance of OFDM systemsby using coherent PSK, we investigate robust channel estimationfor OFDM systems. We derive a minimum mean-square-error(MMSE) channel estimator, which makes full use of the time-and frequency-domain correlations of the frequency responseof time-varying dispersive fading channels. Since the channelstatistics are usually unknown, we also analyze the mismatch ofthe estimator-to-channel statistics and propose a robust channelestimator that is insensitive to the channel statistics. The robustchannel estimator can significantly improve the performance ofOFDM systems in a rapid dispersive fading channel.

Index Terms— Diversity combining, orthogonal frequency-division multiplexing, robust channel estimation, time-varyingdispersive fading.

I. INTRODUCTION

M ULTIMEDIA wireless services require high-bit-ratetransmission over mobile radio channels. To reduce

the effect of intersymbol interference (ISI) caused by thedispersive Rayleigh-fading environment [1], the symbol du-ration must be much larger than the channel delay spread. Inorthogonal frequency-division multiplexing (OFDM) [2]–[9],the entire channel is divided into many narrow subchannels,which are transmitted in parallel, thereby increasing the sym-bol duration and reducing the ISI. Therefore, OFDM is aneffective technique for combating multipath fading and forhigh-bit-rate transmission over mobile wireless channels.

To eliminate the need for channel estimation and tracking,differential demodulation can be used in OFDM systems, atthe expense of a 3–4-dB loss in signal-to-noise ratio (SNR)compared with coherent demodulation. Accurate channel esti-mation [5], [6], [8] can be used in OFDM systems to improvetheir performance by allowing for coherent demodulation.Furthermore, for systems with receiver diversity, optimumcombining can be obtained by means of channel estimators.In [5], [6], and [8], a channel estimator for OFDM systems

Paper approved by N. C. Beaulieu, the Editor for Wireless CommunicationTheory of the IEEE Communications Society. Manuscript received August20, 1997; revised March 16, 1998. This paper was presented in part at IEEEICC’98, Atlanta, GA, June 1998.

The authors are with the Wireless Systems Research Department,AT&T Labs–Research, Red Bank, NJ 07701-7033 USA (e-mail:[email protected]; [email protected]; [email protected]).

Publisher Item Identifier S 0090-6778(98)05169-1.

has been proposed based on the singular-value decompositionor frequency-domain filtering. Time-domain filtering has beenproposed in [8] to further improve the channel estimatorperformance. However, thebest time- or frequency-domainfiltering shapes for channel estimation has not been studied.

In this paper we investigate minimum mean-square-error(MMSE) channel estimation for OFDM systems. We firstderive the MMSE estimator, which makes full use of thecorrelation of the channel frequency response at different timesand frequencies. In particular, for mobile wireless channels, thecorrelation of the channel frequency response at different timesand frequencies can be separated into the multiplication of thetime- and frequency-domain correlation functions. Hence, ourMMSE channel estimator can be a frequency-domain filterusing the fast Fourier transform (FFT), followed by time-domain filters. Since the channel statistics, which depend onthe particular environment, are usually unknown, we present arobustestimator, that is, an estimator that is not sensitive to thechannel statistics. Computer simulation demonstrates that theperformance of OFDM systems using coherent demodulationbased on our channel estimator can be significantly improved.

The paper is organized as follows. Section II introduces thestatistics of the mobile wireless channel and briefly describesthe OFDM system with channel estimation. Then, Section IIIderives the basic MMSE channel estimator for the OFDMsystems. Next, Section IV presents a robust channel estima-tor design approach. Finally, Section V presents computersimulation results to demonstrate the effectiveness of thischannel estimator for OFDM systems in rapid dispersivefading channels.

II. CHANNEL STATISTICS AND OFDM SYSTEMS

Before investigating channel estimation for OFDM systemsin mobile radio channels, we briefly describe the channel sta-tistics, emphasizing theseparation propertyof mobile wirelesschannels, which is crucial for simplifying our MMSE channelestimator. In this section we also briefly describe an OFDMsystem with receiver diversity.

A. Statistics of Mobile Radio Channels

The complex baseband representation [10] of a mobilewireless channel impulse response can be described by

(1)

where is the delay of the th path and is thecorresponding complex amplitude. Due to the motion of the

0090–6778/98$10.00 1998 IEEE

Authorized licensed use limited to: NORTHERN ARIZONA UNIV. Downloaded on February 1, 2010 at 14:55 from IEEE Xplore. Restrictions apply.

