# Radio Frequency Fingerprint Extraction Based on Multidimension Permutation Entropy

Authors: Shouyun Deng; Zhitao Huang; Xiang Wang; Guangquan Huang
Journal: International Journal of Antennas and Propagation
 (2017)

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## Abstract

Radio frequency fingerprint (RF fingerprint) extraction is a technology that can identify the unique radio transmitter at the physical level, using only external feature measurements to match the feature library. RF fingerprint is the reflection of differences between hardware components of transmitters, and it contains rich nonlinear characteristics of internal components within transmitter. RF fingerprint technique has been widely applied to enhance the security of radio frequency communication. In this paper, we propose a new RF fingerprint method based on multidimension permutation entropy. We analyze the generation mechanism of RF fingerprint according to physical structure of radio transmitter. A signal acquisition system is designed to capture the signals to evaluate our method, where signals are generated from the same three Anykey AKDS700 radios. The proposed method can achieve higher classification accuracy than that of the other two steady-state methods, and its performance under different SNR is evaluated from experimental data. The results demonstrate the effectiveness of the proposal.


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## Body

## 1. Introduction

Just like we each have unique fingerprints, radio transmitters also have different radio frequency fingerprints, namely, RF fingerprints [1, 2]. The RF fingerprints come from differences between hardware components of transmitters, and the differences can be reflected in communication signals. The fingerprints can be extracted by processing transient signal or steady-state signal from received RF signals. The method to obtain transmitter hardware characteristics is called RF fingerprint extraction, and the method to identify individual transmitter with fingerprints is called RF fingerprint identification. The RF fingerprints work in physical layer within transmission devices, so they cannot be destroyed or copied.RF fingerprint is a popular area of research in recent decades, and it is widely applied in spectrum resource management, wireless equipment safety certification, the mobile phone network protection, and other fields [3]. The fractal dimensions (box dimension and information dimension) were extracted as RF fingerprints to identify 3 FM stations in [4]. Three fingerprint extraction algorithms based on the Hilbert spectrum were introduced in [5]. RF fingerprints based on dual-tree complex wavelet transform (DT-CWT) features were extracted from the nontransient preamble response of OFDM-based 802.11a signals in [6].In this paper, the inherent nonlinearities of radio transmitters are analyzed, and they can be extracted as RF fingerprints of the signals. As a result, a new RF fingerprinting method based on multidimension permutation entropy is proposed. We design a signal acquisition system to collect signals, and the DSSS signals from the same three radio transmitters are used in identification experiments. The results show that the proposed method is effective in differentiating individual transmitters.


## 2. Proposed Method

### 2.1. Generation Mechanism of RF Fingerprinting

Radio transmitter equipment has a complicated structure, and it is composed of many electronic devices [7]. As shown in Figure 1, baseband signal is processed in digital signal processor block and then goes into analog circuit parts. There are many nonlinear elements and unit circuits in analog circuit parts. Examples of nonlinear elements include power amplifier, nonlinear resistors, diodes, transistors, and field-effect tubes. The unit circuits may contain operational amplifiers, multipliers, absolute value circuits, and so on. The existence of these nonlinear devices makes communication signals have nonlinear components.Figure 1
Architecture of radio transmitter.Special nonlinear components come from device’s tolerance effect, which means that there are a few differences between transmitters produced by the same manufacturers. Even if transmitters have the same modes and production batches, the actual parameters of devices are different, such as oscillator frequency deviation, phase noise, modulation error, nonlinear distortion of power amplifier, and filter distortion. These hardware tolerances are the material basis of RF fingerprint. While in the process of circuit design, we usually consider adopting some measures to compensate nonlinear tolerances [8]. But, in fact, no matter what kind of model is adopted, there must be some errors during the establishment of model, so the nonlinear components of signal cannot be completely eliminated. These nonlinear components are unintentional, inevitably, and they are derived from the physical defects in the devices. Each transmitter device has its own characteristics for the reason that these defects are individual and special, so they can be used as RF fingerprints to identify radio transmitters [9].


