Adapt Modulation

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999 837

An Adaptive Modulation Scheme for SimultaneousVoice and Data Transmission over Fading Channels

Mohamed-Slim Alouini, Member, IEEE, Xiaoyi Tang, and Andrea J. Goldsmith, Member, IEEE

AbstractWe propose a new adaptive modulation technique forsimultaneous voice and data transmission over fading channelsand study its performance. The proposed scheme takes advantageof the time-varying nature of fading to dynamically allocate thetransmitted power between the inphase (

III

) and quadrature (QQQ

)channels. It uses fixed-rate binary phase shift keying (BPSK)modulation on the

QQQ

channel for voice, and variable-rateMMM

-ary amplitude modulation (

MMM

-AM) on theIII

channel for data.For favorable channel conditions, most of the power is allocatedto high rate data transmission on the

III

channel. The remainingpower is used to support the variable-power voice transmission onthe

QQQ

channel. As the channel degrades, the modulation graduallyreduces its data throughput and reallocates most of its available

power to ensure a continuous and satisfactory voice transmission.The scheme is intended to provide a high average spectralefficiency for data communications while meeting the stringentdelay requirements imposed by voice. We present closed-formexpressions as well as numerical and simulation results for theoutage probability, average allocated power, achievable spectralefficiency, and average bit error rate (BER) for both voice anddata transmission over Nakagami-

mmm

fading channels. We alsodiscuss the features and advantages of the proposed scheme. Forexample, in Rayleigh fading with an average signal-to-noise ratio(SNR) of 20 dB, our scheme is able to transmit about 2 Bits/s/Hzof data at an average BER of 10000 5 while sending about 1 Bit/s/Hzof voice at an average BER of 1000 0 2 .

Index Terms Adaptive modulation techniques, integratedvoice and data systems, Nakagami fading.

I. INTRODUCTION

THE RADIO spectrum available for wireless communica-tions is extremely scarce, while demand for mobile andpersonal communications is growing at a rapid pace. Spectral

efficiency is therefore of primary concern in the design of

future wireless communications systems. Furthermore, these

systems will have to support not only voice services but also

Manuscript received January 1997; revised January 1999. The work ofM.-S. Alouini was supported in part by a National Semiconductor GraduateFellowship Award and in part by the Office of Naval Research under GrantNAV-5X-N149510861. The work of X. Tang was supported by a Summer

Undergraduate Fellowship (SURF) award. This is an expanded version ofwork which was presented at the IEEE Vehicular Technology Conference(VTC98), Ottawa, Ont., Canada, May 1998.

M.-S. Alouini was with the Communications Group, Department of Elec-trical Engineering, California Institute of Technology, Pasadena, CA 91125USA. He is now with the Department of Electrical and Computer Engi-neering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:[email protected]).

X. Tang is with the Communications Group, Department of ElectricalEngineering, California Institute of Technology, Pasadena, CA 91125 USA(e-mail: [email protected].

A. J. Goldsmith is with the Department of Electrical Engineering, StanfordUniversity, Stanford, CA 94305 USA (e-mail: [email protected]).

Publisher Item Identifier S 0733-8716(99)03084-X.

data services including facsimile, file transfer, e-mail, and

Internet access.

The need for spectrally efficient communication has recently

led to the development of adaptive transmission techniques.

These techniques take advantage of the time-varying nature

of wireless channels to vary the transmitted power level [1],

symbol rate [2], coding rate/scheme [3], constellation size

[4][8], or any combination of these parameters [9][14]. Their

goal is to improve the link average spectral efficiency (

[Bits/s/Hz]), defined as the average transmitted data rate per

unit bandwidth for a specified average carrier-to-noise ratio

(CNR) and bit error rate (BER). Good performance of theseschemes requires accurate channel estimation at the receiver

and a reliable feedback path between the estimator and the

transmitter. Buffering of the input data may also be required,

since the outage probability of such schemes can be quite high,

especially for channels with low average CNR.

In general, voice transmission has low data rate require-

ments with real-time delay constraints, while data transmis-

sion demands higher rates with less stringent delay require-

ments. This suggests that fixed-rate transmission combined

with power adaptation, where the transmitter adjusts its power

to maintain a constant CNR at the receiver, is well suited

to voice, while bursty variable-rate transmission, which max-

imizes average spectral efficiency, is best suited to datacommunication. In addition, voice and data typically have very

different BER requirements which must be incorporated into

their respective transmission schemes.

