RBF-Equalized Adaptive
Modulation
Having considered the concepts of RBF-assisted channel equalization in Chapter
8,
we are
now ready to amalgamate these concepts with the AQAM philosophy detailed in Part
I
of
the book. Although it is advantageous for the reader to consult Part
I
of the book, before
delving into Part
I1
dedicated to RBF-assisted arrangements, there is sufficient background
information in this part of the book for the reader to be able to dispense with reading Part
I.
Here we will commence by providing
a
brief introduction to the state-of-the-art in AQAM
transmissions over both narrow-band, as well as wide-band channels and then we will refer
back to Part
I
of the book in more detail with the objective of establishing a link betwen the
two parts.
Based on the foundations of the previous chapter, in this chapter the concept of RBF
equalizers is extended to Burst-by-Burst (BbB) Adaptive QAM (AQAM) schemes.
As
dis-
cussed in Part
I
of the book, BbB AQAM schemes employ a higher-order modulation mode in

transmission bursts, when the channel quality is favourable, in order to increase the through-
put and conversely, a more robust but lower-order modulation mode is utilized in those trans-
mission bursts, where the instantaneous channel quality drops. The modem mode switching
regime will be detailed in more depth during our further discourse. We will show that this
RBF-AQAM scheme naturally lends itself
to
accurate channel quality estimation. We will
provide an outline of our various assumptions and the description of the simulation model,
leading to our RBF-AQAM performance studies. This scheme is shown to give a significant
improvement in terms
of
the mean BER and bits per symbol (BPS) performance compared to
that of the individual fixed modulation modes. Let us now commence with a brief background
on adaptive modulation in both narrow- and wide-band fading channel environments.
385
Adaptive Wireless Tranceivers
L. Hanzo, C.H. Wong, M.S. Yee
Copyright © 2002 John Wiley & Sons Ltd
ISBNs: 0-470-84689-5 (Hardback); 0-470-84776-X (Electronic)
386
CHAPTER
9.
RBF-EOUALIZED ADAPTIVE MODULATION
9.1
Background to Adaptive Modulation in a Narrowband
Fading Channel
We summarise here the principles of
adaptive modulation
in a narrow-band Rayleigh fading
channel environment. In a narrow-band channel, as a result of channel fading, the short-term

SNR can be severely degraded. This typically degrades the short-term BER at the receiver.
Again, the concept of adaptive modulation is to employ a higher modulation mode, when
the channel quality is favourable, in order to increase the throughput and conversely, a more
robust modulation mode is employed, in order to provide an acceptable BER, when the chan-
nel exhibits a deep fade. Thus, adaptive modulation is not only used to combat the fading
effects of a narrow-band channel, but it also attempt to maximise the throughput. This idea is
somewhat reminiscent of invoking a coarse power control scheme although without the detri-
mental effects of inflicting increased interferences upon other system users due to powering
up during the intervals of low channel quality. In our work we used a variable number of
modulation levels and again, we refer to this scheme as AQAM, while maintaining a constant
transmitted power.
Adaptive modulation can only be invoked in the context of duplex transmissions, since
some method of informing the transmitter of the quality of the link as perceived by the re-
ceiver is required unless an explicit feedback control channel is provided by the system.
More explicitly, in adapting the modulation mode, a signalling regime has to be implemented
in order to harmonise the operation
of
the transmitter and receiver with regards to the adap-
tive modem mode parameters. The range of signalling options is summarized in Figure 9.1
for both so-called open-loop and closed-loop signalling. For example, adaptive modulation
can be applied in a time division duplex (TDD) arrangement, where the uplink and down-
link transmissions
are
time-multiplexed onto the same carrier as depicted in Figure 9.2. If the
channel quality of the uplink and downlink can be considered similar, an open-loop signalling
system can be implemented, where the modulation mode can be adapted at the transmitter
based on the information about the channel quality acquired during its receiving mode. This
open-loop system is portrayed in Figure 9.l(a). The specific modem mode invoked has to
be explicitly signalled by the transmitter to the receiver along with the reverse-direction in-
formation and it must be strongly protected against transmission errors, in order to avoid

catastrophic BER degradations in case of modem mode signalling errors. By contrast, if the
above channel quality predicability is not applicable
-
for example due to the presence of co-
channel interference, etc.
-
the closed-loop based signalling system shown in Figure 9.l(b)
can be implemented. This would be typical in a frequency division duplex (FDD) based sys-
tem, where the uplink and downlink transmission frequency bands are different. Explicitly,
the receiver has to instruct the remote transmitter concerning the modem mode to be used
for meeting the receiver’s target integrity requirements. The modem mode side-information
signalling requirement is the same for both of the above signalling scenarios. For example,
two bits per transmission burst
are
required to signal four different modem modes. However,
the channel quality information will be based on a more obsolete channel quality estimate in
the dissimilar uplinWdownlink scenario, when the receiver instructs the remote transceiver
concerning the modem mode to be used for meeting the receiver’s BER target. It was shown
in the context of a Kalman-filtered DFE block turbo coded AQAM scheme that it is feasible
to refrain from explicitly signalling the modem modes upon invoking blind mode detection
and hence increase the associated throughput
[215].
9.1.
BACKGROUND TO ADAPTIVE MODULATION
IN
A NARROWBAND FADING CHANNEL
387
I
Uplink
I

*
MS
._____.__ _________
BS
Evaluate perceived
Evaluate perceived
channel quality and
channel quality and
decide the transmission
decide the transmission
Downlink
mode
of
local
TX
Signal modem modes
used by
MS
+
1
Signal modem modes
\
mode
of
local
TX
_._____ ~~~.___ ___
used by
BS
(a)

Open-loop based signalling
MS
Evaluate perceived
channel quality and
signal the requested
transmission mode
to the
BS
TX

Signal modem modes Evaluate perceived
to be used by
BS
channel quality and
signal the requested
Downlink transmission mode
-

to the
MS
TX
Signal modem modes
to be used by
MS
(b)
Close-loop based signalling
Figure
9.1:
Closed- and open-loop signalling regimes
for

AQAM, where BS represents the Base Sta-
tion, MS denotes the Mobile Station and the transmitter is represented
by
TX.
Having discussed briefly the principle
of
adaptive modulation and the associated sce-
narios, where it can be applied, we can now explore the methology used for choosing the
appropriate number of modulation levels.
Torrance
[
1451
used the instantaneous received power as the channel quality measure. The
estimated instantaneous received power was used to select the suitable modulation mode by
comparing the received power against a set of switching thresholds,
l,,
n
=
1,
.
. .
,4,
as de-
picted in Figure
9.3.
These switching thresholds govern the tradeoff between the mean
BER
and the
BPS
performance of the system.

