an adaptive modulation scheme for simultaneous voice and data transmission over fading channels

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-rate MMM -ary amplitude modulation (MMM -AM) on the III 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 ontheQQQ channel. As the channel degrades, the modulation graduallyreduces its data throughput and reallocates most of its availablepower 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 105 while sending about 1 Bit/s/Hzof voice at an average BER of 102.

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. Spectralefficiency is therefore of primary concern in the design offuture wireless communications systems. Furthermore, thesesystems 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 SummerUndergraduate 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 Electrical

Engineering, California Institute of Technology, Pasadena, CA 91125 USA(e-mail: [email protected]. J. Goldsmith is with the Department of Electrical Engineering, Stanford

University, 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, andInternet 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 natureof 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]. Theirgoal is to improve the link average spectral efficiency ([Bits/s/Hz]), defined as the average transmitted data rate perunit 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 receiverand a reliable feedback path between the estimator and thetransmitter. 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 combinedwith power adaptation, where the transmitter adjusts its powerto maintain a constant CNR at the receiver, is well suitedto voice, while bursty variable-rate transmission, which max-imizes average spectral efficiency, is best suited to datacommunication. In addition, voice and data typically have verydifferent BER requirements which must be incorporated intotheir respective transmission schemes.Considerable research efforts have been devoted in recent

years for the integration of voice and data for wireline [15] andwireless communication systems [16][20]. For the latter sys-tems these efforts focused on the development of a variety ofmedia access control (MAC) techniques and protocols such aspacket reservation multiple access (PRMA), idle signal multi-ple access for integrated services (I-ISMA), and dynamic timedivision multiple access (D-TDMA). In this paper we proposea new hybrid adaptive scheme which supports simultaneousvoice and data over fading channels.1 Contrary to the MACsolutions, the proposed scheme offers a link layer solutionto the voice and data integration problem by designing thetransmitted signal modulation to support their respective delay,data rate, and BER requirements. In particular, the proposedadaptive scheme responds to the fading channel fluctuations by

1More 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.

07338716/99$10.00 1999 IEEE

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

giving priority voice communication in one of the quadraturechannels, while devoting the other quadrature component tovariable-rate data communication. For bad channel conditions,most of the transmitted power is allocated to ensure continuousand satisfactory transmission of speech communications. Asthe channel conditions improve, most of the transmitted poweris reallocated to high data rate transmission. Hence the goalof the scheme is to provide a high average spectral efficiencyfor data communications while meeting the stringent delayrequirements of speech communications. The power alloca-tion, as well as the constellations selection for the proposedschemes constant-power, will be discussed in more detail inSection III.The remainder of this paper is organized as follows. Section

II describes the channel model. Section III presents the detailsof the proposed scheme. The performance of this scheme, as-suming perfect channel estimation and negligible time delay, isanalyzed in Section IV. In particular closed-form expressionsfor the outage probability, average allocated power, achievablespectral efficiency, and average BER for both voice and datatransmission are derived. Numerical and simulation results thatallow discussion of the behavior of the proposed scheme arealso presented. Our conclusions are given in Section V.

II. CHANNEL MODELWe consider a slowly varying flat-fading channel changing

at a rate much slower than the symbol data rate, so the channelremains roughly constant over hundreds of symbols. Weassume that the multipath fading environment is characterizedby the Nakagami- probability density function (PDF). Hencethe channel fading amplitude is given by [22, Eq. (11)]

(1)

where is the average received power, is theNakagami fading parameter , and is thegamma function defined by [23, p. 942, Eq. (8.310.1)]

(2)

Given the channel fading amplitude , a signal power ,a signal bandwidth of [Hz], and a noise power densityof [W/Hz], let us define the CNR . Byusing a standard transformation of random variables, it can beshown that the CNR is distributed according to a gammadistribution, , given by

(3)

where is the average CNR.We use the Nakagami- distribution since it can represent

a range of multipath channels via the parameter [22], whichcan be interpreted as the amount of fading on the channel: as

increases the amount of fading on the channel decreases.In particular, the Nakagami- distribution includes the one-sided Gaussian distribution ( , which corresponds toworst-case fading) and the Rayleigh distribution ( )

as special cases. Furthermore, the Nakagami- distributionclosely approximates the Nakagami- (Hoyt) [22, Eq. (59)] andthe Nakagami- (Rice) [22, Eq. (56)] distributions. Finally,and perhaps most importantly, the Nakagami- distributionoften gives the best fit to land-mobile [24][26], indoor-mobile[27] multipath propagation, as well as scintillating ionosphericsatellite radio links [28][32].

