Method for removing spatial and temporal multi-path interference for a receiver of frequency-modulated radio signals
View Patent ↗A method for decreasing multi-path interference, for a vehicle radio receiver including at least two radio reception antennas that each receive a plurality of radio signals composed of time-shifted radio signals resulting from a multi-path effect. The plurality of radio signals combined to deliver a combined radio signal y s to be played, with: y n =W n T [ G 1,n S , X 1,n + G 2,n S , X 2,n ] at time n, where x 1 and x 2 are vectors the components of which correspond to the plurality of signals received by the first antenna and by the second antenna, respectively, G 1,n S and G 2,n S are scalars the components of which are the complex weights of a spatial filter and w n T is the transpose matrix of a vector the components of which are the complex weights of a temporal filter. The method includes implementation of an iterative adaptation algorithm to determine the complex weights of the spatial filter and the complex weights of the temporal filter.
1. A method for decreasing multi-path interference, for implementation thereof in a vehicle radio receiver, said radio receiver being intended to receive an emitted radio signal and comprising at least two radio reception antennas that each receive a plurality of radio signals corresponding to said emitted radio signal, each of said plurality of signals received by each of said antennas being composed of time-shifted radio signals resulting from a multi-path effect, said plurality of radio signals being combined to deliver a combined radio signal y n to be played, with y n ==W n T [ G 1,n S , X 1,n + G 2,n S , X 2,n ] at the time n, where X 1 is a vector the components of which correspond to a plurality of signals received by a first antenna, expressed in complex baseband, X 2 is a vector the components of which correspond to the plurality of signals received by a second antenna, expressed in complex baseband, G 1,n S and G 2,n S are scalars the components of which are the complex weights of a spatial filter and W n T is the transpose matrix of a vector the components of which are the complex weights of a temporal filter, said method comprising:
the implementation of an iterative adaption algorithm to determine said complex weights of the spatial filter and said complex weights of the temporal filter, wherein the respective variations in the components of the matrix the components of which form the complex weights of the temporal filter and in the components of the scalars the components of which form the complex weights of a spatial filter are written:
W
n
+
1
t
=
W
n
t
-
μ
W
y
n
-
R
y
n
y
n
_
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
G
1
,
n
+
1
s
=
G
1
,
n
s
-
μ
G
1
y
n
-
R
y
n
y
n
_
(
W
n
t
_
)
T
X
1
,
n
G
2
,
n
+
1
s
=
G
2
,
n
s
-
μ
G
2
y
n
-
R
y
n
y
n
_
(
W
n
t
_
)
T
X
2
,
n
where μ W , μ G1 , μ G2 are iterative steps chosen for the update of the gains and phases of each of the complex weights.
2. The method as claimed in claim 1 , wherein the iterative adaptation algorithm is configured to minimize a cost function J such that
J=E {(| y n |−R ) 2 }
where R is a constant to be determined, corresponding to the constant modulus of the combined signal y n .
3. The method as claimed in claim 2 , further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written:
∇
J
=
2
y
n
-
R
y
n
[
R
e
[
y
n
_
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
-
Im
[
y
n
_
A
n
t
∘
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
R
e
[
y
n
_
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
-
Im
[
y
n
_
b
1
,
n
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
R
e
[
y
n
_
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
-
Im
[
y
n
_
b
2
,
n
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
]
with
:
W
n
t
=
A
n
t
∘
e
-
j
θ
n
t
,
with
:
A
n
t
=
[
a
0
,
n
a
1
,
n
a
2
,
n
.
.
.
a
K
-
1
,
n
]
T
θ
n
t
=
[
e
-
j
θ
0
,
n
e
-
j
θ
1
,
n
e
-
j
θ
2
,
n
.
.
.
e
-
j
θ
K
-
1
,
n
]
T
,
and
:
G
1
,
n
s
=
b
1
,
n
e
-
j
φ
1
,
n
G
2
,
n
s
=
b
2
,
n
e
-
j
φ
2
,
n
so as to incorporate an interdependence between the real and imaginary parts of said complex weights.
4. The method as claimed in claim 2 , wherein said iterative adaptation algorithm is a constant modulus adaptation algorithm configured to minimize the cost function.