If
low switching thresholds are used, the probability
of employing a high-order modulation mode increases, thus yielding a better
BPS
perfor-
mance. Conversely, if high switching thresholds are used, a low-order modulation mode is
employed more frequently, resulting in an improved mean
BER
performance. In his efforts
to derive upper-bound performance bounds Torrance
[
1451
assumed perfect channel quality
estimation and compensation, perfect knowledge of the modulation mode at the receiver and
perfect estimation of the expected received power prior to transmission.
388
CHAPTER
9.
RBF-EOUALIZED ADAPTIVE MODULATION
Mobile Station Mobile Station
I-
receives
-1-
transmits
-1
<
QAM symbols
QAM symbols
TDD
frames

I
_
-_
-_
QAM symbols QAM symbols
~~
i-

~ delay
~ Propagation
Base Station
A
Base Station

receives
,
transmits
:-
The channel quality required
+:
I
to
be approximately constant
I
Figure
9.2:
The TDD framing structure used in our
AQAM
system.
Short

Term
SNR
Time
p,
64QAM
W
BPSK
No
Transmission
(NO
TX)
Figure
9.3:
Stylised profile
of
the
short-term received
SNR,
which is used
to
choose the next modula-
tion mode
of
the transmitter in
TDD
mode.
9.2.
BACKGROUND ON ADAPTIVE MODULATION IN A WIDEBAND FADING CHANNEL
389
Figure

9.4: Decision-feedback equalizer schematic.
Ik
-
+
Webb and Steele [4] used the received signal strength and the BER as channel quality
measures in a flat Rayleigh-fading environment. The signal to co-channel interference ratio
and the expected delay spread of the channel was used by Sampei, Komaki and Morinaga [59]
as the criteria to switch amongst the modulation modes and the legitimate modulation rates.
They used ;-rate QPSK, ;-rate QPSK, QPSK, 16-QAM, 64-QAM in a narrow-band channel
environment. Sampei, Morinaga and Hamaguchi utilized the signal to noise ratio and the
normalized delay spread as the channel quality measure.
For a review of other work that has been conducted using adaptive modulation, the reader
is referred to the previous chapters.
9.2
Background on Adaptive Modulation in a Wideband
Fading Channel
In this section we will initially extend the AQAM concept to wideband fading channel envi-
ronments by employing conventional channel equalization. We will briefly summarise, how
the performance
of
the equalizer and the AQAM scheme can be jointly optimized.
As expected, the AQAM switching criteria of the narrow-band scenario mentioned in
Section 9.1 has to be modified for the wideband channel environment. In Torrance’s paper
[l451 for example, the quality of the channel was determined on the basis
of
the short-term
SNR, which was then used
as a metric
in
order to choose the appropriate modulation mode

for the transmitter. However, in a wideband environment, the SNR metric is not reliable in
quantifying the quality of the channel, where the existence of the multipath components in
the wideband channel produces not only power attenuation of the transmission burst, but also
intersymbol interference, as discussed
in
Section
8.1.
Even when the channel SNR is high,
QAM transmissions over wideband Rayleigh fading channels are subjected
to
error bursts due
to 1%. Consequently, the metric required to quantify the channel quality has to be redefined,
in order to incorporate the effects of the wideband channel.
Wong and Hanzo [32,296] approached this problem by formulating a two-step method-
ology to mitigate the effects of the dispersive wideband channel. The first step employed a
conventional Kalman-filtering based DFE, in order to eliminate most of the ISI. In the second
390
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
step, the signal to noise plus residual interference ratio at the output of the equalizer was
calculated based on the channel estimate. This ratio was referred to as the
pseudo
SNR,
since
it exhibited
a
Gaussian-like distribution and it was used as a metric to switch the modulation
mode. Again, in [32,296], Wong used the conventional Kalman-filtering based DFE depicted
in Figure 9.4. If the

IS1
due to past detected symbols is eliminated by the feedback filter, then
the wanted signal power, the residual
IS1
signal power and the effective noise power can be
expressed as follows
[
1051:
Wanted Signal Power
=
E
[lq01,1~] , (9.1)
Residual
IS1
Signal
=
c
E
[lqkln-k12]
,
(9.2)
-1
k=-K1
0
Effective Noise Power
=
NO
c
(cj
12,

(9.3)
j=-K,
72
=
-00,.
.
.
,m,
(9.4)
where
qk
=
xj=-KI
cj
fk-3,
cj,
j
=
-K1,
.
.
. ,
0
are the feedforward tap coefficients,
cj,
j
=
1,
.
. .

,
K2
are the feedback tap coefficients,
fk
is the kth impulse response tap of the
channel and
NO
is the noise power. Therefore, the pseudo
SNR
output of the DFE,
TDFE,
can
be calculated as follows:
0
The calculated pseudo
SNR
output of the DFE,
?DE,
is then compared against a set of switch-
ing threshold levels,
l,,
stored in a lookup table. The pseudo SNR output of the DFE,
TDFE,
is used for invoking the appropriate modem mode as follows [296]:
NO TX
if
YDFE
II
BPSK if
11

<
YDFE
<
12
Modulation Mode
=
4-QAM
if
12
<
YDFE
<
13
(9.6)
16-QAM
if
13
<
TDFE
<
14
1
64-QAM if
YDFE
>
14,
where
I,,
n
=

1,
. .
.
,4
are the pseudo-SNR thresholds levels, and Powell’s Multi-dimensional
Line Minimization technique [297] was used to optimize the switching levels
I,
in [32].
9.3
Brief Overview of
Part
I
of
the
Book
In Part
I
of this monograph we commenced by analysing the performance of the DFE using
multi-level modulation schemes, when communicating over static multi-path Gaussian chan-
nels as shown in Figure 2.10. These discussions were further developed in the context of a
multi-path fading channel environment, where the recursive Kalman algorithm was invoked
in order to track and equalize the received linearly distorted data, as evidenced by Figure
3.16. Explicitly, an adaptive CIR estimator and DFE were implemented in two different re-
ceiver structures, as shown in Figure 3.14, while their performances were compared in Figure
9.3. BRIEF OVERVIEW OF PART
I
OF THE
BOOK
391
2.10.

In
this respect, Structure
1,
which utilized the adaptive
CIR
estimator provided a better
performance, when compared to that of Structure
2,
which involved the adaptive DFE, as
evidenced by Table 3.10. Furthermore, the complexity of Structure
2
was higher than that of
Structure
1,
which was studied in Section 3.4. However, these experiments were conducted in
a fast start-up environment, where adaptation was restricted to the duration of the training se-
quence length. By contrast, if the adaptation was invoked over the entire transmission frame
using a decision directed scheme, the complexity advantage of Structure
1
was eroded, as
discussed in Section 3.5. The application of these fast adapting and accurate CIR estimators
was crucial in a wideband AQAM scheme, where the CIR variation across the transmission
frame was slow.
In
these experiments valuable insights were obtained with regards to the de-
sign of the equalizer and to the characteristics of the adaptive algorithm itself. This provided
a firm foundation for the further investigation of the proposed wideband AQAM scheme.
Following our introductory chapters, in
Chapter
4

the concept
of
adaptive modulation
cast in the context of a narrow-band environment was introduced in conjunction with the
application of threshold-based power control. In this respect, power control was applied in
the vicinity of the switching thresholds of the AQAM scheme. The associated performance
was recorded
in
Table 4.4, where the trade-off between the BER and BPS performance was
highlighted. The relative frequency of modulation mode switching was also reduced at the
cost of a slight BER degradation. However, the complexity of the scheme increased due to
the implementation of the power control regime. Moreover, the performance gains portrayed
at this stage represented an upper-bound estimate, since perfect power control was applied.
Consequently, the introduction of threshold-based power control in a narrow-band AQAM
did not offer an attractive complexity versus performance gain trade-off.
The concept of AQAM was subsequently invoked in the context of a wideband channel,
where the DFE was utilized in conjunction with the AQAM modem mode switching regime.
Due to the dispersive multi-path characteristics of the wideband channel, a metric based
on
the output SNR of the DFE was proposed
in
order to quantify the channel’s quality. This
ensured that the wideband channel effects were mitigated by the employment of AQAM
and equalization techniques. Subsequently a numerical model based
on
this criterion was
established for the wideband AQAM scheme, as evidenced by Figures 4.16 and
4.17.
The
wideband AQAM switching thresholds were optimised for maintaining a certain target BER

