Variable Rate Adaptive Trellis Coded QAM
for
High Bandwidth Efficiency
Applications in Rayleigh Fading Channels
Vincent
K.N.
Lau and Malcolm
D.
Macleod
email: knlauOlucent .com, mdmOeng.cam.ac.uk
Signal Processing and Communication Group,
Department of Engineering, University
of
Cambridge, CB2 lPZ,
UK
12
September
1997
Abstract
operation of the ATCQAM scheme. Simulation results are
presented and discussed in section
3.
Finally, in section
4,
we
A
high bandwidth efficiency variable rate adaptive channel conclude with
a
summary of results.
coding scheme, ATCQAM, is proposed. Known pilot symbols
are transmitted periodically to aid demodulation. Past chan-
nel states are fed back to the transmitter with delay. Current
2
Adaptive Trellis Coded QAM
channel state is then predicted
at
the transmitter to decide on
the appropriate modulation mode for the current symbol.
At
good channel states, high level modulation is used to boost
up the average throughput. At bad channel states, low level
There are three main criteria leading to
a
good ATCQAM
scheme. They are decoder complexity, rate compatibility, and
constant bandwidth. They will be addressed
as
follows.
modulation is used to increase error protection. By match-
ing the variable modulation level with
a
variable rate channel
2.1
Design
of
ATCQAM
coder, the physical bandwidth is maintained constant. Design
issues for the ATCQAM are considered. The effects of finite
feedback delay, finite interleaving depth and mobile speed are
investigated.
1
Introduction
Error
correction codes have been widely used to combat the
effect of Rayleigh fading in mobile radio channels. In tra-
ditional
FEC
schemes
[l],
fixed-rate codes were used which
failed to explore the time varying nature of the channel. To
keep the performance
at
a
desirable level, they were designed
for the average or worst case situation. In this paper, we
propose and study
a
high bandwidth efficiency variable rate
adaptive trellis coded QAM (ATCQAM) which varies the
code rate and modulation level according to the channel con-
dition. The receiver estimated the channel states and inform
the transmitter through the use of
a
feedback link. When the
channel state is good, the transmitter increases the through-
put by using
a
higher level QAM. On the other hand, when
the channel state
is
bad, the
transmitter
uses
a
lower
level
QAM to improve the error protection.
We use M-ary QAM since it is more energy efficient than
the M-ary PSK constellations
at
large
M.
Known pilot sym-
bols are periodically inserted
at
the transmitter
[2,
31
to aid
the demodulation. Performance degradations due to finite
feedback delay, finite depth interleaving and mobile speed are
investigated
.
The paper is organized
as
follows. In section
2,
we de-
scribed design issues, different system components and the
The simplified system block diagram of the proposed scheme
is shown in fig. l(a). Information bits are convolutionally
encoded and the coded bits are mapped with the appropriate
M-ary &AM symbol. Known pilot symbols are inserted
at
the transmitter periodically to aid the demodulation
at
the
receiver. By means of an interpolation filter
at
the receiver,
channel states in between the pilot positions are interpolated
and used to demodulate the received symbols. The estimated
channel states
at
pilot positions are fed back to the trans-
mitter via
a
low noise (error protected) feedback link with
certain delay. By means
of
an instantaneous linear prediction
filter, current channel states are predicted
at
the transmitter
and appropriate modulation modes are used for the current
symbol.
By matching the
adaptive channel coder
and the
adaptive
modulator,
all M-ary symbols have the same duration and
hence the occupied bandwidth is constant. The varying in-
stantaneous throughput is achieved by encoding
a
varying
number of information bits per symbol.
The trellis encoder is based on a modified
pragmatic
TCM
design
[4]
using
a
core rate
1/6
encoder. Between each trellis
transition,
a
variable number of uncoded bits are concate-
nated with the coded bits and mapped with the appropriate
M-ary QAM symbol
as
shown in fig. l(b). Hence, we have
a
trellis with
a
fixed number of states but
a
varying number
of
parallel branches between each transition step. The same
Viterbi decoder can be used at the receiver. This reduces
decoder complexity.
Suppose the estimated path (state sequence) diverged from
the correct transmitted path
at
node
1
of the trellis dia-
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gram, the error path will have its Hamming distance (M-ary)
2.5
unaltered irrespective of the subsequent modulation modes.
