A new power control function for multirate DS-CDMA systems

896 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 47, NO. 6, JUNE 1999

A New Power Control Function forMultirate DS-CDMA Systems

Teck H. Hu and Max M. K. Liu

Abstract—This paper proposes a closed-form power controlfunction for the reverse link of a multirate single chip-ratevariable processing gain DS-CDMA system in a mobile radioenvironment that assumes a Rayleigh fading channel with log-normal shadowing and path loss. A closed-form open-loop powercontrol function based on a newly definedtraffic exponent isproposed, and nonlinear programming is used to perform theoptimization. In addition, a user model that allows users todynamically switch traffic rates for different connection appli-cations is implemented. Results obtained using random chipsequences demonstrate improvement in the system capacity withthe new power control function compared to the conventionalpower control function. Furthermore, the proposed function alsosimplifies the power control processing.

Index Terms—DS-CDMA, multirate CDMA, power control.

I. INTRODUCTION

FOR the third-generation wireless system, the traffic in-cludes not only voice, but also data, video, images,

files, or any combination thereof. In this new multimediawireless system, different types of traffic will require differentquality of service (QoS) which will result in different optimalsolutions for voice and data, respectively. To provide over-all optimal performance and throughputs, many approacheshave been proposed and studied [1]–[4]. Studies on packet-switched and circuit-switched PCN systems have considered[3] packet-switched and circuit-switched DS-CDMA systems,respectively. Although both packet and circuit-switched DS-CDMA systems have been proposed for wireless multimediaapplications, studies have been focused on packet DS-CDMAsystems because of the demand for multimedia communica-tions in packet-based wireless networks such as WLAN. Asan example, different admission policies for packet DS-CDMAsystems have been proposed by Yang and Geraniotis [1],Pichnaet al. [2] and Geraniotiset al. [4]. More recently, Wuand Kohno [5] presented a wireless multimedia packet CDMAbased on adaptive power control. All the above proposedand studied a packet-switched solution for multimedia traffic.Although packet switching is more efficient for data, it canresult in less than optimal transmission of voice traffic.

Paper approved by J. Wang, the Editor for Wireless Spread Spectrum ofthe IEEE Communications Society. Manuscript received May 6, 1998; revisedSeptember 29, 1998; January 6, 1999.

T. H. Hu is with Lucent Technologies, Bell Labs Innovations, Whippany,NJ 07981 USA (e-mail: [email protected]).

M. M. K. Liu is with Integrated Technology Express, Inc., Santa Clara, CA95051 USA.

Publisher Item Identifier S 0090-6778(99)05007-2.

Circuit-switched DS-CDMA systems have always beenstudied extensively for single-rate bit stream traffic, such asvoice traffic. Current commercially available CDMA systemsbased on IS-95 operate in circuit mode and also assume ahomogeneous user population, where all users have the sametraffic. System analysis of single-rate circuit-switched DS-CDMA systems have been well researched by Pursley [6] andLehnert [7]. However, these studies concentrated on circuit-switched DS-CDMA systems with single-rate traffic. Lately,a circuit-switched DS-CDMA system with multirate trafficwas analyzed by Yao and Geraniotis [8]. Two discretizedpower control functions which can optimize the capacityperformance of the system were proposed. The purpose ofusing power control is to minimize transmission power subjectto maintaining the QoS for each traffic type. As a result,interference is minimized and the system capacity can bemaximized. Although [8] considered multirate traffic, eachuser was limited to a fixed rate transmission, lacking theflexibility where a user can transmit at multiple bit rates andalso changing the bit rates at any time.

A closed-form power control for a multimedia and multirateDS-CDMA system is first introduced in [9] for an additivewhite Gaussian noise (AWGN) channel. Central to the newclosed-form function is a parameter called the traffic exponent,which can be optimized for maximum throughput and, at thesame time, ensure the QoS. Thus, the difficulty in obtaining anoptimal closed-form power control function in [8] is overcome.In addition, the complexity of feedback information to themobile stations is reduced compared to the discretized powercontrol functions in [8] where this feedback is needed. In [10],the system analysis based on the system SNR for a variablerate DS-CDMA system is presented for a similar channel. Inthis paper, we propose a circuit-switched multirate DS-CDMAsystem based on a new closed-form power control functionwhich will maximize the user capacity of the system and atthe same time, allow the random switching of traffic rates.Results on the system capacity when random code sequencesare used are then presented for various combinations of trafficprobabilities and QoS’s. Both dual-rate and tri-rate trafficcompositions of the user are studied.

