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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, OCTOBER 2002 781

Mitigating Multiple Access Interference andIntersymbol Interference in Uncoded CDMA

Systems With Chip-Level InterleavingRavishankar H. Mahadevappa and John G. Proakis, Life Fellow

AbstractThe presence of intersymbol interference (ISI), in ad-dition to multiple access interference, severely hampers the per-formance of a code-division multiple-access (CDMA) communi-cation system. In such a situation, channel coding can be used toobtain better performance, but at the cost of a reduction in rateof flow of information. In this paper, it is shown with the help ofsimulation results that the chip-Interleaved CDMA system effec-tively combats ISI without requiring additional channel coding.The system differs from the conventional CDMA system in thesense that, the chip sequence resulting from the pseudo noise (PN)sequence modulation is interleaved before transmission. Two re-

ceivers are proposed, one based on the turbo equalization methodwhich employs a Maximum a posteriori equalizer of exponentialcomplexity and the other based on minimum-mean square error-optimized iterative interference cancellation principles which is oflinear complexity. Simulation results are provided which show thaterror rates close to the no-ISI single-user case can beobtained. Theshortcomings of the coded CDMA with turbo detection system inthe presence of ISI are also discussed.

Index TermsIntersymbol interference (ISI), multiple accessinterference (MAI) algorithm, multiuser detection (MUD), seriallyconcatenated systems, turbo detection.

I. INTRODUCTION

D IRECT-sequence spread-spectrum code-division mul-tiple-access (DS-SS-CDMA) systems have foundapplication in several communication scenarios, prominent

among them being wireless communications. In such a sce-

nario, several users share a given bandwidth and time period

to communicate with each other, using pseudo noise (PN)

sequences assigned to them. The low cross-correlation values

of the PN sequences enable them to communicate fairly reliably

even in the presence of multiple access interference (MAI)

due to the other users, using a simple conventional matched

filter at the receiver. Further, in the presence of strong MAI,

more complicated multiuser detectors (MUDs) can be used to

improve performance. However, in a multipath fading channel

which leads to significant intersymbol interference (ISI), the

error rates are often much worse compared with the case where

there is no ISI.

Manuscript received July 25, 20001; revised March 21, 2001 and November16, 2001; accepted November 16, 2001. The editor coordinating the review ofthis paper and approving it for publication is L. Hanzo.

The authors are with the Departmentof Electrical and Computer Engineering,Northeastern University, Boston, MA 02115 USA (e-mail: ravi@ece.neu.edu;proakis@neu.edu).

Digital Object Identifier 10.1109/TWC.2002.804163

The turbo equalization method, presented by Douillard et al.[2] and also studied by Bauch et al. [3], is shown to be effective

in recovering the loss due to ISI for a binary communication

system. At the transmitter, the data is first coded using a con-

volutional encoder, then interleaved and transmitted. The multi-

path channel is seen as a second encoder. The two encoders and

the interleaver together form a serially concatenated system. In

the detector, as in turbo decoders [1], information is exchanged

between two soft-inputsoft-output (SISO) maximum a poste-

riori (MAP) decoders and decisions are made after several iter-ations. It has been demonstrated that error rates close to that of

the no-ISI case can be obtained with such a system.

The turbo decoding idea has been extended to coded CDMA

systems by Wang and Poor [5], Alexander et al. [6], and Valenti

[8], among others. In coded CDMA, the data of each user

is convolutionally encoded, interleaved, and modulated with

a PN sequence before transmission. The combination of PN

sequence modulation and the multipath channel is considered

as the second encoder. It is claimed in [5] that the system

is able to mitigate the detrimental effects of both MAI and

ISI. However, this is achieved by normalizing the composite

sequence obtained by convolving the PN sequence with the

channel impulse response, before transmission. This is not al-ways possible, since, in general, the channel coefficients are not

known at the transmitter. In addition to that, different receivers

see different channels and it is not possible to normalize the

composite sequence as per the requirements of all channels, at

the transmitter. On the other hand, the chip-Interleaved CDMA

(cI-CDMA) system does not require this normalization and yet

is effective in mitigating the MAI and ISI effects.