and BPS performance, as shown in Figure 4.3.5. The wideband AQAM BPS throughput
performance was then compared to that of the constituent fixed modulation modes, where
BPS/SNR gains of approximately
1
-
3dB and
7
-
9dB were observed for target BERs of
1%
and
0.01%,
respectively. However, as a result of the assumption made in Section 4.3.1, these
gains constituted an upper bound estimate. Nevertheless, the considerable gains achieved
provided further motivation for the research of wideband AQAM schemes.
The concept of wideband coded AQAM was presented in
Chapter
5,
where turbo block
coding was invoked in the switching regime for different wideband AQAM schemes. The
key characteristics of these four schemes, namely those of the
FCFI-TBCH-AQAM, FCVI-
TBCH-AQAM, P-TBCH-AQAM
and VR-TBCH-AQAM arrangements, were highlighted
in Table 5.10 in terms of the respective turbo interleaver size and the coding rate utilized. The
general aim of using turbo block coding in conjunction with a high code rates was to increase
the effective BPS transmission throughput, which was achieved, as shown in Table
5.1
1
for

the arrangement that we referred to as the
Low-BER scheme.
In
this respect, all the schemes
produced gains in terms of their BER and BPS performance, when compared to the uncoded
392
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
AQAM scheme, which was optimised for a BER of
0.01%.
This comparison was recorded in
Table 5.1
1
for the four different turbo coded AQAM schemes studied.
The
FCFI-TBCH-AQAM scheme exhibited a better throughput gain, when compared
to the other schemes. This was achieved as a result of the larger turbo interleaver used
in this scheme, which also incurred a higher delay. The size of the turbo interleaver was
then varied, while retaining identical coding rate for each modulation mode, resulting in the
FCVI-TBCH-AQAM scheme, where burst-by-burst decoding was achieved at the receiver.
The BPS throughput performance of this scheme was also compared to that of the constituent
fixed modulation modes, which utilized different channel interleaver sizes, as shown in Fig-
ure 5.1
1.
SNR gains of approximately
1.5
and 5.0dB were achieved by the adaptive scheme
for a target BERs of 0.01%, when compared to the fixed modulation modes using the small-
and large-channel interleavers, respectively. By contrast, for a target BER of

1%
only modest
gains were achieved by the wideband AQAM scheme. These apparently low gains were the
consequence of an ’unfair’ comparison, since sibnificantly larger turbo interleaver and chan-
nel interleaver sizes were utilized by the fixed modulation modes. Naturally, his resulted in
a high transmission delay for the fixed modulation modes. By contrast, the
FCVI-TBCH-
AQAM
scheme employed low-latency instantaneous burst-by-burst decoding, which is im-
portant
in
real-time interactive communications.
The size of the turbo interleaver and the coding rate was then varied according to the
modulation mode, in order to ensure burst-by-burst decoding at the receiver. This resulted
in the
P-TBCH-AQAM scheme, which also incorporated un-coded modes for the sake of
increasing the achievable throughput. Finally, the
VR-TBCH-AQAM scheme activated dif-
ferent code rates in conjunction with the different modulation modes. These schemes pro-
duced a higher maximum throughput due to the utilization of higher code rates. However, the
SNR gains in terms of both the BER and BPS performance degraded, when compared to the
FCFI-TBCH-AQAM scheme as a result of the reduced-size turbo interleaver used. Further-
more, the utilization of higher code rates for the
VR-TBCH-AQAM arrangement resulted
in a higher decoding complexity. Once again, these comparisons are recorded in Table 5.7.
Similar characteristics were also observed
in
the context of the High-BER candidate scheme
and in conjunction with the near-error-free schemes. However, the performance gains of the
High-BER schemes were less than those of the Low-BER schemes. This was primarily

due to the lower channel coding gain achieved at higher BERs and due to the smaller turbo
interleaver size used.
The advantages of burst-by-burst decoding were also exploited in the context
of
blindly
detecting the modulation modes. In this respect, the channel coding information and the
mean square phasor error was utilized in the hybrid SD-MSE modulation mode detection
algorithm of Section 5.6.2 characterized by Equation 5.6. Furthermore, concatenated m-
sequences
[
1691 were used in order to detect the NO TX mode while also estimating the
channel’s quality. The performance of this algorithm was shown in Figure 5.16, where a
modulation mode detection error rate (DER) of
lop4
was achieved at an average channel SNR
of 15dB. However, the complexity incurred by this algorithm was high due to the multiple
channel decoding processes required for each individual modulation mode.
Turbo convolutional coding was then introduced and its performance using fixed modu-
lation modes was compared to that
of
turbo block coding, as shown in Figure 5.23. A BER
versus SNR degradation
of
approximately
1
-
2dB was observed for the turbo convolutional
coded performance at a BER of However, the complexity was significantly reduced,
9.3.
BRIEF OVERVIEW OF PART

I
OF THE
BOOK
393
namely by a factor of seven, when compared to the previously studied turbo block coded
schemes. Turbo convolutional coding was then incorporated in our wideband AQAM scheme
and its performance was compared to that of the turbo block coded AQAM schemes, where
the results were similar, as evidenced by Figure 5.24. Consequently the complexity versus
performance gain trade-off was more attractive for our turbo convolutional coded AQAM
schemes.
In our continued investigations of coded AQAM schemes, turbo equalization was invoked
where BPS/SNR gains of approximately
1
-
2dB were achieved by our AQAM scheme. In
achieving this performance, iterative CIR estimation was implemented based on the LMS
algorithm, which approached the perfect CIR estimation assisted AQAM performance, as
shown in Figure
5.3
1. However, the implementation of this scheme was severely hindered by
the high complexity incurred, which increased exponentially in conjunction with higher-order
modulation modes and longer CIR memory.
The chapter was concluded with a system design example cast in the context of TCM,
TTCM and BICM based AQAM schemes, which were studied under the constraint of a sim-
ilar implementational complexity. The BbB adaptive TCM and TTCM schemes were inves-
tigated when communicating over wideband fading channels both with and without channel
interleaving and they were characterised in performance terms over the COST 207 TU fading
channel. When observing the associated BPS curves, adaptive TTCM exhibited up to 2.5
dB
SNR-gain for a channel interleaver length

of
four transmission bursts in comparison to the
non-interleaved scenario,
as it was evidenced in Figure 5.40. Upon comparing the associated
BPS curves, adaptive TTCM also exhibited up to
0.7
dB
SNR-gain compared to adaptive
TCM of the same complexity in the context of
System
11,
while maintaining a target BER of
less than 0.01
%,
as it was shown in Figure
5.44.
Finally, adaptive TCM performed better,
than the adaptive BICM benchmarker in the context of
System
I,
while the adaptive BICM-
ID scheme performed marginally worse, than adaptive TTCM in the context of
System
11,
as
it
was discussed in Section 5.1 1.5.
In
Chapter
6

following a brief introduction to several fading counter-measures, a general
model was used for describing various adaptive modulation schemes employing various con-
stituent modulation modes, such
as PSK, Star QAM and Square QAM, as one of the attractive
fading counter-measures. In Section 6.3.3.1, the closed
form
expressions were derived for the
average BER, the average BPS throughput and the mode selection probability of the adap-
tive modulation schemes, which were shown to be dependent on the mode-switching levels
as well
as
on the average SNR. In Sections 6.4.1, 6.4.2 and 6.4.3 we reviewed the existing
techniques devised for determining the mode-switching levels. Furthermore,
in
Section 6.4.4
the optimum switching levels achieving the highest possible BPS throughput were studied,
while maintaining the average target BER. These switching levels were developed based on
the Lagrangian optimization method.
Then, in Section 6.5. l the performance of uncoded adaptive PSK, Star QAM and Square
QAM was characterised, when the underlying channel was a Nakagami fading channel. It
was found that an adaptive scheme employing a Ic-BPS fixed-mode
as the highest throughput
constituent modulation mode was sufficient for attaining all the benefits of adaptive mod-
ulation, while achieving an average throughput of up to
Ic
-
1
BPS. For example, a three-
mode adaptive PSK scheme employing No-Tx, l-BPS BPSK and 2-BPS QPSK modes at-
tained the maximum possible average BPS throughput of 1 BPS and hence adding higher-

