# Integrated Communication and Measurement System with BOC-Assisted OFDM
## 3 Reception of the Composite Signal
### Demodulation of the OFDM Signal  
The OFDM signal is the superposition of multiple subchannel signals, and the subcarriers are distinguished by orthogonality. However, when the Doppler frequency offset exceeds a threshold, interference may occur between subchannels, resulting in the degradation of the communication performance. Therefore, reducing the influence of the Doppler frequency offset on the OFDM signal is a key issue for enhancing the performance of UAV communication systems under high-speed mobile conditions. Consequently, we propose an approach for using the BOC signal to assist in the demodulation of the OFDM signal, as shown in Figure 9.  
In Section 3.3, we obtain a Doppler frequency offset with high precision through the SPLL three-loop tracking algorithm. The high-precision Doppler frequency offset tracked by the BOC signal is adopted for carrier Doppler compensation to assist in the demodulation of the OFDM signal.  
Figure 9: Demodulation of the OFDM signal.  
Let the signal received after it passes through the channel be \(r_{OFDM\_BOC}(t)\). Considering that the BOC signal has little influence on OFDM demodulation, the received OFDM signal can be expressed as follows:  
\[r_{OFDM\_BOC}(t)\approx r_{OFDM}(t)=\alpha\cdot\frac{1}{M}\sum_{m=0}^{M-1}S_{k}(m )\cdot e^{j2\pi km/M}\cdot e^{j2\pi(f_{c}+f_{d})t} \tag{19}\]  
Subsequently, carrier stripping and carrier Doppler compensation are performed on the received OFDM signal, as shown in Equation (20):  
\[\begin{split} r_{dop}&=r_{OFDM}(t)\cdot e^{-j2\pi \left(f_{c}+f_{dappler}\right)t}\\ &=\alpha\cdot\frac{1}{M}\sum_{m=0}^{M-1}S_{k}(m)\cdot e^{j2\pi km /M}\cdot e^{j2\pi(f_{c}+f_{d})t}\cdot e^{-j2\pi\left(f_{c}+f_{dappler}\right)t} \\ =&\alpha\cdot\frac{1}{M}\sum_{m=0}^{M-1}S_{k}(m) \cdot e^{j2\pi km/M}\cdot e^{j2\pi\left(f_{d}-f_{dappler}\right)t}\end{split} \tag{20}\]  
where \(f_{c}\) is the carrier frequency, \(f_{d}\) is the channel Doppler frequency, and \(f_{dappler}\) is the high-precision Doppler frequency offset obtained through the SPLL three-loop tracking algorithm. Let \(\xi=f_{dappler}-f_{d}\), when \(f_{dappler}\) becomes infinitely close to \(f_{d}\), \(\xi\approx 0\), and \(e^{j2\pi\left(f_{d}-f_{dappler}\right)t}=e^{j2\pi(\xi)t}\approx 1\).  
Subsequently, the signal is subjected to S/P conversion, and the FFT is applied to obtain parallel subdata bits \(S_{k}^{\prime}(m)\), where \(S_{k}^{\prime}(m)\) denotes the kth symbol received on the mth subcarrier, with \(k=0,1,2,\ldots,\infty\) and \(m=0,1,2,\ldots,M-1\). Channel estimation and channel compensation are further carried out. For channel estimation, least squares (LS) channel estimation based on comb-type pilots [33] is adopted. In Figure 10, the blue subcarriers contain only the main lobe of the BOC signal, the gray subcarriers contain the pilot information, and the white subcarriers contain the received signal to be demodulated. We denote the transmitted pilot information by \(X_{d}=[X_{d}(m)]\) and the pilot information received by \(Y_{d}=[Y_{d}(m)]\), where \(m\) and \(d\) represent the dth symbol received on the mth subcarrier. In this paper, the pilot positions are the 3 rd, 7 th, and 11 th subcarriers. Thus, the channel transmission function of the pilot subcarrier can be estimated as follows:  
\[\hat{H}_{LS}(m)=\frac{Y_{d}(m)}{X_{d}(m)} \tag{21}\]  
Once the channel transmission function \(\hat{H}_{LS}\) of the pilot subcarriers has been estimated, the channel transmission function \(\hat{H}_{LS}^{\prime}\) of the data subcarriers can be obtained through linear interpolation [34]. Subsequently, we perform channel compensation on the received signal  
Figure 10: Comb-type pilots.  
in accordance with the channel transmission function, as shown in Equation (22). Finally, QPSK demodulation and Viterbi decoding are performed to recover the received signal.  
\[S_{compensation}(m)=\frac{S_{K}^{\prime}(m)}{H_{LS}^{\prime}(m)} \tag{22}\]