The cI-CDMA system differs from the conventional CDMA

system in the sense that the chip sequence resulting from the PN

sequence modulation is interleaved before transmission. Chip-

level interleaving was introduced in the early 80s by Tachikawa

and Marubayashi, [19] (and references therein), as a means of

mitigating burst impulsive noise disturbances. Further, in [20],its effectiveness in the presence of wideband on-off jamming

and tone jamming, has been investigated. Frenger et al. in [21],

have compared performance of cI-CDMA with random signa-

ture sequences with low rate code-spread CDMA in single path

and two-path fading channels.

In this paper, the effectiveness of chip-level interleaving cou-

pled with iterative (turbo) detection based receivers, in combat-

ting ISI and MAI, is studied. The PN sequence modulation is

seen as theouter encoder and no additional encoding is required.

The multipath channel is seen as the second encoder. A receiver

1536-1276/02$17.00 2002 IEEE

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782 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, OCTOBER 2002

Fig. 1. Block diagram of a CDMA system with different multipath channels.

is designed along the lines of the turbo equalization method,

involving two MAP decoders working iteratively on the a pos-

teriori probability (APP) outputs of each other. Simulation re-

sults are presented which show that the system performs well

in the presence of ISI and error rates close to that of the no-ISI

case are obtained. The interleaved CDMA system proposed in[9] considered the case where the channels for all the users

were identical. Further, the interleavers were also assumed to

be identical. Such a model could possibly be used to represent

the downlink scenario. However, in general, the channels for the

different users could be different. Here such a general scenario

is considered. The interleavers for the users are also assumed

to be different.

The turbo equalization method based receiver has computa-

tional complexity which is exponential in the number of users

and lengths of the channels. It is, therefore, not practical when

there is a large number of users in the system. An alternative

low-complexity receiver based on minimum-mean square error

(MMSE)-optimized iterative interference cancellation principleis presented here. The detector is a modified version of the

MMSE-optimized iterated soft-decision interference cancellerby Mller and Huber [17]. It has been modified to work at the

chip level and to cancel the ISI in addition to MAI. There are

also some differences in the way the soft estimates are obtained.

Simulation results are provided which show that the low-com-

plexity receiver too performs well, yielding error rates close to

the no-ISI, single-user error rates.

The paper is organized as follows. Section II introduces the

notation used and illustratesthe effect of ISI on a CDMA system

with an example. Section III discusses the shortcomings of the

coded CDMA system in more detail. The cI-CDMA system

transmitter and the turbo-equalization based receiver structures

are presented in Section IV. The MMSE-optimized chip-level

interference canceller (cIC) based receiver is presented in Sec-

tion V. Conclusions and possible future extensions are pointed

out in Section VI.

II. CONVENTIONAL CDMA SYSTEM AND ISI

In this section, it is shown that the conventional CDMA

system is prone to severe loss in performance in the presence

of ISI, with the help of an example. The optimal MAP decoder

is used and it is assumed that the channel coefficients are

known at the receiver, so that there is no loss due to suboptimal

detection or errors in channel estimation.

The block diagram of a -user DS-SS-CDMA system with

associated multipath channels is shown in Fig. 1. The data is

assumed to be transmitted in blocks of length . Each multipath

channel is represented by a tapped delay line filter with delaysequal to the chip period.

The received signal is passed through a chip-matched filter,

the output of which is sampled at chip rate to yield samples

where

(1)

and isa white Gaussiannoisesample. isan arbitrary delay

for each user, which represents the bit-asynchronous nature ofthe system. It takes values from the set , as-

suming the transmission is chip synchronous. It must be noted

that although chip synchronization may be harder to achieve in

practice, it is a closer approximation to an asynchronous system

compared with the bit-synchronous assumption and simplifies

analysis to a large extent. represents the PN sequence of user

. The sequences are assumed to be of equal length and are

normalized. They are binary valued, i.e., ,

where . are the coeffi-

cients of the paths in the multipath channel of the

th user. is the th user energy. represents the th

bit transmitted by the th user and takes values from the bi-

nary alphabet . is the unique value which satisfiesfor a given

.

Due to the bit-asynchronous nature of the transmission and

the multipath channel, the past bits of the th user also

contribute to the transmitted signal in a given bit period. Here

(2)

where represents the smallest integer greater than or equal

to . An example is shown in Fig. 2.

