# Performance Assessment of the Medium Frequency R-Mode Baltic Testbed at Sea near Rostock
## 2 The MF R-Mode System  
One of the main outcomes of the R-Mode Baltic project was the successful establishment of a testbed in the Baltic Sea. At the time of writing, the testbed includes eight operational MF radio beacons transmitting R-Mode signals. Figure 1 shows the map of the testbed area with the position of the R-Mode-enabled radio beacons located in four countries: Germany, Sweden, Poland and Denmark. Figure 1: Enabled MF R-Mode radio beacons (yellow triangles) around the southern Baltic Sea. The MF radio beacon system is based on the Frequency Division Multiple Access (FDMA) scheme. Thus, a channel of 500 Hz is allocated for each terrestrial beacon in the marine frequency band between 283.5 kHz and 315 kHz. These values are valid in European countries and might differ in other regions, where a different frequency allocation strategy has been selected. An important characteristic of the radio waves in the MF band is that they propagate as a ground-wave. This means that the signals are not limited to the line-of-sight (LOS) propagation, as it is for GNSS or VHF signals, but they propagate far beyond the horizon following the curvature of the earth. Therefore, the R-Mode positioning only provides 2D solutions and does not provide any height information. The transmitted signal includes a Minimum Shift Keying (MSK)-modulated signal, which represents the legacy signal carrying the D(ifferential) GNSS information, plus two additional pilot signals, each referred to as a Continuous Wave (CW). Such sinusoidal signals are placed in the fourth zero crossing of the MSK spectrum to minimize interference on the legacy signal and, to be precise, they are spaced by 225 Hz on the left and right of the carrier frequency. Additionally, the signals are synchronized to the R-Mode System Time in order to have a zero-phase crossing to the full seconds, such that synchronization is achieved among all the transmitters. The R-Mode System Time is the reference time for all R-Mode system components. It can be aligned to the GPS time, as it is conducted by the GPS-stabilized rubidium clocks at the moment but also other options are possible, such as the time and frequency transfer using fiber optic cable. The research on cost-efficient synchronization strategies is ongoing [15]. The fundamental idea to obtain pseudorange measurements at the receiver side is to exploit phase estimates of the two CW and to track the evolution of these phases as the vessel moves. This technique is similar to the one used in the GNSS receivers, which exploit carrier phase observations to obtain high-accuracy positioning solutions [16]. The pseudorange \(\rho_{j,k}(t)\) can then be represented as follows  
\[\rho_{j,k}(t)=[N_{j,k}(t)+\phi_{j,k}(t)+\phi_{j,k}^{ck}+\phi_{j,k}^{e}]\lambda _{j,k} \tag{1}\]  
where \(j\) is the station index and \(k=1,2\) is an index which distinguishes between the two CW. \(\lambda\) is the wavelength of the CW. \(N\) represents the integer number of the full wavelengths between the transmitter and the receiver, referred to as the ambiguity in the GNSS domain, and \(\phi_{j,k}\) represents the fractional part of the wavelength. Finally, \(\phi_{j,k}^{ck}\) represents the error caused by the clock at the receiver and transmitter side \(j\), while \(\phi_{j,k}^{e}\) includes the errors introduced by the different impairments encountered by the signal, as will be explained in Section 3. A Software-Defined Radio (SDR) receiver has been developed by the DLR, as described in [14]. The receiver setup is composed of an Ettus X310 connected to an E-field antenna through an amplifier and a filter. These components represent the front-end of the receiver, which provides as an output the discretized digital raw samples to a computer. A C++ and Python-based receiver implementation performs digital signal processing and phase and position estimation on the computer. As explained, the phase measurements are characterized by the presence of the ambiguity, which needs to be estimated.