### 2.2. Multidimension Permutation Entropy

Permutation entropy algorithm was firstly introduced by Christoph Bandt and Bernd Pompe. Permutation entropy is an appropriate complexity measure for chaotic time series, and it is extremely fast and robust when compared with all known complexity parameters such as zero-crossing rate and Lyapunov exponent [10]. As a signal analysis method of nonlinear theory, it can extract and amplify tiny changes in time series and can fast detect the dynamic mutation in complex systems. In addition, it is easy to be implemented and has strong antinoise ability [11]. Its basic principle is as follows.The key to the algorithm is phase space reconstruction. It can reconstruct one-dimensional time series into high dimension vectors in multidimensional state space and find motion rules hidden in the whole system. Then consider a discrete time sequencexi,i=1,2,…,N and the phase space reconstruction of it can be calculated as follows:(1)Xi=xi,xi+l,…,xi+m-1l.m is the embedding dimension (m≥2), and l is the time delay. The variable i should be valued as 1≤i≤N-m-1l. And m components of Xi can be ranged in an ascending order:(2)Xi=xi+j1-1l≤xi+j2-1l≤⋯≤xi+jm-1l.If two values are equal, for example, whenxi+jn1-1l=xi+jn2-1l, they should be ordered by j value firstly. And then each Xi corresponds to a permutation:(3)πi=j1,j2,…,jm.Them independent number is 1,2,…,m, so the number of arrangement ways is m!. In the reconstructed phase space, it is assumed that there are k arrangement ways, and probability of each permutation can be recorded as p1,p2,…,pk. According to the definition of Shannon entropy, permutation entropy Hp is defined as(4)Hp=-∑j=1kpjln⁡pj.It can usually be normalized by the formula:(5)0≤Hp=-∑j=1Kpjln⁡pjlnm!≤1.According to the definition,Hp clearly reflects the randomness of time series on the m dimension. In the above process, the embedding dimension m is a very important parameter; Bandt and Pompe suggest m should be valued between 3 and 7 in [10].Radio transmitter is a complicated system, and it contains different nonlinear characteristics from each analog module. So we cannot reconstruct a complete system phase space using only one dimension. An improved permutation entropy algorithm, which considers multiple dimensions, is proposed in the paper. The improved permutation entropy is called multidimension permutation entropy, and its definition is as follows. The multidimension vectorm is defined as (6)m=m1m2⋯mi⋯mn.m
i is the ith dimension embedded in the signal. The permutation entropy under the ith dimension is(7)Hpi=Hpmi,lln⁡mj!.Finally, the multidimension permutation entropy can be calculated by the formula:(8)H=Hp1Hp2⋯Hpi⋯Hpn.The multidimension permutation entropy is a high dimension feature vector to characterize a sample of signal, and it can reflect complexity of system undern dimensions. The new method reconstructs phase space of signal under different dimensions, so it contains rich nonlinear significance of transmitter and approximates to the real system space of device.


### 2.3. Feature Extraction

Based on the above analysis, we extract the envelope of the radio communication signal and then calculate multidimension permutation entropy of the envelope time series as a radio frequency fingerprint. The fingerprint feature can be calculated by following these steps:(i)
Capture the time slot from the radio communication signal as the signal sample{x(i)}(i=1,2,…,N) for the feature extraction, where N is the signal length.(ii)
Calculate the envelope sequence{ξ(i)}(i=1,2,…,N) from the signal sample {x(i)}.(iii)
Reconstruct phase space of signal envelope sequence{ξ(i)} under n dimensions according to (1).(iv)
Range sequenceXi in an ascending order for different dimensions.(v)
Calculate multidimension permutation entropy of the signal sample according to (5).