III. PROPOSED MODULATION SCHEMEThe proposed modulation scheme is a generalized and adap-

tive version of the unbalanced quadrature phase shift keying(UQPSK) [33], [34, p. 622], which also offers the capabilityof handling two different types of data. For instance, UQPSKwas used by the space shuttle and the tracking and data relaysatellite system (TDRSS) to communicate scientific data onthe inphase ( ) channel and operational/telemetry data on thequadrature ( ) channel. In our case we propose to devote thechannel to data communications while transmitting voice overthe channel. In contrast to UQPSK, where binary phaseshift keying (BPSK) modulation is used on both channels,our scheme uses BPSK on the channel for voice and -ary amplitude modulation ( -AM) [34, p. 219], [35, p. 272][also known as -ary amplitude shift keying ( -ASK)]2 onthe channel for data. The proposed scheme suffers a spectralefficiency penalty compared to -QAM constellations [5],[8], [10]. However the scheme has the advantage of providinga solution which lends itself to simplicity of design andperformance evaluation, as we will see next. In this section wefirst introduce the hybrid BPSK/ -AM modulation scheme.We then present the details of the proposed adaptive scheme.

A. Hybrid BPSK/ -AM Modulation SchemeA block diagram of the proposed hybrid BPSK/ -AM

modulation scheme is shown in Fig. 2. Following the form ofthe UQPSK modulation [34, p. 622], the hybrid BPSK/ -AMtransmitted signal can be written as

(4)

where is the radian carrier frequency, and and arethe powers of the (data) and (voice) components of ,respectively. In (4), and correspond to the data andvoice symbol streams, respectively; that is

(5)

where is a unit power shaping pulse of duration (thesignal bandwidth is hence ). In (5) ( ,

, , ) are the Gray-mapped data symbols of thedata bits (as depicted in Fig. 3) and are the voicebits.

2We use here a symmetric M -AM constellation in which the signal pointsare symmetrically located about the origin as shown in Fig. 1.

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 , aphase shift , and additive white Gaussian noise (AWGN)term with power spectral density [W/Hz]. Hencethe 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 matchedfilters, then sampled (at times ) to form thedecision variables and given by

(7)

where and are independent zero-mean Gaussian noisesamples with the same variance . For uncoded dataand voice streams and independent hard decisions on theand 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 dataand voice instantaneous CNR, respectively, and erfc is thecomplementary error function defined by

erfc (10)


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 amplitudemodulation ( -QAM) with two-dimensional Gray coding, wederived exact BER expressions for the -AM modulationwith Gray coding as shown in Fig. 1. The procedure as well asthe exact BER expressions are given in the Appendix. Theseexact BER expressions are plotted by the solid lines in Fig. 3and are in excellent agreement with Monte Carlo simulatedBER values which are plotted by o on the same Fig. 3. Forlarge CNR, where the probability of symbol error is dominatedby the probability of adjacent symbol error, the BER with Grayencoding can be approximated by [34, p. 210], [35, p. 265]

BERSER (11)

For comparison, the dash lines in Fig. 3 show the BERapproximation (11) for different values of . Note that (11)lower bounds the exact BER expressions (as given in theAppendix) for all values of and the bound is tighter forlow and high CNR. Using the Chernoff-bound on the erfc( )function in (11), it can be shown that (11) is upper-boundedfor large CNR by

BERSER

(12)

For comparison, the BER upper-bound (12) is plotted in Fig. 3by star/solid lines for different values of . Note that (12)tightly upper bounds the exact BER expressions (as given inthe 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 inthe sense that it provides simple expressions for the dataswitching thresholds, as shown in Section III-B.

B. Proposed Adaptive SchemeWe 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 transmissionat the target voice BER BER i.e., the power allocated tovoice is set to just meet the voice BER requirementBER . The remaining available power[W] is dynamically assigned on the channel to supportthe (adaptive) -AM below the target data BER BER .Specifically, based on the channel CNR estimate and on the

3Accurate 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].


Fig. 4. Outage probability for voice P vout

and data P dout

versus the average CNR .

available power , the decision device at the receiverselects the signal constellation size to be transmitted onthe channel, configures the demodulator accordingly, andinforms the transmitter about that decision via the feedbackpath. We now describe the power allocation for voice anddata 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 powerconsumption subject to the peak power constraint. Specifically,voice transmission is not attempted when the powerrequired to meet the target voice BER exceeds the peak powerconstraint , and in this case a voice outage is declared.Furthermore, since the voice has to operate at the targetBER , we see from (9) that the power allocated to voicetransmission must be set to

(or equivalently )otherwise

(13)where erfc BER and erfc denotes theinverse complementary error function. For data the schemeresponds to the instantaneous channel CNR fluctuation byvarying its constellation size as follows. The data CNR rangeis divided into fading regions, and the constellationsize (where is the number of bits per -AMsymbol) is assigned to the th region ( ).When the received data CNR is estimated to be in the thregion, the constellation size is transmitted. The regionboundaries (or switching thresholds) are set to the

