Communications: directive radio wave systems and devices (e.g. – Directive – Beacon or receiver
Reexamination Certificate
2002-04-24
2004-06-01
Tarcza, Thomas H. (Department: 3662)
Communications: directive radio wave systems and devices (e.g.,
Directive
Beacon or receiver
C342S424000, C342S440000
Reexamination Certificate
active
06744407
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention concerns a method for the space-time estimation of one or more transmitters in an antenna network when the wave transmitted by a transmitter is propagated as multipaths.
Multipaths exist when a wave transmitted by a transmitter is propagated along several paths towards a receiver or a goniometry system. Multipaths are due in particular to the presence of obstacles between a transmitter and a receiver.
The field of the invention concerns in particular that of the goniometry of radioelectric sources, the word source designating a transmitter. Goniometry means “the estimation of incidences”.
It is also that of spatial filtering whose purpose is to synthesise an antenna in the direction of each transmitter from a network of antennas.
2. Discussion of the Background
The purpose of a traditional radiogoniometry system is to estimate the incidence of a transmitter, i.e. the angles of arrival of radioelectric waves incident on a network
1
of N sensors of a reception system
2
, for example a network of several antennas as represented in
FIGS. 1 and 2
. The network of N sensors is coupled to a computation device
4
via N receivers in order to estimate the angles of incidence &thgr;
p
of the radioelectric waves transmitted by various sources p or transmitters and which are received by the network.
The wave transmitted by the transmitter can propagate along several paths according to a diagram given in FIG.
3
. The wave k(&thgr;
d
) has a direct path with angle of incidence &thgr;
d
and the wave k(&thgr;
r
) a reflected path with angle of incidence &thgr;
r
. The multipaths are due in particular to obstacles
5
located between the transmitter
6
and the reception system
7
. At the reception station, the various paths arrive with various angles of incidence &thgr;
op
where p corresponds to the p
th
path. The multipaths follow different propagation routes and are therefore received at different times t
mp
.
The N antennas of the reception system receive the signal x
n
(t) where n is the index of the sensor. Using these N signals x
n
(t), the observation vector is built:
x
_
(
t
)
=
[
x
1
(
t
)
.
.
x
n
(
t
)
]
(
1
)
With M transmitters this observation vector x(t) is written as follows:
x
_
(
t
)
=
∑
m
=
1
M
∑
p
=
1
P
m
ρ
mp
a
_
(
θ
mp
)
s
m
(
t
-
τ
mp
)
+
b
_
(
t
)
(
2
)
where
a(&thgr;
mp
) is the steering vector of the p
th
path of the m
th
transmitter. The vector a(&thgr;) is the response of the network of N sensors to a source of incidence &thgr;
&rgr;
mp
is the attenuation factor of the p
th
path of the m
th
transmitter
&tgr;
mp
is the delay of the p
th
path of the m
th
transmitter
P
m
is the number of multipaths of the m
th
transmitter
s
m
(t) is the signal transmitted by the m
th
transmitter
b(t) is the noise vector composed of the additive noise b
n
(t) (1≦n≦N) on each sensor.
The prior art describes various techniques of goniometry, of source separation and of goniometry after the separation of the source.
These techniques consist of estimating the signals s
m
(t−&tgr;
mp
) from the observation vector x(t) with no knowledge of their time properties. These techniques are known as blind techniques. The only assumption is that the signals s
m
(t−&tgr;
mp
) are statistically independent for a path p such that 1≦p≦P
m
and for a transmitter m such that 1≦m≦M. Knowing that the correlation between the signals s
m
(t) and s
m
(t−&tgr;) is equal to order 2 to the autocorrelation function r
sm
(&tgr;)=E[s
m
(t)s
m
(t−&tgr;)*] of the signal s
m
(t), we deduce that the multipaths of a given signal s
m
(t) transmitter are dependent since the function r
sm
(&tgr;) is non null. However, two different transmitters m and m′, of respective signals s
m
(t) and s
m′
(t), are statistically independent if the relation E[s
m
(t) s
m′
(t)*]=0 is satisfied, where E[.] is the expected value. Under these conditions, these techniques can be used when the wave propagates in a single path, when P
1
= . . . =P
M
=1. The observation vector x(t) is then expressed by:
x
_
(
t
)
=
∑
m
=
1
M
a
_
(
θ
m
)
s
m
(
t
)
+
b
_
(
t
)
=
A
s
_
(
t
)
+
b
_
(
t
)
(
3
)
where A=[a(&thgr;
1
) . . . a(&thgr;
M
)] is the matrix of steering vectors of the sources and s(t) is the source vector such that s(t)=[s
1
(t) . . . s
M
(t)]
T
(where the exponent T designates the transpose of vector u which satisfies in this case u=s(t)).
