# An Improved Method for Decision-Directed Blind Equalization Algorithm

Topics: Computational complexity theory, Blind equalization, Hyperbolic function Pages: 16 (1708 words) Published: March 6, 2014
AN IMPROVED METHOD FOR DECISION-DIRECTED
BLIND EQUALIZATION ALGORITHM
Seongmin Kim, Wangrok Oh and Whanwoo Kim
Department of Electronics Engineering
Chungnam National University, Daejeon, Republic of Korea
wwkim@cnu.ac.kr
ABSTRACT
s ( n)

u ( n)

ˆ(
s n)

y ( n)

The decision-directed blind equalization algorithm is often
used due to its simplicity and good convergence property
when the eye pattern is open. However, in a channel
where the eye pattern is closed, the decision-directed
algorithm is not guaranteed to converge. Hence, a
modified decision-directed algorithm using a hyperbolic
tangent function for zero-memory nonlinear function has
been proposed and applied to avoid this problem by Filho
et al. But application of this algorithm includes the
calculation of hyperbolic tangent function and its
derivative or a look-up table which may need a large
amount of memory due to channel variations. To reduce
the computational and/or hardware complexity of Filho’s
algorithm, in this paper, an improved method for the
decision-directed algorithm is proposed. It is shown that
the proposed scheme, when it is combined with decisiondirected algorithm, reduces the computational complexity drastically while it retains the convergence and steadystate performance of the Filho’s algorithm.

Figure 1. Block diagram of a receiver system using
Bussgang blind equalization algorithm.

Index Terms— Blind equalization, decision-directed,
zero-memory nonlinear function.

where W ( n ) = [ w 0 ( n ) … w L −1 ( n ) ] is the tap weight

1. INTRODUCTION

e( n)

η [ ⋅ ]

Bussgang algorithm can be described by the
following equations:
W ( n + 1) = W (n) + μ ( n)e( n) U ( n)

(1)

e(n) = η ⎡ y ( n )⎤ − y ( n )

(2)

T

y (n) = U (n) W(n)

(3)

T

vector of the equalizer at time n , (here, w i ( n) is the i -th equalizer coefficient), L is the equalizer length, μ (n) is the step size; U ( n ) = [u ( n ) u ( n − 1) … u ( n − L + 1) ] is the equalizer input vector of L sample measurements at the

channel output, y ( n ) is the equalizer output, and η [⋅] is a T

Blind equalization algorithms are typically classified into
two categories, depending on whether the adaptation is
performed by a linear or a nonlinear filter. Bussgang
algorithms exploit in the implicit sense the higher order
cumulants that are associated with nonlinear filter [1].
This paper deals with a Bussgang algorithm and its
modified versions that are adequate for real time
processing and simple realization. Bussgang algorithm
can be obtained with the minimization of a nonlinear cost
function which may be achieved by a LMS (least mean
square) algorithm, as in [1], by means of a stochastic
gradient steepest descent algorithm, as in [2] and [3], or
any suitable known optimization method. Especially,
Bussgang-type algorithm with a derivative of zeromemory nonlinear (ZNL) function using a hyperbolic tangent function is described in [2]. We consider this
algorithm to improve the computational complexity in this
paper. The block diagram of a receiver system using
Bussgang blind equalization algorithm is illustrated in
Figure 1.

zero-memory nonlinear (ZNL) function.
Each Bussgang blind equalization algorithm is
determined by choosing the corresponding ZNL function
η [⋅] , which is used to generate the error signal e(n) . When this nonlinearity is chosen as the decision device
D(⋅), the decision-directed (DD) algorithm is obtained.
The DD algorithm is often used in association with
another blind equalization algorithm, due to its good
convergence property and its simplicity when the eye
pattern is open [2]. However, in a channel where the eye
pattern is closed, the DD algorithm is not guaranteed to
converge. Hence, a modified decision-directed (MDD)
algorithm using a hyperbolic tangent function for the ZNL
function has been proposed and applied to avoid this
problem by Filho et al [2]. But...