Specific Radar Recognition Based on Characteristics of Emitted Radio Waveforms Using Convolutional Neural Networks
Abstract
:1. Introduction
2. Description of the Database
2.1. Description of Radar Signal Parameters
 
 Automatic detection direction that finds and monitors the emission sources with a frequency ranging from 500 MHz to 18 GHz;
 
 Signal parameters measured: frequency, pulse width, amplitude, direction of arrival, pulse repetition frequency, antenna rotation period;
 
 Deinterleaving;
 
 Acoustooptical channel of spectrum analyzer 500 MHz and channel of compression spectrum analyzer 40 MHz;
 
 Radio frequency measurement with 1 MHz accuracy;
 
 Instantaneous time parameters measurement with 25 ns accuracy.
2.2. Constructing a Set of Data for Training a Neural Network
 (a)
 The first training dataset consists of time waveforms (TW) of the signals with variable PD, RF and intrapulse modulation. An example of the time waveforms of a signal simulated with the use of a simulation environment (which is described in more detail in Section 5), based on the parameters presented in Table 1, is depicted in Figure 4.
 (b)
 The second training dataset consists of variable PRI waveforms which change depending on the applied interpulse modulation. Below, in Figure 5, these changes of PRI are shown.
 (c)
 The third training dataset consists of variable PD waveforms changing from pulse to pulse.
2.3. The Similarity between the Classes of Signals
3. Proposed Model
4. CNN Learning
Algorithm 1 Batch normalization procedure  
Input: X[N] $,$ 

N, 

$\gamma $, $\beta $, 

$\u03f5$ 

Output: $\mathrm{Y}\left[\mathrm{N}\right]$ 

1: initialize: $\mathrm{i}=0,{\mu}_{B}=0,{\sigma}_{B}^{2}=0,s=0,x=0$  
2: for $\mathrm{i}=0$ in $\mathrm{N}1$ do 

3: ${\mathsf{\mu}}_{\mathrm{B}}={\mathsf{\mu}}_{\mathrm{B}}+\mathrm{X}\left[\mathrm{i}\right]$  
4: end for  
5: ${\mathsf{\mu}}_{\mathrm{B}}={\mathsf{\mu}}_{\mathrm{B}}/N$  
6: for $\mathrm{i}=0$ in $\mathrm{N}1$ do 

7: $s=\mathrm{X}\left[\mathrm{i}\right]{\mathsf{\mu}}_{\mathrm{B}}$  
8: ${\sigma}_{B}^{2}={\sigma}_{B}^{2}+s\cdot s$  
9: end for  
10: ${\sigma}_{B}^{2}={\sigma}_{B}^{2}/N$  
11: for $\mathrm{i}=0$ in $\mathrm{N}1$ do 

12: $x=\frac{X\left[i\right]{\mu}_{B}}{\sqrt{{\sigma}_{B}^{2}+\u03f5}}$  
13: $Y\left[i\right]=\gamma x+\beta $  
14: end for 
5. Simulation Environment
Algorithm 2 Add signals to vector space (Random PRI, PD, RF Modulation)  
Input:$\mathrm{L}=18$ 

$\mathrm{N}$ 

$\mathrm{Cs}\left[\mathrm{L}\right]$ 

$\mathrm{ud}\left(\mathrm{minValue},\mathrm{maxValue}\right)$ 

$\mathrm{rg}$ 

Output: $\mathrm{S}\left[\mathrm{N}\right]$ 

1: initialize: $\mathrm{i}=0$ $\mathrm{sw}$ 

2: for $\mathrm{i}=0$ in (L − 1) do  
3: $\mathrm{cl}=\mathrm{Cs}\left[\mathrm{i}\right]$ 

4: $\mathrm{priRange}=\mathrm{ud}\left(\mathrm{cl}.\mathrm{pri}\_\mathrm{min},\mathrm{cl}.\mathrm{pri}\_\mathrm{max}\right)$ 

5: $\mathrm{pdRange}=\mathrm{ud}\left(\mathrm{cl}.\mathrm{pd}\_\mathrm{min},\mathrm{cl}.\mathrm{pd}\_\mathrm{max}\right)$ 

6: $\mathrm{rfRange}=\mathrm{ud}\left(\mathrm{cl}.\mathrm{rf}\_\mathrm{min},\mathrm{cl}.\mathrm{rf}\_\mathrm{max}\right)$ 

