# Wide-Band Interference Mitigation in GNSS Receivers Using Sub-Band Automatic Gain Control +
## 4 Test Setup
### Estimation of Interference to Noise Ratio  
The output power of the Agilent MXG-series signal generator is selected to be between \(-70\,\mathrm{dBm}\) and \(0\,\mathrm{dBm}\). However, this is not a meaningful measure of the interference power. The interference-to-signal ratio (ISR) is often used to characterize interference tests, but the problem is that each satellite is received at a different \(C/N_{0}\). Therefore, the ISR is not a practical measure when comparing the PVT solutions with each other or different satellites in the same scenario. The INR compares the interference power to the thermal noise of each receiver. It is independent of the satellite signals and is consequently the same for all satellites. The ISR can be converted to the INR for a given satellite if the \(C/N_{0}\) and the bandwidth of the receiver \(B\) are known:  
\[\mathrm{INR}=\mathrm{ISR}\cdot\frac{C/N_{0}}{B} \tag{9}\]  
\[\mathrm{INR}_{\mathrm{dB}}=\mathrm{ISR}_{\mathrm{dB}}+\left(C/N_{0}\right)_{ \mathrm{dB}}-10\log_{10}(B)\quad\mathrm{[dB]} \tag{10}\]  
Although the INR is a better comparison on a single receiver, it is a function of the receiver bandwidth. It makes a comparison invalid, as different receivers have different analog bandwidths. Therefore, the interference-to-noise density ratio (\(I/N_{0}\)), which normalizes the INR to the receiver bandwidth, is the only fair metric regardless of the receiver analog bandwidth and the received signal. The \(I/N_{0}\) is defined as  
\[I/N_{0}=\mathrm{ISR}\cdot C/N_{0}=\mathrm{INR}\cdot B \tag{11}\]  
\[\left(I/N_{0}\right)_{\mathrm{dB}}=\mathrm{ISR}_{\mathrm{dB}}+\left(C/N_{0} \right)_{\mathrm{dB}}=\mathrm{INR}_{\mathrm{dB}}+10\log_{10}(B)\quad\mathrm{ [dBHz]} \tag{12}\]  
The \(I/N_{0}\) is less intuitive, but it is analogous to the \(C/N_{0}\), familiarizing it to the GNSS community. The \(I/N_{0}\) is displayed in the results for consistency, but it is fairly simple to convert to the INR or ISR, as demonstrated in Equation (12). The \(I/N_{0}\) is estimated based on the signal generator power and the spectral separation coefficient (SSC). The effect of the SSC on the \(C/N_{0}\) is the \(\left(C/N_{0}\right)_{\mathrm{eff}}\). This is defined as [26; 27]:  
\[\left(C/N_{0}\right)_{\mathrm{eff}}=\frac{1}{\frac{1}{C/N_{0}}+\frac{\mathrm{ ISR}}{Q_{j}\cdot R_{c}}} \tag{13}\]  
where \(C/N_{0}\) is the interference-free, \(Q_{j}\) the jamming resistive quality factor, which measures how efficient the interference is, and \(R_{c}\) the chipping rate of the GNSS signal. The jamming resistive quality factor \(Q_{j}\) is a function of the GNSS signal power spectral density (PSD) and the interference signal PSD. First, the \(Q_{j}\) is determined for a \(4\,\mathrm{MHz}\) filtered noise interference signal, and a GPS L1 C/A BPSK(1) is determined to be \(Q_{j}=4.11\). Second, the ISR for GPS L1 C/A satellites for the 4 MHz filtered noise interference is determined:  
\[\mathrm{ISR}_{\mathrm{est}}[n,m]=\left(\frac{1}{\left(C/N_{0}\right)_{\mathrm{ NoIM}}[n,m]}-\frac{1}{\left(C/N_{0}\right)_{\mathrm{Roof}}[n,m]}\right)\cdot Q _{j}\cdot R_{c} \tag{14}\]  
where \(\mathrm{ISR}_{\mathrm{est}}[n,m]\) is the estimate for the \(n\)-th observation for the \(m\)-th satellite, \(\left(C/N_{0}\right)_{\mathrm{Roof}}\) is the measurement from the HE roof antenna, and \(\left(C/N_{0}\right)_{\mathrm{NoIM}}\) is the measurements from the HE with the IM switched off. Figure 4 shows the estimated ISR compared to the transmit power. Note the biases between the various satellites. Third, the \(I/N_{0}\) is estimated from the ISR using the roof \(C/N_{0}\) values:  
\[\left(I/N_{0}\right)_{\mathrm{est}}[n,m]=\mathrm{ISR}_{\mathrm{est}}[n,m] \cdot\left(C/N_{0}\right)_{\mathrm{Roof}}[n,m] \tag{15}\]  
Figure 5 shows the estimates. It is clear that the values are similar between the satellites, and the biases from the ISR are removed. Figure 4: Estimated ISR from the 4 MHz bandwidth filtered noise interference scenario. Figure 5: Estimated \(I/N_{0}\) from the 4 MHz bandwidth filtered noise interference scenario.