## 2 Effect of SRBS on GPS Receiver Noise Floor  
Solar flares produce an increase in solar noise, which is measured in units of SFU, \(10^{-22}\) W m\({}^{-2}\) Hz\({}^{-1}\), or \(-220\) dBWHz\({}^{-1}\). These SRBs are wideband noise, which increase the noise power of the receiver and result in a lower \(C/N_{0}\). Measuring the solar radio emission power at the GPS receiver antenna output is critical to the steady operation of the GPS system. The antenna directive gain is defined as the ratio between the power of the actual antenna \(P(\beta)\) and the power of the signal generated by the ideal radiation unit \(P_{0}\) at the same point in space under the conditions of equal input power. This parameter quantitatively describes the degree to which an antenna radiates the input power, which can be defined as  
\[D(\beta)=P(\beta)/P_{0}, \tag{1}\]  
where \(\beta\) is the elevation angle of the GPS signal. Obviously, the directive gain is closely related to the elevation angle of the antenna. The gain is usually computed in units of dB and expressed as \(G(\beta)=10\cdot\lg(D(\beta))\). These-sults [27] for the gain corresponding to different elevation angles are shown in Table 1.  
A GPS antenna needs to be able to receive as many GPS signals as possible so that its gain is very low in all directions. Moreover, the reception cross-section of the GPS antenna is low, especially near the horizon. The antenna effective area is defined as  
\[A_{\rm e}(\beta)=\frac{4\pi\cdot D(\beta)}{\lambda^{2}}, \tag{2}\]  
where \(\lambda\) is the wavelength of the received signal. The calculated results of the antenna effective area \(A_{\rm e}(\beta)\) for different elevation angles at GPS frequency bands are shown in Table 2.  
The radio emissions of a solar flare can be taken as Gaussian white noise for GPS signals. The solar radio emission intensity is constant within the bandwidth \(\Delta F_{n}\), so the radio emission power within the frequency bands of GPS signal can be calculated in a similar way and is defined as  
\[P_{n}=\Delta F_{n}\cdot N_{0}. \tag{3}\]  
Therefore, without considering the polarization loss and atmospheric attenuation, the solar radio noise at the receiver antenna output can be expressed as [12]  
\[P_{n}=\Delta F_{n}\cdot k\cdot N_{0}\cdot A_{\rm e}(\beta), \tag{4}\]  
where \(k\) is the rate of the solar radio emission flux in terms of SFU and \(N_{0}=-10^{-22}\) W m\({}^{-2}\) Hz\({}^{-1}\). Finally, the solar radio noise power at the receiving antenna output for solar elevation angles \(>15^{\circ}\) at the central solar radio emission frequency \(f=1415\) MHz (we assumed \(\lambda=0.212\) m, \(A_{\rm e}=2.253\times 10^{-3}\)m\({}^{2}\)) is calculated and shown in Table 3[12]. Note that the solar radio noise is computed in units of dBW, and the front-end passband of the GPS receiver radio path (\(\Delta F_{\rm GPS}\)) is 3 MHz [27]. \begin{table}
\begin{tabular}{c c c} \hline
**Elevation Angle, \(\beta^{\circ}\)** & \(G(\beta)\)**in (dB)** & \(D(\beta)\)**=\(P(\beta)\)/\(P_{0}\)** \\ \hline \(0<\beta<5\) & \(-7.5\leq G(\beta)\leq-5\) & \(0.1775\leq D(\beta)\leq 0.316\) \\ \(5<\beta<15\) & \(-4.5\leq G(\beta)\) & \(0.354\leq D(\beta)\) \\ \(\beta>15\) & \(-2\leq G(\beta)\) & \(0.63\leq D(\beta)\) \\ \hline \end{tabular}
\end{table} 
Table 1: Directive characteristics of a navigation receiver antenna. \begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Elevation Angle, \(\beta^{\circ}\)**} & \multicolumn{2}{c}{\(A_{\rm e}(\beta)\)**in (m\({}^{2}\))**} \\ \cline{2-3}  & \(\lambda\) = 0.190 in (m) (L1) & \(\lambda\) = 0.244 in (m) (L2) \\ \hline \(0<\beta<5\) & \(5.099\times 10^{-4}\leq A_{\rm e}(\beta)\) & \(8.409\times 10^{-4}\leq A_{\rm e}(\beta)\) \\  & \(\leq 9.077\times 10^{-4}\) & \(\leq 1.497\times 10^{-3}\) \\ \(5<\beta<15\) & \(1.01\times 10^{-3}\leq A_{\rm e}(\beta)\) & \(1.677\times 10^{-3}\leq A_{\rm e}(\beta)\) \\ \(\beta>15\) & \(1.809\times 10^{-3}\leq A_{\rm e}(\beta)\) & \(2.984\times 10^{-3}\leq A_{\rm e}(\beta)\) \\ \hline \end{tabular}
\end{table}