US 8,572,010 B1 · Deciding whether a received signal is a signal of interest

Abstract

A method of deciding whether an observed received signal is a particular signal of interest (SOI) includes the steps of: providing a statistical model of the particular signal of interest and a statistical model of the environment when the particular signal of interest is not present, and processing the observed received signal in accordance with a decision rule that uses the provided statistical models to decide whether the observed received signal is the particular signal of interest. The decision rule is: decision = { SOI if ⁢ ⁢ LLR ⁡ ( y ) > + λ ~ SOI if ⁢ ⁢ LLR ⁡ ( y ) < - λ unsure otherwise ⁢ ⁢ where ⁢ ⁢ LLR ⁡ ( y ) = log ⁢ P ⁢ ( a 1 ⁡ ( y ) · a 2 ⁡ ( y ) , … ⁢ | SOI ) P ⁡ ( a 1 ⁡ ( y ) · a 2 ⁡ ( y ) ⁢ … ⁢ | ~ SOI ) , where LLR is log likelihood ratio, P denotes a probability, a1(y) and a2(y) are functions of first and second attributes of the observed signal y in a sequential order that said attribute functions are presented for computation of LLR(y), and +λ and −λ are real numbers, wherein the statistical model of the particular signal of interest includes functions of attributes that individually have a probability distribution function f1 when the observed received signal is the particular signal of interest such that KL(f1,f0)>0, where f0 is a probability distribution function of the respective individual attribute when the observed received signal is not a signal of interest.

Claims10

Dependent claims

A method of deciding whether an observed received signal is a particular signal of interest (SOI), comprising the steps of:

(a) providing a statistical model of the particular signal of interest and a statistical model of the environment when the particular signal of interest is not present;
and
(b) with a computer, processing the observed received signal in accordance with a decision rule that uses the provided statistical models to decide whether the observed received signal is the particular signal of interest;
wherein the decision rule is:
decision
=
{
SOI
if
⁢
⁢
LLR
⁡
(
y
)
>
+
λ
~
SOI
if
⁢
⁢
LLR
⁡
(
y
)
<
-
λ
unsure
otherwise
⁢
⁢
where
⁢
⁢
LLR
⁡
(
y
)
=
log
⁢
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
SOI
)
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
~
SOI
)
,
where LLR is log likelihood ratio, P denotes a probability, a1(y) and a2(y) are functions of first and second attributes of the observed signal y in a sequential order that said attribute functions are presented for computation of LLR(y), and +λ and −λ are real numbers,
wherein the statistical model of the particular signal of interest includes functions of attributes that individually have a probability distribution function f1 when the observed received signal is the particular signal of interest such that
KL(f1,f0)>0,
where f0 is a probability distribution function of the respective individual attribute when the observed received signal is not a signal of interest;
and
wherein at least one of the attribute functions is expressed as:
a(yC,yR)fc=fc
a(yC,yR)Δf=Δf
a(yC,yR)tc=tc
a(yC,yR)Δt=Δt,
where yC is a sample of the observed signal received by a commutated element of a commutated antenna array, yR is a sample of the observed signal received by a commutated element of the antenna array, f is frequency, and t is time.

99 more elements

A method of deciding whether an observed received signal is a particular signal of interest (SOI), comprising the steps of:

(a) providing a statistical model of the particular signal of interest and a statistical model of the environment when the particular signal of interest is not present;
and
(b) with a computer, processing the observed received signal in accordance with a decision rule that uses the provided statistical models to decide whether the observed received signal is the particular signal of interest;
wherein the decision rule is:
decision
=
{
SOI
if
⁢
⁢
LLR
⁡
(
y
)
>
+
λ
~
SOI
if
⁢
⁢
LLR
⁡
(
y
)
<
-
λ
unsure
otherwise
⁢
⁢
where
⁢
⁢
LLR
⁡
(
y
)
=
log
⁢
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
SOI
)
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
~
SOI
)
,
where LLR is log likelihood ratio, P denotes a probability, a1(y) and a2(y) are functions of first and second attributes of the observed signal y in a sequential order that said attribute functions are presented for computation of LLR(y), and +λ and −λ are real numbers,
wherein the statistical model of the particular signal of interest includes functions of attributes that individually have a probability distribution function f1 when the observed received signal is the particular signal of interest such that
KL(f1,f0)>0,
where f0 is a probability distribution function of the respective individual attribute when the observed received signal is not a signal of interest;
and
wherein at least one of the attribute functions is expressed as one of the following:
a
⁡
(
y
C
,
y
R
)
S
N
=