These methods consist of building a matrix W of dimension (N×M), called separator, generating at each time t a vector y(t) of dimension M which corresponds to a diagonal matrix and, to within one permutation matrix, to an estimate of the source vector s(t) of the envelopes of the M signals of interest to the receiver. This problem of source separation can be summarised by the following expression of the required vectorial output at time t of the linear separator W:
y
(
t
)=
W
H
x
(
t
)=Π&Lgr;
ŝ
(
t
) (4)
where Π and &Lgr; correspond respectively to arbitrary permutation and diagonal matrices of dimension M and where
ŝ
(t) is an estimate of the vector s(t). W
H
designates the transposition and conjugation operation of the matrix W.
These methods involve the statistics of order 2 and 4 of the observation vector x(t).
Order 2 Statistics: Covariance Matrix
The correlation matrix of the signal x(t) is defined by the following expression:
R
xx
=E[x
(
t
)
x
(
t
)
H
] (5)
Knowing that the source vector s(t) is independent of the noise b(t) we deduce from (3) that:
R
xx
=AR
ss
A
H
+&sgr;
2
I
(6)
Where R
ss
=E[s(t) s(t)
H
] and E[b(t) b(t)
H
]=&sgr;
2
I.
The estimate of R
xx
used is such that:
R
^
xx
=
1
T
∑
t
=
1
T
x
_
(
t
)
x
_
(
t
)
H
(
7
)
where T corresponds to the integration period.
Order 4 Statistics: Quadricovariance
By extension of the correlation matrix, we define with order 4 the quadricovariance whose elements are the cumulants of the sensor signals x
n
(t):
Qxx
(
i,j,k,l
)=cum{
xi
(
t
),
xj
(
t
)*,
xk
(
t
)*,
xl
(
t
)} (8)
With
cum
{
y
i
,
y
j
,
y
k
,
y
i
}
=
E
[
y
i
y
j
y
k
y
l
]
-
E
[
y
i
y
j
]
[
y
k
y
l
]
-
E
[
y
i
y
k
]
[
y
j
y
l
]
-
E
[
y
i
y
l
]
[
y
j
y
k
]
(
9
)
Knowing that N is the number of sensors, the elements Q
xx
(i,j,k,l) are stored in a matrix Q
xx
at line number N(j−1)+i and column number N(l−1)+k. Q
xx
is therefore a matrix of dimension N
2
×N
2
.
It is also possible to write the quadricovariance of observations x(t) using the quadricovariances of the sources and the noise written respectively Q
ss
and Q
bb
. Thus according to expression (3) we obtain:
Q
xx
=
∑
i
,
j
,
k
,
l
Q
ss
(
i
,
j
,
k
,
l
)
[
a
_
(
θ
i
)
⊗
a
_
(
θ
j
)
*
]
[
a
_
(
θ
k
)
⊗
a
_
(
θ
l
)
*
]
H
+
Q
bb
(
10
)
where {circle around (x)} designates the Kronecker product such that:
u
_
⊗
v
_
=
[
u
_
v
1
.
u
_
v
K
]
where
v
_
=
[
v
1
.
v
K
]
(
11
)
Note that when there are independent sources, the following equality (12) is obtained:
Q
xx
=
∑
m
=
1
M
Q
ss
(
m
,
m
,
m
,
m
)
[
a
_
(
θ
m
)
⊗
a
_
(
θ
m
)
*
]
[
a
_
(
θ
m
)
⊗
a
_
(
θ
m
)
*
]
H
+
Q
bb
Since Q
ss
(i,j,k,l)=0 for i&ne
Mull F H
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
Tarcza Thomas H.
Thales
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