## 2.1. Generation Mechanism of RF Fingerprinting

Radio transmitter equipment has a complicated structure, and it is composed of many electronic devices [7]. As shown in Figure 1, baseband signal is processed in digital signal processor block and then goes into analog circuit parts. There are many nonlinear elements and unit circuits in analog circuit parts. Examples of nonlinear elements include power amplifier, nonlinear resistors, diodes, transistors, and field-effect tubes. The unit circuits may contain operational amplifiers, multipliers, absolute value circuits, and so on. The existence of these nonlinear devices makes communication signals have nonlinear components.Figure 1
Architecture of radio transmitter.Special nonlinear components come from device’s tolerance effect, which means that there are a few differences between transmitters produced by the same manufacturers. Even if transmitters have the same modes and production batches, the actual parameters of devices are different, such as oscillator frequency deviation, phase noise, modulation error, nonlinear distortion of power amplifier, and filter distortion. These hardware tolerances are the material basis of RF fingerprint. While in the process of circuit design, we usually consider adopting some measures to compensate nonlinear tolerances [8]. But, in fact, no matter what kind of model is adopted, there must be some errors during the establishment of model, so the nonlinear components of signal cannot be completely eliminated. These nonlinear components are unintentional, inevitably, and they are derived from the physical defects in the devices. Each transmitter device has its own characteristics for the reason that these defects are individual and special, so they can be used as RF fingerprints to identify radio transmitters [9].


## 2.2. Multidimension Permutation Entropy

Permutation entropy algorithm was firstly introduced by Christoph Bandt and Bernd Pompe. Permutation entropy is an appropriate complexity measure for chaotic time series, and it is extremely fast and robust when compared with all known complexity parameters such as zero-crossing rate and Lyapunov exponent [10]. As a signal analysis method of nonlinear theory, it can extract and amplify tiny changes in time series and can fast detect the dynamic mutation in complex systems. In addition, it is easy to be implemented and has strong antinoise ability [11]. Its basic principle is as follows.The key to the algorithm is phase space reconstruction. It can reconstruct one-dimensional time series into high dimension vectors in multidimensional state space and find motion rules hidden in the whole system. Then consider a discrete time sequencexi,i=1,2,…,N and the phase space reconstruction of it can be calculated as follows:(1)Xi=xi,xi+l,…,xi+m-1l.m is the embedding dimension (m≥2), and l is the time delay. The variable i should be valued as 1≤i≤N-m-1l. And m components of Xi can be ranged in an ascending order:(2)Xi=xi+j1-1l≤xi+j2-1l≤⋯≤xi+jm-1l.If two values are equal, for example, whenxi+jn1-1l=xi+jn2-1l, they should be ordered by j value firstly. And then each Xi corresponds to a permutation:(3)πi=j1,j2,…,jm.Them independent number is 1,2,…,m, so the number of arrangement ways is m!. In the reconstructed phase space, it is assumed that there are k arrangement ways, and probability of each permutation can be recorded as p1,p2,…,pk. According to the definition of Shannon entropy, permutation entropy Hp is defined as(4)Hp=-∑j=1kpjln⁡pj.It can usually be normalized by the formula:(5)0≤Hp=-∑j=1Kpjln⁡pjlnm!≤1.According to the definition,Hp clearly reflects the randomness of time series on the m dimension. In the above process, the embedding dimension m is a very important parameter; Bandt and Pompe suggest m should be valued between 3 and 7 in [10].Radio transmitter is a complicated system, and it contains different nonlinear characteristics from each analog module. So we cannot reconstruct a complete system phase space using only one dimension. An improved permutation entropy algorithm, which considers multiple dimensions, is proposed in the paper. The improved permutation entropy is called multidimension permutation entropy, and its definition is as follows. The multidimension vectorm is defined as (6)m=m1m2⋯mi⋯mn.m
i is the ith dimension embedded in the signal. The permutation entropy under the ith dimension is(7)Hpi=Hpmi,lln⁡mj!.Finally, the multidimension permutation entropy can be calculated by the formula:(8)H=Hp1Hp2⋯Hpi⋯Hpn.The multidimension permutation entropy is a high dimension feature vector to characterize a sample of signal, and it can reflect complexity of system undern dimensions. The new method reconstructs phase space of signal under different dimensions, so it contains rich nonlinear significance of transmitter and approximates to the real system space of device.


