Digital Signal Processing Reference
In-Depth Information
2.4.2.2
Kalman Detector for Equalization
The channel estimate given by (2.80) is fed into an equalizer for symbol detection.
Another Kalman filter, together with a quantizer, acts as the symbol detector at the
receiver end. The state and the measurement equations are now given by
()
=
( )
+
()
+
()
,
s
n
Φ
s
n
1
Γ
sn
Γ
sn
(2 . 81)
d
d
()
=
()()
+
()
,
hs
T
yn
nnvn
(2.82)
d
d
where
T
()
:=
() ( )
−
( )
,
s
d
ns ns n
1
s nd
()
:=
({}
,,
()
:=
()
−
()
,
sn
sn
Esn
sn sn
T
0
0
0
T
d
T
Φ
:=
,
Γ:=
10
,
d
I
d
d
T
()
:=
( ) ()
ˆ
ˆ
ˆ
;;
( )
−
h
nhn
0
h n
1
h n
L
0
,
d
dL
where integer
d
≥
L
; it will also be the equalization delay. Assume data symbols are zero
mean and white. If
s
(
n
) is a data symbol, we have
s
(
n
) = 0,
˜
(
n
) =
s
(
n
); if
s
(
n
) is a training
symbol,
s
(
n
) =
s
(
n
),
s
(
n
) = 0. Details of Kalman filtering of the system described by (2.81)
and (2.82) can be found in [34].
2.4.3
Symbol-Adaptive Joint Channel Estimation
and Data Detection
Representative approaches in this category are [27, 34] and references therein. A Gauss-
Markov model for channel variations (typically an autoregressive model) is coupled
with a state-space model for received data to form an augmented state-space model with
nonlinear measurement equation. This results in a nonlinear state estimation problem.
In [27] a finite-length minimum mean square error (MMSE) DFE is used during non-
data-aided periods to generate hard decisions. Reference [34] presents a low-complexity
turbo equalization receiver for coded signals where a nonlinear Kalman filtering-based
adaptive equalizer is coupled with a soft-in soft-out decoder. These approaches work well
so long as the channel does not fade too fast.
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