-
Equalization Algorithm in MIMO
System
——
Based on Minimum
Mean Square Error
Name:Cui
Hao(
崔浩
)
Number
：
4
system
In
radio,
multiple-input
and
multiple-output,
or
MIMO,
is
a
method
for
multiplying the capacity of a radio
link using multiple transmit and receive antennas
to exploit multipath has become an
essential element of wireless
communication standards.
At
one
time,
in
wireless
the
term
referred
to
the
use
of
multiple
antennas at the
transmitter and the receiver. In modern usage,
refers to a practical technique for
sending and receiving more than one data signal
simultaneously
over
the
same
radio
channel
by
exploiting
multipath
propagation.
MIMO
is
fundamentally
different
from
smart
antenna
techniques
developed
to
enhance the performance
of a single data signal, such as beamforming and
diversity.
MIMO
can
be
sub-divided
into
three
main
categories,
precoding,
spatial
multiplexing (SM),
and diversity coding.
RX
Figure system
H is the channel matrix of the
Nt
and
Nr
columns, the elements of
which are
independent
of
each
other
and
subject
to
cyclic
symmetric
complex
Gaussian
distribution
with
mean
0
and
variance
1
(ie,
0.5
for
the
real
and
the
imaginary
variance),
ie
the
channels
are
independent
flat
Rayleigh
fading
channel
and
the
receiving end already knows the channel
state information.
By figure 1 , we can
get Rayleigh fading channel
H
?
h
11<
/p>
?
h
?
21
H
?
?
?
...
?
?
?
?
h
Nt
1
h
12
h
22
...
h
Nt
2
...
h
1
Nr
?
...
h
2
Nr
?
?
?
...
...
?
?
?
...
h
NtN
r
?
?
Nr1
Nt2
…
Ntn
Nt1
Nt2
…
Ntn
h
11
h
12
h
1
n
h
21
h
2
2
h
2
n
h<
/p>
31
h
32
h<
/p>
3
n
By
(0)
Where
H
NtNr
denotes
the
channel
Rayleigh
fading
coefficient
from
the
Nt
-th
transmitting antenna to the
Nr
-th receiving antenna.
Equalization
2.1
Equalization
The insertion of a tunable
filter in a digital communication system can
correct
and
compensate
for
system
characteristics
and
reduce
the
impact
of
intersymbol
interference. This compensating filter
is called an equalizer.
Equalizers
are
usually
implemented
using
filters,
which
use
a
filter
to
compensate for distorted
pulses. The demodulator output samples obtained by
the
decider are samples that have been
corrected by the equalizer or have cleared the
inter-symbol
interference.
Adaptive
equalizer
directly
from
the
transmission
of
the
actual
digital
signal
in
accordance
with
an
algorithm
to
adjust
the
gain,
which
can
adapt
to the random channel changes, so that the
equalizer is always the best state,
which has better distortion
compensation performance.
2.2 Minimum
Mean Square Error
In
statistics
and
signal
processing,
a
minimum
mean
square
error
(MMSE)
estimator
is
an
estimation
method
which
minimizes
the
mean
square
error
(MSE),
which is a common
measure of estimator quality, of the fitted values
of a dependent
variable.
In
the
Bayesian
setting,
the
term
MMSE
more
specifically
refers
to
estimation with quadratic
loss function. In such case, the MMSE estimator is
given by
the
posterior
mean
of the parameter
to
be estimated.
Since
the
posterior
mean
is
cumbersome to calculate, the form of
the MMSE estimator is usually constrained to
be within a certain class of functions.
Linear MMSE estimators are a popular choice
since they are easy to use, calculate,
and very versatile.
2.3 MMSE of a
fading model
System Model:
Where:
y
: received
signal vector ,
y =
[
y
1
,
y
2
,
... ,
y
Nr
].
n
: interference
and noise ,
n =
[
n
1
,
n
2
,
... ,
n
Nr
].
x
: input signal vector ,
x =
[
x
1
,
x
2
,
... ,
x
Nt
].
H
: fading channel , please
watch equation (0).
It is assumed that
n
is statistically
independent to
x
.
y
?
Hx
?
n
(1)
We want to
estimate
x
from
y
by linear operation:
x
?
?
G
H
y
(2)
where the
G
is selected to minimize
the estimation error
e
=
x
-
x
?
(3)
MMSE criterion is to minimize the
following equation
J = E
(
e
H
e
)
= tr
{
E
(
e
H
e
)}
(4)