Generalized MLP/BP-based MIMO DFEs for Overcoming ISI and ACI in Band-limited Channels

Abstract

In this work, we base on generalized multi-layered perceptron neural networks with backpropagation algorithm (generalized MLP/BP) to construct multi-input multi-output (MIMO) decision feedback equalizers (DFEs). The proposal is used to recover distorted nonreturn-to-zero (NRZ) data in wireline parallel band-limited channels. From the simulations, we note that the proposed design can recover severe distorted NRZ data as well as suppress intersymbol interference (ISI), adjacent channel interference (ACI) and background noise. The better BER performance as compared to a set of LMS DFEs and an MLP/BP-based MIMO DFE is achieved in the wireline parallel band-limited channels where the data rate is ten times as much as the channel bandwidth.

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* Works supported by MOEA and NSC of Taiwan, ROC, under Grant
95-EC-17-A-01-S1-031 and NSC-95-2221-E-009-291, respectively.
Generalized MLP/BP-based MIMO DFEs for
Overcoming ISI and ACI in Band-limited Channels
Terng-Ren Hsu1, 2, Chi-Shi Chen1, 3, Terng-Yin Hsu4, and Chen-Yi Lee1
1Department of Electronics Engineering, National Chiao Tung University
1001, University Road, Hsinchu 300, Taiwan
2Department of MicroElectronics Engineering, Chung Hua University
707, Sec.2, WuFu Rd, Hsinchu 300, Taiwan
3National Chip Implementation Center (CIC), National Applied Research Laboratories, Taiwan
7F, No.26, Prosperity Rd. 1, Science Park, Hsinchu 300, Taiwan
4Department of Computer Science and Information Engineering, National Chiao Tung University
1001, University Road, Hsinchu 300, Taiwan
Tel: +886-3-5712121 Ext. 54789; Fax: +886-3-5724176
Email: trhsu@royals.ee.nctu.edu.tw
cschen@royals.ee.nctu.edu.tw
tyhsu@csie.nctu.edu.tw
cylee@cc.nctu.edu.tw
ABSTRACT
In this work, we base on generalized multi-layered perceptron
neural networks with backpropagation algorithm (Generalized
MLP/BP) to construct multi-input multi-output (MIMO) decision
feedback equalizers (DFEs). The proposal is used to recover
distorted nonreturn-to-zero (NRZ) data in wireline parallel band-
limited channels. From the simulations, we note that the proposed
design can recover severe distorted NRZ data as well as suppress
intersymbol interference (ISI), adjacent channel interference (ACI)
and background noise. The better BER performance as compared
to a set of LMS DFEs and an MLP/BP-based MIMO DFE is
achieved in the wireline parallel band-limited channels where the
data rate is ten times as much as the channel bandwidth.
I. INTRODUCTION
In wireline data communications, the source data are
transmitted over intersymbol interference (ISI) channels, corrupted
by noise, and then received as distorted nonreturn-to-zero (NRZ)
ones. Besides, adjacent channel interference (ACI) will lead to
more distortions and worse performance. In addition, the additive
white Gaussian noise (AWGN) is used to model the background
noise.
In this work, we consider several parallel band-limited channels
where the data rate is ten times as much as the channel bandwidth.
In such channels, the tail of each pulse in the received signal will
be elongated, resulting in lack of zero crossing for the received
signal. Besides, adjacent signals result in color noises; the received
signal will be tainted by such color noises. Intersymbol
interference and adjacent channel interference make the received
signal with large distortion. Therefore, it is necessary to apply data
equalizers to recover the original waveform from the distorted one
in practical communication systems [1].
Conventionally, the NRZ signal recovery is based on either
linear equalizers (LEs) [1], or decision feedback equalizers [1-2].
The linear equalizer can restore the originally transmitted signal in
a band-limited wireline channel, but also amplifies high-frequency
noise that severely degrades the system performance. The DFE
employing previous decisions to remove the ISI on the current
symbol has been extensively exploited to serve intersymbol
interference rejection. The least mean squares (LMS) algorithm is
used to estimate the coefficients of the equalizer [1-2] whose
accuracy determines the system performance.