LI et al.: ROBUST CHANNEL ESTIMATION FOR OFDM SYSTEMS 903

vehicle, ’s are wide-sense stationary (WSS) narrow-band complex Gaussian processes, which are independent fordifferent paths.

We assume that has the same normalized correlationfunction for all and, therefore, the same normalizedpower spectrum Hence

(2)

where is the average power of theth path.Using (1), the frequency response of the time-varying radio

channel at time is

(3)

Hence, the correlation function of the frequency response fordifferent times and frequencies is

(4)

where is the total average power of the channel impulseresponse defined as

(5)

(6)

It is obvious that Without loss ofgenerality, we also assume that , which, therefore,can be omitted from (4).

From (4), the correlation function of can be sep-arated into the multiplication of atime-domain correlation

and afrequency-domain correlation isdependent on the vehicle speed or, equivalently, the Dopplerfrequency, while depends on the multipath delayspread. With the separation property, we are able to simplifyour MMSE channel estimator described in the next section.

For an OFDM system with block length and tone spacing(subchannel spacing) , the correlation function for differentblocks and tones can be written as

(7)

where

(8)

From Jakes’ model [11]

(9)

where is the zeroth-order Bessel function of the first

(a)

(b)

Fig. 1. OFDM system with channel estimator. (a) Transmitter. (b) Diversityreceiver.

kind, and its Fourier transform (FT) is

if

otherwise(10)

In the above expression , and is theDopplerfrequency, which is related to the vehicle speedand thecarrier frequency by

(11)

where is the speed of light. For example, for a system withcarrier frequency GHz, Hz when the useris moving at 60 mi/h.

B. OFDM Systems with Channel Estimator

The OFDM system with channel estimation considered inthis paper is shown in Fig. 1. The Reed–Solomon (RS) codeacross tones is utilized in the system to correct the burst errorsresulting from frequency-selective fading. Since the phase ofeach subchannel can be obtained by the channel estimator,coherent phase-shift keying (PSK) modulation is used here toenhance the system performance.

For a diversity receiver, the signal from theth antenna atthe th tone and the th block can be expressed as

(12)

In the above expression is additive Gaussian noisefrom the th antenna at theth tone and the th block, withzero-mean and variance We also assume is inde-pendent for different ’s, ’s, or ’s. , the frequencyresponse at theth tone and the th block corresponding tothe th antenna, is assumed independent for different’s,but with the same statistics. is the signal modulatingthe th tone during the th block and is assumed to have unitvariance and be independent for different’s and ’s.

With knowledge of the channel parameters, can beestimated as by an MMSE combiner

(13)

However, the multipath channel parameters are time varying



and are usually unknown. Hence, a channel estimation algo-rithm must be derived to obtain accurate estimation of thechannel parameters.

Since the channel corresponding to each antenna has thesame statistics, the channel estimator for each antenna hasthe same coefficients. Furthermore, the estimator for eachantenna works independently since the signal from the otherantennas carries no information about the channel parameterscorresponding to this antenna. Therefore, the subscriptiseliminated from in the next two sections.

III. MMSE CHANNEL ESTIMATION

If the reference generator in Fig. 1 can generate an idealreference , then a temporal estimation of canbe obtained as

(14)

where the superscript denotes the complex conjugate. Asindicated in the previous section, ’s for different ’sand ’s are correlated; therefore, an MMSE channel estimatorcan be constructed as follows:

(15)

where ’s are selected to minimize

(16)

in the above expression is the number of tones in eachOFDM block.

Denote

...

...

(17)

(18)

(19)

Then, using the separation property (7), it can be shown (seethe Appendix) that the estimator coefficients are given by

(20)

In the above expression is a diagonal matrix with theth diagonal element

(21)

where is a stable one-sided FT

(22)

Fig. 2. Channel estimator for OFDM systems.

which is uniquely determined by

(23)

The direct current (dc) component in can be foundby

(24)

The ’s and ’s are the corresponding eigenvalues andeigenvectors of the frequency-domain correlation matrix,defined as

......

.. ....

(25)

is obviously a unitary matrix.The MMSE channel estimator derived from (20) is shown

in Fig. 2. The unitary linear inverse transform and trans-form in the figure perform the eigendecomposition of thefrequency-domain correlation. The estimator turns off the zeroor small ’s to reduce the estimation noise. For those large

’s, linear filters are used to take advantage of the time-domain correlation.