II. SYSTEM MODEL

The system model for a multirate DS-CDMA system isshown in Fig. 1. For simplicity, a coherent BPSK modulation[6] is assumed and only the reverse link (uplink) transmissionin a single cell is considered. Assume the spread bandwidth foreach connection is fixed at (Hz) and there are a total number

0162–8828/93$03.00 1993 IEEE

HU AND LIU: POWER CONTROL FUNCTION FOR MULTIRATE DS-CDMA SYSTEMS 897

Fig. 1. The DS-CDMA system model.

of active users in the system with the ability of transmittingany one of source bandwidths (Hz)corresponding to different types of multimedia traffic. Theprocessing gain for the different typesof traffic is thus and are the bitperiod and chip duration, respectively.

The transmission signal shown in Fig. 1 can beexpressed as

(1)

where is the th usertransmission power given by

(2)

where is the power control function for user withbaseband data of rate, and is the common power term.

is the periodic DS sequence for usergiven by

where is the th signature periodic sequence of elements( 1, 1), and is the chip waveform which is a time signallimited to is the baseband signal for traffic type

and is an arbitrary phase angle. Since the user may setup a call session for a particular traffic type and modify itstype during the call, the bandwidth for the baseband signal

is a discrete random variable equal to at a certainprior probability That is,

(3)

with probability andBecause user may modify its traffic during a call session, itsprocessing gain (PG), varies correspondingly.In a single-rate DS-CDMA system, the PG of the signal isequal to the code sequence period given by[6]. However,in a multirate DS-CDMA system with multiple PG’s for thedifferent traffic types, is greater than or equal to the largestPG’s since all the different traffic is spread by the same codesequence. Higher rate traffic will have PG smaller than theIn this paper, we highlight the difference betweenand ,generalizing the analysis.

The received signal at the base station is given by

(4)

where is the AWGN with two-sided spectral density, is due to path loss with being the propagation

exponent dependent on the environment andbeing thedistance between the BS and the MS, is the propagationdelay of the th user, and is due to the multipath signalsarriving at the MS, which is modeled as Rayleigh fading withvariance of The factor in (4) representsthe effect of the lognormal shadowing, and is a Gaussianrandom variable with zero mean and variance

The Rayleigh fading and the lognormal shadowing are as-sumed to be mutually independent and independent ofTheyare also assumed to be invariant during the data bit duration,which occurs during slow fading. Channel measurement by thereceiver through some forms of control channels is assumed,enabling the receiver to determine the traffic type (e.g., voiceor data) from the received signal. The derivation to obtainthe system SNR is similar to the analysis presented in [10]for an AWGN channel, and thus will not be fully repeatedhere. Standard Gaussian approximation [6] is used where themultiple access interference from other users is assumed to berandom and treated as additional Gaussian noise to the system.

The for user 0 with rate is

(5)

where is the system multiple access interference (MAI)derived in the Appendix. as derived in the Appendix isgiven by

(6)

(7)

(8)

(9)


and

(10)

and (11), shown at the bottom of the page, whereand

The discrete partial-period aperiodic cross-correlation func-tions and are de-fined by

(12)

(13)

(14)

and

(15)

To facilitate the performance evaluation for the powercontrol method in a multirate DS-CDMA system proposedin the next section, an approximation method to the interusercorrelations or cross correlations by assuming random codesequences is provided here. This allows us to obtain a muchsimplified SNR expression. When the sequences are random,each consists of a sequence of mutually independentrandom variables taking values in [1, 1] with equal prob-ability, and the sequences assigned to different users aremutually independent. With these assumptions, the expectation

of and can bederived and the results are given below

(16)

(17)

(18)

and

(19)

From these results, can be approximated by itsexpected value or ensemble average. Taking the expectationof and substituting the results from (16)–(19), weobtain

(20)

We see that the expected value of is the same forboth and This is intuitively meaningfulbecause the randomness of the sequences means that thepartial-period cross correlation is independent of the user codesequence period. The above result is also consistent with thewell-known result obtained by [6] for the single-rate DS-CDMA system when we substitute with

III. B IT ERROR PROBABILITY

The BER of the system, averaging overand is expressedas

(21)

where is given in (6) and is a Gaussian distributed randomvariable with mean and variance

