Multi-modulus Blind Equalization Algorithm
based on high-order QAM genetic optimization
Youcong Ni,Xin Du, Ruliang Xiao
Faculty of software
Fujian Normal University
Fuzhou, China
youcongni@foxmail.com
Chengwang Xie
School of software
East China JiaoTong University
Nanchang,China
chengwangxie@163.com
Abstract—A multi-modulus blind equalization algorithm based
on genetic algorithm is proposed in this paper. It combines the
advantages of multi-mode blind equalization algorithm and
decision directed algorithm, uses genetic algorithm to optimize
the weight vector of equalizer and gets better balanced results.
Theoretical analysis and computer simulations indicate that the
proposed algorithm outperforms multi-modulus blind
equalization algorithm in convergence rate and steady-state
convergence residual.
Keywords
—
Genetic Algorithm, Blind equalization, Multi-modulus
algorithm, QAM
I. INTRODUCTION
With high-speed development of wireless broadband
communication technology, in communication system, in
order to eliminate inter symbol interference(ISI) aroused by
communication channel bandwidth limitations and multi-path
propagation, receiver need to introduce equalization. The
traditional equalization methods use training sequence to
complete initialization of tap coefficients, and then switch to
decision directed algorithm for auto-adaptive tracking. Under
the time-variable channel environment, the sender needs to
send periodical training sequence to obtain time-varying
characteristics of the channel. Because the blind balanced
algorithm does not need to send the training sequence, which
greatly improves the bandwidth utilization. However, its slow
convergence rate is slower, and its static error is also bigger
[1,2]
. Genetic algorithm(GA for brevity)
[3-5]
is an auto-adapted
probability search algorithm based on global optimization, has
stronger robustness and global random search abilities, and
can find global optimal solution in complex, multi-peak, non-
differentiable large vector space effectively and quickly,
which makes the possibility of falling into local convergence
greatly reduced.. Therefore, it is used to optimize weight
vector of equalizer, improve the performance of the equalizer,
and obtain the global optimal solution.
Based on the above analysis, a multi-modulus blind
equalization algorithm based on genetic optimization (GA-
MMA for brevity) is proposed in this paper. This algorithm
uses cost function of GA-MMA as the fitness function of GA,
uses GA to solve cost function of the equalizer and find
optimal individual. Compared with multi-modulus blind
equalization algorithm (MMA for brevity), GA-MMA has
better convergence rate.
II. M
ULTI-MODULUS BLIND EQUALIZATION
ALGORITHM
(MMA)
First, we w
ill introduce the blind equalization system,
which is shown in Figure 1. In this system,
()kα
is the
transmitting signal and can be denoted as
() nnkaibα =+⋅
,
where
na
is real part,
nb
is imaginary part,
()kv
is additive
white Gaussian noise, R(k) is the input signal of blind
equalizer. w(k) is weight vector of equalizer and its length is L,
that is
0() [ (), , , ()]L
T
kk kWw w= ⋅⋅⋅ ⋅⋅⋅
, where
[]
T
⋅
represents
transposition operation. Let y(k) be the output signal of blind
equalizer, then y(k)=W(k)R(k). z(k) is output sequence that we
want to transmit through the blind equalization system.
Constant modulus algorithm (CMA for brevity) as a
comparative mature blind equalization algorithm, has better
convergence performance under appropriate conditions, and
now has been widely used. Its cost function is as follows:
22
{(| ( ) | )}CMA
CMA
JEykR=−
(1)
where
242
E{| ( ) | } E{| ( ) | }
CMA
Rakak=
represent signal modulus
value.
CMA only uses equalizer to output amplitude signal
information. It has phase ambiguity, slower convergence rate
and bigger static error. So, only in the initial stage, equalizer
will use CMA to provide appropriate initial conditions under
the low signal-to-noise ratio environment or in processing
higher order QAM signal time.
Figure 1. Blind equalization system
The difference between MMA[6-8] and CMA is that MMA
divides the output y(k) of equalizer into real part and imaginary