It should be noted that a channel estimator described in[5] uses only the frequency-domain correlation functions.However, the MMSE estimator described here exploits thechannel correlations in both the time- and frequency-domains,resulting in better performance than the estimator in [5].

As shown in the appendix, the average MMSE of thechannel estimator is

(26)

For Jakes’ model, Then by direct calcu-lation

(27)

(28)



where

(29)

if

if

(30)

If the time-domain correlation is ideal -band-limited, i.e.,

if

otherwise(31)

then

(32)

(33)

For any -band-limited function satisfying

(34)

we have

(35)

with equality if and only if almost everywhere.

In the above derivation the inequality for all

has been used. Hence

(36)

The above inequality suggests that a channel with an ideal

band-limited time-domain correlation gives the worst mean-square-error (MSE) performance among all channels.

IV. ROBUST CHANNEL ESTIMATOR DESIGN

Once the channel statistics, such as the time-domain corre-lation and frequency-domain correlation, are known, the opti-mum channel estimator can be designed. However, in mobilewireless links the channel statistics depend on the particularenvironments, for example, indoor or outdoor, urban or sub-urban, and change with time. Hence, it is not robust to designa channel estimator thattightly matches the channel statistics.

In this section we first analyze the performance degradationdue to a mismatch of the estimator to the channel statistics anddevelop a robust estimator design approach. Then, we brieflydiscuss the design of finite-tap robust estimators.

A. Mismatch Analysis

If an MMSE channel estimator is designed to match achannel with time- and frequency-domain correlationsand , respectively, then its coefficients aredetermined from (20) by

(37)

where the definitions of and are similar to those ofand except that and there are replaced by

and , respectively.For a channel with time- and frequency-domain correlations

and , rather than and , from (16), theMSE for the designed channel estimator is

(38)

where and

ifotherwise.

(39)

Substituting (37) into (38), we obtain a general formula for



the MSE of the mismatched channel estimator

(40)

1) Time-Domain Correlation Mismatch:Assume that thefrequency-domain correlation of the channel estimator matchesthat of the channel, i.e.,

(41)

for , and the time-domain correlation ismismatched. Then

(42)

and

(43)

The first term in the above expression represents the MSEvariation due to the mismatch. By means of (24) and (21),

can be further simplified into

(44)

If , that is, the time-domain correlation ofthe designed estimator is ideal -band-limited, then, for anychannels with zero outside and

(45)

we have

(46)

Therefore

(47)

Hence, if an OFDM channel estimator is designed usingas the time-domain correlation, then the time-domain

correlation mismatch of the estimator will not degrade itsperformance. This suggests that a robust channel estimatorshould use as the time-domain correlation.

2) Frequency-Domain Correlation Mismatch:To analyzethe frequency-domain correlation mismatch, we assume thatthe time-domain correlation of the designed estimator is thesame as that of the channel, that is, , and thefrequency-correlation matrix of the designed estimator has thesame eigenvectors as that of the channel. That is,can beeigendecomposed into

or (48)

where and . and forare generally different.

Although the second assumption seems strange, it is, in fact,reasonable. As indicated in [5], with tolerable leakage, bothmatrices and can be approximated by the discrete FT(DFT) matrix that is defined as

......

(49)

The leakage of the above approximation depends on the guardinterval and the channel multipath delay profile. If the delay

of a path is an integer multiple of the sampling interval,that is, , then all of the energy from the path will bemapped to Otherwise, if the delay is a noninteger multipleof the sampling interval, that is, , then mostof its energy will be contained in and , although theenergy will leak to all ’s. Hence, if the maximum delayspread is , then for all ,where is the symbol duration of OFDM.



Applying the above two assumptions to (40), we get

(50)

where

(51)

In the above derivation we have used (23) and (21). From itsdefinition, and for any

If the channel estimator is designed such that

forfor

(52)

then, for any channel with for and, we have

(53)

However, if

(54)

then

(55)

since for anyFrom the above discussion, a robust estimator, which is

insensitive to the channel statistics, should have an idealband-limited time-domain correlation

and a frequency-domain correlation matrix

......

