## 3 Signal Acquisition and Preprocessing
### Signal Acquisition  
Wireless signals are often collected through universal software radio peripheral (USRP). After the wireless signals are collected, it is necessary to capture and separate each frame conforming to the OFDM PPDU frame format from the collected signals for subsequent analysis, and at the same time the interference of other standard signals that may exist in the air should be also considered.  
Considering that the PHY preamble has a fixed repetition structure, and especially the time domain waveform of 10 repeated short training symbols has obvious distinction, which can be used as the search target for fast acquisition, the method of cross-correlation operation with the local ideal signal can be adopted to realize the signal capture. Since the real-time requirement for capturing valid signal frames from the received signals needs to be satisfied in practical work, the way of sliding a small window to receive the signal can be taken, in which the collected signal is sent to the processor in sequence, and its conjugate correlation value is calculated with a local ideal short training symbol. If the correlation value exceeds the threshold value and the energy of the received signal also exceeds the threshold value, it can be considered that the signal acquisition is successful.  
In the IEEE 802.11p protocol, a short training symbol lasts for 1.6 \(\upmu\)s and occupies 32 sampling points at a sampling rate of 20 MHz. Using a window with a length of 32 sampling points for sliding and performing correlation operations have low overhead  
Figure 2: IEEE 802.11p OFDM PPDU frame format.  
and can basically meet the demands of real time. Suppose a local short training symbol is \(x(n)\), and the received signal taken out by sliding window and sent to the processor is \(y(n)\). In order to facilitate the comparison with the decision thresholds, the amplitudes of the two sequences are normalized first. The two normalized sequence signals are  
\[x_{short\_symbol}(n)=\frac{x(n)}{\frac{1}{L}\sum\limits_{n=0}^{L-1}\lvert x(n )\rvert} \tag{3}\]  
\[y_{short\_symbol}(n)=\frac{y(n)}{\frac{1}{L}\sum\limits_{n=0}^{L-1}\lvert y(n )\rvert} \tag{4}\]  
where \(n=0,1,\ldots,L-1\), \(L\) denotes the sampling points of a short training symbol. The complex conjugate correlation value of two normalized signals is expressed by  
\[r_{short\_symbol}=\sum\limits_{n=0}^{L-1}y_{short\_symbol}(n)x_{short\_symbol }^{*}(n) \tag{5}\]  
where \(x_{short\_symbol}^{*}(n)\) is the conjugate of \(x_{short\_symbol}(n)\). Only when the calculated value \(r_{short\_symbol}\) exceeds the threshold \(TH\), can it be considered that a short training symbol has been captured. In addition, since the correlation value of the noise part after the normalization may also exceed the threshold, the energy of the received signal itself  
\[P=\frac{1}{L}\sum\limits_{n=0}^{L-1}\lvert y(n)\rvert^{2} \tag{6}\]  
also needs to exceed a threshold value. According to the above acquisition rules, when the correlation values of continuous multi-segment signals with local ideal signal and their own energy both exceed the threshold, it means that a frame of IEEE 802.11p PPDU signal has been acquired.