throughput modes, such as 3-BPS 8-PSK to the three-mode adaptive PSK scheme resulting
394
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
in a four-mode adaptive PSK scheme did not achieved a better performance across the
1
BPS
throughput range. Instead, this four-mode adaptive
PSK
scheme extended the maximum BPS
throughput achievable by any adaptive PSK scheme to 2 BPS, while asymptotically achieving
a throughput of 3 BPS, as the average SNR increases.
On the other hand, the relative SNR advantage of adaptive schemes in comparison to
fixed-mode schemes increased as the target average BER became lower and decreased as the
fading became less severe. More explicitly, less severe fading corresponds to an increased
Nakagami fading parameter
m,
to an increased number of diversity antennas, or to an in-
creased number of multi-path components encountered in wide-band fading channels. As the
fading becomes less severe, the average BPS throughput curves of our adaptive Square QAM
schemes exhibit undulations owing to the absence of 3-BPS, 5-BPS and 7-BPS square QAM
modes.
The comparisons between fixed-mode MC-CDMA and adaptive OFDM (AOFDM) were
made based on different channel models. In Section 6.5.4 it was found that fixed-mode
MC-
CDMA might outperform adaptive OFDM, when the underlying channel provides sufficient
diversity. However, a definite conclusion could not be drawn since in practice MC-CDMA
might suffer from MU1 and AOFDM might suffer from imperfect channel quality estimation
and feedback delays.

systems were investigated in Section 6.5.5. The coded schemes reduced the required average
SNR by about 6dB-7dB at a throughput of
1
BPS, achieving near error-free transmission. It
was also observed in Section 6.5.5 that increasing the number of transmit antennas in adap-
tive schemes was not very effective, achieving less than 1dB SNR gain, due the fact that the
transmit power per antenna had to be reduced in order to limit the total transmit power for the
sake of a fair comparison.
The practical issues regarding the implementation of the advocated wideband AQAM
scheme was analysed in
Chapter
7. The impact of error propagation in the DFE was high-
lighted in Figure 7.2, where the BER degradation was minimal and the target BERs were
achieved without any degradation to the transmission throughput performance. The impact of
channel quality estimation latency was also studied, where the sub frame based TDDRDMA
system of Section 7.2.
l
was implemented. In this system, a channel quality estimation delay
of 2.3075ms was imposed and the channel quality estimates were predicted using a linear pre-
diction technique. In this practical wideband AQAM scheme, SNR gains
of
approximately
1.4dB and 6.4dB were achieved for target BERs of 1% and
0.01%,
when compared to the per-
formance of the constituent fixed modulation modes. This was shown graphically in Figure
7.11.
CC1 was then subsequently introduced in Section 7.3, where in terms of channel quality
estimation, the minimum average SIR that can be tolerated by the wideband AQAM scheme
was approximately lOdB, as evidenced by Figure 7.14. In order to mitigate the impact of

CC1 on the demodulation process, the JD-”SE-BDFE scheme using an embedded con-
volutional encoder was invoked, where the performance was shown in Figure 7.21 and 7.22
for the fixed modulation modes and for the wideband AQAM scheme, respectively. The per-
formance gains achieved by the wideband AQAM scheme were approximately 2
-
4dB and
7
-
9dB for the target BERs of
1%
and
0.01%,
when compared to the performance of the as-
sociated fixed modulation modes. However, these gains constituted an upper bound estimate,
since perfect channel estimation of the reference user and the interferer was assumed.
Concatenated space-time block coded and turbo convolutional-coded adaptive multi-carrier
9.4.
JOINT
ADAPTIVE MODULATION AND
RBF
BASED EQUALIZATION
395
Noise
l
I
Look-up
Table
Switching Threshold Burst
Short Term
of

Bit
Error
Probability
of
the Data Burst
Figure
9.5:
System schematic
of
the joint adaptive modulation and
RBF
equalizer scheme.
The concept of segmented wideband AQAM was then introduced, in order to reduce
the impact of CCI. In this scheme, the inner and outer switching thresholds were developed
based on a noise and interference limited environment, respectively, for any given average
channel SNR and average SIR. A channel quality estimation delay of 2.3075ms was imposed
in estimating the instantaneous SIR and the associated performance was displayed in Figure
7.24.
By employing this segmented AQAM scheme, accurate estimation of the instantaneous
SIR was needed, which was provided by the Kalman-filter based mid-amble assisted CIR
estimation. However, information regarding the interferer was not required for reducing the
impact
of
CCI, which was a substantial advantage.
Having studied a whole host of the associated aspects of AQAM-assisted wireless com-
munications in Part I of the book, in the forthcoming chapters we will focus our attention
on using RBF-aided equalizers as described in Section 8.9, instead of employing the conven-
tional DFE. The joint adaptive modulation and RBF equalization scheme will be described
next, followed by our simulation results.
9.4

Joint Adaptive Modulation and
RBF
Based Equalization
In this section, we will describe the joint AQAM and RBF network based equalization scheme
and the switching metric employed. We commence by exploring the joint AQAM and RBF
equalizer scheme’s best-case performance. Finally, the performance of this scheme and that
of the individual fixed modulation modes is compared in terms of their mean BER and BPS.
9.4.1
System
Overview
The schematic of the joint AQAM and RBF network based equalization scheme is depicted
in Figure 9.5. We use the RBF DFE described in Section 8.11 in this scheme. At the receiver,
the RBF DFE is trained using the method described in Section 8.9.3 and then the corrupted
received signal is equalized. The short-term probability of bit error
or
short-term BER of the
transmitted burst is calculated from the output of the sub-RBF network, and is used as the
switching metric. Section 9.4.2 will highlight this issue in more detail. The short-term BER
is compared to a set of switching BER values corresponding to the modulation mode of the
396
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
received data burst. Consequently, a modulation mode is selected for the next transmission,
assuming channel quality similarity for the uplink and downlink transmissions. This implies
that the similarity of the short-term BER
of
consecutive uplink and downlink data bursts can
be exploited, in order to set the next modulation mode. The modulation modes utilized in
our system are BPSK, 4-QAM, l6-QAM, 64-QAM and no transmission

(NO
TX), similarly
to Equation 9.6. Therefore, the modulation mode is switched according to the estimated
short-term BER, as follows:
1
NO
TX if
Phit,
short-term
2
pp
BPSK if
P2M
>
&it, short-term
2
Pp
Modulation Mode
=
4-QAM if
Pp
>
Pbit,
short-term
2
PIS
M
16-QAM
if
>

Phit,
short-term
2
PE
64-QAM
if
PE
>
Phit,
short-term,
(9.7)
where
PzM,
i
=
2,4,16,64
are
the switching BER thresholds corresponding to the various
M-QAM modes.
9.4.2
Modem
Mode
Switching Metric
The RBF equalizer based on the optimal Bayesian decision function of Equation 8.17, as
described in Chapter
8,
is capable of providing the ’on-line’ estimation of the BER in the
receiver without the knowledge of the transmitted symbols. This is possible, since the equal-
izer is capable
of

estimating the
a
posteriori probability of the transmitted symbols, if the
CIR is known and provided that the centres
of
the RBF network are assigned the values of
the channel states, as it was originally suggested in Section 8.9.
Referring to Section 8.9.2 and Figure 8.19, the output of the RBF networks provides the
conditional probability density function of each legitimate QAM symbol,
Zi,
i
=
1,
. .
.
,
M
which is described by Equation 8.85. The
a
posteriori probability
y(k)
of the transmitted
symbols, can be evaluated from the conditional density function,
(~(k)
as follows:
Si(k)
=
P(1k-r
=
ZilVk)

