Fuzzy Adaptive Blind Equalizer Using Extended Kalman Filter
Based Adaptation Algorithm For Powerline Channel
Wai Kit Wong and Heng Siong Lim
Faculty of Engineering and Technology, Multimedia University, Jln Ayer Keroh Lama,
75450 Melaka, Malaysia. Tel:+60 06-2523258
Email:wkwong@mmu.edu.my;hslim@mmu.edu.my
Abstract
Fuzzy adaptive equalizer (FAE) is a knowledge based equalizer
operating on linguistic variables. The advantages of using fuzzy
logic adaptation scheme with respect to more traditional
adaptation schemes in powerline communication system are the
simplicity of the approach and the use of knowledge (fuzzy IF-
THEN rules and input output pairs information) about the
communication medium. This paper presents a new adaptive blind
equalization method based on fuzzy logic for powerline channel.
We introduce a new type of fuzzy adaptive blind equalizer (FABE)
using extended Kalman filter (EKF) based adaptation algorithm
for powerline channel equalization. The proposed blind equalizer
for powerline channel has the following merits: It is new and
simple in design, and it does not requires training sequence. In a
changeable distorted powerline channel, data transmission is
continuous and do not stop for training the equalizer. The
performance of EKF-based FABE is compared with two other
types of FABEs based on the recursive least squares (RLS) and
the least mean squares (LMS) adaptation algorithm. The
simulation results show that EKF-based FABE has faster
convergent and lower steady state probability of error compared
to the other two FABEs. The bit error rate (BER) of the EKF-
based FABE is close to that of the optimal equalizer.
I. INTRODUCTION
The term equalizer or filter in powerline communication system is
commonly referred to a device that is designed to perform signal
processing operations by extracting information about a
prescribed quantity of interest from noisy and intersymbol
interfered data [1]. In conventional equalization process, initial
acquisition of the equalizer’s parameters is usually accomplished
using learning sequences transmitted periodically in time.
However, for the sake of simplicity in system design and
convenience in system implementation, it is sometimes desirable
to let the receivers start up without the aid of the transmitter. For
certain powerline communication system, it is impractical to
utilize a training sequence of long duration and the system cost
involved to train the equalizer with repeated transmission of a
known sequence is typically high. Hence a brilliant way to
overcome such problems is by applying blind equalization
technique.
Blind channel equalization, or more formally, unsupervised
equalization, is a type of equalization technique that depends only
on the received samples and assumptions on the input data to
identify the channel [1]. The idea of blind equalization systems
dates back to the pioneering works of Sato [2], [3] and Godard [4],
[5]. The Sato algorithm for blind equalization was introduced
originally to deal with one-dimensional multilevel pulse
amplitude modulation (M-ary PAM) signals, which is more robust
than a decision-directed algorithm [1]. Godard algorithm is
considered to be the most successful among the Bussgang family
of blind equalization algorithms, as demonstrated by the
comparative studies done in [6] and [7]. The Godard algorithm is
more robust than other Bussgang algorithm due to the fact that
cost function used for its derivation is based solely on received
signals’ amplitudes [8]. Under steady state conditions, blind
equalizer using Godard algorithm attains a mean square error that
is the lowest among all the Bussgang algorithm existed in the
world nowadays [8].
In this paper, we modify on a class of Bussgang-type
equalizers that employ the Godard algorithm. In particular, we
have replaced the transversal filter in the conventional Bussgang-
type equalizer with a fuzzy adaptive filter. The modified
Bussgang type equalizers (i.e., fuzzy adaptive blind equalizer
(FABE)) operate on the received signals sampled at the baud rate.
Unlike most of the blind equalizers recently proposed, FABE is a
knowledge based system operating on linguistic variables.
Linguistic information (fuzzy IF-THEN rules) and numerical
information (input-output pairs) can be combined into the blind
equalizer. We further derive a FABE that uses an extended
Kalman filter (EKF) adaptation algorithm [9] for equalization of
powerline channel. Simulation results show that this type of
FABE has faster convergent speed compared to both RLS-based
FABE and LMS-based FABE.
The paper is organized as follows: Section II briefly comments
on powerline data transmission system using FABE. Section III
describes the structure of the proposed FABE and the adaptation
algorithm. Section IV contains some computer simulation results
and Section V summarizes the work.
II. POWERLINE DATA TRANSMISSION SYSTEM
USING FABE
The baseband powerline data transmission system using FABE
is shown in Fig. 1.
noise
n(k)
The channel includes the effects of the transmission filter,
powerline communication (PLC) channel and reception filter. The
+
message
signal s(k)
CHANNEL
Fuzzy Adaptive
Filter
g (f(x(k)))
+
Adaptation Algorithm
f(x(k))
+ -
y(k)
ê(k)
x(k)
equalizer
output
FABE, a modified Bussgang type equalizer
Fig 1: Powerline data transmission with fuzzy adaptive blind
equalization
IV 449 142440469X/06/$20.00 ©2006 IEEE ICASSP 2006