This corresponds to the rate compatibility.
Therefore, the There are
7
odda at ion
modes in the Proposed
ATCQAM.
proposed adaptive pragmatic TCM satisfied the mentioned They are listed
as
follow.
design criteria. The only disadvantage of the design is the
presence of parallel branches. Although parallel branches are
Mode
O:
detrimental to the performance of the fixed rate TCM un-
der Rayleigh fading, it is not the performance bottleneck of
the ATCQAM by careful mapping of the signal constellation
[4,51. symbols.
Operation
of
the ATCQAM
ThroughPut-1/3, 6 Coded bits carried by
3
QAM
symbols.
Mode
1:
ThrOWhPut-1/2, 4 coded bits carried by 2 QAM
2.2
Interleaving
Interleaving is used to convert the bursty fading into inde-
pendent fading. Since a variable number of information bits
are carried per trellis transition, the interleaving design is
not trivial. The simplified block diagram for the interleaver
is shown in
fig.
l(b). Information bits are passed to the
core encoder and the coded bits are interleaved'. At the time
of transmission, an appropriate number of uncoded bits are
drawn from the buffer. The uncoded bits and the interleaved
coded bits are mapped with the appropriate M-ary QAM
symbol.
At
the receiver, received symbols are de-interleaved
and decoded. The uncoded bits are further re-scrambled to
resume the original order.
2.3
Channel State Interpolation
To avoid severe degradation in QAM performance caused by
fast Rayleigh fading, the transmitter inserted known pilot
symbol periodically (1 pilot every
Np
symbols) to aid the
receiver demodulation. The receiver stored
a
number
of
re-
ceived pilot symbols and made use of an
interpolation filter
to estimate the fading in between the pilots.
Let
ET,i
be the complex fading
at
frame position
r
of the
i-th frame. Using
a
2Pl
+
l-th order linear
FIR
interpolation
filter, the interpolated fading
at
the r-th frame position (in
between the pilot instants) of the i-th frame,
Zr,i,
is given by:
Zr,i
=
[Er,i
+
Z,i]
+
6,i
r
E
11,
Np
-
11
(1)
Note that
ET.i
is modeled as
a
Gaussian
residual
noise with
Mode
2:
Throughput-1, 2 coded bits carried by
1
QAM
symbol.
Mode
3:
Throughput-2,1 uncoded bits
+
2
coded bits car-
ried by
1
8PSK
symbol.
Mode
4:
Throughput-3,2 uncoded bits
+
2 coded bits car-
ried by
1
l6QAM symbol.
Mode
5:
Throughput-4,3 uncoded bits
+
2 coded bits car-
ried by
1
32QAM symbol.
Mode
6:
Throughput-5,4 uncoded bits
+
2 coded bits car-
ried by
1
64QAM symbol.
The predicted channel state
is
partitioned into
7
segments
with each segment corresponds to one of the above modes.
Let
%
be the average symbol energy to noise ratio. Mode
m
is chosen if the predicted SNR
E
[Cm,
Cm+l].
Note that
CO
=
0
and
57
=
00.
There are two different ways to operate the ATCQAM,
namely the
constant
BER
operation and the
constant through-
put
operation. For the constant
BER
operation, we set the
switching thresholds
so
as to maintain
a
relatively constant
BER
over
a
range of
2.
For simplicity, the ATCQAM is
specified by a single parameter,
51.
For the constant throughput operation, we set the thresh-
olds
so
as to maintain
a
constant average throughput. This
can be achieved if
c1
0:
e.
variance
o:(;)
due to imperfect filtering,
Er,i
is
a
Gaussian
noise with variance
U:.
Hence, the interpolated fading esti-
with Gaussian noise,
ET,i
and the residual noise,
ET,i.
The re-
ceiver use
Z,i
to perform match filtering and to computt: the
decision metrics to be used in the Viterbi decoder.
mate,
ZT,i,
can be modeled as
a
correct fading,
ET,i,
corrupted
3
Results and Discussion
Due to the varying throughput in the ATCQAM scheme, we
use the average symbol energy to noise ratio,
%,
instead of
the usual bit energy to noise ratio as
a
reference for compar-
2.4
Channel State Prediction
It is essential for the transmitter to know the current fad-
ing instantaneously to decide on the appropriate modulation
mode. The interpolation filtering, although very accurate,
suffers from
a
processing delay of
(PI
-
1)/2 pilot symbols.