- -
P(VkJI&,
=
Zz)
.
P(1&
=
Ti)
p(vk)
The
a
posteriori probability
<(k)
of
the detected symbol can be obtained without the knowl-
edge of the term
P(vk), if the
a
posteriori probability has unity support (i.e. the sum of the
a
posteriori probabilities of all symbols is unity):
(9.9)
9.4.
JOINT
ADAPTIVE MODULATION AND
RBF
BASED EQUALIZATION
397
and the overall probability of symbol error of the detector is given by:
Similarly, the probability of a bit error can be obtained from the a posteriori probability

of the bits representing the QAM symbols. Below we provide an example for the 4-QAM
scheme. The a posteriori probability of the
4
symbols,
11,
12,
13
and
14,
is estimated by
the RBF networks as
cl,
Q,
Q
and
~4,
respectively. A 4-QAM symbol is denoted by the bits
UoU1
and the symbols
11,
Z2,Zs
and
14
correspond to 00,01,
10
11, respectively. Thus, the
a posteriori probability of the bits is given as follows:
P(U0
=
1)

=
P(UoU1
=
11
U
UOUI
=
10)
=
c4
+
<3,
P(&
=
0)
=
P(UoU1
=
01
U
Ul)U,
=
00)
=
Q
+
51,
P(U1
=
1)

=
P(UoU1
=
11
U
UoU1
=
01)
=
Q
+Q,
P(U1
=
0)
=
P(UoU1
=
10
U
UOU1
=
00)
=
c3
+Cl.
(9.12)
In general, the average probability of bit error for the detected symbol at signalling instant
IC
is given by:
(9.13)

where BPS denotes the number of bits per symbol and
bi
is the value (either
0
or 1) of the ith
bit of the symbol exhibiting the maximum a
posteriori
probability. The overall probability of
bit error for the detector
is
given by:
For our joint RBF based equalization and AQAM scheme, we are unable to obtain the
true probability of bit error for the detector, namely
Pbit averaged over all data bursts, since
we need to collect a large number of received samples for an accurate estimation. We can
only obtain the short-term probability of bit error,
Pbit,
short-term, which is the average bit error
probability over a data burst that was received, i.e.,
(9.15)
where
LD
is the number of data symbols per burst. Thus, we could estimate the channel
quality on a BbB basis, relying on the estimated
short-term value. The short-term probability
of bit error or BER is only an estimate of the actual
Pbit
of the system for the duration of the
data burst. The accuracy of the estimation is dependent on the number of data symbols
LD

in the burst. This issue will not be discussed further for now.
Having described the switching metric used by the joint AQAM and RBF equalizer
scheme, we will further investigate this scheme with the aim of producing a best-case perfor-
mance estimate. Before proceeding, the next section will present the assumptions used, when
we employ this scheme in a wideband channel environment.
398
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
9.4.3
Best-case Performance Assumptions
In deriving the best-case performance of this joint adaptive modulation and RBF based equal-
ization scheme, the following assumptions are made:
1.
2.
3.
4.
5.
Perfect CIR estimation or channel state estimation is assumed at the receiver. The
RBF’s centres are assigned the values of the channel states. The associated CIR and
channel state estimation techniques were presented in Section 8.9.3, 8.9.4 and 8.9.5.
We note that incorrect estimation of the channel states will degrade the performance
of the constituent fixed modulation modes, as
it
was demonstrated by our simulation
results in Section 8.12. This degradation is neglected here with the aim of deriving a
best-case performance estimate.
The CIR is time-invariant for the duration of the transmission burst, but varies from
burst to burst, which corresponds to assuming that the channel is slowly varying. How-
ever, if the CIR changes during the transmission burst or if the estimation algorithm

gives an inaccurate channel estimate, the effect of the channel variations can be con-
sidered by modifying the noise variance estimate, as discussed
in
[259,298]. Let
us
briefly summarize this idea. We define the error between the noisy channel output 2/k
and the estimated noiseless channel state output
ijk
as follows:
(9.16)
where
A,
(.)
is an error function caused by an inaccurate estimate of the channel im-
pulse response
fa,
n
=
0,
.
.
.
,
L.
Having determined this noise term, the RBF equal-
izer uses the noise variance in its width parameter seen in Equation
8.80
in order to
compute the conditional probability densities of each legitimate
QAM

symbols. There-
fore, by computing the ’noise variance’ as the average of
e:,
and substituting these
values in Equation
8.80
yields p
=
2E
[e:].
Hence we translated the CIR estimation
error to a noise-like term.
We assume furthermore that the receiver has perfect knowledge of the modulation
mode used in its received transmission burst. For a practical system, control sym-
bols must be used to convey the modulation mode employed by the transmitter to the
receiver [21,26].
The RBF
DFE
used in the system neglects error propagation by feeding the correct
symbol to be used for RBF subset centre selection or space translation, as described
in
Section
8.1
1.
However, at low target BERs, we will expect low performance degrada-
tion due to decision feedback error propagation, as it was demonstrated in Figure 8.42.
The short-term probability of error estimate, namely
short-term,
is known prior to
transmission for all the modulation modes used in the system. This can be assumed

in
9.4.
JOINT ADAPTIVE MODULATION AND
RBF
BASED EQUALIZATION
399
a TDD scenario, where the channel can be considered similar in the uplink and down-
link transmission and when the channel is slowly varying. We also assume that given
the estimated
&,
shofi-tem for a particular modulation mode, the transmitter knows the
corresponding short-term probability of bit error for the other modulation modes used
in the system under the same channel conditions. Thus, the transmitter
of
a base station
for example, can utilize its receiver’s
Phit, shofi-tem estimation for its next transmission,
provided that there is a high channel quality correlation between the transmitter and
receiver slots. Note however that the latency between the transmitter and receiver slots
can affect the quality of the estimation. This latency is mitigated, when employing slot-
by-slot TDD
-
as in the third generation IMT-2000 and UTRA [299-3011 proposals
-
where any TDD-slot can be configured as an uplink or downlink slot, hence reducing
the latency of channel quality estimates.
During our further discourse we will gradually remove these idealistic assumptions.
Having described the assumptions stipulated, in order to derive the best-case performance
of
this joint adaptive modulation and RBF based equalization scheme, we now describe our

simulation model.
9.4.4 Simulation Model for Best-case Performance
In our experiments, pseudo-random symbols were transmitted in a fixed-length burst for all
modulation modes over the burst-invariant wideband channel to fulfil assumptions 2 and
5.
The receiver received each data burst having different modulation modes and equalized each
one
of
them independently. The estimated short-term probability of bit error or BER was
obtained for each modulation mode, as described in Section 9.4.2. The highest-order mod-
ulation mode,
M*
that provided a short-term BER
Pbyihort.tem,
which was below the target
BER
Phit, target, when:
was chosen to be the actual modulation mode that was used by the transmitter and the received
equalized burst was used for the BER estimation of the system. The notation
PhFshon-tem
represents the short-term BER of M-QAM. However, if all the modulation mode could not
provide the targetted BER performance, i.e.
P&,
>
NO
TX mode is utilized.
Figure
9.6
shows the simulation schematic of the joint AQAM and RBF DFE scheme used
in our best-case BER performance evaluation. The next section will present our simulation

results and analysis.
9.4.5 Simulation Results
The simulation parameters are listed in Table 9.1, noting that we analysed the joint AQAM
and RBF equalizer scheme over a two-path Rayleigh fading channel. The wideband fading
channel was burst-invariant. The RBF DFE used in our simulations had a feedforward order
of
m
=
2, feedback order of
n
=
1
and delay of
T
=
1.
Figure 9.7 portrays the short-term BER of the burst-invariant channel versus symbol in-
dex, as estimated by the RBF DFE. For the simulated scenario, i.e., for a Doppler frequency of
400
CHAPTER
9.
RBF-EOUALIZED ADAPTIVE MODULATION
BPSK
4QAM Burst
16QAM
64QAM
Choose frame
with highest-
Short Term
invariant

