Pulse or digital communications – Receivers – Interference or noise reduction
Reexamination Certificate
2000-07-24
2003-11-18
Ghebretinsae, Temesghen (Department: 2631)
Pulse or digital communications
Receivers
Interference or noise reduction
C375S348000, C455S296000
Reexamination Certificate
active
06650716
ABSTRACT:
RELATED APPLICATIONS
U.S. patent application entitled “Minimum Mean-Squared Error Block-Decision Feedback Sequence Estimation in Digital Communication Systems” by Ratnarajah et al., filed on same date, and assigned to the assignee of the present application, discloses and claims subject matter related to that of the present invention and is herein incorporated by reference.
FIELD OF THE INVENTION
This invention relates to digital communication systems, and more particularly to the estimation of the sequence of transmitted symbols in such systems.
BACKGROUND OF THE INVENTION
In EDGE (Enhanced Data Rates for GSM Evolution) cellular communication systems a sequence of symbols is transmitted as an 8 Phase Shift Keying (8-PSK) modulated signal. The signal may propagate along several propagation paths to a receiver. If the time delay between the various propagation paths is comparable to the intersymbol period, then the'signal received by the receiver will contain intersymbol interference. The attenuation along each path will vary, as will phase changes due to reflections, so the intersymbol interference will not be merely additive. In addition, transmitted symbols in neighbouring cells in Time Division Multiple Access systems can cause co-channel interference. Finally, the received signal will contain noise, which is assumed to be additive white Gaussian noise.
The receiver must estimate the transmitted sequence of symbols s from the received sequence of signal samples x. In a diversity receiver having M antennae, the M spatially distinct received signal samples at any discrete time k can be represented as a vector X
k
=[x
1
, . . . , x
M
]k
T
. A hybrid receiver considers the contributions of co-channel interference and intersymbol interference separately. The hybrid receiver includes a space-time filter which acts on the M received signal samples x
k
to mitigate co-channel interference, and an equalizer which then corrects for intersymbol interference. The output of the equalizer is an estimated sequence of symbols ŝ which ideally is equal to the transmitted sequence of symbols s.
If the space-time filter takes L+1 delayed time-taps of the received signal, then the spatially distinct received signal samples x
k
can be extended to include temporal distinctions. If ordered sequentially, the received signal samples can be represented as a space-time stacked vector of vectors x
k
=[x
k
T
, . . . , x
k−L
T]
T
of length M(L+1), or
x
_
k
=
[
x
1
,
k
⋮
x
M
,
k
x
1
,
k
-
1
⋮
x
M
,
k
-
1
⋮
x
1
,
k
-
L
⋮
x
M
,
k
-
L
]
where for each element of the vector the first subscript refers to the antenna at which the signal sample was received, and the second subscript refers to the time-tap.
An intermediate signal sample y
k
can be defined as an output of the space-time filter such that y
k
=w
T
x
k
where w is a vector of M(L+1). space-time filter coefficients, w=[w
1, 1
, . . . , w
M,1
, . . . , w
1,L+1
, . . . , w
M,L+1
]
T
. For a sequence of N received signal samples, the space-time stacked vector x
k
is extended to form a matrix X=[x
k
, . . . , x
k+N−1
], or
X
=
[
x
1
,
k
x
1
,
k
+
1
⋯
x
1
,
k
+
N
-
1
⋮
⋮
⋯
⋮
x
M
,
k
x
M
,
k
+
1
…
x
M
,
k
+
N
-
1
x
1
,
k
-
1
x
1
,
k
…
x
1
,
k
+
N
-
2
⋮
⋮
…
⋮
x
M
,
k
-
1
x
M
,
k
…
x
M
,
k
+
N
-
2
⋮
⋮
…
⋮
x
1
,
k
-
L
x
1
,
k
+
1
-
L
…
x
1
,
k
+
N
-
1
-
L
⋮
⋮
…
⋮
x
M
,
k
-
L
x
M
,
k
+
1
-
L
…
x
M
,
k
+
N
-
1
-
L
]
∈
C
M
(
L
+
1
)
×
N
and an intermediate sequence of singal samples y of length N is then produced by the space-time filter such that y
T
w
T
X.