Recently, various equalizer designs based on artificial neural
networks have been applied to the severely distorting signal
recoveries. Having the capability of classifying the sampling
pattern and fault tolerance, neural-based schemes provide better
performance than conventional equalization techniques.
Based on the MLP/BP neural networks [3], the feedforward
equalizers [4-5], and the decision feedback equalizers [6] have
been widely used to NRZ signal recovery in severe ISI channels.
Moreover, Perceptron neural networks have been used as data
equalizers in ISI and ACI channels [7-8]. For high-speed wireline
data communications, it is common to use waveform equalization
technique to improve the data rate or decrease the error rate [9-11].
In practice circuits, interconnect paths of parallel data I/O would
cause the adjacent channel interference. The receiver must detect
correct data under ISI, ACI, and AWGN conditions.
In our previous study [12], we use MLP/BP-based DFEs to
tolerate sampling clock skew and channel response variance in
wireline band-limited channels. Also, we use an MLP/BP-based
MIMO DFE [13] to suppress ISI, ACI, and AWGN in wireline
parallel band-limited channels. This work is based on above
studies and the generalized MLP/BP neural networks [14-15]. We
use a generalized MLP/BP-based MIMO DFE to recover the
distorted NRZ signal in wireline parallel band-limited channels.
From the simulations, better performances as compared to a set of
LMS DFEs and an MLP/BP-based MIMO DFE are achieved.
This paper is organized as follows. The equivalent channel
model, and the proposed approach are presented in section 2 while
section 3 shows the simulation results. Finally, the conclusions are
presented in section 4.
II. PROPOSED ARCHITECTURE
In this section, an equivalent channel model is presented first
followed by the proposed approach. The architecture and
configuration of the generalized MLP/BP-based MIMO DFE are
discussed in detail.
A. Channel Models
If the data rate is higher than the channel bandwidth, the
received signal pulse is unable to complete its transition within a
symbol interval. Besides, interconnect paths of parallel I/O
channels would cause the adjacent channel interference and taint
the received signals. The equivalent model for the ISI channels
with ACI and AWGN is shown in Fig. 1 where finite impulse
response (FIR) filters are used to model the ISI channel responses
and ACI responses with the AWGN.
The ISI responses and ACI responses with AWGN can be
written as follows:
1031-4244-0583-1/07/$20.00 ©2007 IEEE

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L
L z
?
?
f...zf
?
zff(z)H
???
???????
?
?
?
i
?
2
2
1
100
(1)
M
rMrrrr
zg...zgzgg(z)A
???
?????
2
2
1
10
(2)
?
??
L
ikik
xfy
0
0 (3)
?
?
j
?
?
??
M
r
kjj
r
k
xga
0
(4)
kkkk
nayy
ˆ
??
(5)
where H0(z) is the transfer function of the ISI channel responses; L
is the length of the ISI channel response; Ar(z) is the transfer
function of the ACI responses; M is the length of the ACI response;
xk
of r-th ACI response; yk is the channel output which is warped by
ISI only; ak is the sum of adjacent channel interference; nk is the
AWGN; ?k is the received signal which is distorted by ISI, ACI
and AWGN.
ois the input sequence of ISI response; xk
ris the input sequence
ISI Response
ACI Response
Weight #12
Weight #1M
Weight #11
RX
TX
2-PAM Signal
ISI Response
ACI Response
Weight #22
Weight #2M
Weight #21
RX
TX
2-PAM Signal
ISI Response
ACI Response
Weight #M2
Weight #MM
Weight #M1
RX
TX
2-PAM Signal
AWGN
AWGN
AWGN
NRZ Signal
NRZ Signal
NRZ Signal
ISI
ACI
Fig. 1. Equivalent model for the band-limited channels with
adjacent channel interference.