7: $\mathrm{shift}=0$  
8: $\mathrm{msl}=\mathrm{cl}.\mathrm{pd}\_\mathrm{max}\cdot \mathrm{N}$ 

9: while $\left(\left(\mathrm{shift}+\mathrm{msl}\right)<N\right)$ do  
10: $\mathrm{cPRI}=\mathrm{priRange}\left(\mathrm{rg}\right)$ 

11: $\mathrm{cPD}=\mathrm{pdRange}\left(\mathrm{rg}\right)$ 

12: $\mathrm{cRF}=\mathrm{rfRange}\left(\mathrm{rg}\right)$ 

13: $\mathrm{cWL}=\mathrm{currentPD}\cdot \mathrm{N}$ 

14: $\mathrm{sw}=\mathrm{generate}\left(\mathrm{cPD},\mathrm{cRF}\right)$ 

15: $\mathrm{AS}2\mathrm{VS}\left(\mathrm{S},\mathrm{sw},\mathrm{cWL}\right)$ 

16: $\mathrm{shift}=\mathrm{shift}+\mathrm{cPRI}\cdot \mathrm{N}$ 

17: end while  
18: end for 
Algorithm 3 Add signal to vector space (random PRI modulation)  
Input:$\mathrm{S}\left[\mathrm{N}\right]$ 

$\mathrm{signalWaveform}\left[\mathrm{currentWaveformLength}\right]$ 

$\mathrm{currentWaveformLength}$ 

shift 

Output: $\mathrm{S}\left[\mathrm{N}\right]$ 

1: initialize: $\mathrm{i}=0$  
2: for $\mathrm{i}=0$ in (currentWaveformLength − 1) do  
3: $\mathrm{S}\left[\mathrm{i}+\mathrm{shift}\right]=\mathrm{S}\left[\mathrm{i}+\mathrm{shift}\right]+\mathrm{signalWaveform}\left[\mathrm{i}\right]$ 

11: end for 
Algorithm 4 Filter all signals  
Input: $\mathrm{S}\left[\mathrm{N}\right]$ 

$\mathrm{L}=18$ 

$\mathrm{filtersFIR}\left[\mathrm{L}\right]$ 

1: initialize: $\mathrm{i}=0$ $\mathrm{filteredSignalVector}\left[\mathrm{N}\right]$ 

2: for $\mathrm{i}=0$ in (L − 1) do  
3: $\mathrm{firFilter}=\mathrm{filtersFIR}\left[\mathrm{i}\right]$ 

4: $\mathrm{outputSignalVector}=\mathrm{firFilter}.\mathrm{filter}\left(\mathrm{S}\right)$ 

5: $\mathrm{DNN}\_\mathrm{isClassSignal}\left(\mathrm{outputSignalVector}\right)$ 

11: end for 
6. Experiment Results
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Class Number  PRI $\left[\mathbf{m}\mathbf{s}\right]$  PD $\left[\mathsf{\mu}\mathbf{s}\right]$  RF $\left[\mathrm{GHz}\right]$  SP [s] 

0  0.877–0.878  0.929–1.725  2.800–2.832  3.97–4.00 
1  1.229–1.230  3.958–4.492  1.255–1.368  2.85–2.87 
2  1.223–1.223  2.512–2.863  1.221–1.339  5.80–5.96 
3  1.223–1.223  3.277–3.277  1.228–1.330  2.86–2.88 
4  1.248–1.250  2.512–3.015  1.215–1.351  2.86–2.87 
5  1.247–1.250  3.216–3.571  1.248–1.303  2.85–2.88 
6  1.250–1.252  3.727–3.885  1.308–1.365  2.87–2.88 
7  1.751–1.752  0.431–0.705  3.144–3.162  2.81–2.92 
8  1.251–1.252  2.018–2.379  2.816–2.842  5.04–5.08 
9  0.768–0.768  1.308–3.384  2.832–2.854  3.96–3.99 
10  1.738–1.739  2.811–3.514  1.203–1.254  6.02–6.07 
11  1.775–1.778  3.482–3.482  1.220–1.240  9.72–9.76 
12  1.856–1.858  1.727–4.592  3.040–3.092  6.03–6.09 
13  1.905–1.905  0.888–1.466  2.219–2.235  9.85–9.91 
14  2.150–2.150  4.898–5.570  1.100–1.389  5.41–5.53 
15  2.225–2.228  5.280–5.529  1.180–1.205  5.44–5.47 
16  2.224–2.226  4.138–4.917  1.633–1.650  5.43–5.59 
17  2.375–2.375  5.440–5.548  1.171–1.190  5.42–5.76 
Number of Signal Class  Number of Overlapping Signals in PRI  Number of Overlapping Signals in PD  Number of Overlapping Signals in the RF  Number of Overlapping Signals in the SP 