... (56)

where

, and Notethat is the DFT matrix defined in (49). In this case theaverage MSE of the robust estimator is

(57)

For any channel with and , the averageMSE should be

Fig. 3 shows the MSE of the robust estimator that matchesdifferent Doppler frequencies and delay spreads. As shown, theMSE is almost a constant if is fixed. In particular, let

(58)

where is the baud of the OFDM system. ForOFDM systems satisfying and ,the average MSE of the robust channel estimator is

(59)

If the channel estimator is designed to match the Dopplerspectrum given by (10) and the’s given by (52), then

for

for(60)

(61)

and therefore, from (28), we have

(62)

Hence, compared with the estimator that tightly matches theDoppler spectrum, the performance degradation of the robustchannel estimator is negligible.

B. FIR Channel Estimator

Here, we briefly introduce the design of finite-tap robustestimators. Note that from the previous section, for a robust



(a)

(b)

Fig. 3. Normalized MSE of channel estimator versus Doppler frequency(a) whenSNR = 10 dB and td = 0, 5, 10, 20, and 40�s and (b) whenSNR = 10 dB andfdtd = 0:00008, 0:0008, and0:008, respectively.

estimator

(63)

Let

...

...

...

...

(64)

...

...

...

...

(65)

where is the coefficient of the designed channelestimator. Then, from (A.15), for the FIR channel estimator

with length , we have

(66)

for where

ifotherwise.

(67)

From (66), it is obvious that for For

(68)

where

(69)

......

.. .. . .

.... . .

(70)

(71)

Using derivations similar to those in Section III, the FT ofthe coefficient matrix of the designed FIR channel estimatoris determined by

(72)

where is a diagonal matrix with

(73)

and is the FT of The estimation error of the FIRestimator can be found by

(74)

Hence, for the robust FIR channel estimator, thein Fig. 2is the DFT matrix and the ’s for are

In Fig. 4 the average MSE of a robust FIR channel estimatoris shown as a function of its length. From the figure, for theestimator matching a 40-Hz maximum Doppler frequency, a50-tap FIR estimator is needed to exploit the time-domaincorrelation of the channel parameters, while for one matching a200-Hz maximum Doppler frequency, only a five-tap channelestimator is sufficient.

V. REFERENCEGENERATION AND COMPUTER SIMULATION

In this section we demonstrate the performance improve-ment of an OFDM system with our robust channel estimator.First, we briefly describe the simulated OFDM system.



(a) (b)

(c) (d)

Fig. 4. Normalized MSE versus the length of FIR channel estimator under different channel conditions.

A. System Parameters

In our simulation, we use a two-path Rayleigh-fading chan-nel model [12] with delay from 0 to 40 s and Dopplerfrequency from 10 to 200 Hz. The channels correspondingto different receivers have the same statistics. Two antennasare used for receiver diversity.

To construct an OFDM signal, assume that the entirechannel bandwidth, 800 kHz, is divided into 128 subchannels.The four subchannels on each end are used as guard tones andthe rest (120 tones) are used to transmit data. To make the tonesorthogonal to each other, the symbol duration is 160s. Anadditional 40- s guard interval is used to provide protectionfrom ISI due to channel multipath delay spread. This resultsin a total block length s and a subchannel symbolrate kBd.

To compare the performance of the OFDM system with andwithout the channel estimation, PSK modulation with coherentdemodulation and differential PSK (DPSK) modulation withdifferential demodulation are used, respectively. As in [4], a(40,20) RS code, with each code symbol consisting of threequadrature PSK/differential quadrature PSK (QPSK/DQPSK)symbols grouped in frequency, is used in the system. Hence,each OFDM block forms an RS codeword. The RS decoder

erases ten symbols, based on signal strength, and corrects fiveadditional random errors. Hence, the simulated system cantransmit data at 1.2 Mb/s before decoding or 600 kb/s afterdecoding, over an 800-kHz channel.

B. Reference Generation

An ideal reference is assumed in the derivation of the chan-nel estimator in Section III. In practical systems a reference canbe generated during a training block. In subsequent blocks areference is generated using the received signals. We considerfour possible reference generating schemes.

1) Undecoded/Decoded Dual Mode Reference:If the RSdecoder can successfully correct all errors in an OFDMblock, the reference for the block can be generated bythe decoded data; hence Otherwise,

2) Undecoded Reference: , no matterwhether the RS decoder can successfully correct allerrors in a block or not.