(11)


Finally, forward error correction is provided by anblock code capable of correcting up toerrors. In particular,we assume that the (23, 12) Golay code is used, which cancorrect up to three channel errors. The BER can then beapproximated by

(22)

IV. PROPOSEDPOWER CONTROL FUNCTION

The key strategy toward power control in a multirate DS-CDMA system is based on reducing the transmission power ofthe traffic with higher PG while still maintaining its requiredminimum BER or QoS. Therefore, a “forced”near–fareffectamong the different traffic types is intentionally applied, wherethe received signal powers of the different traffic types areunequal. This is achieved by controlling the transmissionpower level of each of the different types of traffic and atthe same time attempting to maximize the system capacity.

First, two of the three parameters in the proposed powercontrol function will be explained. The first parameter,,is the power compensation due to path loss between the MSand the BS. This is the only power compensation consideredin the conventional power control function. The objective of

, defined in (10), is to increase the bit energy of traffic withlower bit energy. Therefore, the bit energy of higher bit ratetraffic will be increased to the same level as the bit energy ofthe traffic with lowest bit rate The overall objective ofthe second parameter is therefore to achieve equal bit energyamong all the different traffic types that have different bit rates.

Before introducing the new power control function, let usdefine

traffic exponent

where is a positive unitless parameter that is a function ofthe traffic The proposed power control function for thethuser with traffic type is

(23)

where

is the normalized bit rate Since is themaximum bit rate, is less than or equal to 1.0, and asa result, Thus, depending on , the transmissionpower level of each traffic type is reduced proportionately.

The objective is therefore to effectively reduce the transmis-sion power of lower bit rate traffic while still maintaining itsQoS and at the same time, increase the overall system capacity.

V. OPTIMIZATION

In the previous sections, we have derived the BER expres-sion for a multirate DS-CDMA system with matched filterdetection of BPSK, and we have proposed a new closed-formpower control function based on the newly defined parameter

Given the QoS of traffic , QoS , the proposed power

TABLE ISYSTEM PARAMETERS: DUAL-RATE SYSTEM, CASE I

control function should meet the corresponding QoS require-ment. Under these constraints, the power control function withthe optimum must be obtained so that the objective ofmaximizing the system capacity can be achieved.

Using nonlinear programming, the objective function andthe constraints are defined. The objective of the power controlfunction is to maximize the average number of users that canbe supported by the system

(24)

by optimizing under the QoS constraints

(25)

and

A successive quadratic programming algorithm availablethrough IMSL is adapted to perform the optimization. Using(21) and (22), for each of the traffic types are evaluated.The optimization assumes initial values of, and based onthe constraints of the QoS of each traffic type, the valuesof and are varied in a process to maximize the value

Therefore, the largest value is searched subject to theconstraints of each traffic BER, while are varied. Onceconvergence is achieved, the maximum is obtained inaddition to the optimum for each of the different traffictypes.

VI. RESULTS AND DISCUSSION

The performance of the new power control function willbe evaluated in this section, comparing it with other proposedmethods. In addition, the effects and advantages of the newfunction will also be highlighted.

In order to evaluate the proposed power control function,we applied the multirate DS-CDMA system to the FCC’s un-licensed band at 1.91–1.93 GHz with 20 MHz bandwidth. Thechannel Rayleigh fading and lognormal shadowing parametersare and ,1 respectively. We first assumed adual-rate system with two different traffic types, labeled by thedifferent medium number 0 and 1. Medium 0 could be voicetraffic, and medium 1 could be data traffic. Table I shows thesystem parameters for the two different traffic types.

In the subsequent results, three different power controlfunctions are compared; the conventional method:the equal bit energy method: and the newlyproposed power control function.

1The system is assumed to have undergone closed-loop power control,hence the small shadowing standard deviation used.


Fig. 2. BER versus number of usersK for a dual-rate system withp(k)0 = 0:5 andp(k)1 = 0:5:Eb;max=No = 20 dB, �2 = 0:5; and�� = 1:

Figs. 2–4 show the BER performance for both medium0 and 1 using the three power control functions and withthree different sets of users’ traffic probabilities. Specifically,

and are used. TheQoS for each medium is given in Table I, and an arbitrarytraffic exponent is used for the new power controlfunction. Therefore, the values of used inFigs. 2–4 are not obtained from the optimization process asdiscussed in the previous section. Setting the to20 dB, Fig. 2 shows the BER performance of both medium 0and 1 for the three power control functions when their trafficprobabilities are equal.