0    9, 13  8  9 
1    12, 16  2, 3, 4, 5, 6, 14  3, 4, 5, 6, 7 
2  3  4, 9, 10, 12  1, 3, 4, 5, 6, 10, 11, 14   
3  2  5, 9, 10, 12  1, 2, 4, 5, 6, 10, 11, 14  1, 4, 5, 6, 7 
4  5  2, 9, 10, 12  1, 2, 3, 5, 6, 10, 11, 14  1, 3, 5, 6, 7 
5  4  3, 9, 10, 11, 12  1, 2, 3, 4, 10, 14  1, 3, 4, 6, 7 
6  8  12  1, 2, 3, 4, 14  1, 3, 4, 5, 7 
7        1, 3, 4, 5, 6 
8  6  9, 12  0, 9   
9    0, 2, 3, 4, 5, 8, 10, 12, 13  8  0 
10    2, 3, 4, 5, 9, 11, 12  2, 3, 4, 5, 11, 14, 15  12 
11    5, 10, 12  2, 3, 4, 10, 14   
12    1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 16    10 
13    0, 9     
14    15, 16, 17  1, 2, 3, 4, 5, 6, 10, 11, 15, 17  15, 16, 17 
15  16  14, 17  10, 14, 17  14, 16, 17 
16  15  1, 12, 14    14, 15, 17 
17    14, 15  14, 15  14, 15, 16 
Layer Number  Layer Type  Layer Dimension  Activation Function 

0  B     
1  R ^{1}     
2  C_1D ^{2}  [KS ^{3}: 5, NK ^{4}: 5, SS ^{5}: 1]  ReLU [20,62] 
3  B ^{6}     
4  MP_1D ^{7}  [SS: 2]   
5  C_1D  [KS: 3, NK: 9, SS: 1]  ReLU 
6  B     
7  MP_1D  [SS: 2]   
8  C_1D  [KS: 2, NK: 6, SS: 1]  ReLU 
9  B     
10  MP_1D  [SS: 2]   
11  F     
12  D ^{8}    ReLU 
13  B     
14  Dropout     
15  D    Softmax [20] 
16  B     
Input Vectors:  

PD Samples (PostProcessing)  PRI Samples (PostProcessing)  TW Samples (Raw Acquired Signal Samples)  
Structure CNN for PD parameter ^{9}  Structure CNN for PRI parameter  Structure CNN for TW parameter  
Associated Outputs in CNN for PD, PRI and TW Parameters  
Layer number  Layer type  Dimensions of layer  Activation function 
0  D    ReLU 
1  B     
2  D    Softmax 
3  B     
Layer Number  Layer Type  Dimensions of Layer  Activation Function 

0  R     
1  C_1D  [KS: 5, NK: 30, SS: 1]  ReLU 
2  B     
3  MP_1D  [SS: 2]   
4  C_1D  [KS: 4, NK: 30, SS: 2]  ReLU 
5  B     
6  MP_1D  [SS: 2]   
7  C_1D  [KS: 3, NK: 30, SS: 3]  ReLU 
8  B     
9  MP_1D  [SS: 2]   
10  C_1D  [KS: 4, NK: 30, SS: 2]  ReLU 
11  B     
12  C_1D  [KS: 5, NK: 30, SS: 1]  ReLU 
13  B     
14  MP_1D  [SS: 2]   
15  F     
16  D    Softmax 
Processing Network  Input Tensor Size  Number of Layers  Number of Weights  Size on Disk  Processing Time for a Single Tensor [s]  GPU Processor 

TW or PD or PRI  (1, 128)  17  2248  63 kB  0.015  Geforce 1060 GTX 6GB 
TW + PRI + PD  (3, 128)  3 × 17 (In parallel) + 3 (Output) = 54  2248 × 3 + 1332 = 8076  (63 × 3 + 18) kB = 207 kB  0.046 
Input Size of ANN:  512  

