adapt modulation
TRANSCRIPT
-
8/6/2019 Adapt Modulation
1/14
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.
07338716/99$10.00 1999 IEEE
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
2/14
-
8/6/2019 Adapt Modulation
3/14
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)
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
4/14
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].
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
5/14
ALOUINI et al.: ADAPTIVE MODULATION SCHEME 841
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.
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
6/14
842 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999
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)
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
7/14
ALOUINI et al.: ADAPTIVE MODULATION SCHEME 843
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)
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
8/14
844 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999
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)
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
9/14
ALOUINI et al.: ADAPTIVE MODULATION SCHEME 845
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)
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
10/14
846 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999
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
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
11/14
ALOUINI et al.: ADAPTIVE MODULATION SCHEME 847
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 .
Fig. 10. Average BER for voice h BERv
i and data h BERd
i versus the average CNR for Rayleigh fading ( m = 1 ).
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
12/14
848 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999
Fig. 11. Average BER for voice h BERv
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
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
13/14
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 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.
REFERENCES
[1] J. F. Hayes, Adaptive feedback communications, IEEE Trans. Com-mun. Technol., vol. COM-16, pp. 2934, Feb. 1968.
[2] J. K. Cavers, Variable-rate transmission for Rayleigh fading channels,IEEE Trans. Commun., vol. COM-20, pp. 1522, Feb. 1972.
[3] B. Vucetic, An adaptive coding scheme for time-varying channels,IEEE Trans. Commun., vol. 39, pp. 653663, May 1991.
[4] S. Otsuki, S. Sampei, and N. Morinaga, Square-QAM adaptive modula-tion/TDMA/TDD systems using modulation level estimation with Walshfunction, Electron. Lett., vol. 31, pp. 169171, Feb. 1995.
[5] W. T. Webb and R. Steele, Variable rate QAM for mobile radio, IEEETrans. Commun., vol. 43, pp. 22232230, July 1995.
[6] Y. Kamio, S. Sampei, H. Sasaoka, and N. Morinaga, Performanceof modulation-level-controlled adaptive-modulation under limited trans-mission delay time for land mobile communications, in Proc. IEEE
Veh. Technol. Conf. VTC95, Chicago, IL, July 1995, pp. 221225.[7] J. M. Torrance and L. Hanzo, Upper bound performance of adaptive
modulation in a slow Rayleigh fading channel, Electron. Lett., vol. 32,pp. 718719, Apr. 1996.
[8] M.-S. Alouini and A. Goldsmith, Adaptive M-QAM modulation overNakagami fading channels, in Proc. Communication Theory Mini-Conf. (CTMC-VI) in conjunction with IEEE Global Commuication Conf.GLOBECOM97, Phoenix, AZ, Nov. 1997, pp. 218223.
[9] V. O. Hentinen, Error performance for adaptive transmission on fadingchannels, IEEE Trans. Commun., vol. COM-22, pp. 13311337, Sept.1974.
[10] A. Goldsmith and P. Varaiya, Increasing spectral efficiency throughpower control, in Proc. IEEE Int. Conf. on Commun. ICC93, Geneva,Switzerland, June 1993, pp. 600604.
[11] S. M. Alamouti and S. Kallel, Adaptive trellis-coded multiple-phased-shift keying for Rayleigh fading channels, IEEE Trans. Commun., vol.42, pp. 23052314, June 1994.
[12] A. Goldsmith and S. G. Chua, Adaptive coded modulation for fadingchannels, IEEE Trans. Commun., vol. 46, pp. 595602, May 1998.[13] T. Ue, S. Sampei, and N. Morinaga, Symbol rate and modulation level
controlled adaptive modulation/TDMA/TDD for personal communica-tion systems, in IEICE Trans. Commun., vol. E78-B, pp. 11171124,Aug. 1995.
[14] H. Matsuoka, S. Sampei, N. Morinaga, and Y. Kamio, Adaptivemodulation system with variable coding rate concatenated code for highquality multi-media communication systems, IEICE Trans. Commun.,vol. E79-B, pp. 328334, Mar. 1996.
[15] G. Bremer and K. D. Ko, Simultaneous voice and data on the generalswitched telephone network using framed QADM, IEEE Commun.
Mag., vol. 34, pp. 5863, Dec. 1996.[16] D. J. Goodman, R. A. Valenzuela, K. T. Gayliard, and B. Ramamurthi,
Packet reservation multiple access for local wireless communications,IEEE Trans. Commun., vol. 37, pp. 885890, Aug. 1989.
[17] K. Zhang and K. Pahlavan, An integrated voice/data system for mobileindoor radio networks, IEEE Trans. Veh. Technol., vol. 39, pp. 7582,Feb. 1990.