Hence, to obtain an instantaneous estimate of the current fad-
ing given the past fading, we use
a
linear predictor of order
p2.
lThe two coded
bits
are
not
broken
up
in
the interleaver.
ison. We assumed
Np
=
91 (pilot period),
Pl
=
21 (inter-
polation filter order),
PZ
=
16 (prediction filter order) and
Nu
=
8
(user per TDMA frame). The overhead due to pilot
symbols is about
1%.
Convolutional code of constraint length
5 is used to construct the ATCQAM. Its performance is com-
pared with that
of
the optimal fixed rate TCM2 Hence, the
comparison is fair.
20ptimal in the sense
of
the maximal diversity order that could be
achieved. For example, the fixed rate
8PSK-TCM
has a diversity order
of
3
which is the best
out
of
constraint length 5 convolutional code.
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3.1
Performance of ATCQAM in TDMA
Zero Feedback Delay
(A
=
0):
As
an
illustration, we as-
sumed zero feedback delay, 100
x
500 block interleaving
and
fdTs
=
1
x
The BER and the throughput of
the ATCQAM-TDMA scheme using
constant
BER
con-
trols are shown in fig. 2(a) and (b). Under the
constant
BER
control, the BER remains approximately constant
when
e
is within the range of adaptation
as
shown in
fig. 2(a). The level of BER and the adaptation range
depends on the initial control threshold,
cl.
Along the
BER curves of the ATCQAM, the throughput varied
as
3~
as illustrated in fig. 2(b). At high
2,
we trade BER
Zth
a
higher throughput. To compare with the perfor-
mance of the fixed rate TCM, we have to consider the
relative throughput gain of the ATCQAM
at
the same
e
and BER. The BER against the relative throughput
gains of the ATCQAM w.r.t. the fixed rate 8PSK-TCM
and 16QAM-TCM are plotted in fig. 3(a). For exam-
ple, at
.fj,
=
the throughput gains relative to the
8PSK-TCM and the 16QAM are 1.95 and 1.54 times re-
spectively. However, when compared to QPSK-TCM,
Frame
always out-performs the corresponding fixed rate codes.
For example,
at
Pb
=
with 100x100 interleaving, the
gain in
2
is 8.7dB w.r.t. 8PSK-TCM.
At
Pb
=
4
x
with 35x35 interleaving, the gain in
2
is 10dB. Hence,
the proposed ATCQAM also shows significant gains in
systems with small interleaving depth.
Effects of Mobile Speed:
Fig. 6(a) shows
pb
against
%
for the ATCQAM-TDMA scheme and the fixed rate
16QAM-TCM
at
fdTs
=
6
x
It is apparent that
an
irreducible
error floor
at
pb
=
3
x
10-~
appears.
Note that above the error floor, ATCQAM always out-
performs the fixed rate codes.
The reason of the presence of the error floor is because of
aliasing. At this high fading rate, the Nyquist sampling
criteria is exceeded and aliasing causes severe degrada-
tion in the interpolation process at the receiver. This is
particularly serious for high density signal constellations
like 64QAM. Hence,
go,
is non-zero even in the absence of
channel noise and this causes the
irreducib2e
error floor.
This can be avoided by reducing the pilot period
at
the
expense of increased pilot symbol overheads.
3.2
Performance of ATCQAM in FDMA
there is negligible gain
as
opposed to the results in [7]
under ideal conditions. This is because of the degraded
gains in the ATCQAM due to errors in the channel state
estimation and prediction.
The ATCQAM-FDMA behaves in
a
similar
way
as the
On the other hand, when operating under the
constant
ATCQAM-TDMA. However, they do have some differences
throughput
control, the throughput of the ATCQAM is in terms of performance.
maintained
at
2
and
3
for comparison with fixed rate
8pSK-TCM and 16QAM-TcM. The
5
gain ofthe
ATC-
Tx-Rcv Synchronization:
AS discussed in section
2,
only
QAM relative
to
8PSK-TCM and 166AM-TCM is plot-
quasi-closed
loop
control can be applied to maintain the
ted
in
fig,
3(b). For example, there
are
7.1dB and 9.3dB
synchronization of the transmitter and the receiver by
gains
in
5
at
pb
=
10-4
relative
to
8PSK-TCM and synchronizing the feedback delay
at
the receiver.