Considerable research efforts have been devoted in recent

years for the integration of voice and data for wireline [15] and

wireless communication systems [16][20]. For the latter sys-

tems these efforts focused on the development of a variety of

media access control (MAC) techniques and protocols such as

packet reservation multiple access (PRMA), idle signal multi-

ple access for integrated services (I-ISMA), and dynamic time

division multiple access (D-TDMA). In this paper we proposea new hybrid adaptive scheme which supports simultaneous

voice and data over fading channels.1 Contrary to the MACsolutions, the proposed scheme offers a link layer solution

to the voice and data integration problem by designing the

transmitted signal modulation to support their respective delay,

data rate, and BER requirements. In particular, the proposed

adaptive scheme responds to the fading channel fluctuations by

1 More generally the proposed scheme is capable of handling two inde-pendent information streams which are inherently different: i.e., they may begenerated by different sources and may also differ in their delay and BERrequirements.

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ALOUINI et al.: ADAPTIVE MODULATION SCHEME 839

Fig. 1. Gray mapping for the M -AM constellations.

Fig. 2. Block diagram of the proposed adaptive system.

The channel introduces a multiplicative fading gain , a

phase shift , and additive white Gaussian noise (AWGN)

term with power spectral density [W/Hz]. Hence

the received signal can be written as

(6)

Assuming perfect channel estimation ( and ),

the received signal is first coherently demodulated, then the

(data) signal is passed through an adaptive gain controller

(AGC). Both and signals are passed through matched

filters, then sampled (at times ) to form the

decision variables and given by

(7)

where and are independent zero-mean Gaussian noise

samples with the same variance . For uncoded data

and voice streams and independent hard decisions on the

and channels (see Fig. 2), the conditional (conditioned on

) symbol error rate (SER), SER , for data and BER,

and BER , for voice are given by [34, p. 631]

SER erfc (8)

BER erfc (9)

where , and are the data

and voice instantaneous CNR, respectively, and erfc is the

complementary error function defined by

erfc (10)



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840 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999

Fig. 3. Bit error rate versus received CNR for M -AM.

The data symbol estimates are then passed through an -

ary Gray demapper to obtain an estimate of the source data bits

. Using the same procedure described in [36], [37, Ch. 5] to

obtain the exact BER of square -ary quadrature amplitude

modulation ( -QAM) with two-dimensional Gray coding, wederived exact BER expressions for the -AM modulation

with Gray coding as shown in Fig. 1. The procedure as well as

the exact BER expressions are given in the Appendix. These

exact BER expressions are plotted by the solid lines in Fig. 3

and are in excellent agreement with Monte Carlo simulated

BER values which are plotted by o on the same Fig. 3. For

large CNR, where the probability of symbol error is dominated

by the probability of adjacent symbol error, the BER with Gray

encoding can be approximated by [34, p. 210], [35, p. 265]

BERSER

(11)

For comparison, the dash lines in Fig. 3 show the BER

approximation (11) for different values of . Note that (11)

lower bounds the exact BER expressions (as given in the

Appendix) for all values of and the bound is tighter for

low and high CNR. Using the Chernoff-bound on the erfc( )

function in (11), it can be shown that (11) is upper-bounded

for large CNR by

BERSER

(12)

For comparison, the BER upper-bound (12) is plotted in Fig. 3

by star/solid lines for different values of . Note that (12)

tightly upper bounds the exact BER expressions (as given in

the Appendix) for all values of and for BER ,

which is the BER range of interest for data transmission.Hence we will use this upper-bound (12) to derive closed-

form expressions which upper-bound the average data BER.

In addition, (12) has the advantage of being invertible in

the sense that it provides simple expressions for the data

switching thresholds, as shown in Section III-B.

B. Proposed Adaptive Scheme

We now describe the details of our proposed system shown

in Fig. 2. Assuming a perfect channel fading amplitude esti-

mate 3 (equivalently, a perfect channel CNR estimation

) and a peak power constraint of [W], variable-

power [W] is used on the BPSK of thechannel to ensure continuous fixed-rate voice transmission

at the target voice BER BER i.e., the power allocated to

voice is set to just meet the voice BER requirement

BER . The remaining available power

[W] is dynamically assigned on the channel to support

the (adaptive) -AM below the target data BER BER .

Specifically, based on the channel CNR estimate and on the

3 Accurate channel fading estimation can be obtained via two techniques:transparent tone in band (TTIB) or pilot symbol assisted modulation (PSAM).The usage of these two techniques over fading channels is described in detailsin [37, Sect. 10.3].