## 2.3. Feature Extraction

Based on the above analysis, we extract the envelope of the radio communication signal and then calculate multidimension permutation entropy of the envelope time series as a radio frequency fingerprint. The fingerprint feature can be calculated by following these steps:(i)
Capture the time slot from the radio communication signal as the signal sample{x(i)}(i=1,2,…,N) for the feature extraction, where N is the signal length.(ii)
Calculate the envelope sequence{ξ(i)}(i=1,2,…,N) from the signal sample {x(i)}.(iii)
Reconstruct phase space of signal envelope sequence{ξ(i)} under n dimensions according to (1).(iv)
Range sequenceXi in an ascending order for different dimensions.(v)
Calculate multidimension permutation entropy of the signal sample according to (5).


## 3. Experimental Results

### 3.1. Signal Acquisition

To evaluate the performance of the proposed method, an experimental system shown in Figure2 is implemented. The test equipment comprises PCs, Anykey AKDS700 radios, a digital receiver, and an oscilloscope. Two digital radios are, respectively, a transmitter and a receiver, and the distance between them is ten meters due to laboratory space limitation. There is no obstacle between the transmitter and the receiver, and signals propagate in HF line-of-sight (LOS) channel. Then, real time wireless communication is performed between the transmitting side and the receiving side. The bandwidth of the channel is fixed at 5 M, and the bandwidth of receiver is 20 M. Following this, a digital oscilloscope connected with the digital receiver is utilized to collect the radio’s RF signals which are DSSS modulation signals, and its capturing bandwidth is fixed at 10 M. We collect communication signals from the same three model digital radios named R1, R2, and R3.Figure 2
The scheme of experiment.


### 3.2. Feature Extraction and Classification Result

In the experiment, one hundred sets of data are collected for each radio. The time domain waveform of radio’s DSSS signal is shown in Figure3, and a complete waveform period comprises transient portion, steady-state portion, and hand-shaking portion. The transient portion which indicates power turns on is very short and difficult to be detected precisely. However, the steady-state and hand-shaking portions come out under stable communication state and are easy to be found out. The steady-state portion includes the random communication data payload, and the hand-shaking portion includes the fixed protocol data payload. To make the performance comparison between fixed and random payload, both the steady-state portion and hand-shaking portion of signal are used for extracting RF fingerprint. We use the average power of signal and noise within the same capturing bandwidth 10 M to calculate S/N on the postcollection phase, and their average SNR is 20 dB.Figure 3
The time domain waveform of radio signal.Multidimension permutation entropy of each signal sample is calculated as RF fingerprint. The multidimension vectorm=[34567] is used in the experiment according to permutation entropy theory, so each radio transmitter has a feature set composed of 100 vectors whose dimension is 5. Then we use a support vector machine (SVM) classifier with RBF kernel [12, 13] to classify these feature vectors. 1000 classification experiments are conducted with feature vectors of each radio transmitter divided equally into two groups for training and testing, and each group constitutes fifty percent of the total. The final average percentages of classification results for steady-state and hand-shaking signals are given by Tables 1 and 2 separately.Table 1
Classification confusion matrix for random payload data: steady-state signal of radios (%).
True class
Classified
R
1
R
2
R
3
R
1
94.7000
4.7251
1.6168
R
2
2.1518
90.9079
2.8132
R
3
3.1482
4.3670
95.5700Table 2
Classification confusion matrix for fixed payload data: hand-shaking signal of radios (%).
True class
Classified
R
1
R
2
R
3
R
1
95.1300
3.9310
1.5484
R
2
2.3702
91.0810
3.0253
R
3
2.4998
4.9880
95.4263As we can see from Tables1 and 2, when analyzing steady-state signals or hand-shaking signals, correct recognition rates are all above 90% for the three Anykey AKDS700 radios. And according to 500 testing inputs for SVM classifier, we use preconfigured functions to return class confidences for the three classes. Then we take the maximum class confidence 98.7% as the generalized confidence of classification results eventually. The classification results demonstrate that the proposed method for extracting RF fingerprint is an effective and stable technique to identify the individual radio transmitter at a minimum amount of 3 and it is little affected by fixed or random payload data.