3) Decoded/CMA Dual Mode Reference:The constantmodulus algorithm (CMA) is one of the most effectiveadaptive blind equalization algorithms [13], [14]. Itcan be also used to generate a reference for the



(a)

(b)

Fig. 5. (a) WER and (b) NMSE of robust estimator with different referencesversus SNR for the system without training blocks when the 50-tap channelestimator matches the channel withfd = 40 Hz andtd = 20�s.

OFDM channel estimator. If the RS decoder cansuccessfully correct all errors in a block, the referencefor the block can be generated from the decoded data;hence Otherwise, the reference canuse the projection of on the unit circle, i.e.,

4) Error Removal Reference:If the RS decoder can suc-cessfully correct all errors in a block, the referencefor the block can be generated by the decoded data.Otherwise, the ’s are used instead of ’sfor , respectively.

C. Simulation Results

Figs. 5–8 demonstrate the performance of the channel es-timator using different references under different channelconditions. To get insight into the average behavior of thechannel estimator, we have averaged the performance over10 000 OFDM blocks.

(a)

(b)

Fig. 6. (a) WER and (b) NMSE of robust estimator with different referencesversus SNR for the system with 1% training blocks when the 50-tap channelestimator matches the channel withfd = 40 Hz andtd = 20�s.

Fig. 5 shows the word-error rate (WER) and normalizedMSE (NMSE) for the OFDM system with only the first blockas a training or synchronizing block and for a channel with

Hz and s. From the figure, whendB, the channel estimator using the decoded/undecoded dualmode reference or the undecoded reference can estimate thechannel parameters with NMSE as small as22 dB. Hence,the WER of the system is almost the same as the performanceassuming ideal knowledge of the channel parameters, which isabout 3 dB better than using differential detection. However,due to error propagation through the references, there is a noisethreshold for the channel estimator. For the estimators with thedecoded/undecoded dual mode reference and the undecodedreference, the noise thresholds are 7 and 8 dB, respectively.For the estimators using the other two reference schemes, thenoise thresholds are 12 and 19 dB, respectively. Once the SNRis larger than the noise threshold, the system performance willbe significantly better than that of the OFDM system usingDQPSK.



(a)

(b)

Fig. 7. (a) WER and (b) NMSE of robust estimator with different referencesversus SNR for the system with 1% training blocks when the 50-tap channelestimator matches the channel withfd = 200 Hz andtd = 5�s.

To suppress the error propagation, training blocks are pe-riodically inserted in the data stream. Fig. 6 illustrates theWER and NMSE for the systems with 1% training blocks.In this situation the noise threshold disappears and, hence, theOFDM system with channel estimation has better performancethan the one without channel estimation when the SNR rangesfrom 0 to 20 dB.

For a channel with a Doppler frequency as large as 200 Hz,as indicated in Fig. 7, if 1% training blocks are used, thenthe OFDM system with channel estimation has about a 1.5-dB SNR improvement compared to the one without channelestimation. If the training blocks are increased from 1% to10% of the data, then the required SNR foris reduced by 1 dB compared with the one with 1% trainingblocks, but the required SNR for is almost thesame as before, as shown in Fig. 8.

Figs. 9 and 10 illustrate the robustness of our channelestimator. As indicated in the analysis in Section IV, if achannel estimator is designed to match the channel with 40-Hz maximum Doppler frequency and 20-s maximum delay

(a)

(b)

Fig. 8. (a) WER and (b) NMSE of robust estimator with different referencesversus SNR for the system with 10% training blocks when the five-tap channelestimator matches the channel withfd = 200 Hz andtd = 5�s.

spread, then for all channels with Hz and s,the system performance is not worse than the channel with

Hz and s, as indicated by Fig. 9. However,for channels with Hz or s, such asHz and s or Hz and s, thesystem performance degrades dramatically. On the other hand,as indicated in Fig. 10, if the estimator is designed to match aDoppler frequency or delay spread larger than the actual ones,the system performance degrades only slightly compared withestimation that exactly matches the channel Doppler frequencyand delay spread.

VI. CONCLUSIONS

We have presented the design of robust channel estimatorsfor OFDM systems that make full use of the time- andfrequency-correlations of the rapid dispersive fading wirelesschannel and are insensitive to the channel statistics. Com-puter simulation demonstrates that channel estimation givesabout 2.5-dB improvement when the Doppler frequency is



(a)

(b)

Fig. 9. (a) WER and (b) NMSE of the 50-tap channel estimator matchingfd = 40 Hz andtd = 20�s for channels with differentfd’s and td’s.

