# In-Band Medium-Frequency R-Mode Signal Quality Estimation +
## 5 Real Data Analysis  
Real data are used to validate the usability of the defined \(C/N_{0}\) as a measure of the signal quality under optimal propagation conditions, i.e., without biases. In this paper, we use data from a measurement campaign conducted in September 2023 at a static location on Fehmann island. The map represented in Figure 4 shows the location of the monitor receiver as an orange triangle, and the MF beacons, which were received as blue circles. As is visible in the map, four stations were received, namely, Gross Mohrdorf, Hammerodde, Zeven, and Helgoland, for a total of eight CW signals. We are aware that during the measurement, the setup was experiencing some issues that could have caused a noise level increase. Despite the ranging performance loss, this allowed us to evaluate whether the \(C/N_{0}\) parameter could still be used for monitoring purposes under non-nominal noise conditions. The measurements were obtained with a 1 Hz sampling rate. The standard deviation of the phase error was computed such that a comparison with the predicted accuracy could be carried out. Even if in a static location the phase estimation is in general quite stable, due to the fact that a high accurate rubidium clock  
Figure 3: Ranging accuracy for the two described cases compaerd with the CRLB and the \(C/N_{0}\)-based predicted accuracy. is used in the receiver, biases can still be introduced by the station hardware itself. To compensate for these biases, a moving averaging filter is used. Figure 5 presents the phase estimation of both CWs (blue and orange) for the four stations. It appears clear that for some stations, i.e., Helgoalnd and Zeven, time varying biases arise, which must be properly compensated for to achieve optimal positioning performance. In the future, this compensation parameter will be computed by the R-Mode service provider and transmitted to the users with the navigation message. On the contrary, the phase estimation for Gross Mohrdorf and Hammerode was quite good and stable. Once the biases are removed, the standard deviation of the phase can be evaluated and compared with the expected ranging accuracy by using the estimated \(C/N_{0}\) in Equation (8). Figure 6 shows the 2D histogram of the phase standard deviation (\(1\sigma\)) evaluated over a moving window of 30 samples as a function of the estimated \(C/N_{0}\). To reduce the noise of the \(C/N_{0}\) estimation, a moving averaging filter of 30 samples length is applied. Moreover, the \(C/N_{0}\) estimate of all the eight CWs is aggregated and used to build the histogram. The data are represented by the gray scale points. Due to the fact that the data were recorded in a static location, the full range of \(C/N_{0}\) values was not observable, which explains the presence of data gaps in the histogram. The predicted accuracy, estimated with Equation (8), is also visible as a red dashed line. As it appears in the figure, the estimated accuracy becomes noisier when the actual \(C/N_{0}\) decreases. This is reasonable as the variance of estimated signal amplitude phase variance increases with the increase in the noise [9]. On the other hand, if the true \(C/N_{0}\) increases or, equivalently, the noise level decreases, its estimate also improves. This agrees with the results obtained in the simulation. In general, it can be observed that the data fit the theoretical curve quite well, which means that the estimated \(C/N_{0}\) is a valuable measure of the signal quality under optimal propagation conditions and can be used to predict signal ranging performance. Nevertheless, a small bias between the data and the theoretical lower bound is visible, especially for smaller values of \(C/N_{0}\). To compensate for this bias and to cover the potential  
Figure 4: Location of the monitor station (orange triangle) and MF R-Mode transmitters (blue circles) processed at the monitor side. residual error due to AGDF mismatch or transmitter instabilities, an inflation factor could be considered to scale up the actual predicted variance of the measurements.