-
mode, such
modulation
BER
RBF
DFE
channel
Calculation
that its short-
term BER
5
targeted BER
t
Frame chosen
for actual BER
and BPS calculation
Figure 9.6:
The simulation schematic of the joint AQAM and RBF DFE arrangement used for best-case
BER
performance estimation.
Number of data symbols per burst,
LD
Number of training symbols per burst,
LT
Transmission Frequency
Transmission Rate
Vehicular Speed
Normalized Doppler Frequency
Channel weights
RBF DFE feedforward order,

m
RBF DFE feedback order,
n
RBF DFE decision delay,
T
144
27
1.9GHz
2.6MBd
30 mph
0.707
+
0.7072-1
2
1
1
3.3
x
10-5
Table
9.1:
Simulation parameters.
3.3
x
lop5
the short-term BER is slowly varying and it is relatively predictable for a number
of
consecutive data bursts. Thus, assumption 2 of Section 9.4.3 is valid for this scenario.
The probability density function (PDF) of the BER estimation error of the RBF DFE for
various channel SNRs is shown in Figure

9.8
for BPSK transmission bursts. The actual BER
is the ratio of the number of bit errors encountered in a data burst to the total number
of
bits transmitted in that burst. Figure
9.8
suggests that the RBF DFE provides a good BER
estimation, especially for high channel SNRs. We note, however that the accuracy of the
actual BER evaluation is limited by the burst-length of 144 bits and its resolution is
1/144.
Hence at high SNRs the actual number of errors registered is often
0,
which portrays the BER
estimation algorithm of Equation
9.1
S
in
a
less accurate light in the PDF of Figure
9.8,
than
it is in reality.
We will now analyse the best-case performance of the joint
AQAM
and RBF DFE scheme
in more detail, using the simulation model described
in
Section 9.4.4 and the assumptions
listed in Section 9.4.3. We designed two systems, a higher integrity scheme, having a target
BER

of
lo-*,
which can be rendered error-free by error correction coding and hence we refer
to this arrangement as a data transmission scheme; the lower integrity scheme was designed
for maintaining a BER of
lo-’,
which is adequate for speech transmission especially in con-
junction with FEC. The target BPS values of these schemes were 3 and
4.5
bits per symbol,
respectively, although these values can only be attained for sufficiently high SNRs.
Figure 9.9(a) and Figure 9.9(b) show the simulated best-case performance of the joint
9.4.
JOINT ADAPTIVE MODULATION AND
RBF
BASED EOUALIZATION
401
L
7=
4oooO
SoooO
12oooO 160000
Number
of
symbols
(a)
BPSK
~ OdB
10 dB
30 dB