An optimal MAP receiver which does joint equalization

and multiuser detection can be designed to detect the data.

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M AHADEVAPPA AND PROAKIS: M ITIGAT ING M AI AND INT ER SYMBOL INTE RF ERE NCE IN UNCODE D C DMA S YS TEM S 78 5

Fig. 5. Coded CDMA system.

would result in a deterioration in performance. In the convolu-tion process, the overlapping parts of the PN sequence might

add constructively too, depending on the values of the PN se-

quence and the channel coefficients. This would result in an im-

provement in performance. However, if path gains are modified

such that the composite sequence has unit norm, as is done in

[5], then there is practically no loss. This requires knowledge of

the channel coefficients at the transmitter, which is not always

available. In addition to that, there may be multiple receivers

which see different channels and it is not possible to normalize

the composite sequence as per the requirement of each channel

at the transmitter. In the absence of such a normalization opera-

tion, coded CDMA systems, as shown in Fig. 5, are not effective

in mitigating ISI. In fact, the 4-dB loss seen in the previous sec-

tion remains.

The loss can also be explained intuitively by the observa-

tion that the interleaver in Fig. 5 is not effective in dispersing

the data information throughout the block, since it operates at

the bit level. In other words, the redundancy provided by the

spreading sequence protects the correct bits and the errors re-

sulting from the channel equally so that the outer decoder cannot

effectively recover the loss due to ISI. It may be theoretically

possible to find particular PN sequences which result in con-

structive overlapping for a given ISI channel. However, if the

channel is time-varying, then the transmitter will have to adapt

to the varying conditions and change the PN sequences appro-priately. Further, the transmitter requires feedback from the re-

ceiver in order to realize the gain, which then would require

more bandwidth and lead to other associated expenses. On the

other hand, by introducing chip-level interleaving, the chips are

redistributed in the block so that not all combinations of chipsresult in destructive overlapping. In the next section, it is seen

that this recovers most of the loss due to ISI.

IV. cI-CDMA

A block diagram of the cI-CDMA system is shown in Fig. 6.

The data is transmitted in blocks of length as before, by each

of the -users. The transmission is bit-asynchronous and chip-

synchronous. Each users data is modulated by its respective PN

sequence, resulting in a chip stream of length . This stream

is interleaved and then transmitted.

Here the channel alone is considered as the inner encoder,

as by Douillard et al. [2] and by Bauch et al. [3]. The PN se-quence modulation is seen as the outer encoder. Although for

each user themodulation appears as a simplerepetition code, the

-user combined modulation is actually an block

code with nonbinary output. The optimal receiver for the system

is exponentially complex, not only in terms of the number of

users, but also in terms of the length of the frame. If one has to

find bit sequences which result in minimum error, one has

to consider possible sequences. This complexity is due to

the interleaving operation. The problem is alleviated by using

the turbo equalization method presented in [2], where the data

estimation is done iteratively. Although the method is subop-

timal, it has been shown that, for large interleaver lengths the

performance is very good. A receiver can be built along thelines of the turbo equalization method, with a MAP equalizer

and single-user detectors, as shown in Fig. 6. The symbol de-

tector in [2] is replaced with a MAP equalizer and the channel

decoder is replaced with single-user detectors.

(14)

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788 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, OCTOBER 2002

Fig. 7. Comparison oferrorratesobtainedfor thecI-CDMAsystemwithturboequalization based receiver. .

dB.

Extrinsic information and a priori input to the equalizer for

the next iteration are computed using (17).

Final decisions are made, after several iterations, by passing

the log APP ratio estimates through a sign detector.

C. When s and Channels Are Identical

The particular case of identical interleavers and identical

channels for the -users is explained in detail in [9]. When

the interleavers are identical, one cannot make the assumption

that the variables are independent over , given .

Therefore, the joint APPs

were computed by the MAP equalizer in [9], instead of the

marginal APPs . Further, since the channelswere assumed to be identical, the a posteriori distribution of

the variable

for different combinations of the vector

was computed by the equalizer. A MAP MUD was

required to process the joint APPs and compute the log APP

ratios .

The complexity of the equalizer could be reduced by com-

puting the APP of for fewer than the possible values,

without much loss in performance. In the general case where

the interleavers are not identical, such a method for reducing

complexity cannot be used. However, there is reduction in com-plexity since the MAP MUD is replaced by SUDs.