This
control by embedding
a
control word in the frame can be
gain relative to QPSK-TCM due to the same reason.
used in ATCQAM-TDMA. This simplified the synchro-
nization task at the expense of increased overheads.
Frame
16QAM-+CM respectively. Similarly, there is negligible
increase
the
On
the
other hand, closed loop
Effects of Finite Feedback Delay:
The
pb
of the ATC-
QAM under finite feedback delay
at
fdTs
=
1
x
loe3
and
fdTs
=
6
x
are shown in in fig. 4(a) and (b) respec-
tively with
5
=
60 and
[
=
3.
The ATCQAM schemes
(FDMA and TDMA), are robust to the feedback delay
at slow fading (see fig. 4(a)). For example,
at
A
=
40,
pb
of the ATCQAM schemes are approximately 30 times
smaller than the BER of the fixed rate 16QAM.
At
higher fading rate (see fig. 4(b)), the ATCQAM-
TDMA become more sensitive to the feedback delay. At
A
=
40,
pb
for the ATCQAM-TDMA
is
the same
as
the
fixed rate
BER.
Effects of Block Interleaving:
Fig. 5(a) and
(b)
shows
pb
and
fj
against
5
for the ATCQAM-TDMA scheme
and the fixed rate 8PSK-TCM at various interleaving
depths.
Pb
increases gradually as the interleaving depth
decreases. However,
at
all interleaving depths, although
the absolute
Pb
degrades, the ATCQAM-TDMA scheme
3This
corresponds
to
a
mobile
speed
of
24kmlhr and baud rate
of
40kbaud.
Feedback Delays and
BER
Performance:
Under most
circumstances, BER for the ATCQAM-TDMA is always
lower than the FDMA counterpart. Their difference ex-
agerates at high fading rate (see fig. 4(a) and (b)).
At
fdTs
=
6
x
BER of the ATCQAM-FDMA is
even higher than that of the fixed rate l6QAM at all
A.
Hence, the ATCQAM-FDMA is totally not effective
at
fdTg
=
6
X
This
is
due
to
the difference in their prediction errors.
The prediction filter for the TDMA scheme only has to
predict the channel states for part of the physical frame
(assigned timeslot)
at
the vicinity of the pilot symbol.
This is more accurate compared with the FDMA system
where the channel states across the whole physical frame
have to be predicted.
The relative prediction errors
at
the transmitter for the
ATCQAM-TDMA scheme and the ATCQAM-FDMA
schemes are shown in fig.
7
(a)
and (b). As seen from
the figures, the predicted channel states for the FDMA
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system is less accurate.
It
is more likely for symbols to
be transmitted using an unsuitable mode for the FDMA
system. Hence, its BER degrades. As the fading rate in-
creases, the difference in their prediction errors increases
and this enlarges their differences in
Pb.
Irreducible Error Floor:
At
high fading rate,
irreducible
error floor appears in the BER curves. The error floor
depends on the fading rate. However,
at
the same fad-
ing rate, we found that ATCQAM-TDMA always has
a
lower error
floor
than ATCQAM-FDMA. This
is
illus-
trated in fig.
6(b).
At
fdT.
=
6
x
the error
floors
of the ATCQAM-TDMA and the ATCQAM-FDMA are
3
x
and
2
x
respectively. This means that
ATCQAM-TDMA
is
more robust to high fading rate as
well.
4
Conclusions
Seven modes ATCQAM scheme is proposed to exploit the
time varying nature of the mobile radio channel. By means
of an instantaneous linear prediction filter, current channel
states are predicted
at
the transmitter and appropriate mod-
ulation modes are used for the current symbol. Two ways of
operation of the ATCQAM, namely the
constant BER
oper-
ation and the
constant throughput
operation, are introduced.