The intermediate sequence of signal samples y can also be expressed as y
T
=h
T
S+e
T
where h is a vector of effective channel coefficients, S is a matrix of transmitted symbols of the form
S
=
[
s
k
s
k
+
1
…
s
k
+
N
-
1
s
k
-
1
s
k
…
⋮
⋮
⋮
⋰
⋮
s
k
-
v
-
L
…
…
s
k
-
v
-
L
+
N
-
1
]
∈
C
(
v
+
L
+
1
)
×
N
,
v+1 is the number of propagation paths being considered for the environment in which the signal propagates, v+L+1 is the number of effective channels which will be considered by the equalizer, and e is a disturbance. The effective channel coefficients are used in the equalizer, as discussed below. From the perspective of the equalizer y is a received sequence of signal samples having passed through v+L+1 effective channels with impulse response coefficients given by h, the effective channels consisting of the propagation paths and the effects of the space-time filter.
Combining the two expressions for y, it is seen that the disturbance can be expressed as e
T
=w
T
X−h
T
S. A signal-to-interference-plus-noise ratio SINR can be defined as
SINR
=
&LeftDoubleBracketingBar;
h
_
T
S
&RightDoubleBracketingBar;
2
&LeftDoubleBracketingBar;
e
_
&RightDoubleBracketingBar;
2
SINR
=
&LeftDoubleBracketingBar;
h
_
T
S
&RightDoubleBracketingBar;
2
&LeftDoubleBracketingBar;
w
_
T
X
-
h
_
T
S
&RightDoubleBracketingBar;
2
The filter coefficients w and the effective channel coefficients h are jointly optimized by maximizing the SINR with respect to w and h to produce optimal coefficients w
opt
and h
opt
. Using the technique of separation of variables, h
opt
is found to be
h
_
opt
=
arg
max
h
_
h
_
H
S
*
S
T
h
_
h
_
H
S
*
P
*
S
T
h
_
∈
C
(
v
+
L
+
1
)
×
1
where P=(I−X
H
(XX
H
)
−1
X), I is an identity matrix, the superscript H indicates the Hermitian of the matrix or vector to which it refers, and the superscript indicates the complex conjugate of the matrix or vector to which it refers. This is a generalized eigenvalue problem, and h
opt
is the eigenvector corresponding to the largest eigenvalue of (S*P*S
T
)
−1
S*S
T
. w
opt
is then found from
w
opt
T
=h
opt
T
SX
H
(
XX
H
)
−1
h
opt
and w
opt
can be found if the matrices S and X are formed from known training data. Unfortunately the eigenvalue problem is a complex one, and an efficient method of determining h
opt
is needed.
Once w
opt
and h
opt
are determined the estimated sequence of symbols ŝ can be determined. The intermediate sequence of signal samples y produced by the space-time filter is found from y
T
=w
T
X where X is now the matrix of received sequences of signal samples for user data rather than for training data, having N+v+L columns where N is the number of symbols in the transmitted sequence (which is half a slot in EDGE systems). From the perspective of the equalizer, y=Hs+e where H is a matrix of effective channel coefficients having the form
H
=
[
h
1
h
0
0
…
…
…
0
h
2
h
1
h
0
⋯
⋯
⋯
0
h
3
h
2
h
1
⋯
…
…
0
⋮
⋮
⋮
⋰
⋰
⋰
⋮
h
v
+
L
h
v
+
L
-
1
h
v
+
L
-
2
…
…
…
0
0
h
v
+
L
h
v
+
L
-
1
…
…
…
0
⋮
⋮
⋮
…
…
…
⋮
]
∈
C
(
N
+
v
+
L
)
×
N
and the values of the matrix elements hi are given by h
opt
, determined earlier during the joint optimization.
One method of estimating the transmitted sequence of symbols in the presence of intersymbol interference is the Maximum Likelihood Sequence Estimation (MLSE) method. For each of the possible transmitted symbols, the received signal is compared with the signal that should have been received if it was that symbol that had been transmitted. Based on these comparisons, the MLSE method then selects the symbol which was most likely to have been trans
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