D. Simulation Results/Observations

The error rates obtained with the cI-CDMA system, for the

same specifications used in Section II-B are plotted in Fig. 7.

Random interleavers were generated for each frame and each

user. The performance of the system is compared with that with

no ISI. It is seen that the error rates with ISI are close to that

obtained when there is no ISI as SNR increases.

It is seen that there is a slight degradation compared with the

results given in [9], where the interleavers were identical, for

the same channel coefficients for both users. The reason for this

Fig. 8. Comparison oferrorratesobtained forthe cI-CDMA systemwith thoseof the conventional CDMA system. dB. as before and

.

is that the two equalizers are different, as pointed out in pre-

vious section. A posteriori distributions of joint events are used

in [9], whereas here they are approximated by marginal distri-

butions. This approximation is more accurate for larger inter-

leaver lengths. In fact, it was observed that the error rates for the

fifth-iteration were even closer to the no-ISI case with frames of

length .

Fig. 8 shows the error rates obtained for the conventional

CDMA system and cI-CDMA system with the channel coef-

ficients used in [2].

These results show that the system is indeed effective against

both ISI and MAI. One of the disadvantages of the system

is the complexity of the receiver. The order of complexity is

for the equalizer, which is prohibitive for a large

number of users. Alternative detectors, which work with a

smaller number of states, like the M-algorithm could be used

for the equalizer. Alexander et al. have presented a SISO

version of the M-algorithm in [6]. In the next section, a SISO

detector of linear complexity is presented.

V. MMSE-OPTIMIZED CHIP-LEVEL INTERFERENCE

CANCELLER (cIC)

An interference canceller is a SISO device which takes in softestimates of interfering bits, cancels their effect in the received

signal and provides a soft estimate for the desired bit. They arefound to be a very good low complexity alternative for detectingdata in CDMA systems, especially when used in an iterativefashion. The iterative detectors can be classified into two cat-egories, based on the way the ICs are used: parallel and serialICs. PICs have been studied by Divsalar et al. [13], Buehrer andWoerner [14]. Here, bits of all users are estimated in parallel ateach stage and their effect is cancelled from the received sam-ples for the next iteration of estimation. In serial ICs [15][17],the most recent estimates of the interferers are used to cancelthe interference. The detector of Patel and Holtzman [15] is notiterative since it stops when all users bits are estimated once,but it could be extended. The detectors based on the expectation

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790 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, OCTOBER 2002

Fig. 9. MRC and SISO equalizer for the th user receiver.

variance of the combined noise and residual interference in (33).It is estimated using the past soft estimates of the interferingchips obtained from the SUDs

(35)

The MMSE estimate can be considered as themean value for a particular distribution on the alphabet

, i.e.

for some and (36)

From (34) and (36), we get

(37)

Note that is in the form of a log APP ratio.is deinterleaved to get which is fed to the SUDs

for further processing. The SUD is essentially similar to the onedescribed in Section IV-B, with additional computations for ob-taining soft estimates of the bits and chips. The relevant opera-tions are described here in terms of , for convenience. Newestimates and chips are computed using

(38)

and

where

for (39)

To summarize, the cIC based cI-CDMA receiver can be givenby the following steps.

1. Obtain MRC outputs using (32).2. Initialize chip estimates , for all and .3. For each ,

For each ,obtain using (33) and requiredcompute new log APP ratio estimates using

(37).

Fig. 10. Comparison of error rates obtained forthe cI-CDMA system with cICbased receiver. dB.

EndObtain by deinterleaving .For each ,

compute estimates using (38)compute estimates using (39)

EndInterleave estimates to get new estimates .End

4. Jump to step 3 for the next iteration.5. Make hard decisions on after sufficient iterations.

C. Simulation Results/Observations

A two-user cI-CDMA system with the low complexityreceiver described above was simulated. The channelsconsidered in Section IV-D were used for these simu-lations too. Fig. 10 shows the error rates obtained for

andFig. 11 shows the error rates obtained with as aboveand . By comparingwith the corresponding optimal error rates for conventionalCDMA system shown in Figs. 4 and 8, it can be inferred thatthe cICbased receiver also effectively removes ISI and MAI.

