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.
Just like we each have unique fingerprints, radio transmitters also have different radio frequency fingerprints, namely, RF fingerprints [
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 [
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.
Radio transmitter equipment has a complicated structure, and it is composed of many electronic devices [
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 [
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 [
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 sequence
If two values are equal, for example, when
The
It can usually be normalized by the formula:
According to the definition,
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 vector
Finally, the multidimension permutation entropy can be calculated by the formula:
The multidimension permutation entropy is a high dimension feature vector to characterize a sample of signal, and it can reflect complexity of system under
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: Capture the time slot from the radio communication signal as the signal sample Calculate the envelope sequence Reconstruct phase space of signal envelope sequence Range sequence Calculate multidimension permutation entropy of the signal sample according to (
To evaluate the performance of the proposed method, an experimental system shown in Figure
The scheme of experiment.
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 Figure
The time domain waveform of radio signal.
Multidimension permutation entropy of each signal sample is calculated as RF fingerprint. The multidimension vector
Classification confusion matrix for random payload data: steady-state signal of radios (%).
True class | Classified | ||
---|---|---|---|
|
|
|
|
|
94.7000 | 4.7251 | 1.6168 |
|
2.1518 | 90.9079 | 2.8132 |
|
3.1482 | 4.3670 | 95.5700 |
Classification confusion matrix for fixed payload data: hand-shaking signal of radios (%).
True class | Classified | ||
---|---|---|---|
|
|
|
|
|
95.1300 | 3.9310 | 1.5484 |
|
2.3702 | 91.0810 | 3.0253 |
|
2.4998 | 4.9880 | 95.4263 |
As we can see from Tables
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 [ Calculate the envelope sequence of the signal sample Put the signal envelope sequence in the unit square box and then calculate box dimension according to its definition. Reconstruct the signal envelope sequence. 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 [ For each signal sample Use real-valued wavelet domain coefficients to form the sequence of complex sampled WD signal. Calculate the variance, skewness, and kurtosis of these WD signal sequences. 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 Table
Comparing classification accuracies.
Method | Average classification accuracy (%) |
---|---|
Multidimension permutation entropy | 93.73 |
Fractal dimension | 76.43 |
Dual-tree complex wavelet transform | 84.56 |
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. Figure
Classification accuracies for different SNR.
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 (
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.
The authors declare that they have no conflicts of interest.
This work is supported by the National Natural Science Foundation of China (Grant no. 61401490).