[18] S. Nanda, Analysis of packet reservation multiple access: Voice dataintegration for wireless networks, in Proc. IEEE Global Commun. Conf.GLOBECOM90, San Diego, CA, pp. 19841988.
[19] N. Wilson, R. Ganesh, K. Joseph, and D. Raychaudhuri, Packet CDMAversus dynamic TDMA for multiple access in an integrated voice/dataPCN, IEEE J. Select. Areas Commun., vol. 11, pp. 870884, Aug. 1993.
[20] G. Wu, K. Mukumoto, and A. Fukud, Analysis of an integrated voiceand data transmission system using packet reservation multiple access,
IEEE Trans. Veh. Technol., vol. 43, pp. 289297, May 1994.[21] B. C. Kim and C. K. Un, An efficient wireless voice/data integrated ac-
cess algorithm in noisy channel environments, IEICE Trans. Commun.,vol. E79-B, pp. 13941403, Sept. 1996.
[22] M. Nakagami, The m -distributionA general formula of intensitydistribution of rapid fading, in Statistical Methods in Radio WavePropagation. Oxford, UK: Pergamon, 1960, pp. 336.
Authorized licensed use limited to: Stanford University. Downloaded on June 30,2010 at 01:09:03 UTC from IEEE Xplore. Restrictions apply.
-
8/6/2019 Adapt Modulation
14/14
850 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 17, NO. 5, MAY 1999
[23] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, andProducts, 5th ed. San Diego, CA: Academic, 1994.
[24] H. Suzuki, A statistical model for urban multipath propagation, IEEETrans. Commun., vol. COM-25, pp. 673680, July 1977.
[25] T. Aulin, Characteristics of a digital mobile radio channel, IEEETrans. Veh. Technol., vol. VT-30, pp. 4553, May 1981.
[26] W. R. Braun and U. Dersch, A physical mobile radio channel model,IEEE Trans. Veh. Technol., vol. 40, pp. 472482, May 1991.
[27] A. U. Sheikh, M. Handforth, and M. Abdi, Indoor mobile radio channelat 946 MHz: Measurements and modeling, in Proc. IEEE Veh. Technol.
Conf. VTC93, Secaucus, NJ, May 1993, pp. 7376.[28] S. Basu, E. M. MacKenzie, S. Basu, E. Costa, P. F. Fougere, H. C.Carlson, and H. E. Whitney, 250 MHz/GHz scintillation parametersin the equatorial, polar, and aural environments, IEEE J. Select. AreasCommun., vol. SAC-5, pp. 102115, Feb. 1987.
[29] E. J. Fremouw and H. F. Bates, Worldwide behavior of average VHF-UHF scintillation, Radio Sci., vol. 6, pp. 863869, Oct. 1971.
[30] H. E. Whitney, J. Aarons, R. S. Allen, and D. R. Seeman, Estima-tion of the cumulative probability distribution function of ionosphericscintillations, Radio Sci., vol. 7, pp. 10951104, Dec. 1972.
[31] E. J. Fremouw, R. C. Livingston, and D. A. Miller, On the statisticsof scintillating signals, J. Atmos. Terrest. Phys., vol. 42, pp. 717731,Aug. 1980.
[32] P. K. Banerjee, R. S. Dabas, and B. M. Reddy, C-band and L-bandtransionospheric scintillation experimentSome results for applicationsto satellite radio systems, Radio Sci., vol. 27, pp. 955969, June 1992.
[33] M. K. Simon, Error probability performance of unbalanced QPSKreceivers, IEEE Trans. Commun., vol. COM-26, pp. 13901397, Sept.
1978.[34] M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communica-
tion TechniquesSignal Design and Detection. Englewood Cliffs, NJ:Prentice Hall, 1995.
[35] J. G. Proakis, Digital Communications, 2nd ed. New York, NY:McGraw Hill, 1989.
[36] P. M. Fortune, L. Hanzo, and R. Steele, On the computation of16-QAM performance in Rayleigh-fading channels, IEICE Trans. Com-mun., vol. E75-B, pp. 466475, June 1992.
[37] W. T. Webb and L. Hanzo, Modern Quadrature Amplitude Modulation.New York: IEEE Press, 1994.
[38] A. J. Goldsmith and S. G. Chua, Variable-rate variable-power M-QAMfor fading channels, IEEE Trans. Commun., vol. 45, pp. 12181230,Oct. 1997.
[39] D. L. Goeckel, Adaptive coding for fading channels using outdatedchannel estimates, in Proc. IEEE Veh. Technol. Conf., VTC98, Ottawa,Ont. Canada, May 1998, pp. 19251929.
[40] P. T. Brady, A model for generating on-off speech patterns in two-wayconversation, Bell Syst. Tech. J., vol. 48, pp. 24452472, Sept. 1969.
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.