In this work, the band-limited channels with ACI are used to
verify the proposed approaches. Such channel condition is
practical in many wireline communication systems, whose the
transfer function of the band-limited channels is H0(z) = 0.4665 +
0.2489z-1+ 0.1328z-2 + 0.0708z-3 + 0.0378z-4 and the transfer
function of the ACI is Ar(z) = 0.408 + 0.816z-1 + 0.408z-2. The
frequency responses of them are illustrated in Fig. 2.
Fig. 2. Frequency responses of ISI and ACI.
We assume that these parallel interconnection paths lay on a
plane within a chip or within a PCB. Because the effect of ACI
should be proportional to the distance with an inverse ratio, it is a
worse case that uses sorted uniform distribution random values
between 1 and 0 to simulate the effects between different channels.
And we assume the self-interference of ACI is zero. With these
conditions, we construct an N?N symmetric matrix and normalize
this matrix to make the sum of squares of all elements be N. The
weighting of ACI between different channels is shown in Table 1
where N is equal to 8.
The received signals include the intersymbol interference that
caused by the band-limited channel, and the adjacent channel
interference that caused by crosstalk between different channels.
The transmitted signal is expected to be deteriorated substantially
by ISI, ACI, and AWGN.
Table 1. Weighting of ACI among different channels.
Ch 1 2 3 4 5 6 7 8
1
0 0.7070 0.5984 0.3760 0.3112 0.1641 0.1576 0.1338
2
0.70700 0.4131 0.3155 0.2690 0.1800 0.1398 0.0215
3
0.5984 0.41310 0.5883 0.4451 0.3705 0.2296 0.0353
4
0.3760 0.3155 0.58830 0.6650 0.4303 0.4189 0.0002
5
0.3112 0.2690 0.4451 0.6650 0 0.5375 0.2003 0.1160
6
0.1641 0.1800 0.3705 0.4303 0.5375 0 0.3726 0.1420
7
0.1576 0.1398 0.2296 0.4189 0.2003 0.3726 0 0.6319
8
0.1338 0.0215 0.0353 0.0002 0.1160 0.1420 0.63190
B. Generalized MLP/BP-based MIMO DFEs
Artificial neural networks are systems that are deliberately
constructed to employ some organizational principles resembling
from human brain. An artificial neural network consists of a set of
highly interconnected neurons such that each neuron output is
connected to other ones or/and to itself through weights with or
without lag. Recently, many different artificial neural networks
have been proposed, but the MLP/BP neural network is the most
important and popular one [3]. In this work, we base on the
MLP/BP neural network model and make a key modification to
propose a new approach, the generalized MLP/BP neural network.
This new method is applied to the waveform equalization and
results in a significant improvement in performance.
To achieve better performance, a multivariate power series is
used to replace a first order multivariate polynomial as the
summation function of the MLP/BP neural networks, leading to a
significant modification for the traditional MLP/BP neural network.
Therefore, regarded as a general form of the MLP/BP neural
network, the proposed model can be termed as a generalized
MLP/BP neural network. The corresponding backpropagation
algorithm of the proposed approach is deduced by the gradient
steepest descent method. The assumptions and the recursive
formulas are shown in Appendix. [14-15]
The application of MLP/BP-like neural networks to solve
problems includes two phases, one is training procedure and
another is test procedure. In the training phase, we use the gradient
steepest descent method to minimize the error function for
updating the weights. After that we apply the training results to
obtain the network response in the test phase. The outcome is
really a sub-optimal solution.
Similar to the traditional MLP/BP neural network, the training
procedure of the proposed approach attains different performance
by varying initial conditions, learning rates, network parameters
and summation function orders. Moreover, designers could
perform numerous independent training runs and select the most
suitable result as the final solution. In this work, we execute fifty
independent runs and select the best one as the final result.
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The block diagram of the generalized MLP/BP-based MIMO
DFE is shown in Fig. 3. It employs the single hidden layer MLP
architecture. The inputs of the proposed approach consist of feed-
forward signals, which come from the input symbols by tapped-
delay-line registers, and feedback signals, which come from
previous decisions by other tapped-delay-line registers.