<
y
C
,
y
R
>

2

y
C

2
⁢

y
R

2
-

<
y
C
,
y
R
>

2
,
(
i
)
where yC is a sample of the observed signal received by a commutated element of a commutated antenna array and yR is a sample of the observed signal received by a commutated element of the antenna array;
a(yC,yR)AOA=arg maxΦColor*U(U*diag(Energy)U)−1U*Color
where
Un=ukn(Φ)
Colorn=<yC,yR>Rn
Energyn=<yR,yR>Rn (ii)
yC is a sample of the observed signal received by a commutated element of a commutated antenna array and yR is a sample of the observed signal received by a commutated element of the antenna array;
a
⁡
(
y
,
k
)
Sinusoids
=

Y
⁡
(
k
)
⁢
w

2

y
⁡
(
k
)
-
Y
⁡
(
k
)
⁢
w

2
⁢
⁢
where
⁢
⁢
w
=
(
Y
⁡
(
k
)
*
Y
⁡
(
k
)
)
-
1
⁢
Y
⁡
(
k
)
*
y
⁡
(
k
)
(
iii
)
and k is the k in k-means;
a(y,k)PSK k-ary 1=a(yk,k)Sinusoids, (iv)
and k is the k in k-means;
a
⁡
(
y
,
k
)
PSK
⁢
⁢
k
-
ary
⁢
⁢
2
=
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
Δ
⁢
⁢
y
)
(
v
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
PSK
⁢
⁢
k
-
ary
⁢
⁢
3
=
max
T
~
∈
[
1
2
⁢
Δ
~
⁢
⁢
f
·
2
Δ
~
⁢
⁢
f
]
⁢
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
⋃
i
⁢
s
i
′
)
,
(
vi
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
QAM
⁢
⁢
k
-
ary
⁢
⁢
1
=
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
y
2
)
(
vii
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
QAM
⁢
⁢
k
-
ary
⁢
⁢
2
=
max
T
~
∈
[
1
2
⁢
Δ
⁢
⁢
f
,
2
Δ
⁢
⁢
f
]
⁢
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
⋃
i
⁢
s
i
′
)
(
viii
)
k is the k in k-means, f is the frequency of the signal, and U denotes a union operator;
a
⁡
(
y
)
AM
=

〈
V
⁡
(
ω
~
c
,
y
,
ω
)
,
V
⁡
(
ω
~
c
,
y
,
-
ω
)
〉

2

V
⁡
(
ω
~
c
,
y
,
ω
)

2
⁢

V
⁡
(
ω
~
c
,
y
,
-
ω
)

2
-

〈
V
⁡
(
ω
~
c
,
y
,
ω
)
,
V
⁡
(
ω
~
c
,
y
,
-
ω
)
〉

2
⁢
⁢
ω
~
c
=
argmax
ω
e
⁢

〈
V
⁡
(
ω
c
,
y
,
ω
)
,
V
⁡
(
ω
c
,
y
,
-
ω
)
〉

2
(
ix
)
and ω is frequency.

646 more elements

A non-transitory computer readable storage medium for use with a computer in a system for deciding whether an observed received signal is a particular signal of interest (SOI), wherein the computer readable storage medium contains computer executable program instructions for causing the computer to perform the step of:

(a) processing the observed received signal in accordance with a decision rule that uses a statistical model of the particular signal of interest and a statistical model of the environment when the particular signal of interest is not present to decide whether the observed received signal is the particular signal of interest;
wherein the decision rule is:
decision
=
{
SOI
if
⁢
⁢
LLR
⁡
(
y
)
>
+
λ
~
SOI
if
⁢
⁢
LLR
⁡
(
y
)
<
-
λ
unsure
otherwise
⁢
⁢
where
⁢
⁢
LLR
⁡
(
y
)
=
log
⁢
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
SOI
)
P
⁡
(
a
1
⁡
(
y
)
,
a
2
⁡
(
y
)
,
…
|
~
SOI
)
,
where LLR is log likelihood ratio, P denotes a probability, a1(y) and a2(y) are functions of first and second attributes of the observed signal y in a sequential order that said attribute functions are presented for computation of LLR(y), and +λ and −λ are real numbers,
wherein the statistical model of the particular signal of interest includes functions of attributes that individually have a probability distribution function f1 when the observed received signal is the particular signal of interest such that
KL(f1,f0)>0,
where f0 a is a probability distribution function of the respective individual attribute when the observed received signal is not a signal of interest;
wherein at least one of the attribute functions is expressed as one of the following:
a
⁡
(
y
C
,
y
R
)
S
N
=

〈
y
C
,
y
R
〉

2

y
C

2
⁢

y
R

2
-

〈
y
C
,
y
R
〉

2
,
(
i
)
where yC is a sample of the observed signal received by a commutated element of a commutated antenna array and yR is a sample of the observed signal, received by a commutated element of the antenna array;
a(yC,yR)AOA=arg maxΦColor*U(U*diag(Energy)U)−1U*Color
where
Un=ukn(Φ)
Colorn=<yC,yR>Rn
Energyn=<yR,yR>Rn (ii)
yC is a sample of the observed signal received by a commutated element of a commutated ated antenna array and yR is a sample of the observed signal received by a commutated element of the antenna array;
a
⁡
(
y
,
k
)
Sinusoids
=

Y
⁡
(
k
)
⁢
w

2

y
⁡
(
k
)
-
Y
⁡
(
k
)
⁢
w

2
⁢
⁢
where
⁢
⁢
w
=
(
Y
⁡
(
k
)
*
Y
⁡
(
k
)
)
-
1
⁢
Y
⁡
(
k
)
*
y
⁡
(
k
)
(
iii
)
and k is the k in k-means;
a(y,k)PSK k-ary 1=a(yk,k)Sinusoids, (iv)
and k is the k in k-means;
a
⁡
(
y
,
k
)
PSK
⁢
⁢
k
-
ary
⁢
⁢
2
=
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
Δ
⁢
⁢
y
)
(
v
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
PSK
⁢
⁢
k
-
ary
⁢
⁢
3
=
max
T
~
∈
[
1
2
⁢
Δ
⁢
⁢
f
,
2
Δ
⁢
⁢
f
]
⁢
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
⋃
i
⁢
s
i
′
)
,
(
vi
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
QAM
⁢
⁢
k
-
ary
⁢
⁢
1
=
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
y
2
)
(
vii
)
and k is the k in k-means;
a
⁡
(
y
,
k
)
QAM
⁢
⁢
k
-
ary
⁢
⁢
2
=
max
T
~
∈
[
1
2
⁢
Δ
⁢
⁢
f
,
2
Δ
⁢
⁢
f
]
⁢
∑
i
⁢
Mean
⁡
(
C
i
)
2
∑
i
⁢
Variance
⁡
(
C
i
)
⁢
⁢
where
⁢
⁢
{
C
i
}
=
k
-
means
⁡
(
⋃
i
⁢
s
i
′
)
(
viii
)
k is the k in k-means, f is the frequency of the signal, and U denotes a union operator;
a
⁡
(
y
)
AM
=

〈
V
⁡
(
ω
~
c
,
y
,
ω
)
,
V
⁡
(
ω
~
c
,
y
,
-
ω
)
〉

2

V
⁡
(
ω
~
c
,
y
,
ω
)

2
⁢

V
⁡
(
ω
~
c
,
y
,
-
ω
)

2
-

〈
V
⁡
(
ω
~
c
,
y
,
ω
)
,
V
⁡
(
ω
~
c
,
y
,
-
ω
)
〉

2
⁢
⁢
ω
~
c
=
argmax
ω
e
⁢

〈
V
⁡
(
ω
c
,
y
,
ω
)
,
V
⁡
(
ω
c
,
y
,
-
ω
)
〉

2
(
ix
)
and ω is frequency.

641 more elements

Dependencies are inferred from the claim text.

Deciding whether a received signal is a signal of interest

Life of this patent

Deciding whether a received signal is a signal of interest

Life of this patent

Abstract

Claims10