# A Fast Acquisition Algorithm for Hybrid Signals of 5G and BeiDou B1
## 2 Proposed Method
### Compatibility Analysis of 5G and BeiDou B1 Signal
#### 2.1.3 5G and BeiDou B1 Band Compatibility Analysis  
ITU proposes that navigation systems operating in the 1559-1610 MHz band (BeiDou B1 band) should avoid interference from other radio systems in the surrounding frequencies [31,32]. External broadband interference's total power spectral density must comply with the corresponding protection standards for receivers in different applications. According to the 3 GPP description of mobile communication signal spatial propagation, 5G signals in the propagation of the path model usually have UMi, Uma, RMa, and InH. These models usually consider the multipath effect, size scale fading for the propagation distance in a more than 50 m scenario. Using the free-space loss model if the 5G signal propagation distance is closer (less than 50 m). At the same time, the ITU recommends  
Figure 4: Base station operating band unwanted radiation frequency applicable range. Figure 3: Implementation principle of FBMC with N subcarriers. that when studying the interference size of other radio systems in the frequency band adjacent to the navigation signal, the spatial propagation of the interference signal should be selected using the free-space radiation model [33]:  
\[LOSS=20\log_{10}(f(\mathrm{MHz}))+20\log_{10}(d(\mathrm{m}))-27.55 \tag{7}\]  
Essentially, Equation (7) is free-space path loss (FSPL). It describes the propagation loss between the BeiDou receiver antenna and the source of interference of the 5G signal. It also provides a calculation or estimation method for this nominal path loss. The nominal path loss between the antenna and interference source refers to the estimated average loss in signal power between the antenna and the source of interference, measured in decibels (dB). In wireless communication, signals experience path loss during propagation, resulting in a decrease in signal strength with increasing distance. It is a nominal or theoretically predicted value used to estimate the average path loss between the antenna and the interference source under specific conditions. Path loss occurs due to factors such as damping, scattering, and attenuation that the signal encounters during propagation through space. It can be estimated using various models based on environmental characteristics and frequency bands, to determine the attenuation of the signal. The free-space path loss (FSPL) formula states that in a radio system consisting of a transmitting antenna transmitting radio waves to a receiving antenna, the ratio of radio wave power received \(P_{r}\) to the power transmitted \(P_{t}\) is:  
\[\frac{P_{r}}{P_{t}}=D_{t}D_{r}(\frac{\lambda}{4\pi d})^{2} \tag{8}\]  
where \(D_{t}\) is the directivity of the transmitting antenna, \(D_{r}\) is the directivity of the receiving antenna, \(\lambda\) is the signal wavelength, and \(d\) is the distance between the antennas. The distance between the antennas \(d\) must be large enough that the antennas are in the far field of each other \(d\)\(\gg\)\(\lambda\). The free-space path loss is the loss factor in this equation that is due to distance and wavelength, or in other words, the ratio of power transmitted to power received assuming the antennas are isotropic and have no directivity (\(D_{t}=D_{r}=1\)):  
\[FSPL=(\frac{4\pi d}{\lambda})^{2} \tag{9}\]  
A convenient way to express the FSPL is in terms of decibels (dB):  
\[FSPL(dB)=10\log_{10}((\frac{4\pi df}{c})^{2})=20\log_{10}(d)+20\log_{10}(f)-27.55 \tag{10}\]  
For \(d\),\(f\) in meters and megahertz (MHz), respectively, the constant becomes \(-27.55\). Based on the traversal simulation data, it can be found that if the 5G signal interferes with BeiDou, the BeiDou receiver needs to be close enough to the 5G base station. According to the path propagation model introduced by 3 GPP and ITU, the nominal path loss of 5G signals should be calculated according to the free-space loss. The spatial distribution of 5G signals is calculated using Equation (7).