Two frame formats, namely the TDMA and the FDMA
formats, for the ATCQAM scheme are considered. Two dif-
ferent methods to maintain transmitter-receiver synchroniza-
tion, namely the
quasi-closed
loop
control and the
closed
loop
control, are discussed. Under normal operating conditions,
the ATCQAM has relative throughput gains around
1.5
-
1.9
times and relative
2
gains around
7
-
9dB
w.r.t. the fixed
rate codes
at
Pb
=
The effects of finite feedback link de-
lay, finite depth interleaver and mobile speed are considered.
It is found that ATCQAM-TDMA is in general more robust
than ATCQAM-FDMA.
At
fdTs
=
6
x
irreducible error
floor
occurs but the performance of the ATCQAM-TDMA is
degraded less than the ATCMQAM-FDMA.
References
[l]
J.
G. Proakis,
Digital Communications.
McGraw Hill In-
ternational Editions,
NY,
third ed.,
1995.
[2] J.
K.
Cavers, “An Analysis of Pilot Symbol Assisted Mod-
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IEEE
Trans. on
Vehicular Tech.,
vol.
40,
pp.
686-693,
Nov.
1991.
[3]
S.
Sampei and T. Sunaga, “Rayleigh Fading Compensa-
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IEEE Trans. on Vehicular Tech.,
vol.
42,
pp.
137-147,
May.
1993.
[4]
A.
J.
Viterbi,
J.
K.
Wolf, E. Zehavi, and R. Padovani,
“A
pragmatic approach to trellis-coded modulation,”
IEEE
Communs. Magazine,
pp.
11-19,
July
1989.
(a) Simplified Block Diagram
of
the
ATCQAM
Scheme.
I
I
(b) Block Diagram
for
Variable Rate Interleaver.
Figure
1:
Overall Block Diagrams of the ATCQAM Scheme.
[5]
K. N. Lau and M. D. Malcolm, “Variable Rate Adaptive
Trellis Coded QAM
for
High Bandwidth Efficiency Ap-
plications under Rayleigh Fading Channel,”
Submitted
to
IEEE Trans. on Communs.
[6]
C.
W.
Therrien,
Discrete Random Signals and Statistical
[7]
S.
Alamouti and
S.
Kallel, “Adaptive Trellis-Coded
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pp.
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June
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Signal Processing.
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NJ,
first ed.,
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IEEE
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(a) Average BER against
(b)
Average Normalized
SNR at
various
under Throughputs against
the
constant
BER
opera- SNR at various
G.
tion.
(a)
Pb
against
%
at
var-
ious
interleaving depths.
(b)
fj
against
2
at var-
ious interleaving depths
for
ATCQAM-TDMA.
Figure
2:
Performance
of
ATcQAM-TDMA
relative
to
Figure
5:
Effects
of
the Interleaving Depths on the perfor-
8PSK-TCM and 16QAM-TCM. Dotted lines represent ATC-
&AM. Solid lines represent fixed rate codes.
mance of the ATCQAM.
(a) Relative through-
put gains
of
ACTQAM
w.r.t. 8PSK-TCM and
16QAM-TCM.
(b)
Relative
EA
gains
of
the AYCQAM
w.r.t. 8PSK-TCM and
16QAM-TCM.
(a) BER of the
(b)
BER
of
the
ATCQAM-TDMA ATCQAM-FDMA
at
fdTs
=
6
X
w3.
at
fdTs
=
6
X
Figure 6: Effects of mobile speed and the fading rate on the
Figure
3:
Normalized performance of ATCQAM-TDMA rela- BER performance of the ATCQAM-FDMA and ATCQAM-
tive to 8PSK-TCM and 16QAM-TCM. Dotted lines represent TDMA schemes.
ATCQAM. Solid lines represent fixed rate codes.
I
I
I
(a)
Predicted channel
(b)
Predicted channel
(a)
Effects
of
feedback
(b)
Effects
of
feedback
states (dotted line) and states (dotted line) and
delay on the BER of the delay on the BER of the actual channel states actual channel states
ATCQAM-FDMA and ATCQAM-FDMA and (FDMA). (TDMA).
ATCQAM-TDMA at ATCQAM-TDMA at
fdTS
=
lov3.
fdTs
=
6
X
lop3.
Figure
7:
Illustration of the difference in prediction error be-
tween the ATCQAM-TDMA and the ATCQAM-FDMA sys-
tem.
Figure
4:
Effects of Feedback Delay
on
the performance of
the ATCQAM.
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