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M AHADEVAPPA AND PROAKIS: M ITIGAT ING M AI AND INT ER SYMBOL INTE RF ERE NCE IN UNCODE D C DMA S YS TEM S 79 1

Fig. 11. Comparison of error rates obtained for thecI-CDMA system with cIC based receiver. as before and

dB.

It is also seen that the error rates close to the no-ISI,single-user error rates are reached with as few as five iterations,in both cases. Further, the receiver complexity was linearin number of users and length of the channel, whereas thecomplexity of the MAP equalizer was exponential in the sameparameters. From these results, it appears that the cI-CDMA,even with a simple linear complexity receiver, is a very goodalternative to the conventional CDMA system, when there issignificant ISI in the channel.

The cI-CDMA system is effective in single path fading chan-nels too. Although such channels do not introduce ISI, it is seen

that the conventional CDMA system suffers heavy losses, due todeep fading. In the cI-CDMA system, by using sufficiently largeinterleavers, one can ensure on an average that all the chips ofa particular bit do not undergo severe fading, thus, improvingthe average performance. The actual amount of loss recoveredwould depend on the length of the interleaver, the spreadingfactor , the Doppler spread and the number of users in thesystem.

VI. CONCLUDING REMARKS

A modified version of the CDMA communication system,

called the cI-CDMA system was presented. It was shown thatthis system is effective in mitigating both ISI and MAI. Tworeceivers were presented. The turbo equalization method basedreceiver is computationally intensive, since it requires a MAPequalizer whose complexity is exponential in the number ofusers and the lengths of the channels. The MMSE-optimizedcIC based receiveris able to achieve performance close to that ofthe turbo equalization method, with computational complexitylinear in number of users and channel lengths. The results pre-sented assumed that the channel coefficients were known at thereceiver. The effect of channel estimation, convergence charac-teristics of the receiver, effect of Doppler spread, and capacityof the system are topics which require some study.

REFERENCES

[1] C. Berrou and A. Glavieux, Near optimum error-correcting coding anddecoding: Turbo codes,IEEE Trans. Commun., vol. 44, pp. 12611271,Oct. 1996.

[2] C. Douillard, M. Jzquel, C. Berrou, A. Picart, P. Didier, and A.Glavieux, Iterative correction of intersymbol interference: Turboequalization, Eur. Trans. Telecomm., vol. 6, pp. 507511, Sept.Oct.1995.

[3] G. Bauch,H. Khorram, andJ. Hagenauer, Iterative equalization andde-

coding in mobile communication systems, in Proc. Eur. Personal Mo-bile Commun. Conf., Sept. 1997, pp. 307312.

[4] L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linearcodes for minimizing symbol error rate, IEEE Trans. Inform. Theory,vol. IT-20, pp. 284287, Mar. 1974.

[5] X. Wang and H. V. Poor, Iterative (turbo) soft interference cancellationand decoding for coded CDMA, IEEE Trans. Commun., vol. 47, pp.10461061, July 1999.

[6] P. D. Alexander, M. C. Reed, J. A. Asenstorfer, and C. B. Schlegel, It-erative multiuser interference reduction: Turbo CDMA, IEEE Trans.Commun., vol. 47, pp. 10081014, July 1999.

[7] J. G. Proakis, Digital Communications. New York: McGraw-Hill,1995.

[8] M. C. Valenti, Iterative Detection and Decoding for Wireless Commu-nications, Ph.D. Dissertation, Dept. Elect . Eng., Virginia PolytechnicalInst., Blacksburg, VA, July 1999.

[9] R. H. Mahadevappa and J. G. Proakis, Turbo equalization method formitigating multiple access interference and intersymbol interference in

uncoded CDMA systems, in Proc. 2000 Conf. Information SciencesSystems, Princeton, NJ, Mar. 2000, pp. FA6.1FA6.6.

[10] S. Vasudevan and M. K. Varanasi, Optimum diversity combiner basedmultiuser detection for time-dispersive Rician fading CDMA channels,

IEEE J. Select. Areas Commun., vol. 12, pp. 580591, May 1994.[11] U. Fawer and B. Aazhang, A multiuser receiver for code division

multiple access communications over multipath channels, IEEE Trans.Commun., vol. 43, pp. 15561565, Feb./Mar./Apr. 1995.