## 3.1. Signal Acquisition

To evaluate the performance of the proposed method, an experimental system shown in Figure2 is implemented. The test equipment comprises PCs, Anykey AKDS700 radios, a digital receiver, and an oscilloscope. Two digital radios are, respectively, a transmitter and a receiver, and the distance between them is ten meters due to laboratory space limitation. There is no obstacle between the transmitter and the receiver, and signals propagate in HF line-of-sight (LOS) channel. Then, real time wireless communication is performed between the transmitting side and the receiving side. The bandwidth of the channel is fixed at 5 M, and the bandwidth of receiver is 20 M. Following this, a digital oscilloscope connected with the digital receiver is utilized to collect the radio’s RF signals which are DSSS modulation signals, and its capturing bandwidth is fixed at 10 M. We collect communication signals from the same three model digital radios named R1, R2, and R3.Figure 2
The scheme of experiment.


## 3.2. Feature Extraction and Classification Result

In the experiment, one hundred sets of data are collected for each radio. The time domain waveform of radio’s DSSS signal is shown in Figure3, and a complete waveform period comprises transient portion, steady-state portion, and hand-shaking portion. The transient portion which indicates power turns on is very short and difficult to be detected precisely. However, the steady-state and hand-shaking portions come out under stable communication state and are easy to be found out. The steady-state portion includes the random communication data payload, and the hand-shaking portion includes the fixed protocol data payload. To make the performance comparison between fixed and random payload, both the steady-state portion and hand-shaking portion of signal are used for extracting RF fingerprint. We use the average power of signal and noise within the same capturing bandwidth 10 M to calculate S/N on the postcollection phase, and their average SNR is 20 dB.Figure 3
The time domain waveform of radio signal.Multidimension permutation entropy of each signal sample is calculated as RF fingerprint. The multidimension vectorm=[34567] is used in the experiment according to permutation entropy theory, so each radio transmitter has a feature set composed of 100 vectors whose dimension is 5. Then we use a support vector machine (SVM) classifier with RBF kernel [12, 13] to classify these feature vectors. 1000 classification experiments are conducted with feature vectors of each radio transmitter divided equally into two groups for training and testing, and each group constitutes fifty percent of the total. The final average percentages of classification results for steady-state and hand-shaking signals are given by Tables 1 and 2 separately.Table 1
Classification confusion matrix for random payload data: steady-state signal of radios (%).
True class
Classified
R
1
R
2
R
3
R
1
94.7000
4.7251
1.6168
R
2
2.1518
90.9079
2.8132
R
3
3.1482
4.3670
95.5700Table 2
Classification confusion matrix for fixed payload data: hand-shaking signal of radios (%).
True class
Classified
R
1
R
2
R
3
R
1
95.1300
3.9310
1.5484
R
2
2.3702
91.0810
3.0253
R
3
2.4998
4.9880
95.4263As we can see from Tables1 and 2, when analyzing steady-state signals or hand-shaking signals, correct recognition rates are all above 90% for the three Anykey AKDS700 radios. And according to 500 testing inputs for SVM classifier, we use preconfigured functions to return class confidences for the three classes. Then we take the maximum class confidence 98.7% as the generalized confidence of classification results eventually. The classification results demonstrate that the proposed method for extracting RF fingerprint is an effective and stable technique to identify the individual radio transmitter at a minimum amount of 3 and it is little affected by fixed or random payload data.