Number of Samples ^{10}:  190  Number of Tests ^{11}:  1900  $\mathit{\eta}$^{12}:  0.0001 
Epochs ^{13} [B:S:E] ^{14}  Batch Size [B:S:E]  Prediction ^{15} [Min–Max]  
60  10:10:90  0.056–0.111  
70  10:10:90  0.055–0.111  
80  10:10:90  0.056–0.056  
90  10:10:90  0.056–0.111  
100  10:10:90  0.056–0.056  
110  10:10:90  0.056–0.056  
110:10:240  90  0.056–0.167 
Input Size of ANN:  512  

Number of Samples:  190  Number of Tests:  1900  $\mathit{\eta}$:  0.0001 
Number of Epochs  Batch Size [B:S:E]  Prediction [Min–Max]  
60  10:10:90  0.000–0.333  
70  10:10:90  0.056–0.500  
80  10:10:90  0.056–0.333  
90  10:10:90  0.056–0.556  
100  20:10:90  0.056–0.611  
110  20:10:90  0.056–0.778  
120  20:10:90  0.056–0.500  
130  20:10:90  0.111–0.722  
140  20:10:90  0.056–0.667  
150  20:10:90  0.111–0.556 
Input Size of ANN:  93  

Number of Samples:  190  Number of Tests:  1900  $\mathit{\eta}$:  0.0001 
Number of Epochs [B:S:E]  Batch Size [B:S:E]  Prediction [Min–Max]  
60  10:10:90  0.294–0.584  
70  10:10:90  0.334–0.538  
80  10:10:90  0.343–0.607  
90  10:10:90  0.392–0.589  
100  10:10:90  0.363–0.633  
110  10:10:90  0.447–0.664  
120  10:10:90  0.440–0.672  
130  10:10:90  0.474–0.667  
140  10:10:90  0.467–0.717  
150  10:10:90  0.463–0.652 
Input Size of ANN (TW):  93  

Number of Samples:  190  Number of Tests:  1900  $\mathit{\eta}$:  0.0001 
Number of Epochs [B:S:E]  Input Size (PRI, PD) [B:S:E]  Prediction [Min–Max]  
128  128:32:288  0.774–0.889  
128  320:32:480  0.776–0.944  
128  512:32:672  0.808–0.944  
128  704:32:864  0.670–0.889  
128:32:160  896:32:928  0.778–0.889  
160:32:224  960:32:992  0.832–0.923  
256  128:32:288  0.722–0.944  
256  320:32:480  0.722–1.000 
Input Size of ANN:  $3.3554\ast {10}^{5}$  

Number of Samples  80  Number of Tests  80  Batch Size:  40  $\mathit{\eta}$:  $5\ast {10}^{5}$ 
Number of Epochs  Prediction  Disruption Level  
256  0.991  0.1  
0.969  0.2  
0.943  0.3  
0.803  0.4  
0.644  0.5  
0.631  0.6  
0.328  0.7  
0.454  0.8  
0.446  0.9  
Input Size of ANN:  $8.3886\cdot {10}^{5}$  
499  0.922  0.9 
Input Size of ANN:  $3.3554\ast {10}^{5}$  

Number of Epochs:  256  Number of Samples:  80  Number of Tests  80  Batch Size  40  $\mathit{\eta}$:  $5\ast {10}^{5}$ 
Prediction  Disruption Level  
0.999  0.1  
1.000  0.2  
0.997  0.3  
0.997  0.4  
0.999  0.5  
0.984  0.6  
0.956  0.7  
0.660  0.8  
0.753  0.9 
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Share and Cite
Matuszewski, J.; Pietrow, D. Specific Radar Recognition Based on Characteristics of Emitted Radio Waveforms Using Convolutional Neural Networks. Sensors 2021, 21, 8237. https://doi.org/10.3390/s21248237
Matuszewski J, Pietrow D. Specific Radar Recognition Based on Characteristics of Emitted Radio Waveforms Using Convolutional Neural Networks. Sensors. 2021; 21(24):8237. https://doi.org/10.3390/s21248237
Chicago/Turabian StyleMatuszewski, Jan, and Dymitr Pietrow. 2021. "Specific Radar Recognition Based on Characteristics of Emitted Radio Waveforms Using Convolutional Neural Networks" Sensors 21, no. 24: 8237. https://doi.org/10.3390/s21248237