For medium 0, we can see that the conventional methodyields the best performance and the new method the worst.The equal bit energy method yields intermediary performance.Because for medium 0, its bit energy is reduced,resulting in higher BER. Contrary to medium 0, the BER per-formance when conventional and new power control functionsare used is reversed for medium 1. This improvement is due tothe reduction in the system MAI variance when the bit energyof medium 0 is reduced. Lower MAI variance contributed tothe better BER performance. For the equal bit energy powercontrol method, both medium 0 and 1 have the same BERas a result of the objective of maintaining equal BER for alltraffic types. An additional advantage of the new power controlfunction is its ability to take into consideration situations whenthe user has different and unequal traffic probabilities. Someresults on those situations are shown next.

In Fig. 3, traffic probabilities equal toare used. Comparing Figs. 2 and 3, we see that when theprobability of the medium 0 (medium with larger PG) isincreased, the BER of both medium 0 and 1 also decreaseswhen the new power control function is used. This is due to thereduction in bit energy of medium 0 which resulted in higher

Fig. 3. BER versus number of usersK for a dual-rate system withp(k)0 = 0:7 andp(k)1 = 0:3: Eb;max=No = 20 dB, �2 = 0:5; and�� = 1:

Fig. 4. BER versus number of usersK for a dual-rate system withp(k)0 = 0:3 andp(k)1 = 0:7: Eb;max=No = 20 dB, �2 = 0:5; and�� = 1:

reduction in total power when the probability of medium 0increases. This reduction in the system total variance willalso lead to better BER performance and eventually, highercapacity, as will be shown later. The increase in BER can beobserved in Fig. 4 when the traffic probabilities are changedto

Assuming an unoptimized value of one for theof medium0 and 1, previous figures showed the effects of differenttraffic probabilities on the traffic BER when different powercontrol functions are used. In the following results that willbe shown, optimized ’s have been obtained and used in the


Fig. 5. Case I. System capacity comparison for a dual-rate integratedvoice/data 1 DS-CDMA system.p0 = p1 = 0:5; �2 = 0:5; and�� = 1:

Fig. 6. Case I. System capacity comparison for a dual-rate integratedvoice/data 1 DS-CDMA system.p0 = 0:7; p1 = 0:3; �

2 = 0:5; and�� = 1:

capacity computation. Figs. 5–7 compare the system capacityfor a dual-rate system when the three different power controlfunctions are employed. Using equal traffic probabilities formediums 0 and 1, Fig. 5 compares the system capacity amongthe three methods. It can be seen that the new power controlfunctions clearly achieve higher capacity than the other twomethods.

The effects of different traffic probabilities on the capacityare shown in Figs. 6 and 7. As the users transmit more medium0 than medium 1 , from Figs. 5 and 6, the number of

Fig. 7. Case I. System capacity comparison for a dual-rate integratedvoice/data 1 DS-CDMA system.p0 = 0:3; p1 = 0:7; �

2 = 0:5; and�� = 1:

TABLE IISYSTEM PARAMETERS: TRI-RATE SYSTEM, CASE II

users that can be supported at dB increasesfrom eight users to 11. Increase in capacity is possible becauseof the higher reduction is system MAI variance when islarger. For the same reason, capacity improvement is less when

is small, as shown in Fig. 7 forNevertheless, in all three cases, the new power control

function achieves higher capacity than both the equal bitenergy and conventional power control methods. For example,Fig. 5 shows capacity improvement is up by 166% comparedto conventional method at and up by 33% com-pared to equal bit energy method when dB.

In the following results, the power control function isapplied to a system with three different bit rates. Threedifferent cases for traffic with varying QoS are analyzed.The system parameters (Case II) for a tri-rate system areshown in Table II. The three different mediums 0, 1, and2 are differentiated by their different PG’s and their QoSrequirements. Medium 2 represents the traffic with the highestbit rate (lowest PG) and highest QoS requirement, and medium0 the lowest bit rate traffic with the lowest QoS.