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Fig. 4. Outage probability for voice P vo u t

and data P do u t

versus the average CNR .

available power , the decision device at the receiver

selects the signal constellation size to be transmitted on

the channel, configures the demodulator accordingly, and

informs the transmitter about that decision via the feedback

path. We now describe the power allocation for voice and

data as well as the constellation size assignment for datatransmission in more detail.

Our proposed modulation scheme uses the channel state

information at the transmitter to minimize its average power

consumption subject to the peak power constraint. Specifically,

voice transmission is not attempted when the power

required to meet the target voice BER exceeds the peak power

constraint , and in this case a voice outage is declared.

Furthermore, since the voice has to operate at the target

BER , we see from (9) that the power allocated to voice

transmission must be set to

(or equivalently )

otherwise(13)

where erfc BER and erfc denotes the

inverse complementary error function. For data the scheme

responds to the instantaneous channel CNR fluctuation by

varying its constellation size as follows. The data CNR range

is divided into fading regions, and the constellation

size (where is the number of bits per -AM

symbol) is assigned to the th region ( ).

When the received data CNR is estimated to be in the th

region, the constellation size is transmitted. The region

boundaries (or switching thresholds) are set to the

CNR required to achieve the target BER using M -AM over

an AWGN channel. Specifically from (12) we have

BER

(14)

If during voice transmission the remaining available power

is not able to support BPSK on the

channel, then no data is transmitted and a data outage is

declared. Hence the power allocated to data transmission can

be written as

equivalently

otherwise.

(15)

IV. PERFORMANCE ANALYSISIn this section we analyze the performance of the proposed

scheme and we present both numerical and simulation results

which are in perfect agreement, as can be seen in Figs. 411.

All our numerical and simulation results are plotted as a

function of the average CNR for different values of the

Nakagami fading parameter and for different maximum

constellation sizes (levels). Note that all these numerical and

simulation results assume a target uncoded voice BER, BER ,

of 10 , and a target uncoded data BER, BER of 10 . We

used these values to speed up our simulations, however our

analytic derivations apply to any set of BER requirements.



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Fig. 5. Average power allocation for voice h Pv

i = P and data h Pd

i = P versus the average CNR .

We use the MATLAB Communication Toolbox for our

computer simulations. The powers allocated for voice and

data as well as the constellation size for data transmission

are determined at each symbol time according to the fading

level, as explained in Section III. We assume perfect channel

estimation,4 coherent phase detection at the receiver, and Graycoding for bit mapping on the -AM constellations, as shown

in Fig. 1. All our simulations use a 4 level modem which is

able to support up to 16-AM modulation for data transmission.

A. Outage Probability

Since no voice is sent when the required power

exceeds , the voice transmission suffers an outage probability

of

(16)

Substituting (3) in (16), then using [23, p. 364, Eq. (3.381.3)],we can express as

(17)

where is the complementary incomplete

gamma function (or Pryms function) defined by [23, p. 949,

4 We do not address in this paper the effect of channel estimation errors.However, the analytical tools used in [8], [38], and [39] to characterize theeffect of channel estimation errors and feedback delay on adaptive M -QAMmodulations can be used to study the performance of our proposed hybridscheme under imperfect channel estimate conditions.

Eq. (8.350.2)]

(18)

For positive integers [23, p. 949, Eq. (8.352.2)],

(19)

where denotes the degree polynomial defined by

(20)

Thus if we restrict ourselves to integer values of , (17) can

be expressed as

(21)

For the special case of the Rayleigh fading channel ( ),(21) reduces to

(22)

Since no data is sent when the available power is insuf-

ficient to support BPSK on the channel, data transmission

suffers an outage probability of

(23)



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Fig. 6. Overall normalized average power h P i = P allocated to both voice and data versus the average CNR .

where is the first data switching threshold. If we restrict

ourselves to integer values of , (23) can be expressed as

(24)

Hence for the special case of the Rayleigh fading channel

( ), (24) reduces to

(25)

Fig. 4 shows the outage probability and for voice

and data transmission, respectively. In the high average CNR

region (i.e., higher than 4 dB for voice and higher than 9 dB

for data), the higher the average CNR, the lower the outage

probability, as expected. In addition, the scheme meets the

more stringent delay requirements of voice since for a fixed

data suffers a higher outage probability than voice at all

average CNRs. Although these outage curves appear simple

and intuitive, they will in fact be crucial to explain many ofour subsequent performance results.

