## 4 Target Model and Frequency Offset Extraction Method
### Target Detection Processing Method
#### 4.2.3 Interference Suppression  
1. Direct wave and multipath clutter suppression  
The signals received by the receiving antenna include target echoes, direct waves from the transmitting antenna, and multipath signals reflected by other obstacles in the environment. After the signal is synchronized, the delay and frequency offset of the direct wave are both 0. According to Equation (12), the direct wave will add a constant to the corresponding symbol and subcarrier position in the matrix \(H(n,m)\). The delay of the multipath signal relative to the direct wave is \(\tau\), and the frequency offset is 0, which is expressed as a constant complex number in \(H(n,m)\). So, a strong peak will appear in the spectrum at zero frequency. Therefore, it is necessary to suppress the zero-frequency component of the signal to obtain the Doppler frequency offset of the target, which can be achieved by removing the average value of the signal or using a filter. Using the rotation model shown in Figure 5, the target echo intensity is set to 0 dB, the direct wave intensity is set to 20 dB, and the signal-to-noise ratio is 15 dB. In the simulation, the period of the CSI-RS signal is set to five time slots, that is, 50 ms. Figure 10a,b shows the time-frequency analysis results and extracted frequency offset curve after removing the signal mean value. Figure 10c shows the error between the actual measurement value and the theoretical value. It can be seen that the error is small and random, which has a small impact on the measurement of the frequency offset variation period. For the filter, the equal ripple design method is used to design a bandpass filter with an order of 226. After filtering, delay compensation is performed on the signal. The time-frequency analysis results and the extracted frequency offset curve are shown in Figure 11a-c and show the error between the actual measurement value and the theoretical value. The reason why the starting position in Figure 11b is 0 for tens of milliseconds is that the filter initially acts on the signal, resulting in poor filtering performance. In data processing, it is possible to discard data with poor filtering performance at the forefront of the wave. Figure 11: (**a**) Time–frequency analysis results after filter processing; (**b**) frequency offset curve after filter processing; (**c**) the error between the actual measurement value and the theoretical value. Figure 10: (**a**) Time–frequency analysis results after removing the signal mean value; (**b**) frequency offset curve after removing the signal mean value; (**c**) the error between the actual measurement value and the theoretical value. Random phase noise suppression  
In the experiment, the signal-receiving and transmitting antennas are separated, which would lead to the problem of clock desynchronization. Clock desynchronization may result in random phase shifts that need to be processed to obtain more accurate Doppler shifts. Multiple antennas can be used to receive signals in the experiment. If two receiving antennas share a crystal oscillator, the clock offset of the two antennas at the same time will be the same. Taking advantage of this characteristic, the cross-antenna cross-correlation (CACC) method or the cross-antenna signal ratio (CASR) method can be used to eliminate random phase shifts [25; 26]. In this paper, we use the CASR method to eliminate random phase shifts. Taking the channel response extracted from a subcarrier as an example, the channel response can be divided into static path components and dynamic path components. For the i-th antenna, the obtained channel response can be written as follows [25]:  
\[h^{i}(t)=\left[h^{i}_{s}(t)+h^{i}_{d}(t)\exp(j2\pi f_{d}t)\right]\exp[j\theta(t)] \tag{16}\]  
where \(h^{i}_{s}(t)\) is the static path component in the i-th antenna channel response, \(h^{i}_{d}(t)\exp(j2\pi f_{d}t)\) is the dynamic path component, \(h^{i}_{d}(t)\) is a constant in the dynamic path component, and \(\theta(t)\) is a random phase offset.