Machine Learning for RF Fingerprinting Extraction . . .
195
Imag
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
Real
A1
A2
A3
A4
C3
Fig. 3. Constellation diagram for QPSK with SNR = 10 dB
The constellation of QPSK signal when SNR = 10 dB is showed as Fig. 3.
The average of the four constellation point sets is taken to form a quadrilateral.
And A 1 , A 2 , A 3 , A 4 represent the length of each side separately, K 1 , K 2 represent
two diagonals as Fig. 3 shows.
The constellation features are defined as follows
– c 1 represents the ratio of the longest to the shortest side length and can be
expressed as
c 1 =
max (A 1 , A 2 , A 3 , A 4 )
min (A 1 , A 2 , A 3 , A 4 )
.
(9)
– c 2 represents the longest to shortest ratio of the diagonal and can be expressed
as
c 2 =
max (K 1 , K 2 )
min (K 1 , K 2 )
.
(10)
– c 3 indicates the maximum angle between the diagonals and can be expressed
as
c 3 = π − arccos
K 1 · K 2
|K 1 | × |K 1 |
.
(11)
3.4 SNR Estimation
In order to better analyze the classification results, SNR is selected as the performance measurement parameter, based on the practical need for signal detection
under noncooperative communication conditions. In this paper, a small prior
knowledge SNR estimation algorithm based on high-order moments is selected
from many SNR estimation methods [10].
195
Imag
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
Real
A1
A2
A3
A4
C3
Fig. 3. Constellation diagram for QPSK with SNR = 10 dB
The constellation of QPSK signal when SNR = 10 dB is showed as Fig. 3.
The average of the four constellation point sets is taken to form a quadrilateral.
And A 1 , A 2 , A 3 , A 4 represent the length of each side separately, K 1 , K 2 represent
two diagonals as Fig. 3 shows.
The constellation features are defined as follows
– c 1 represents the ratio of the longest to the shortest side length and can be
expressed as
c 1 =
max (A 1 , A 2 , A 3 , A 4 )
min (A 1 , A 2 , A 3 , A 4 )
.
(9)
– c 2 represents the longest to shortest ratio of the diagonal and can be expressed
as
c 2 =
max (K 1 , K 2 )
min (K 1 , K 2 )
.
(10)
– c 3 indicates the maximum angle between the diagonals and can be expressed
as
c 3 = π − arccos
K 1 · K 2
|K 1 | × |K 1 |
.
(11)
3.4 SNR Estimation
In order to better analyze the classification results, SNR is selected as the performance measurement parameter, based on the practical need for signal detection
under noncooperative communication conditions. In this paper, a small prior
knowledge SNR estimation algorithm based on high-order moments is selected
from many SNR estimation methods [10].