Machine Learning for RF Fingerprinting Extraction . . .
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waveform. In [8], the box dimension in fractal theory can reflect the geometric
scale of the fractal set. The information dimension can reflect the distribution
of the fractal set in the regional space. And the wireless communication signal
as a time series can be characterized by the fractal dimension.
The calculation processes of the wireless communication source signal box
dimension are shown as follows. The signal sequence {s (i) , i = 1, 2, . . . , N} is
obtained by preprocessing the communication signal and extracting the signal
envelope, where N is the length of the signal sequence; place the signal sequence
{s (i)} in the unit square, and the minimum interval on the abscissa is d = 1/N ,
let
N (d) = N +
N −1
i=1
max [s (i) , s (i + 1)]d −
N −1
i=1
min [s (i) , s (i + 1)]d
d 2
. (3)
Calculate box dimension:
D b = −
ln N (d)
ln d
.
(4)
The fractal box dimension only reflects the geometric scale. In order to utilize the distribution information of the fractal set in the regional space, the
calculation processes of wireless communication source signal fractal dimension
are shown as follows: preprocess the communication signal, extract the signal
envelope, and obtain a signal sequence {s (i) , i = 1, 2, . . . , N}, where N is the
length of the signal sequence; the signal sequence is reconstructed according to
the following method to reduce the influence of part of the in-band noise, and
at the same time, it is convenient to calculate the information dimension
s 0 (i) = s (i + 1) − s (i) , i = 1, 2, . . . , N − 1.
(5)
Calculate fractal dimension, let S =
N −1
i=1
s 0 (i) p (i) =
s0(i)
S , thus
D I = −
N −1
i=1
{p (i) × lg [p (i)]}.
(6)
Box dimension and information dimension are used to measure the complexity of the signal spectrum shape, which contains the information of the signal
amplitude, frequency, and phase.
3.2 Phase Noise Spectrum
Phase noise [9] is an important indicator reflecting the frequency stability and
frequency reliability of signal sources. In phase noise measurement technology,
power spectrum estimation is an indispensable part of any phase noise measurement system.
193
waveform. In [8], the box dimension in fractal theory can reflect the geometric
scale of the fractal set. The information dimension can reflect the distribution
of the fractal set in the regional space. And the wireless communication signal
as a time series can be characterized by the fractal dimension.
The calculation processes of the wireless communication source signal box
dimension are shown as follows. The signal sequence {s (i) , i = 1, 2, . . . , N} is
obtained by preprocessing the communication signal and extracting the signal
envelope, where N is the length of the signal sequence; place the signal sequence
{s (i)} in the unit square, and the minimum interval on the abscissa is d = 1/N ,
let
N (d) = N +
N −1
i=1
max [s (i) , s (i + 1)]d −
N −1
i=1
min [s (i) , s (i + 1)]d
d 2
. (3)
Calculate box dimension:
D b = −
ln N (d)
ln d
.
(4)
The fractal box dimension only reflects the geometric scale. In order to utilize the distribution information of the fractal set in the regional space, the
calculation processes of wireless communication source signal fractal dimension
are shown as follows: preprocess the communication signal, extract the signal
envelope, and obtain a signal sequence {s (i) , i = 1, 2, . . . , N}, where N is the
length of the signal sequence; the signal sequence is reconstructed according to
the following method to reduce the influence of part of the in-band noise, and
at the same time, it is convenient to calculate the information dimension
s 0 (i) = s (i + 1) − s (i) , i = 1, 2, . . . , N − 1.
(5)
Calculate fractal dimension, let S =
N −1
i=1
s 0 (i) p (i) =
s0(i)
S , thus
D I = −
N −1
i=1
{p (i) × lg [p (i)]}.
(6)
Box dimension and information dimension are used to measure the complexity of the signal spectrum shape, which contains the information of the signal
amplitude, frequency, and phase.
3.2 Phase Noise Spectrum
Phase noise [9] is an important indicator reflecting the frequency stability and
frequency reliability of signal sources. In phase noise measurement technology,
power spectrum estimation is an indispensable part of any phase noise measurement system.