## 4 RFF Extraction and Identification Methods  
### Preamble Field-Based RFF Extraction Method  
After the signal acquisition and preprocessing steps are completed, the features of the radio frequency fingerprint can be extracted. In the mobility environment, if stable RFFs need to be obtained, the most challenging problem to be solved is to eliminate the time-varying influence of the channel. This paper proposes an RFF extraction method for IEEE 802.11p-based DSRC signals, which utilizes the characteristics of the preamble field of the OFDM PHY frame, superimposes part of the time domain waveform of the short preamble and the long preamble, and then divides the spectrum of them to remove the multi-channel and the added noise in the mobile environment, resulting in a purer device fingerprint. First, four signal sequences are taken out from the preprocessed OFDM preamble field in order to extract the fingerprint for each frame of received signal. Considering that the first short training symbol may be affected by the initial transient response, and that the IFFT transformation period is 6.4 us, equivalent to four times of the period of the short training symbol, the second to fifth symbols are taken and named as the sequence STF1. Accordingly, the seventh to tenth symbols are taken as the sequence STF2. For local signal sequence, STF1 and STF2 are theoretically identical, each containing 12 subcarriers. For long preamble, regardless of the cyclic prefix part, the first long training symbol is taken as the sequence LTF1, and the second long training symbol is taken as the sequence LTF2. Theoretically, LTF1 and LTF2 are also identical, each containing 52 non-DC subcarriers. As described in Section 3.1, the four sequences are identical in length and each last for 6.4 us, totaling 128 sampling points at a sampling rate of 20 MHz. However, in practice, the preamble field signals transmitted by each device are not the same, because the RFF information of the transmitter will be parasitized in the signal it sends. In addition, when the transmitter sends the wireless signal, it will experience wireless channel and generate convolution relationship with the multipath effect in it. Moreover, the final received signal will be affected by various types of noise dominated by additive noise. The following part will discuss and deduce how the method proposed in this paper can not only preserve and enhance the RFF features, but also eliminate the mobile multipath interference and additive noise. The formation of RFF can be ideally modeled as a local time domain baseband signal passing through a filter, in which the local ideal signal and fingerprint are in a convolution relationship, and the received signal can be expressed as  
\[y(n)=x(n)*f^{t}(n)*h(n)*f^{r}(n)+v(n) \tag{14}\]  
where \(n=0,1,\ldots,N-1,N\) denotes the length of the sequence. In the four signal sequences mentioned above, each sequence lasts 6.4 us and thus \(N=128\) if the sampling rate is 20 MHz. Besides, \(y(n)\) denotes the received signal, \(x(n)\) denotes the local ideal signal, \(f^{t}(n)\) denotes the RFF of signal transmitter, \(f^{r}(n)\) denotes the RFF of signal receiver, \(h(n)\) denotes the multipath channels experienced by the sequence, \(v(n)\) denotes the additive noise, and \(*\) denotes a linear convolution operation. Specifically, the received signal of the four sequences STF1, STF2, LTF1, and LTF2 are represented as  
\[y_{STF1}(n) =x_{STF1}(n)*f^{t}_{STF1}(n)*h(n)*f^{r}(n)+v_{STF1}(n) \tag{15}\] \[y_{STF2}(n) =x_{STF2}(n)*f^{t}_{STF2}(n)*h(n)*f^{r}(n)+v_{STF2}(n)\] (16) \[y_{LTF1}(n) =x_{LTF1}(n)*f^{t}_{LTF1}(n)*h(n)*f^{r}(n)+v_{LTF1}(n)\] (17) \[y_{LTF2}(n) =x_{LTF2}(n)*f^{t}_{LTF2}(n)*h(n)*f^{r}(n)+v_{LTF2}(n) \tag{18}\]  
Since the local signal \(x_{STF1}(n)\) and \(x_{STF2}(n)\) are the same sequence, the RFF generated by the transmitter \(f^{t}_{STF1}(n)\) and \(f^{t}_{STF2}(n)\) are also the same. Similarly, \(f^{t}_{LTF1}(n)\) and \(f^{t}_{LTF2}(n)\) are the same.