20 dB
~~~~~~.
40000 S0000
l20000
Number
of
symbols
(c)
16-QAM
160000
20 dB
30 dB
I"
0
40000 SO000 120000 160000
Number
of
symbols
(b)
4-QAM
to-'
e,
lo.s
a
v)
10"
~
-
;:::
~

30 dB


i

::
0
40000
SO000
120000 160000
_-_
.
,.
._
.
Number
of
symbols
(d)
64-QAM
Figure
9.7:
Short-term BER versus symbol index as estimated by the RBF
DFE
over the two-path
equal-weight, symbol-spaced Rayleigh fading channel of Table
9.1.
The RBF DFE had a
feedforward order of
m

=
2,
feedback order of
n
=
1
and decision delay
of
7
=
l
symbol.
Perfect channel impulse response estimation is assumed and the error propagation due to
decision feedback is ignored. The transmitted burst of Figure
8.44
consists of
171
symbols
(144
data symbols and
27
training symbols).
402
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
11
I
I
l

I
I
I
0.9
-0.03
-0.02 -0.01
0
0.01
0.02
0.03
Error
between actual
BER
and estimated
BER
Figure
9.8:
Discretised PDF
of
the error between the actual BER
of
the data
burst
and the BER esti-
mated
by
the RBF DFE for the two-path Rayleigh fading channel
of
Table
9.1

using BPSK.
AQAM and RBF DFE scheme for the target BER of
lop2
designed for speech transmis-
sion and for the target BER of
10W4
created for data transmission, respectively. The BER
performance of the constituent fixed modulation modes is also depicted in both figures for
comparison. The best-case performance was evaluated for two different adaptive modulation
schemes. In the first scheme, the transmitter always transmitted data without transmission
blocking, i.e. the NO TX mode of Equation 9.7 was not invoked. By contrast, in the second
scheme, dummy data was transmitted, whenever the estimated short-term BER was higher
than the target BER, a scenario, which we referred to as transmission blocking. The trans-
mission of dummy data during blocking allowed us to keep monitoring the BER, in order to
determine when to commence transmission and in which modem mode.
We will commence by analysing Figure 9.9(a), where the joint AQAM and RBF DFE
scheme was designed for speech transmission, i.e. for
a
BER of
10p2.
For the adaptive
scheme, which did not incorporate transmission blocking, the performance of adaptive mod-
ulation was better or equivalent to the performance of BPSK in terms of the mean BER and
mean BPS for the SNR range between OdB and 9dB. At the channel SNR of 9dB, even though
the mean BER performance was equivalent for the adaptive scheme and the BPSK scheme,
the mean BPS for the adaptive scheme improved by a factor of
1
S,
resulting in a mean BPS
of

1.5.
In the SNR range of 9dB to 16dB, the adaptive scheme outperformed the 4-QAM
scheme in terms
of
the mean BER performance. At the channel SNR of 16dB, the mean
BERs of both schemes are equivalent, although the mean BPS of the adaptive scheme is 2.7,
resulting in a BPS improvement by a factor of 1.35, when compared to 4-QAM. At the chan-
nel
SNR
of 26dB, the mean BPS improvement of the adaptive scheme is by a factor of 1.3 for
an equivalent mean BER. The adaptive scheme that utilized transmission blocking achieved a
mean BER below
1%.
At the channel SNR of 12dB, even though the mean BER performance
was equivalent for the BPSK scheme and the adaptive scheme with transmission blocking,
the mean BPS for the adaptive scheme improved by a factor of 2. As the
SNR
improved,
the performance of the adaptive schemes both with and without transmission blocking con-
9.4.
JOINT ADAPTIVE MODULATION AND RBF BASED EQUALIZATION
403
verged, since the probability of encountering high short-term BERs reduced. The mean BER
and mean BPS performance
of
both adaptive schemes converged to that of 64-QAM for high
SNRs, where 64-QAM becomes the dominant modulation mode.
Similar trends were observed for data-quality transmission, i.e. for the
lop4
target BER

scheme in Figure 9.9(b). However, we note that for the SNR range between 8dB to 20dB,
the mean BER of the adaptive scheme without transmission blocking was better, than that of
BPSK. This phenomenon was also observed in the narrowband adaptive modulation scheme
of
[l451 and in the wideband joint AQAM and DFE scheme of [32,296], which can be
explained
as
follows. The mean BER of the system is the ratio
of
the total number of bit
errors to the total number of bits transmitted. The mean BER will decrease with decreasing
number of bit errors and with increasing number
of
total bits transmitted in the data burst.
For
a
fixed number of symbols transmitted, the number of total bits transmitted in
a
data
burst is constant for the BPSK scheme, while for the AQAM scheme the total number of bits
transmitted in
a
data burst increased, when
a
higher-order AQAM mode was used. However,
in this case the BER increased. If the relative bits per symbol increment upon using AQAM is
higher than the relative bit error ratio increment, then the mean BER of the adaptive scheme
will be improved. Consequently the adaptive mean BER can be lower than that
of
BPSK.

The probability of encountering each modulation mode employed in the adaptive scheme
based
on
the estimated short-term BER switching mechanism is shown in Figure 9.10 and
Figure 9.1
1
for the BER
=
lo-’
and BER
=
lop4
schemes, respectively. As expected, the
sum of the probabilities at each particular SNR is equal to one. At low SNRs, the lower order
modulation modes (NO TX or BPSK) are dominant, producing
a
robust system. At higher
SNRs, the higher order modulation modes become dominant, yielding
a
higher mean BPS
and yet
a
reduced mean BER. From Figure 9.1 1 (b), we observe that the transmission blocking
mode was dominant in the SNR range of OdB to 4dB and thus the mean BER performance
was not recorded in that range of SNRs in Figure 9.9(b).
Comparing Figure 9.10(a) and Figure 9.1 l(a), the probability of transmission blocking
was higher for data-quality transmission, in order to achieve
a
lower target BER due to the
associated more stringent BER requirements of

lop4. The probability of transmission block-
ing was close to zero, once the channel SNR increased to about 16dB and 20dB for the BER
=
lo-’
and BER
=
lop4
schemes, respectively. These are the points, where the performance
of the adaptive schemes with and without transmission blocking converged,
as demonstrated
in Figure 9.9. We observed that the probabilities of the 4-QAM, 16-QAM and 64-QAM
modes being utilized for the adaptive scheme with and without transmission blocking were
fairly similar. This is because introducing transmission blocking will predominantly affect
the probability
of
BPSK, which will be utilized instead
of
no
data transmission.
In summary, the AQAM RBF DFE scheme has its advantages, when compared to the indi-
vidual fixed modulation modes in terms
of
the mean BER and mean BPS performance. Note
however for the adaptive scheme without transmission blocking that the target performance
of BER
=
lo-’
and BER
=
lOW4

can only be achieved, if the channel SNR is higher than
9dB and 18dB, respectively. The target mean BERs for speech transmission (BER
=
lo-’)
and data transmission (BER
=
10W4)
were achieved for all channel SNRs, when we utilized
transmission blocking. The target performance for speech (BER
=
lo-’)
and data (BER
=
lop4)
transmission in terms
of
mean BPS
(4.5
and 3, respectively) can only be achieved for
the AQAM scheme with and without transmission blocking, if the channel SNR is in excess
of about 22dB. Thus, the advantage
of
using
an
adaptive scheme with transmission blocking
404
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
BPSK BER

AQAM
RBF DFE
AQAM
RBF DFE
4
QAM
BER
-
BER:
16
QAM
BER
0

TX
blocking
64
QAM
BER
* without TX
blocking
*

without TX
blocking
1
-
BPS:
0
-

TX
blocking
loo
l
I_ s/O
5 10 15 20 25 30 35
40
SNR
(dB)
(a)
Target BER is
lo-’
(mean BER for speech transmission)
l
BPSKBER
1
AQAM
RBF DFE
~1
AQAM
Bps
:
RBF DE
4
QAM
BER
I6
QAM
BER ~
1

3
-
TX
blocking
~~~~~~
-
BER:
0
-
TX
blocking
,
~~~
MQAM
BER
1
*
without TX
blocking
,,
*
.
wlthoutTX
blocking
10-70
5
10
15
20
25 30 35

40
SNR (dB)
(b)
Target BER is
lop4
(mean BER for data transmission)
Figure
9.9:
The simulated best-case performance
of
the AQAM RBF DFE showing also the BER per-
formance of the constituent fixed modulation schemes, namely
BPSK,
4-QAM, 16-QAM
and 64-QAM, over the two-path Rayleigh-fading channel
of
Table 9.1 and using the as-
sumptions
of
Section 9.4.3.
9.4.
JOINT ADAPTIVE MODULATION AND
RBF
BASED EQUALIZATION
405
0
5
10
I5 25
30

35
40
SNc(dB)
0
5
10
I5
20
25
30
35
40
SNR
(dB)
(a)
With transmission blocking
(b)
Without transmission blocking
Figure 9.10: The probability of encountering the various
M-QAM
modulation modes in the joint
AQAM
and RBF DFE scheme for best-case performance during speech-quality trans-
mission (target BER
of
0.01) over the two-path equal-weight, symbol-spaced Rayleigh
fading channel using the simulation parameters listed in Table
9.1
and the assumptions
stated in Section 9.4.3.

IOK~
;i
0
-
NoTX
A
~~
4QAM
V

WQAM
08
(a)
With transmission blocking
(b)
Without transmission blocking
Figure 9.11: The probability of encountering the
various
M-QAM
modulation modes in the joint
AQAM
and RBF DFE scheme for best-case performance during data-quality trans-
mission (target BER
of
lop4)