40 Hz, and about 1.5-dB improvement when the Dopplerfrequency is as large as 200 Hz. This channel estimationused together with antenna arrays has the potential to providesignificant suppression of cochannel interference in OFDMsystems.

APPENDIX

DERIVATION OF MMSE CHANNEL ESTIMATOR

By the orthogonality principle [15], the ’s aredetermined by

(A.1)

Direct calculation shows that (A.1) is equivalent to

(a)

(b)

Fig. 10. (a) WER and (b) NMSE of the 50-tap channel estimator matchingdifferent fd’s and td’s for the channel withfd = 10 Hz andtd = 5�s.

or

(A.2)

for andwhere

(A.3)

With the separation property (7) of the correlation of thechannel frequency response, (A.2) can be simplified to

(A.4)



Let

...

...

...

...

(A.5)

(A.6)

Then, (A.4) can be written in vector form as

(A.7)

Let the eigendecomposition of be

(A.8)

where is a unitary matrix and is a diagonal matrix with

diagonal elements It is clear that

(A.9)

Substituting (A.8) into (A.7) gives

(A.10)

Consequently

(A.11)

The in the above expression is the pseudoinverse of,

which is also a diagonal matrix with elements

ifif

(A.12)

Denote

(A.13)

then

(A.14)

or

(A.15)

for , where and are the th

elements of and , respectively.

For the with , from [16, Appendix A]

(A.16)

where is a stable one-sided FT

(A.17)

which is uniquely determined by

(A.18)

The dc component in can be found by

(A.19)

For the with , we have for

, which can be also written as (A.16).

Therefore, from (A.13)

(A.20)

where is a diagonal matrix with theth diagonal element

(A.21)

which is zero for the with If we define

(A.22)



then

(A.23)

The MMSE channel estimator for OFDM systems derived(A.23) is shown in Fig. 2.

Substituting (A.2) into (16), the MMSE for the estimationof is

(A.24)

Let

...(A.25)

Then, from (A.23)

(A.26)

where is a diagonal matrix with theth diagonal element

(A.27)

The average MMSE is

(A.28)

where denotes the trace of matrix, defined as the sumof the diagonal elements of the matrix.

ACKNOWLEDGMENT

The authors would like to thank J. Chuang and V. Tarokh fortheir insightful comments, and J. Winters and L. Ariyavisitakulfor helpful discussions.

REFERENCES

[1] J. C.-I. Chuang, “The effect of time delay spread on portable radiocommunications channels with digital modulation,”IEEE J. Select.Areas Commun., vol. SAC-5, pp. 879–889, June 1987.

[2] L. J. Cimini, Jr., “Analysis and simulation of a digital mobile channel us-ing orthogonal frequency division multiplexing,”IEEE Trans. Commun.,vol. COM-33, pp. 665–675, July 1985.

[3] L. J. Cimini, Jr., B. Daneshrad, and N. R. Sollenberger, “ClusteredOFDM with transmitter diversity and coding,” inProc. 1996 IEEEGlobal Telecommunications Conf., London, U.K., Nov. 1996, pp.703–707.

[4] L. J. Cimini, Jr. and N. R. Sollenberger, “OFDM with diversity andcoding for advanced cellular internet services,” inProc. 1997 IEEEGlobal Communications Conf., Phoenix, AZ, Nov. 1997, pp. 305–309.

[5] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O.Borjesson, “On channel estimation in OFDM systems,” inProc. 45thIEEE Vehicular Technology Conf., Chicago, IL, July 1995, pp. 815–819.

[6] , “OFDM channel estimation by singular value decomposition,” inProc. 46th IEEE Vehicular Technology Conf., Atlanta, GA, Apr. 1996,pp. 923–927.

[7] I. Kalet, “The multitone channel,”IEEE Trans. Commun., vol. 37, pp.119–124, Feb. 1989.

[8] V. Mignone and A. Morello, “CD3-OFDM: A novel demodulationscheme for fixed and mobile receivers,”IEEE Trans. Commun., vol.44, pp. 1144–1151, Sept. 1996.

[9] S. B. Weinstein and P. M. Ebert, “Data transmission by frequency-division multiplexing using the discrete Fourier transform,”IEEE Trans.Commun., vol. COM-19, pp. 628–634, Oct. 1971.

