Determination of signal characteristics
A method of determining an estimate of a signal-to-noise ratio characteristic of a signal by receiving samples of the signal; extracting, from the samples, values of two or more features indicative of the signal-to-noise ratio characteristic; providing the two or more extracted feature values as inputs to a machine learning agent; and causing the machine learning agent to process the extracted feature values to provide the estimate of the signal-to-noise ratio characteristic.
1 . A method of determining an estimate of a signal-to-noise ratio characteristic of a signal, the method, executed by a processor, comprising:
receiving samples of a signal;
extracting, from the samples, values of two or more features indicative of a signal-to-noise ratio characteristic;
providing the two or more extracted feature values as inputs to a machine learning agent;
prior to the step of providing the two or more extracted feature values to the machine learning agent, adjusting a relative weightings of at least two of the two or more extracted feature values; and
causing the machine learning agent to process the two or more extracted feature values to provide an estimate of the signal-to-noise ratio characteristic.
2 . The method of claim 1 , further comprising:
prior to the step of providing the two or more extracted feature values to the machine learning agent, normalizing at least two of the two or more extracted feature values.
3 . The method of claim 2 , wherein the step of normalizing comprises:
rescaling each extracted feature value based on a pre-determined mean, a standard deviation, or both for the respective extracted feature value.
4 . The method of claim 3 , wherein after normalization, for each extracted feature value, a mean of the two or more extracted feature values is equal to zero and a standard deviation of the two or more extracted feature values is equal to one.
5 . The method of claim 1 , wherein the signal-to-noise ratio characteristic is a ratio of a signal power to a noise power, expressed either on a decibel scale or a linear scale.
6 . The method of claim 1 , wherein a signal-to-noise ratio characteristic is a signal-to-noise ratio per bit, E b /N 0 .
7 . The method of claim 1 , wherein the machine learning agent comprises an artificial neural network, ANN.
8 . The method of claim 1 , wherein the two or more extracted feature values comprise a maximum received signal amplitude, or a minimum received signal amplitude, or both.
9 . The method of any preceding claim , wherein the two or more extracted feature values comprise an in-phase part, μ r , of a mean of the signal samples, M 1 or a quadrature part μ l of a mean of the signal samples, or both, and
wherein
M
1
=
µ
r
+
j
•
µ
i
=
1
N
∑
t
=
0
t
=
N
-
1
z
t
,
wherein N is a total number of samples, z t .
10 . The method of claim 1 , wherein the two or more extracted feature values comprise a variance, M 2 , of the signal samples,
wherein
M
2
=
1
N
∑
t
=
0
t
=
N
-
1
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
,
wherein M 1 is a mean of the signal samples, z t , and N is a total number of samples.
11 . The method of claim 1 , wherein the two or more extracted feature values comprise am in-phase part, α r , of a third moment of the signal samples, M z , wherein
α
r
=
1
N
•
M
2
3
/
2
∑
t
=
0
t
=
N
-
1
(
x
t
-
μ
r
)
3
,
a quadrature part, α l , of a third moment, wherein
α
i
=
1
N
•
M
2
3
/
2
∑
t
=
0
t
=
N
-
1
(
y
t
-
μ
i
)
3
,
or both, and,
wherein M 2 is a variance of the signal samples z t =x t +jy t and N is a total number of samples.
12 . The method of claim 1 , wherein the two or more extracted feature values comprise a fourth moment of a signal samples, M 4 , wherein
M
4
=
1
N
∑
t
=
0
t
=
N
-
1
[
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
]
2
,
N is a total number of samples z t , and M 1 is a first moment.
13 . The method of claim 1 , wherein the two or more extracted feature values comprise a Kurtosis value, which is given by a fourth moment of the signal samples, M 4 , normalized by a second moment squared of the signal samples, M z 2 ,
wherein
M
4
=
1
N
∑
t
=
0
t
=
N
-
1
[
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
]
2
,
N is a total number of samples z t ,
M
2
=
1
N
∑
t
=
0
t
=
N
-
1
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
,
and
wherein M 1 is a mean of the signal samples.
14 . The method of claim 1 , wherein the two or more extracted feature values comprise a critical part, λ, of an M 2 M 4 estimator of the signal samples,
wherein
λ
=
2
•
M
2
2
-
M
4
,
wherein
M
4
=
1
N
∑
t
=
0
t
=
N
-
1
[
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
]
2
,
N is a total number of samples z t ,
M
2
=
1
N
∑
t
=
0
t
=
N
-
1
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
,
and
wherein M, is a mean of the signal samples.
15 . The method of claim 1 , wherein the two or more extracted feature values comprise a critical part, β, of a signal to variance ratio,
wherein
β
=
α
M
4
-
α
,
and
α
=
∑
(
z
n
z
n
*
)
(
z
n
-
1
z
n
-
1
*
)
.
wherein
M
4
=
1
N
∑
t
=
0
t
=
N
-
1
[
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
]
2
,
N is a total number of samples z t ,
M
2
=
1
N
∑
t
=
0
t
=
N
-
1
(
z
t
-
M
1
)
(
z
t
-
M
1
)
*
,
wherein M, is a mean of the signal samples.
16 . The method of claim 1 , further comprising:
prior to the step of providing the two or more extracted feature values as inputs to the machine learning agent, performing an initial training process of the machine learning agent,
wherein the initial training process is continued until a pre-determined accuracy is achieved.
17 . The method of claim 16 , further comprising:
periodically updating a training of the machine learning agent when in use.
18 . The method of claim 17 , wherein updating the training of the machine learning agent is performed on based on the received signal samples.
19 . A non-transitory computer readable media storing a computer program comprising a set of instructions, which, when executed by a computerized apparatus, cause the computerized apparatus to perform a method of determining an estimate of a signal-to-noise ratio characteristic of a signal, the method comprising:
receiving samples of a signal;
extracting, from the samples, values of two or more features indicative of a signal-to-noise ratio characteristic;
providing the two or more extracted feature values as inputs to a machine learning agent;
prior to the providing the two or more extracted feature values to the machine learning agent, adjusting a relative weightings of at least two of the two or more extracted feature values and
causing the machine learning agent to process the two or more extracted feature values to provide an estimate of the signal-to-noise ratio characteristic.
20 . An apparatus for determining an estimate of a signal-to-noise ratio characteristic of a signal, the apparatus comprising:
a processor configured to:
receive samples of a signal;
extract, from the samples, values of two or more features indicative of a signal-to-noise ratio characteristic;
provide the two or more extracted feature values as inputs to a machine learning agent;
prior to providing the two or more extracted feature values to the machine learning agent, adjust a relative weightings of at least two of the two or more extracted feature values and
cause the machine learning agent to process the two or more extracted feature values to provide an estimate of the signal-to-noise ratio characteristic.