## 4. Performance Comparison

### 4.1. Comparison with Other Methods

A series of experiments are conducted to evaluate the performance of the proposed method. Two other different steady-state based techniques are used in the experiments. And the classification experiments of two techniques are implemented under the same conditions with the proposed method. As in [4], we extract the envelop of an individual signal and then compute the box dimension and information dimension as individual fractal dimension features. And the average classification accuracy achieves 76.43%, which is almost as many as [4]. Its implementation process is as follows:(i)
Calculate the envelope sequence of the signal sample{x(i)}.(ii)
Put the signal envelope sequence in the unit square box and then calculate box dimension according to its definition.(iii)
Reconstruct the signal envelope sequence.(iv)
Use the reconstructed signal sequence to calculate the information dimension according to its definition.However, unlike the dual-tree complex wavelet transform which is implemented in [6], we extract features from steady-state communicational portions of DSSS signals rather than the preamble response of OFDM-based 802.11a signals. Then we calculate fingerprint features on the wavelet domain based on DT-CWT. Its implementation process is as follows:(i)
For each signal sample{x(i)}, get real-valued wavelet domain coefficients from two real-valued filter banks for dual-tree complex wavelet transform.(ii)
Use real-valued wavelet domain coefficients to form the sequence of complex sampled WD signal.(iii)
Calculate the variance, skewness, and kurtosis of these WD signal sequences.(iv)
Use the statistics vector including variance, skewness, and kurtosis to generate DT-CWT fingerprints.Eventually, the average classification accuracy reaches 84.56% by training SVM classifier. The compared average classification accuracies for the three methods are given in Table3. The experiment results show that average classification accuracy of the proposed method is higher than that of methods based on fractal dimension and dual-tree complex wavelet transform for three radio transmitters under our experiment scene.Table 3
Comparing classification accuracies.
Method
Average classification accuracy (%)
Multidimension permutation entropy
93.73
Fractal dimension
76.43
Dual-tree complex wavelet transform
84.56


### 4.2. The Effect of Noise

In order to test the performance of the proposed method in different SNR, the Gaussian white noise simulated by MATLAB is added directly to the steady-state signals for comparison. Figure4 shows the average classification accuracies for the three radio transmitters under different simulation SNR. As can be seen from Figure 4, the classification accuracy begins to degrade obviously when SNR is below 10 dB and the classification accuracy of the proposed method is greater than 90% when SNR is above 10 dB. Because RF fingerprints of steady-state signals are minor components hidden in signals, they will be overwhelmed more seriously if the noise is greater. And when SNR is above 10 dB, noise is too weak to overwhelm fingerprints. As a result, the proposed method based on multidimension permutation entropy has a good performance, especially when SNR is above 10 dB.Figure 4
Classification accuracies for different SNR.


### 4.3. Computational Complexity Analysis

From the process of extracting RF fingerprint characteristics, computation of the algorithm is mainly concentrated on the calculation of the multidimension permutation entropy, and other calculation on data preprocessing is negligible. From (1), we can know that phase space reconstruction needs N-m-1l addition operations, so the computational complexity for (1) is ON-m-1l. And according to (2), the sort operation needs a complexity of ON∗mlogm. Then according to (4) and (8), the complexity for calculating the value of multidimension permutation entropy is Onk. So the total computational complexity for the method is about ON-m-1l+ON∗mlogm+Onk. From the complexity analysis, we can know that when data length N is fixed, computational complexity for the method is mainly effected by embedding dimension m and dimension’s number n. Obviously, the larger m and n are, the higher the computational complexity will be. Large dimension parameters can make RF fingerprint characteristics contain more abundant information representing individual. Therefore, in practice, the m and n values should be compromised between calculation and classification ability.