[12] S. E. Bensley and B. Aazhang, Subspace-based channel estimation forcode division multiple access communication systems, IEEE Trans.Commun., vol. 44, pp. 10091020, Aug. 1996.

[13] D. Divsalar, M. K. Simon, and D. Raphaeli, Improved parallel inter-ference cancellation for CDMA, IEEE Trans. Commun., vol. 46, pp.258268, Feb. 1998.

[14] M. Buehrer and B. D. Woerner, Analysis of adaptive multistage inter-ference cancellation for CDMA using an improved Gaussian approxi-mation, IEEE Trans. Commun., vol. 44, pp. 13081321, Oct. 1996.

[15] P. Patel and J. Holtzman, Analysis of a simple successive interference

cancellation scheme in a DS/CDMA system, IEEE J. Select. AreasCommun., vol. 12, pp. 796807, June 1994.

[16] L. B. Nelson and H. V. Poor, Iterative multiuser receivers for CDMAchannels: An EM-based approach, IEEE Trans. Commun., vol. 44, pp.17001710, Dec. 1996.

[17] R. R. Mllerand J. B. Huber, Iteratedsoft-decision interference cancel-lation for CDMA, in Broadband Wireless Communications, M. Luiseand S. Pupolin, Eds. New York: Springer-Verlag, 1998, pp. 110115.

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

[19] S. Tachikawa and G. Marubayashi, Spread time spread spectrum com-munication systems, in PROC.IEEE GLOBECOM87, vol. 16.5, Nov.1987, pp. 617619.

[20] X. Gui and T. S. Ng, A novel chip-interleaving DS SS system, IEEETrans. Veh. Technol., vol. 49, pp. 2127, Jan. 2000.

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Ravishankar H. Mahadevappa received theB.Tech. degree in electrical and computer engi-neering from the Indian Institute of Technology,Madras, INDIA, in 1994 and the M.S.E.E. degreefrom Northeastern University, Boston, MA, in 1998.

His research interests are in multiuser communica-tions, signal processing, and information theory.

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John G. Proakis (S58M62SM82F84LF97)received the B.S.E.E. degree from the University ofCincinnati, OH, in 1959, the M.S.E.E. degree fromMassachusetts Institute of Technology (MIT), Cam-bridge, in 1961, and the Ph.D. degree from HarvardUniversity, Cambridge, MA, in 1967.

He is currently an Adjunct Professor at theUniversity of California, San Diego, and ProfessorEmeritus at Northeastern University, Boston, MA.

From 1969 to 1998, he was a Faculty Memberat the Electrical and Computer Engineering De-partment, Northeastern University and held the positions of DepartmentChair (19841997), Associate Dean and Director of the Graduate School ofEngineering (19821984), and Acting Dean (19921993). Prior to joiningNortheastern University, he was with GTE Laboratories and the MIT LincolnLaboratory. His professional experience and interests are in the general areas ofdigitalcommunications anddigital signalprocessing. He is theauthor ofDigitalCommunications (New York: McGraw-Hill, 1983, 1st ed.; 1989, 2nd ed.; 1995,3rded.; 2001, 4thed.) andcoauthorofIntroduction to Digital Signal Processing(New York: Macmillan, 1988, 1st ed.; 1992, 2nd ed.; 1996, 3rd ed.); DigitalSignal Processing Laboratory (Englewood Cliffs, NJ: Prentice-Hall, 1991);

Advanced Digital Signal Processing (New York: Macmillan, 1992); Algorithmsfor Statistical Signal Processing (Englewood Cliffs, NJ: Prentice-Hall, 2002);Discrete-Time Processing of Speech Signals (New York: Macmillan, 1992,IEEE Press, 2000); Communication Systems Engineering, (Englewood Cliffs,NJ: Prentice-Hall, 1994, 1st ed.; 2002, 2nd ed.); Digital Signal Processing

Using MATLAB V.4 (Boston, MA: Brooks/Cole-Thomson Learning, 1997,2000); Contemporary Communication Systems Using MATLAB (Boston, MA:Brooks/Cole-Thomson Learning, 1998, 2000). He holds five patents and haspublished over 150 papers.