The system capacity with different medium probabilities iscompared for the three power control methods in Figs. 8–10.Higher system capacity is achieved with the new power controlfunction, compared to both the conventional and equal bitenergy power control function. As in the dual-rate system,higher capacity is obtained when the medium with the larger


Fig. 8. Case II. System capacity comparison of a tri-rate DS-CDMA systemwith p0 = p1 = p2 = 1=3; �2 = 0:5; and�� = 1:

Fig. 9. Case II. System capacity comparison of a tri-rate DS-CDMA systemwith p0 = 0:5; p1 = 0:3; andp2 = 0:2; �2 = 0:5 and�� = 1:

PG has a larger probability than the medium with lower PG.Therefore, a tri-rate system which transmits predominantlyvoice will be able to support more users with the new powercontrol function.

In the following, two different scenarios of traffic withdifferent QoS requirements are analyzed. They are labeled asCases III and IV. In Table III, the new mediums 3 and 4 aredefined. Medium 3 represents low bit rate traffic that requiresa high required QoS and medium 4 represents high bit ratetraffic with a low required QoS. They represent two possibleextreme situations.

Fig. 10. Case II. System capacity comparison of a tri-rate DS-CDMA systemwith p0 = 0:2; p1 = 0:3; andp2 = 0:5; �2 = 0:5 and�� = 1:

TABLE IIISYSTEM PARAMETERS: MEDIUMS 3 AND 4

The performance of the new power control on these twocases will not be shown here but instead, the effect of thenew power control method on the three cases will be shown.Fig. 11 compares the system capacities of the different cases,where for Cases III and IV, medium 2 of Case II is replacedby mediums 3 and 4, respectively. In both cases, because ofthe different PG’s and QoS requirements of the third medium,their system capacities are different.

From medium 2 to medium 3, the PG has increased from63 to 255, although their QoS’s remain the same. Since higherPG traffic has lower BER, Case III is able to satisfy the QoSrequirement specified in Table III better than Case II. In CaseIV, the QoS is compared to in Case II.A lower QoS means that the BER of users can be higher,which occurs when more users are supported by the system.Therefore, Case IV will also perform better than Case II interms of capacity. Fig. 11 shows that Cases III and IV yieldhigher numbers of users that can be supported in the system.This is a direct result of the different medium in the systemand their different QoS’s.

On the other hand, the comparison between Cases III andIV is much more complicated. Fig. 11 shows Case IV withhigher capacity when dB and Case III withhigher capacity when dB. Further studies areneeded to explain this and to predict their performance relativeto their different QoS’s and PG’s.


Fig. 11. System capacity comparison of tri-rate system withp0 = p1 = p2 = 1=3; �2 = 0:5; and�� = 1:

TABLE IVOPTIMUM �’s

The optimum values of ’s for the different cases arepresented in Table IV for the dual-rate DS-CDMA system(Case I) and the different tri-rate DS-CDMA systems (CasesII–IV). These values are obtained using the optimizationtechnique with the objective and constraints explained earlier.We found that different values of ’s are obtained forCases II–IV, because of the different PG’s and QoS’s ofthe third medium. By changing the QoS of just one traffictype, from Cases II–IV, the optimum ’s for the othertraffic types are affected as well. Similarly, when the bitrate of one of the traffic types is increased or decreased, theoptimization resulted in a different set of ’s for all thetraffic types. Therefore, the optimum ’s are a function ofthe following:

• the number of different traffic types with their differentbit rates;

• the PG of each of the different traffic types;• the QoS of each of the different traffic types.

On the other hand, the optimum ’s are independent of thevalue K and the system SNR.

The ’s obtained are also not dependent on the transmis-sion probabilities of the different traffic types. However, thecapacity improvement or the effectiveness of the proposedfunction is very much dependent on the probabilities of thedifferent traffic types, as evidenced in the results presented.

Without using the proposed power control function, trafficwith larger PG will have better BER or performance thantraffic with lower PG. As a result, the disparity between thesystem performance and the required QoS of each traffic typewill become worse. For example, voice traffic will have BERbetter than that required, and the data or video traffic will suffersince their BER’s are much higher than required. Furthermore,different traffic compositions of the user do not have any effecton the system performance. The power control proposed inthis paper corrects the problem by increasing the bit energy ofthe traffic with low PG and decreasing the bit energy of thehigher PG traffic. The correction process consists of two steps.First, by increasing the bit energy of the lower PG traffic,its required QoS can be attained. Second, excessive powerfrom the higher PG traffic is shaved off to a level that is onlynecessary to maintain its BER. The benefit is therefore a lowersystem multiple access interference that resulted in a highersystem capacity. The reduction in the multiple access variancewill be dependent on the traffic probabilities, and it is clear thathigher capacity is obtained when the medium with the largerPG has a larger probability than the medium with lower PG.