Because the order of the neuron of the generalized MLP/BP
neural networks is more than one, it is necessary to generate the
power terms for the inputs in each layer. Although the complexity
of the generalized MLP/BP-based MIMO DFE is higher than that
of the MLP/BP-based MIMO DFE, the generalized MLP/BP-based
MIMO DFE provides better performance.
Z-1
Z-1
Z-1
X-2
X-1
X0
X-n
Z-1
Y1
Y2
Ym
Z-1
Z-1
Ch-1
Output
Input Layer
Hidden Layer
Output Layer
Generalized MLP/BP Neural Network
Threshold
Ch-1
Input
Ch-n
Output
Threshold
Ch-nFeedback
Ch-1
Feedback
Z-1
Z-1
Z-1
X-2
X-1
X0
X-n
Z-1
Y1
Y2
Ym
Z-1
Z-1
Ch-n
Input
Power Term Generator
Power Term Generator
Fig. 3. The generalized MLP/BP-based MIMO DFEs.
III. SIMULATION RESULTS
The performance of the generalized MLP/BP-based MIMO
DFE is evaluated through the simulations for the distorted NRZ
signal recovery in the band-limited channels with co-channel
interference. The data rate is ten times of the channel bandwidth. It
is a wireline application so we can select a longer training set to
achieve better performance.
All equalization schemes in this work have 11 symbols per
channel in the forward part and 5 symbols per channel in the
feedback part. We assume there are 8 parallel channels in this
system. The number of neurons in the input layer is equal to 128
(16×8). All neural-based approaches exploit the single hidden
layer MLP architecture. The number of neurons in the hidden layer
is 16. Since all the proposed equalization schemes have a single
output per channel, the number of neurons in the output layer is
equal to 8 (1×8).
In the training procedure, the length of the training set is equal
to 104 symbols and the total training epochs are 102. The two-
phase learning is used with the learning rate of 0.5 (2-1) when the
mean square error of the training set is larger than 10-3, and the
learning rate of 0.125 (2-3), otherwise. When the training epochs
exceed 80 percent of the total epochs, the best parameters will be
recorded to achieve the lowest mean square error of the training set
in the last 20 percent of the training epochs. Hence the steady-state
training results can be recognized. In fact, the simulations indicate
no unstable problems as all training processes are converged.
Because different initial conditions lead to different effects, the
non-training evaluation set that has 8×105 symbols is used to
examine the training quality of numerous independent simulation
outcomes. After numerous independent training and evaluation
runs, those yielding better outcomes will be chosen to perform a
long trial with the test set, and then the best one will be the final
test result. The length of the test set is 8×106 symbols, and the
evaluation set is its subset. In this work, we execute 50
independent runs and select the best one as the final result.
Also, we compare the performance of our proposed approach
with that of a set of LMS DFEs. We use a LMS DFE without cross
inputs for a channel among these parallel channels.
In this work, the ISI response indicates that the data rate is ten
times of the channel bandwidth. The training noise and the
evaluation noise are assumed to be SNR=20dB, and SNR of the
test signal is between 10dB and 25dB. The signal to adjacent
channel interference ratio (SIR) is equal to 10, 12.5, 15, 17.5, and
20, respectively.
Fig. 4 shows the comparisons of the BER vs. SNR performance
for a set of LMS DFEs, the MLP/BP-based MIMO DFE, and the
generalized MLP/BP-based MIMO DFE in the wireline band-
limited channels with different SIR conditions. We find that the
generalized MLP/BP-based MIMO DFE outperform the MLP/BP-
based MIMO DFE under small background noise with large
adjacent channel interference.
Fig. 4. BER vs. SNR performance at SIR=10, 15 and 20dB.
