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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-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
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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.
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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 , 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)
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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
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].
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ALOUINI et al.: ADAPTIVE MODULATION SCHEME 841
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.
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842 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17,
NO. 5, MAY 1999
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)
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ALOUINI et al.: ADAPTIVE MODULATION SCHEME 843
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)
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844 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17,
NO. 5, MAY 1999
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)
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ALOUINI et al.: ADAPTIVE MODULATION SCHEME 845
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)
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846 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17,
NO. 5, MAY 1999
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
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ALOUINI et al.: ADAPTIVE MODULATION SCHEME 847
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.
Fig. 10. Average BER for voice hBERv
i and data hBERd
i versus the average CNR for Rayleigh fading (m = 1).
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848 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17,
NO. 5, MAY 1999
Fig. 11. Average BER for voice hBERv
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
-
ALOUINI et al.: ADAPTIVE MODULATION SCHEME 849
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.