CNR required to achieve the target BER using M -AM overan AWGN channel. Specifically from (12) we have

BER

(14)If during voice transmission the remaining available power

is not able to support BPSK on thechannel, then no data is transmitted and a data outage is

declared. Hence the power allocated to data transmission canbe 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 resultswhich are in perfect agreement, as can be seen in Figs. 411.All our numerical and simulation results are plotted as afunction of the average CNR for different values of theNakagami fading parameter and for different maximumconstellation sizes (levels). Note that all these numerical andsimulation results assume a target uncoded voice BER, BER ,of 10 , and a target uncoded data BER, BER of 10 . Weused these values to speed up our simulations, however ouranalytic derivations apply to any set of BER requirements.


Fig. 5. Average power allocation for voice hPv

i=P and data hPd

i=P versus the average CNR .

We use the MATLAB Communication Toolbox for ourcomputer simulations. The powers allocated for voice anddata as well as the constellation size for data transmissionare determined at each symbol time according to the fadinglevel, as explained in Section III. We assume perfect channelestimation,4 coherent phase detection at the receiver, and Graycoding for bit mapping on the -AM constellations, as shownin Fig. 1. All our simulations use a 4 level modem which isable to support up to 16-AM modulation for data transmission.

A. Outage ProbabilitySince no voice is sent when the required power

exceeds , the voice transmission suffers an outage probabilityof

(16)

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

(17)

where is the complementary incompletegamma function (or Pryms function) defined by [23, p. 949,

4We 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) canbe 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 transmissionsuffers an outage probability of

(23)


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

where is the first data switching threshold. If we restrictourselves 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 voiceand data transmission, respectively. In the high average CNRregion (i.e., higher than 4 dB for voice and higher than 9 dBfor data), the higher the average CNR, the lower the outageprobability, as expected. In addition, the scheme meets themore stringent delay requirements of voice since for a fixed

data suffers a higher outage probability than voice at allaverage CNRs. Although these outage curves appear simpleand intuitive, they will in fact be crucial to explain many ofour subsequent performance results.

B. Average Power AllocationThe normalized average power allocated for voice trans-

mission is given by

(26)

If we restrict ourselves to integer values of , (26) canbe 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 transmissionis given by

(31)


Fig. 7. Achievable spectral efficiency for voice hRv

i=W and data hRd

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) canbe 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 powerallocated for voice transmission . This figure alsodisplays in solid lines the normalized average power allocatedfor data transmission, . The overall normalized averagepower is shown in Fig. 6. Thebehavior of the curves in Fig. V, which varies in the differentregions of average CNR, can be explained by the outagecurves in Fig. 4. In particular, we see in Fig. 4 that at low sboth voice and data suffer a large outage probability. Hence,since there is no transmission during outage, the correspondingpower consumptions in Figs. 5 and 6 are low. Consider nowthe 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 consumptionfor voice decreases. This can be explained by the followingargument. At these extremely low values of note from Fig. 4that the outage probability for voice is essentially the same forall values. However, when voice transmission is possible

channels with a higher amount of fading will require morepower to maintain a constant voice CNR . Thus, in thisregion power consumption for voice increases relative to theamount of fading. In the medium CNR region (i.e., 2.5 dB

dB), we see that a larger value of correspondsto a larger power consumption for voice and a smaller one fordata. 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 andtherefore we must allocate a larger percentage of our powerto voice. In the region of high average CNR (i.e., 12.5 dB

), voice outage probability is small, and since the channelis quite good, a small fraction of the total power is needed forthe voice transmission. Thus most of the power is allocated todata transmission. In this favorable region a large (i.e., asmall amount of fading) implies that less power is needed forvoice transmission and therefore more power can be allocatedto high rate -ary data transmission.

C. Achievable Spectral EfficiencyThe average link spectral efficiency for voice transmission

is given by

(34)

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

(35)


which reduces to

(36)for the special Rayleigh fading case ( ). The averagelink spectral efficiency for data transmission is justthe sum of the data rates ( ) associated with theindividual 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 fadingcase (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 highaverage CNRs (above 15 dB) the scheme provides a higherspectral efficiency for data then for voice and can thereforemeet the higher data rate requirements for data transmission.The overall average spectral efficiency defined asthe sum of the voice and data average spectral efficiencies(i.e., ), is shown in Fig. 8. Athigh average CNR a large corresponds to a large overallaverage spectral efficiency for voice and data. However, at lowaverage CNR (i.e., less than 4 dB for voice and less than 10dB for data) a large corresponds to a low overall averagespectral efficiency. This may seem surprising at first but can be

explained by the following argument. Channels with a smallexhibit significant fading and a corresponding wide range

of CNR values. Channels with a large will have most oftheir CNR concentrated around the average CNR which issmall in the low average CNR region. Hence channels with asmaller fading parameter will have a slightly higher spectralefficiency since the larger CNR fluctuation results in a lowerprobability of outage in this low average CNR region (as canbe seen in Fig. 4).