VII. CONCLUSIONS

This paper analyzes the performance of a multirate DS-CDMA system using a new closed-form power control func-tion, based on the optimization of a newly defined parametercalled traffic exponent. The new multirate model assumes aprobability for each traffic type of bit rate for the user ,and the user can vary its traffic according to the probabilities ofeach of the different traffic types. It has been demonstrated thatthe proposed power control function performs better than theconventional and equal bit energy methods, while its closed-form expression greatly simplifies computation in adaptingtransmission power in contrast to the method proposed in[8] which required feedback information from the MS’s.Consequently, the MS transceiver design complexity is muchreduced. It has also been shown that the traffic exponent ofthe proposed power control function can be computed withrelative ease using standard optimization techniques and isapplicable to more than two different traffic types with varyingQoS requirements.

One interesting extension of the results presented in thispaper would be to study if the proposed power control functionconverges to a minimum total transmitted power and how thisconvergence is affected by the traffic type probabilities.

The results presented in this paper can also be extended toa multicell environment where intercell interference becomesa factor in the system capacity. The effectiveness of the trafficexponent in reducing the intercell interference needs to bestudied. In the area of power control, the effect of imperfectpower control on the system performance can be furtherinvestigated. For example, because the optimum’s dependon the varying traffic composition, it is important to know thesensitivity of the system capacity to error in computation ofthese parameters. Finally, to apply to bursty multimedia traffic,it is useful to extend the work to a packed-switched CDMAsystem.


APPENDIX

The derivations leading to given in (6) are provided here.The desired signal is

and the system MAI variance to user 0 can be written as

where

and Thus, we can write

where and The MAI variance,following the derivation presented in [10] is given by

where is the ensemble average over all the possibledistances ; the distance between the MS and the BS.Substituting and above into (5) would complete theSNR derivation.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for thecomments and suggestions on the original manuscript thathelped to improve the clarity of the paper.

REFERENCES

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[3] D. Raychaudhuri and N. Wilson, “Multimedia personal communicationnetworks (PCN): System design issues,”Future Directions, pp. 289–304.

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[5] J. Wu and R. Kohno, “Performance evaluation of wireless multimediaCDMA networks using adaptive power control,”IEEE J. Select. AreasCommun., vol. 14, pp. 1688–1697, Dec. 1996.

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[10] , “DS-CDMA system with variable-rate traffic,”IEEE Commun.Lett., vol. 2, no. 3, pp. 64–66, Mar. 1998.

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Teck H. Hu received the B.Eng. degree withfirst class honors from the University of Malaya,Malaysia, in 1989 and the M.Eng. degree fromthe National University of Singapore, Singapore,in 1992. He obtained the Ph.D. degree in electricalengineering from the University of Arizona, Tucson,in 1997.

He is currently a Member of the Technical Staffat Lucent Technologies, Whippany, NJ, where he isresponsible for analyzing intersystem interferenceand spectrum coordination issues for the AirLoop

system. His research interests include performance analysis of widebandCDMA systems and spreading code design.

Max M. K. Liu was born in Taiwan, R.O.C. Hereceived the B.S.E.E. degree from National TaiwanUniversity in 1981 and the M.S. and Ph.D. degreesfrom University of California, Berkeley, in 1985 and1987, respectively.

From 1987 to 1989, he was a Member of Tech-nical Staff at Bellcore, Red Bank, NJ. He wasinvolved in SONET and B-ISDN standards devel-opment. From 1989 to 1995, he was an AssistantProfessor at the University of Arizona, Tucson. Hehad active research work in the areas of optical

communications, video networking, and wireless communications. From 1995to 1997, he was an Engineering Manager at Quickturn Design Systems, SanJose, CA. He was responsible for telecommunication projects for advancedIC system development. Since 1997, he has been with Integrated TelecomExpress (ITeX), Santa Clara, CA. He currently serves as the Vice Presidentand leads the ADSL technology development. He is also active in ANSIT1E1.4 and ITU-T standard meetings. He is an author of the bookPrinciplesand Applications of Optical Communications(Irwin, 1996).

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A new power control function for multirate DS-CDMA systems