[10] R. Steele,Mobile Radio Communications. New York: IEEE Press,1992.

[11] W. C. Jakes, Jr., Ed.,Microwave Mobile Communications. New York:Wiley, 1974.

[12] Y. (G.) Li, J. H. Winters, and N. R. Sollenberger, “Spatial-temporalequalization for IS-136 TDMA systems with rapid dispersive fading andco-channel interference,”IEEE Trans. Veh. Technol., to be published.

[13] D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,”IEEE Trans. Commun., vol.COM-28, pp. 1867–1875, Nov. 1980.

[14] J. R. Treichler and B. G. Agee, “A new approach to multipath correctionof constant modulus signals,”IEEE Trans. Acoust., Speech, SignalProcessing, vol. ASSP-31, pp. 349–372, Apr. 1983.

[15] A. Papoulis,Probability, Random Variables, and Stochastic Processes,3rd ed. New York: McGraw-Hill, 1991.

[16] J. Salz, “Optimum mean-square decision feedback equalization,”BellSyst. Tech. J., vol. 52, pp. 1341–1371, Oct. 1973.

Ye (Geoffrey) Li (S’92–M’95–SM’97) was born inJiangsu, China. He received the B.S.E. and M.S.E.degrees from the Department of Wireless Engi-neering, Nanjing Institute of Technology, Nanjing,China, in 1983 and 1986, respectively, and thePh.D. degree from the Department of ElectricalEngineering, Auburn University, Auburn, AL, in1994.

From 1986 to 1991 he was a Teaching Assistantand then a Lecturer with Southeast University, Na-jing, China. From 1991 to 1994 he was a Research

and Teaching Assistant with Auburn University, Auburn, AL. From 1994to 1996 he was a Postdoctoral Research Associate with the Universityof Maryland, College Park, MD. Since 1996 he has been with AT&TLaboratories—Research, Red Bank, NJ. His general research interests includestatistical signal processing and wireless mobile systems with emphasis onsignal processing in communications.

Dr. Li is currently serving as a guest editor for a special issue on signalprocessing for wireless communications for the IEEE JOURNAL ON SELECTED

AREAS IN COMMUNICATIONS and as an Editor for Wireless CommunicationTheory for the IEEE TRANSACTIONS ON COMMUNICATIONS.



Leonard J. Cimini, Jr. (S’77–M’72–SM’89) wasborn in Philadelphia, PA, on April 19, 1956. Hereceived the B.S.E. (summa cum laude), M.S.E.,and Ph.D. degrees in electrical engineering from theUniversity of Pennsylvania, Philadelphia, in 1978,1979, and 1982, respectively.

Since 1982 he has been with AT&T Laborato-ries—Research, Red Bank, NJ, where his currentresearch interests are in wireless communicationssystems. He is also an Adjunct Professor at theUniversity of Pennsylvania.

Dr. Cimini is a member of Tau Beta Pi and Eta Kappa Nu. He has beenvery active in the IEEE Communications Society and is currently servingas Area Editor for Wireless Communications for the IEEE TRANSACTIONS

ON COMMUNICATIONS and Editor-in-Chief of the IEEE JOURNAL ON SELECTED

AREAS IN COMMUNICATIONS Wireless Communications Series. He received aNational Science Foundation Fellowship during his graduate work.

Nelson R. Sollenberger(S’78–M’81–SM’90–F’96)received the B.S.E. degree from Messiah College,Grantham, PA, in 1979, and the M.S.E. degree fromCornell University, Ithaca, NY, in 1981, both inelectrical engineering.

He currently heads the Wireless Systems Re-search Department, AT&T Laboratories—Research,Red Bank, NJ. His department performs research onnext-generation wireless systems concepts and tech-nologies including high-speed transmission meth-ods, smart antennas and adaptive signal processing,

system architectures and radio link techniques to support wireless multimedia,and advanced voice services. From 1979 through 1986 he was a member ofthe Cellular Radio Development Organization, Bell Laboratories, where heinvestigated spectrally efficient analog and digital technologies for second-generation cellular radio systems. In 1987 he joined the Radio ResearchDepartment, Bellcore, where he was Head of the department from 1993to 1995. At Bellcore, he investigated concepts for the Personal AccessCommunications System (PACS).


Robust Channel Estimation For Ofdm Systems With Rapid...

Documents

Transcript of Robust Channel Estimation For Ofdm Systems With Rapid...