D. Average Bit Error RateVoice transmission is always operating at the target BER,

BER . On the other hand, since the choice of the constellationsize for data transmission is done in a conservative fashion,data is transmitted at an average BER, BER smaller thanBER . This average BER can be computed exactly as the ratioof the average number of bits in error over the total averagenumber of transmitted bits

BER

BER

(41)

where

BER BER (42)

It can be shown using (3) and (12) in (42) that BER isupper-bounded as shown in (43) at the bottom of the pagewhere

When is restricted to integer values these bounds become

BER

BER

(44)

BER

BER (43)


Fig. 8. Overall spectral efficiency hRi=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 thatvoice transmission is always operating at the target BER,BER . On the other hand, data is transmitted at an averageBER BER smaller than the target BER , as expectedfrom our conservative choice of constellation size. Sincedata transmission uses the largest constellation often whenthe average CNR is high, the average BER prediction asincreases becomes dominated by the BER performance of thatconstellation. In addition, at high average CNR as increasesthe 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 behaviormay seem surprising at first, but can be explained by the factthat for dB a large implies that only a small amountof power is allocated to data transmission, as can be seen inFig. 5. Hence since data can only use a small fraction of thepower, 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 theanalytical calculations. However, the simulated BERs for data

transmission are slightly lower than the analytical calculationssince the latter are based on the upper-bound (12) of theBER performance of -AM with Gray coding. The fact thatthis bound is tighter (12) for lower (see Fig. 3) combinedwith the fact that the scheme often uses the smallest availableconstellation at low average CNRs explains why the overallaverage BER upper-bound for data transmission is tighter atlow average CNRs.

V. CONCLUSIONWe have proposed an adaptive modulation scheme which

offers a simple and energy-efficient solution to voice anddata integration over fading channels. The proposed designis intended to provide the user with a high average spectralefficiency for data communications while meeting the stringentdelay requirements imposed by voice. For favorable chan-nel conditions, most of the power is allocated to high ratedata transmission by using -AM with a large constellationsize. As the channel degrades, the modem reduces its datathroughput and reallocates most of its available power toensure a continuous and satisfactory voice transmission. Weevaluated the performance of our proposed scheme in termsof outage probability, average allocated power, achievablespectral efficiency, and average BER for both voice and datatransmission.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 ofimproving the spectral efficiency of the proposed scheme. One


Fig. 9. Average BER for voice hBERv

i and data hBERd

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


i and data hBERd

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



i and data hBERd

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

possibility is to multiplex the voice and data bit streams andto use adaptive symmetric -QAM constellations. Besideshaving several parameter choices to optimize, this multiplexingscheme will exhibit some performance and complexity trade-offs relative to our proposed technique. Another area of furtherstudy 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 datacommunication and further reducing the outage probability ofvoice. Design and performance evaluation of multiresolutionadaptive modulations where the constellation of voice anddata are superimposed on the top of one another would alsobe another interesting future research direction. Finally, theuse of a speech activity detector (SAD), which segments aconversation speech into talkspurts and silences [40], can alsoimprove the overall spectral efficiency. A SAD can be usedin conjunction with an adaptive multimode modem to sendadaptive -QAM [8], [10] for data transmission during thesilences when voice is not transmitted on the channel,and our proposed scheme for simultaneous voice and datatransmission can be used during the talkspurts.

APPENDIXEXACT BER EXPRESSIONS FOR-AM OVER AN AWGN CHANNEL

In this Appendix we derive the exact BER expression for4-AM with Gray coding over an AWGN channel, and give theexact 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, isthe symbol duration, is the distance between twoadjacent symbols, and the dashed vertical lines represent thedecision boundaries. Since we consider an AWGN channelwith a noise power spectral density of , the noise isnormally distributed with zero mean and variance

.

Consider first the left bit of each 4-AM symbol, as shown inFig. 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 whenthe noise is larger than . Hence its probability of error

is given by

(46)

where is the Gaussian -function which is related to theerror complementary function as defined in (10) by

erfc (47)

Similarly, , and .Assuming each of the four symbols has equal probability, theerror probability of the left bit is

(48)

Consider now the right bit of each 4-AM symbol as shown inFig. 1. Following the same procedure it can be shown that its


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 BERof 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)

ACKNOWLEDGMENTThe 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 itsapplications. They would also like to thank the anonymousreviewers for their valuable comments and for the suggestedalternative 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 submarine

systems 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 Ka

-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 Graduate

Fellowship 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 CAREER

Development 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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