B. Average Power Allocation

The normalized average power allocated for voice trans-

mission is given by

(26)

If we restrict ourselves to integer values of , (26) can

be expressed as

(27)

For we have [23, p. 951, Eq. (8.359.1)]

(28)

where is the exponential-integral of first order functiondefined as

(29)

Thus for the special case of the Rayleigh fading channel

( ), using (28) in (26) we obtain

(30)

The normalized average power allocated for data transmission

is given by

(31)



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Fig. 7. Achievable spectral efficiency for voice h Rv

i = W and data h Rd

i = W versus the average CNR : (a) m = 1 , (b) m = 2 , and (c) m = 4 .

If we restrict ourselves to integer values of , (31) can

be expressed as

(32)

For the particular case of the Rayleigh fading channel ( ),

using (28) in (31) we get

(33)

Fig. 5 shows in dash lines the normalized average power

allocated for voice transmission . This figure also

displays in solid lines the normalized average power allocated

for data transmission, . The overall normalized average

power is shown in Fig. 6. The

behavior of the curves in Fig. V, which varies in the different

regions of average CNR, can be explained by the outagecurves in Fig. 4. In particular, we see in Fig. 4 that at low s

both voice and data suffer a large outage probability. Hence,

since there is no transmission during outage, the corresponding

power consumptions in Figs. 5 and 6 are low. Consider now

the region of extremely low average CNR (i.e., dB).

Observe that for a fixed in this region, as increases

(i.e., the amount of fading decreases) the power consumption

for voice decreases. This can be explained by the following

argument. At these extremely low values of note from Fig. 4

that the outage probability for voice is essentially the same for

all values. However, when voice transmission is possible

channels with a higher amount of fading will require more

power to maintain a constant voice CNR . Thus, in this

region power consumption for voice increases relative to the

amount of fading. In the medium CNR region (i.e., 2.5 dB

dB), we see that a larger value of corresponds

to a larger power consumption for voice and a smaller one for

data. This can be explained by observing that in Fig. 4 the dataoutage probability in this region is essentially independent of

but the voice outage probability decreases as increases.

Thus, as increases, we are transmitting voice more often and

therefore we must allocate a larger percentage of our power

to voice. In the region of high average CNR (i.e., 12.5 dB

), voice outage probability is small, and since the channel

is quite good, a small fraction of the total power is needed for

the voice transmission. Thus most of the power is allocated to

data transmission. In this favorable region a large (i.e., a

small amount of fading) implies that less power is needed for

voice transmission and therefore more power can be allocated

to high rate -ary data transmission.

C. Achievable Spectral Efficiency

The average link spectral efficiency for voice transmission

is given by

(34)

When is restricted to integer values (34) may be written as

(35)



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which reduces to

(36)

for the special Rayleigh fading case ( ). The average

link spectral efficiency for data transmission is just

the sum of the data rates ( ) associated with the

individual regions, weighted by the probability

that the data CNR falls in the th fading region

(37)

where the s can be expressed using [23, p. 364, Eq.

(3.381.3)] as

(38)

in the most general case and may be written as

(39)

when is restricted to integer values. For the Rayleigh fading

case (39) reduces to

(40)

The dashed lines in Fig. 7 show the average spectral ef-

ficiency for voice transmission . This figure alsoshows the average spectral efficiency for data transmission

for different maximum constellation sizes. For high

average CNRs (above 15 dB) the scheme provides a higher

spectral efficiency for data then for voice and can therefore

meet the higher data rate requirements for data transmission.

The overall average spectral efficiency defined as

the sum of the voice and data average spectral efficiencies

(i.e., ), is shown in Fig. 8. At

high average CNR a large corresponds to a large overall

average spectral efficiency for voice and data. However, at low

average CNR (i.e., less than 4 dB for voice and less than 10

dB for data) a large corresponds to a low overall average

spectral efficiency. This may seem surprising at first but can be

explained by the following argument. Channels with a small

exhibit significant fading and a corresponding wide range

of CNR values. Channels with a large will have most of

their CNR concentrated around the average CNR which is

small in the low average CNR region. Hence channels with a

smaller fading parameter will have a slightly higher spectral

efficiency since the larger CNR fluctuation results in a lower

probability of outage in this low average CNR region (as can

be seen in Fig. 4).