5. The method as claimed in claim 4 , further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written:
∇
J
=
2
y
n
-
R
y
n
[
R
e
[
y
n
_
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
-
Im
[
y
n
_
A
n
t
∘
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
R
e
[
y
n
_
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
-
Im
[
y
n
_
b
1
,
n
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
R
e
[
y
n
_
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
-
Im
[
y
n
_
b
2
,
n
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
]
with
:
W
n
t
=
A
n
t
∘
e
-
j
θ
n
t
,
with
:
A
n
t
=
[
a
0
,
n
a
1
,
n
a
2
,
n
.
.
.
a
K
-
1
,
n
]
T
θ
n
t
=
[
e
-
j
θ
0
,
n
e
-
j
θ
1
,
n
e
-
j
θ
2
,
n
.
.
.
e
-
j
θ
K
-
1
,
n
]
T
,
and
:
G
1
,
n
s
=
b
1
,
n
e
-
j
φ
1
,
n
G
2
,
n
s
=
b
2
,
n
e
-
j
φ
2
,
n
so as to incorporate an interdependence between the real and imaginary parts of said complex weights.
6. The method as claimed in claim 1 , further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written:
∇
J
=
2
y
n
-
R
y
n
[
R
e
[
y
n
_
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
-
Im
[
y
n
_
A
n
t
∘
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
R
e
[
y
n
_
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
-
Im
[
y
n
_
b
1
,
n
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
R
e
[
y
n
_
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
-
Im
[
y
n
_
b
2
,
n
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
]
with
:
W
n
t
=
A
n
t
∘
e
-
j
θ
n
t
,
with
:
A
n
t
=
[
a
0
,
n
a
1
,
n
a
2
,
n
.
.
.
a
K
-
1
,
n
]
T
θ
n
t
=
[
e
-
j
θ
0
,
n
e
-
j
θ
1
,
n
e
-
j
θ
2
,
n
.
.
.
e
-
j
θ
K
-
1
,
n
]
T
,
and
:
G
1
,
n
s
=
b
1
,
n
e
-
j
φ
1
,
n
G
2
,
n
s
=
b
2
,
n
e
-
j
φ
2
,
n
so as to incorporate an interdependence between the real and imaginary parts of said complex weights.
7. The method as claimed in claim 6 , wherein the respective variations in the components of the matrix the components of which form the complex weights of the temporal filter and in the components of the scalars the components of which form the complex weights of a spatial filter are written:
A
n
+
1
t
=
A
n
t
-
μ
A
y
n
-
R
y
n
Re
[
y
n
_
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
θ
n
+
1
t
=
θ
n
t
+
μ
θ
y
n
-
R
y
n
Im
[
y
n
_
A
n
t
∘
e
j
θ
n
t
∘
(
G
1
,
n
s
_
X
1
,
n
+
G
2
,
n
s
_
X
2
,
n
)
]
b
1
,
n
+
1
=
b
1
,
n
-
μ
b
1
y
n
-
R
y
n
Re
[
y
n
_
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
φ
1
,
n
+
1
=
φ
1
,
n
+
μ
φ1
y
n
-
R
y
n
Im
[
y
n
_
b
1
,
n
e
j
φ
1
,
n
(
W
n
t
_
)
T
X
1
,
n
]
b
2
,
n
+
1
=
b
2
,
n
-
μ
2
,
n
y
n
-
R
y
n
Re
[
y
n
_
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
φ
2
,
n
+
1
=
φ
2
,
n
+
μ
φ2
y
n
-
R
y
n
Im
[
y
n
_
b
2
,
n
e
j
φ
2
,
n
(
W
n
t
_
)
T
X
2
,
n
]
where μ A , μ θ , μ b1 , μ b2 , μ φ1 , μ φ2 are iterative steps chosen for the update of the gains and phases of each of the complex weights, and the operator “º” is defined as carrying out the multiplication of two vectors, component by component, the resultant being a vector.
8. The method as claimed in claim 1 , wherein the temporal filter is an impulse response filter.
9. A radio receiver comprising a microcontroller configured to implement the method as claimed in claim 1 .
10. A motor vehicle comprising a radio receiver as claimed in claim 9 .