Considering different SIR conditions in the wireline band-
limited channels at SNR=15dB and 20dB, Fig. 5 also shows the
comparisons of the BER vs. SIR performance for the LMS DFEs,
the MLP/BP-based MIMO DFE, and the generalized MLP/BP-
based MIMO DFE. As compared with LMS DFEs and the
MLP/BP-based MIMO DFE, the generalized MLP/BP-based
MIMO DFE can improve the SIR tolerance about 2.5dB and 0.3dB
at BER=10-3. Besides, we find that the suitable summation
function order is equal to two when small interference presented,
or three when large distortion appeared.
Fig. 5. BER vs. SIR performance at SNR= 15 and 20dB.
Because the architecture of the proposed approach involves a
large number of addition and multiplication, such requests cause
high hardware complexity. For hardware implementations, the
architecture of the generalized MLP/BP-based MIMO DFEs is
more complex than that of the conventional methods. However, we
think that the rapid progress of VLSI technology will afford more
complex approaches for better performance.
IV. CONCLUSION
According to the simulation results, the generalized MLP/BP-
based MIMO DFE can recover severe distorted NRZ signals as
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well as suppress ISI, ACI and AWGN to achieve better BER
performance than a set of LMS DFEs and an MLP/BP-based
MIMO DFE in wireline parallel band-limited channels in which
the data rate is ten times as much as the channel bandwidth. Also
the proposed scheme is MIMO architecture, we can extend the
input and output number for more complex system. Overall, the
generalized MLP/BP-based MIMO DFE can yield a substantial
improvement over the MLP/BP-based MIMO DFE that performs
better than a set of LMS DFEs.
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APPENDIX
The Generalized MLP/BP Neural Networks
The network architecture of the generalized MLP/BP neural
networks is the same as the traditional. However, the construction
of neurons of the both is different. A neuron of this new approach
is shown in Fig. 6.
f(.)
Wj11
Wj12
[A(n-1)1]1
[A(n-1)1]2
[A(n-1)i]1
Anj
[A(n-1)n]m
?
Wji1
Wjnm
Fig. 6. Neuron of the generalized MLP/BP neural networks.
To achieve better performance, the multivariate power series is
used as the summation function of this new approach. The
corresponding backpropagation algorithm is deduced by the
gradient steepest descent method. The assumptions and the
recursive formulas are shown as follows. [14-15]
nj??

??
) f(netAOutput
nj
(6)
j
im
m
n
(
ijim nj
AWFunction Summation_ net
????
? ) 1
(7)
?
j
????
njj
ATFunctionErrorE
2)(
2
1
_
(8)
m
n
( ?
i nj
jim
jim
A
W
E
W
) 1
?????????
?
?
?
(9)
??
for output layer:
?
?
? ?
j nj
? ? ?
(10)
)( ')(
nj njjnj
netfAT
??
(11)
for hidden layer:
)( '][
1
1
1
nj
k
p
m
m
nj kjm )k(nnj
netfAWm
??
???????
?
?
?
(12)
where Anj is the output of neuron j in the n-th layer; f(.) is the
transfer function for obtaining the output of a neuron; netnj is the
output of the summation function of neuron j in the n-th layer; m is
the order of the summation function; Wjim represents the weight of
the connection between neuron j in the n-th layer and neuron i in
the (n-1)-th layer corresponding to order m; ?j is the threshold (bias)
of neuron j; Tj is the desired output of the neuron j in the output
layer; E is the error function; ?Wjim is the update quantity of Wjim;
??j is the update quantity of ?j; ? is the learning rate, and ?nj is the
error signal of neuron j in the n-th layer.
The proposed method is actually equivalent to the traditional
MLP/BP neural network when m=1, indicating that later is a
special case of former. Thus the approach being presented is a
generalized model. Moreover, the network configuration of this
scheme has more degrees of freedom than the traditional one.
Because the summation function of the generalized MLP/BP
neural networks is a multivariate power series (nonlinear function),
the boundaries of neighbors become either nonlinear or piecewise
nonlinear. As the nonlinear summation function within each
neuron is materialization in each layer of the generalized MLP/BP
neural networks, the proposed approaches present continuous
nonlinear pattern space mapping potential.
106