D. Average Bit Error Rate

Voice transmission is always operating at the target BER,

BER . On the other hand, since the choice of the constellation

size for data transmission is done in a conservative fashion,

data is transmitted at an average BER, BER smaller than

BER . This average BER can be computed exactly as the ratio

of the average number of bits in error over the total average

number of transmitted bits

BER

BER

(41)

where

BER BER (42)

It can be shown using (3) and (12) in (42) that BER is

upper-bounded as shown in (43) at the bottom of the page

where

When is restricted to integer values these bounds become

BER

BER

(44)

BER

BER (43)



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Fig. 8. Overall spectral efficiency h R i = W versus the average CNR : (a) m = 1 , (b) m = 2 , and (c) m = 4 .

which reduces in the Rayleigh case ( ) to

BER

BER (45)

Fig. 9 shows the average BER for both voice and data,

for different maximum constellation sizes or levels. Note that

voice transmission is always operating at the target BER,

BER . On the other hand, data is transmitted at an average

BER BER smaller than the target BER , as expected

from our conservative choice of constellation size. Since

data transmission uses the largest constellation often when

the average CNR is high, the average BER prediction as

increases becomes dominated by the BER performance of that

constellation. In addition, at high average CNR as increases

the average BER for data decreases, as one might expect.

However, at low average CNR (i.e., dB) the averageBER for data actually increases as increases. This behavior

may seem surprising at first, but can be explained by the fact

that for dB a large implies that only a small amount

of power is allocated to data transmission, as can be seen in

Fig. 5. Hence since data can only use a small fraction of the

power, its BER increases.

We show the simulated BER for Rayleigh fading ( )

and for Nakagami fading with in Figs. 10 and 11,

respectively. The BER simulation results for voice trans-

mission in these figures are in perfect agreement with the

analytical calculations. However, the simulated BERs for data

transmission are slightly lower than the analytical calculations

since the latter are based on the upper-bound (12) of the

BER performance of -AM with Gray coding. The fact that

this bound is tighter (12) for lower (see Fig. 3) combined

with the fact that the scheme often uses the smallest available

constellation at low average CNRs explains why the overall

average BER upper-bound for data transmission is tighter at

low average CNRs.

V. CONCLUSION

We have proposed an adaptive modulation scheme which

offers a simple and energy-efficient solution to voice and

data integration over fading channels. The proposed design

is intended to provide the user with a high average spectral

efficiency for data communications while meeting the stringent

delay requirements imposed by voice. For favorable chan-

nel conditions, most of the power is allocated to high rate

data transmission by using -AM with a large constellation

size. As the channel degrades, the modem reduces its datathroughput and reallocates most of its available power to

ensure a continuous and satisfactory voice transmission. We

evaluated the performance of our proposed scheme in terms

of outage probability, average allocated power, achievable

spectral efficiency, and average BER for both voice and data

transmission.

Although the design and analyses for our proposed scheme

is quite simple, this simplicity comes at the expense of a spec-

tral efficiency penalty compared to -QAM constellations [5],

[8], [10]. We are currently looking at other possibilities of

improving the spectral efficiency of the proposed scheme. One



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Fig. 9. Average BER for voice h BERv

i and data h BERd

i versus the average CNR : (a) m = 1 , (b) m = 2 , and (c) m = 4 .


i and data h BERd

i versus the average CNR for Rayleigh fading ( m = 1 ).



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i and data h BERd

i versus the average CNR for Nakagami fading ( m = 2 ).

possibility is to multiplex the voice and data bit streams and

to use adaptive symmetric -QAM constellations. Besides

having several parameter choices to optimize, this multiplexing

scheme will exhibit some performance and complexity trade-

offs relative to our proposed technique. Another area of further

study is unequal error protection codes which can be used inconjunction with adaptive modulation to achieve different lev-

els of error protection while improving the throughput of data

communication and further reducing the outage probability of

voice. Design and performance evaluation of multiresolution

adaptive modulations where the constellation of voice and

data are superimposed on the top of one another would also

be another interesting future research direction. Finally, the

use of a speech activity detector (SAD), which segments a

conversation speech into talkspurts and silences [40], can also

improve the overall spectral efficiency. A SAD can be used

in conjunction with an adaptive multimode modem to send

adaptive -QAM [8], [10] for data transmission during the

silences when voice is not transmitted on the channel,and our proposed scheme for simultaneous voice and data

transmission can be used during the talkspurts.

APPENDIX

EXACT BER EXPRESSIONS FOR

-AM OVER AN AWGN CHANNEL

In this Appendix we derive the exact BER expression for

4-AM with Gray coding over an AWGN channel, and give the

exact BER expressions for 8-AM and 16-AM.

