RADIAL BASIS FUNCTION DECISION FEEDBACK EQUALISER ASSISTED
BURST-BY-BURST ADAPTIVE MODULATION
M. S. Yee, L. Hanzo
Dept. of Electr. and Comp. Sc., Univ. of Southampton, SO17 1BJ, UK.
Tel: +44-703-593 125, Fax: +44-703-594 508
Email:lh@ecs.soton.ac.uk, http://www-mobile.ecs.soton.ac.uk
ABSTRACT
The performance of radial basis function decision
feedback equalised burst-by-burst adaptive modu-
lation is presented for transmission over dispersive
wideband mobile channels. Radial Basis Function
(RBF) network based channel equalisers have a close
relationship with Bayesian schemes. The RBF de-
cision feedback equaliser (RBF DFE) is capable of
estimating the 'short term bit error rate' of the
received data burst and this estimate is used as
the modem mode switching criterion in order to
switch between dierent modulation schemes. This
scheme is shown to give a signicant improvement
in terms of mean bit error rate (BER) and bits per
symbol (BPS) performance compared to that of the
individual xed modulation schemes.
1. BACKGROUND
Burst-by-burst Adaptive Quadrature Amplitude Modula-
tion (AQAM) schemes employ a higher-order modulation
scheme, when the channel quality is favourable, in order to
increase the throughput and conversely, a more robust lower
order modulation scheme is utilized to improve the mean
BER performance, when the channel envelope encounters
a deep fade. The principles of AQAM scheme were sum-
marized for example by Wong [1] et al. In this paper, we
present a novel adaptive modem scheme for transmissions
over wideband mobile channels, which employs a Radial
Basis Function (RBF) based channel equaliser with deci-
sion feedback, in order to mitigate the eects of the disper-
sive wideband channel. Chen, McLaughlin, Mulgrew and
Grant [2] proposed a range of so-called RBF network based
channel equalisers, which are potentially capable of error-
freely detecting the received signalling symbols even in a
scenario, where the phasors become linearly non-separable
due to the inter-symbol interference (ISI) in
icted by the
channel. In this situation conventional equalisers would be
unable to remove the eects of ISI and hence would exhibit
a residual BER. Additionally, Chen et al. [3] introduced de-
cision feedback in their RBF-based equaliser, in order to re-
duce its computational complexity. The RBF decision feed-
back equaliser (RBF DFE) was then extended to higher-
order QAM schemes, which were investigated in [5]. The
The nancial support of the following organisations is grate-
fully acknowledged: Motorola ECID, Swindon, UK; European
Community, Brussels, Belgium; Engineering and Physical Sci-
ences Research Council, Swindon, UK; Mobile Virtual Centre of
Excellence, UK.
reader is referred to the above references for background
reading.
2. SYSTEM OVERVIEW
The structure of the joint AQAM and RBF network based
equalisation scheme is portrayed in Figure 1. The receiver
rst extracts the modulation mode used in its received data
burst. At the same time the corrupted received data burst
is equalised, the BER of the transmitted burst is calcu-
lated at the output of the RBF DFE and it is used as the
AQAM modem mode switching criterion in order to deter-
mine the modem mode to be used during the next transmis-
sion burst. This regime assumes a Time Division Duplex
(TDD) arrangement, where the uplink (UL) channel qual-
ity is estimated on the basis of the Downlink (DL) channel
quality.
Modulation
Mode
Switch
Switching
Threshold
Look-up Table
Modulation
Level
Estimator
Modulation
Mode of Data
Burst
Short Term
Probability of
Bit Error of the
Data Burst
Equalised
DataDFE
RBFData Transmitter
Noise
Channel Receiver
Figure 1: System schematic of the joint adaptive modula-
tion and RBF equaliser scheme
2.1. Switching Criterion
The M-QAM RBF equaliser of [5] consists of M RBF net-
works that provide the conditional probability density func-
tion of each legitimate QAM symbol, I
i
; i = 1; : : : ;M, if the
channel impulse response (CIR) is known. Furthermore, the
centers of the RBF network are assigned the values of the
channel states. The outputs of the RBF networks are given
by [2, 3, 5]:

i
(v
k
) =
n
s
X
j=1
w
j
'
j
(v
k
);
'
j
(v
k
) = exp(kv
k
c
j
k
2
=2
2
);
i = 1; : : : ;M (1)
where  is the RBF width, w
j
are the RBF weights, c
j
are the RBF centers and n
s
is the number of the hidden
RBF nodes, which are represented by '
j
. The a-posteriori
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