Deciding whether a received signal is a signal of interest
View Patent ↗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, a 1 (y) and a 2 (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 f 1 when the observed received signal is the particular signal of interest such that KL ( f 1 ,f 0 )>0, where f 0 is a probability distribution function of the respective individual attribute when the observed received signal is not a signal of interest.
1. 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, a 1 (y) and a 2 (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 f 1 when the observed received signal is the particular signal of interest such that
KL ( f 1 ,f 0 )>0,
where f 0 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 ( y C ,y R ) f c =f c
a ( y C ,y R )Δ f=Δf
a ( y C ,y R ) t c =t c
a ( y C ,y R )Δ t=Δt,
where y C is a sample of the observed signal received by a commutated element of a commutated antenna array, y R is a sample of the observed signal received by a commutated element of the antenna array, f is frequency, and t is time.
2. A method according to claim 1 , wherein the attribute functions a 1 (y),a 2 (y), . . . are presented for computation of LLR(y) in an order that is in accordance with the time cost of observing the attributes.
3. A method according to claim 1 , wherein the attribute functions a 1 (y),a 2 (y), . . .are presented for computation of LLR(y) in an order that is in accordance with the time cost of computation.
4. A method according to claim 1 , wherein the attribute functions a 1 (y),a 2 (y), . . . are presented for computation of LLR(y) in an order that is in accordance with the time cost of communicating the observed attribute.
5. 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, a 1 (y) and a 2 (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 f 1 when the observed received signal is the particular signal of interest such that
KL ( f 1 ,f 0 )>0,
where f 0 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 ( y C ,y R ) f c =f c
a ( y C ,y R )Δ f=Δf
a ( y C ,y R ) t c =t c
a ( y C ,y R )Δ t=Δt,
where y C is a sample of the observed signal received by a commutated element of a commutated antenna array, y R is a sample of the observed signal received by a commutated element of the antenna array, f is frequency, and t is time.
6. 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, a 1 (y) and a 2 (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 f 1 when the observed received signal is the particular signal of interest such that
KL ( f 1 ,f 0 )>0,
where f 0 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 y C is a sample of the observed signal received by a commutated element of a commutated antenna array and y R is a sample of the observed signal received by a commutated element of the antenna array;
a ( y C ,y R ) AOA =arg max Φ Color* U ( U* diag(Energy) U ) −1 U* Color
where
U n = u k n ( Φ )
Color n =<y C ,y R > R n
Energy n =<y R ,y R > R n (ii)
y C is a sample of the observed signal received by a commutated element of a commutated antenna array and y R 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 ( y k ,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.
7. A method according to claim 6 , wherein the attribute functions a 1 (y), a 2 (y), . . . are presented for computation of LLR(y) in an order that is in accordance with the time cost of observing the attributes.
8. A method according to claim 6 , wherein the attribute functions a 1 (y), a 2 (y), . . . are presented for computation of LLR(y) in an order that is in accordance with the time cost of computation.
9. A method according to claim 6 , wherein the attribute functions a 1 (y), a 2 (y), . . . are presented for computation of LLR(y) in an order that is in accordance with the time cost of communicating the observed attribute.
10. 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, a 1 (y) and a 2 (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 f 1 when the observed received signal is the particular signal of interest such that
KL ( f 1 ,f 0 )>0,
where f 0 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 y C is a sample of the observed signal received by a commutated element of a commutated antenna array and y R is a sample of the observed signal, received by a commutated element of the antenna array;
a ( y C ,y R ) AOA =arg max Φ Color* U ( U* diag(Energy) U ) −1 U* Color
where
U n = u k n ( Φ )
Color n =<y C ,y R > R n
Energy n =<y R ,y R > R n (ii)
y C is a sample of the observed signal received by a commutated element of a commutated ated antenna array and y R 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 ( y k ,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.