For 4-AM the four symbols are symmetrically distributed

about zero with equal distance between two adjacent symbols

as shown in Fig. 1. In Fig. 1, is the amplitude level, is

the symbol duration, is the distance between two

adjacent symbols, and the dashed vertical lines represent the

decision boundaries. Since we consider an AWGN channel

with a noise power spectral density of , the noise is

normally distributed with zero mean and variance.

Consider first the left bit of each 4-AM symbol, as shown in

Fig. 1. A bit error occurs when the bit 1, corrupted by noise,

falls into the boundaries of bit 0 or vice versa. For example,

the left bit of the symbol 10, i.e., 1, will be interpreted 0 when

the noise is larger than . Hence its probability of error

is given by

(46)

where is the Gaussian -function which is related to the

error complementary function as defined in (10) by

erfc (47)

Similarly, , and .

Assuming each of the four symbols has equal probability, the

error probability of the left bit is

(48)

Consider now the right bit of each 4-AM symbol as shown in

Fig. 1. Following the same procedure it can be shown that its



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probability of error is given by

(49)

Hence the average BER for 4-AM is given by

BER -

(50)

On the other hand the average power per symbol is

(51)

Thus

where is the signal bandwidth. The exact BER

of 4-AM can hence be rewritten in terms of average CNR,

, as

BER -

(52)

The exact BER expressions for 8-AM and 16-AM can be

calculated in a similar way and are given by

BER -

(53)

BER -

(54)

ACKNOWLEDGMENT

The authors would like to thank Dr. M. K. Simon of

the NASA Jet Propulsion Laboratory (JPL), Pasadena, CA,

for early discussions regarding unbalanced QPSK and its

applications. They would also like to thank the anonymous

reviewers for their valuable comments and for the suggested

alternative method of multiplexing voice and data bits.

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Mohamed-Slim Alouini (S94M99) was bornin Tunis, Tunisia. He received the Dipl. Ing.degree from the Ecole Nationale Superieure desTelecommunications (TELECOM), Paris, France,and the Diplome dEtudes Approfondies (DEA)degree in electronics from the University of Pierre& Marie Curie (Paris VI), Paris, France, bothin 1993. He received the M.S.E.E. degree fromthe Georgia Institute of Technology (GeorgiaTech), Atlanta, in 1995, and the Ph.D. degree inelectrical engineering from the California Institute

of Technology (Caltech), Pasadena, in 1998.

While completing the DEA thesis, he worked with the optical submarinesystems research group of the French National Center of Telecommunications(CNET-Paris B) on the development of future transatlantic optical links.While at Georgia Tech, he conducted research in the area of K

a

-band satellitechannel characterization and modeling. From June to August 1998, he was apostdoctoral fellow with the Communications Group at Caltech, carrying outresearch on adaptive modulation techniques and on CDMA communications.He joined the Department of Electrical and Computer Engineering, Universityof Minnesota, Minneapolis, in September 1998, where his current researchinterests include statistical modeling of multipath fading channels, adaptivemodulation techniques, diversity systems, and digital communication overfading channels.

Dr. Alouini is the recipient of a National Semiconductor GraduateFellowship Award.

Xiaoyi Tang will receive the B.S. degree in elec-trical engineering from the California Institute ofTechnology (Caltech), Pasadena, in June 1999.

Currently, he is an Undergraduate Research As-sistant with the Communications group at Caltech.

Andrea J. Goldsmith (S94M95) received theB.S., M.S., and Ph.D. degrees in electrical engineer-ing from the University of California, Berkeley in1986, 1991, and 1994, respectively.

From 1986 to 1990, she was with Maxim Tech-nologies, where she worked on packet radio andsatellite communication systems, and from 1991 to1992, she was with AT&T Bell Laboratories, whereshe worked on microcell modeling and channel esti-mation. She was an Assistant Professor of electricalengineering at the California Institute of Technol-

ogy, Pasadena, from 19941998, and is currently an Assistant Professor ofelectrical engineering at Stanford University, Stanford, CA. Her researchincludes work in capacity of wireless channels, wireless communicationtheory, adaptive modulation and coding, joint source and channel coding,and resource allocation in cellular systems.

Dr. Goldsmith is a recipient of the National Science Foundation CAREERDevelopment Award, the ONR Young Investigator Award, two NationalSemiconductor Faculty Development Awards, an IBM Graduate Fellowship,and the David Griep Memorial Prize from the University of California,Berkeley. She is an Editor for the IEEE TRANSACTIONS ON COMMUNICATIONSand the IEEE PERSONAL COMMUNICATIONS MAGAZINE.

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