over the two-path equal-weight, symbol-spaced Rayleigh
fading channel using the simulation parameters listed in Table 9.1 and the assumptions
stated in Section 9.4.3.
406
CHAPTER

9.
RBF-EQUALIZED ADAPTIVE MODULATION
is that the performance of the joint AQAM and RBF DFE scheme can be 'tuned' to a certain
required mean BER performance. However, the disadvantage is that the utilization of trans-
mission blocking results in transmission latency, an issue, which was addressed for example
in [40,41]. Specifically, the interdependency of the required buffer size, doppler frequency
and latency was analysed. Furthermore, frequency hopping was proposed for reducing the
average duration of NO TX mode at low Doppler frequencies, where the latency and the
buffer size may become excessive.
Let us now embark on a comparative analysis between the joint AQAM RBF DFE scheme
and the Kalman-filtering based joint AQAM DFE scheme introduced by Wong
et
al.
[32] for
wideband channels. The joint AQAM DFE scheme in [32] used the
pseudo-SNR
at the output
of the DFE as the switching metric, an issue discussed briefly in Section 9.2. The pseudo-
SNR at the output of the DFE was compared to a set
of
pseudo-SNR thresholds optimized
using Powell's method [297]. Table 9.2 gives the results of the optimization process invoked,
in order to achieve transmission integrities of
lop2
and 10W4 over the two-path Rayleigh-
fading channel of Table 9.1 [32]. The conventional DFE used
in
the adaptive scheme had
a feedforward order of
m

=
15, feedback order of
R
=
2 and decision delay of
T
=
15
symbols. The parameters
m,
R
and
T
of the conventional DFE were chosen such that it
exhibited the best possible performance for our simulation scenario and hence further increase
of the feedforward order would not give a significant performance improvement. We note
again that for our best-case performance comparisons, the switching metric used for both
schemes
-
namely the short-term BER for the AQAM RBF DFE scheme and the pseudo
SNR for the AQAM DFE scheme
-
was estimated perfectly prior to transmission and the
appropriate AQAM mode was chosen for the data burst to be transmitted, which satisfied the
target BER requirement.
ll(dB)
23.051 16.8846 10.4541
8.30459 Data
17.8342 11.7181 6.3488
3.68026

Speech
b(dB) /3(dB)
l2(dB)
Table
9.2:
The optimized switching levels
1,
of
the joint adaptive modulation and DFE scheme
for
speech and data transmission in the two-path Rayleigh fading channel
[32].
The target mean
BER
and
BPS performance
for
speech was
lo-'
and
4.5,
respectively, while
for
computer
data,
lop4
and
3,
respectively.
Figure 9.12 provides the BER performance comparison of the conventional DFE and the

RBF DFE over the two-path Rayleigh fading channel of Table 9.1 for the constituent fixed
modulation modes. The BER performance of the RBF DFE for BPSK and 4-QAM was better
than that of the conventional DFE, as the SNR increased. By contrast, the BER performance
of the RBF DFE was inferior compared to that of the conventional DFE for 16- and 64-QAM.
The performance of the RBF DFE can be, however, improved by increasing both the decision
delay
T
and the feedforward order
m,
as argued
in
Section
S.
1
1,
at the expense of increased
computational complexity. However, the present parameter values for the conventional DFE
and RBF DFE are convenient, since they yield similar BER performances.
The performance comparison of the adaptive schemes, i.e. that of the AQAM DFE and
AQAM RBF DFE, is given in Figure 9.13. For the target BER system, the AQAM
RBF DFE provides a better BER performance, than the Kalman-filtering based AQAM DFE
9.4.
JOINT ADAPTIVE MODULATION AND
RBF
BASED EQUALIZATION
407
in the SNR range from OdB to 28dB at the expense of a lower BPS performance, especially
for higher SNRs. As the SNR exceeds 28dB, the BER performance of the AQAM DFE
scheme becomes superior to that of the AQAM RBF DFE. This is because at higher SNRs
the 64-QAM modulation mode prevails and since the 64-QAM BER performance of the

conventional DFE was better, than that of the RBF DFE in Figure 9.12, hence the mean BER
improvement of the AQAM DFE is expected, when compared to that of the AQAM RBF
DFE.
For the
lop4
target BER system, the BER performance of the AQAM DFE and AQAM
RBF DFE is fairly similar in the SNR range from 5dB to 12dB, but the BPS performance of
the AQAM RBF DFE is better, than that of the AQAM DFE in that range. In this SNR range
the lower-order modulation modes dominate. Since the RBF DFE can provide a better BER
performance, than that of the conventional DFE for the lower-order modulation modes, the
BPS performance of the AQAM RBF DFE can be improved, while maintaining a similar BER
performance to that
of
the AQAM DFE. As the SNR exceeds 12dB, the BER performance
of
the AQAM RBF DFE remains better at the expense of a lower BPS performance.
The overall results of our simulations show that the AQAM RBF DFE is capable
of
per-
forming similarly to the AQAM DFE at a lower decision delay and lower feedforward and
feedback order. However, the computational complexity of the RBF DFE is dependent on the
modulation mode, since the number of RBF centres increases with the number of modulation
levels, as discussed in Section 8.7. This is not
so
in the context of the conventional DFE,
where the computational complexity is only dependent on the feedforward and feedback or-
der. Table 9.3 compares the computational complexity of the RBF DFE
(m
=
2,

n
=
1,
T
=
1)
and the conventional DFE
(m
=
15,
n
=
2)
used in our simulations. The complexity
analysis of the RBF DFE is based on Table
8.10.
The high computational cost incurred by the
RBF DFE in the high-order
M-ary modulation modes presents
a
drawback for the AQAM
RBF DFE scheme.
Operation
0
4096 256
16 4
division
17
12288 768
48

12
multiplication
16
16320 1008 60 15
subtraction and addition
Conv. DFE
RBF DFE
BPSK
64-QAM 16-QAM 4-QAM
exPO
0
4096 256 16
4
Table
9.3:
Computational complexity of RBF DFE and conventional
DFE
per equalized output sample.
The RBF
DFE
has
a
feedforward order of
m
=
2,
feedback order
of
n
=

1
and decision
delay
of
T
=
1
symbol. The number of RBF hidden units
ns,3
is dependent on the order
of
the
M-QAM
modes and the channel memory
L
where
nzs,3
=
The channel
memory is assumed to be
L
=
1.
The complexity analysis of the RBF
DFE
is based on
Table
8.10.
The conventional
DFE

has
a
feedforward order
of
m
=
15,
feedback order of
n
=
2
and decision delay of
T
=
15
symbols.
Nevertheless, we note that unlike the conventional DFE, the AQAM RBF DFE is capable
of performing well over channels, which result in non-linearly separable received phasor
constellations.
408
CHAPTER
9.
RBF-EQUALIZED ADAPTIVE MODULATION
Conventional
DE
:
BPSK
4 QAM
64 QAM



16 QAM
_
RBFDFE
:
0
.
BPSK
0
4 QAM
n
16 QAM
0

64 QAM
5
10
15
20
25
SNR
(dB)
30
35
40
Figure 9.12:
BER versus
SNR
performance of the conventional DFE and the RBF
DFE

over the two-
path equal-weight symbol-spaced Rayleigh-fading channel of Table
9.1
for different
M-
QAM
schemes. The conventional DFE has a feedforward order of
m
=
15,
feedback
order of
n
=
2
and decision delay of
7
=
15
symbols. The RBF DFE has
a
feedforward
order of
m
=
2,
feedback order
of
7c
=

1
and decision delay
of
T
=
1
symbols.
9.4.6
Discussion
In the above sections, BbB adaptive modulation was applied in conjunction with the RBF
DFE
of
Section
8.11
in a wideband channel environment. The short-term BER of Equa-
tion
9.15
estimated by the RBF DFE was used as the modem mode switching metric in order
to switch between different modulation modes. The validity
of
using this metric was tested in
Section
9.4.5
and in Figure
9.8
it was shown that the RBF DFE gives a good BER estimate for
the adaptive scheme to maintain the target mean BER performance. The simulation results
also showed that there was
a
performance improvement in terms

of
the mean
BER
and mean
BPS, when compared to the constituent fixed modulation modes. The performance of the
joint
AQAM RBF
DFE
scheme was then compared to that of the joint AQAM conventional
DFE scheme investigated by Wong
[32].
The AQAM RBF
DFE
having
a
lower feedforward
and feedback order and a smaller decision delay, showed comparable performance to the
9.4.
JOINT ADAPTIVE MODULATION AND
RBF
BASED EOUALIZATION
409
Conventional DFE
:
Speech Transmission
:
mean BER performance
mean BPS performance
Data Transmission
:

mean BER performance
mean BPS performance
RBF DFE
:
Speech Transmission
:
x
~ mean BER performance
0
~ ~ mean BPS performance
Data Transmission
:
.
mean BER performance
0
-
-
-
mean BPS performance
SNR
(dB)
Figure
9.13:
Simulated best-case performance of the
AQAM
lU3F DFE scheme and the numerical
best-case performance of the joint
AQAM
conventional DFE scheme for speech- and data-
transmission

[32], using the parameters listed in Table 9.1 and the assumptions stated in
Section
9.4.3. The modem mode switching levels used for the joint
AQAM
conventional
DFE scheme are listed in Table
9.2. The
RBF
DFE had
a
feedforward order of
m
=
2,
feedback order of
n
=
1
and decision delay of
T
=
1
symbol and the conventional DFE
had a feedforward order of
m
=
15,
feedback order of
n
=

2
and decision delay of
7
=
15
symbols.