## 4.1. Comparison with Other Methods

A series of experiments are conducted to evaluate the performance of the proposed method. Two other different steady-state based techniques are used in the experiments. And the classification experiments of two techniques are implemented under the same conditions with the proposed method. As in [4], we extract the envelop of an individual signal and then compute the box dimension and information dimension as individual fractal dimension features. And the average classification accuracy achieves 76.43%, which is almost as many as [4]. Its implementation process is as follows:(i)
Calculate the envelope sequence of the signal sample{x(i)}.(ii)
Put the signal envelope sequence in the unit square box and then calculate box dimension according to its definition.(iii)
Reconstruct the signal envelope sequence.(iv)
Use the reconstructed signal sequence to calculate the information dimension according to its definition.However, unlike the dual-tree complex wavelet transform which is implemented in [6], we extract features from steady-state communicational portions of DSSS signals rather than the preamble response of OFDM-based 802.11a signals. Then we calculate fingerprint features on the wavelet domain based on DT-CWT. Its implementation process is as follows:(i)
For each signal sample{x(i)}, get real-valued wavelet domain coefficients from two real-valued filter banks for dual-tree complex wavelet transform.(ii)
Use real-valued wavelet domain coefficients to form the sequence of complex sampled WD signal.(iii)
Calculate the variance, skewness, and kurtosis of these WD signal sequences.(iv)
Use the statistics vector including variance, skewness, and kurtosis to generate DT-CWT fingerprints.Eventually, the average classification accuracy reaches 84.56% by training SVM classifier. The compared average classification accuracies for the three methods are given in Table3. The experiment results show that average classification accuracy of the proposed method is higher than that of methods based on fractal dimension and dual-tree complex wavelet transform for three radio transmitters under our experiment scene.Table 3
Comparing classification accuracies.
Method
Average classification accuracy (%)
Multidimension permutation entropy
93.73
Fractal dimension
76.43
Dual-tree complex wavelet transform
84.56


## 4.2. The Effect of Noise

In order to test the performance of the proposed method in different SNR, the Gaussian white noise simulated by MATLAB is added directly to the steady-state signals for comparison. Figure4 shows the average classification accuracies for the three radio transmitters under different simulation SNR. As can be seen from Figure 4, the classification accuracy begins to degrade obviously when SNR is below 10 dB and the classification accuracy of the proposed method is greater than 90% when SNR is above 10 dB. Because RF fingerprints of steady-state signals are minor components hidden in signals, they will be overwhelmed more seriously if the noise is greater. And when SNR is above 10 dB, noise is too weak to overwhelm fingerprints. As a result, the proposed method based on multidimension permutation entropy has a good performance, especially when SNR is above 10 dB.Figure 4
Classification accuracies for different SNR.


## 4.3. Computational Complexity Analysis

From the process of extracting RF fingerprint characteristics, computation of the algorithm is mainly concentrated on the calculation of the multidimension permutation entropy, and other calculation on data preprocessing is negligible. From (1), we can know that phase space reconstruction needs N-m-1l addition operations, so the computational complexity for (1) is ON-m-1l. And according to (2), the sort operation needs a complexity of ON∗mlogm. Then according to (4) and (8), the complexity for calculating the value of multidimension permutation entropy is Onk. So the total computational complexity for the method is about ON-m-1l+ON∗mlogm+Onk. From the complexity analysis, we can know that when data length N is fixed, computational complexity for the method is mainly effected by embedding dimension m and dimension’s number n. Obviously, the larger m and n are, the higher the computational complexity will be. Large dimension parameters can make RF fingerprint characteristics contain more abundant information representing individual. Therefore, in practice, the m and n values should be compromised between calculation and classification ability.


## 5. Conclusions

In this paper, we propose a new RF fingerprint method based on multidimension permutation entropy. The proposed method is based on the principle that the inherent nonlinear components within transmitters are unintentional, inevitably, and individual can designate the unique transmitter. Multidimension permutation entropy contains rich nonlinear characteristics of transmitter and can be used to extract RF fingerprint of transmitter. Then, classification experiments for three radios are conducted by a signal acquisition system. The experimental result demonstrates that the proposed method is effective for both fixed and random payload at a minimum of 3 transmitters, and the comparison experiment results show that the method works better than the fractal dimension and dual-tree complex wavelet transform techniques under our experiment scene. Also, the proposed method can achieve a good performance when SNR is above 10 dB. The method provides a new convenient and effective solution for radio frequency communication protection and other security fields.



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*Source: 1538728-2017-08-28.xml*