## 3 Frequency Selection  
The frequency at which the experiments will take place has to be considered first, because of its significant impact on the design. On one hand, the sensor can only measure the signal of the probes when NVIS propagation is present for a large part of each day. This puts an upper limit on the frequency used. Lowering the frequency, on the other hand, will increase the absorption in the D-region and the ambient electromagnetic noise (radio noise) level and therefore require significantly more probe power. A lower frequency also implies a larger antenna, which will make the deployment more difficult. For NVIS propagation the peak plasma frequency of the ionosphere must be higher than the frequency of the electromagnetic wave. The local plasma frequency is directly related to the local electron density in the ionosphere [32] and the highest frequency at which the ordinary wave is reflected vertically is:  
\[f_{oF2}=\frac{1}{2\pi}\sqrt{\frac{e^{2}N_{max}}{\varepsilon_{0}m_{e}}}\approx 8.98\sqrt{N_{max}} \tag{1}\]  
where \(f_{oF2}\) is the critical frequency in Hz, \(N_{max}\) the peak electron density in electrons/m\({}^{3}\), \(e\) the charge of an electron (\(1.602\times 10^{-19}\) C), \(\varepsilon_{0}\) the permittivity of free space (\(8.854\times 10^{-12}\) F/m), and \(m_{e}\) the mass of an electron (\(9.109\times 10^{-31}\) kg). The critical frequency \(f_{xF2}\) of the extraordinary wave is slightly higher [32]:  
\[f_{xF2}=f_{oF2}\sqrt{1+\left(\frac{f_{H}}{2f_{oF2}}\right)^{2}}+\frac{f_{H}}{2} \tag{2}\]  
where \(f_{H}\) is the electron gyrofrequency in Hz, which ranges from 1.0 to 1.2 MHz at 220 km height in the Netherlands and Spain, so that Equation (2) can be approximated as:  
\[f_{xF2}\approx f_{oF2}+0.55\;\mathrm{MHz} \tag{3}\]  
There is no propagation when \(f_{xF2}\) is lower than the probe frequency \(f_{probe}\). Only the extraordinary wave propagates when \(f_{xF2}>f_{probe}>f_{eF2}\). And both waves propagate when \(f_{oF2}>f_{probe}\). The electron production in the ionosphere is driven by solar radiation [4] and therefore \(f_{xF2}\) and \(f_{xF2}\) follow a diurnal cycle, increasing in the morning when the sun starts to illuminate the ionosphere and decreasing in the afternoon, as shown in Figure 4. In this example, NVIS propagation is possible from 09:00-18:00 h. The minimum and maximum values depend on the location on Earth, the day of the year and the position in the 11-year solar sunspot cycle [7]. The experiments were planned in the winter to take advantage  
Figure 3: Experiment topology: (**a**) An example of a star-shaped deployment (Catalonia, Spain); (**b**) The inclination of the Earth’s magnetic field changes with latitude. Map courtesy of Free World Maps.  
of the higher electron densities caused by the 'winter anomaly' in the northern hemisphere [33]. After analysing ionospheric sounding data from the Royal Observatory of Belgium (50.1\({}^{\circ}\)N, 4.6\({}^{\circ}\)E) and the Ebre Observatory in Spain (40.8\({}^{\circ}\)N, 0.5\({}^{\circ}\)E), the critical frequency \(f_{oF2}\) was expected to remain above 7 MHz during at least 8 h of each day. Therefore, an experimental license was obtained in the Netherlands to use a clear frequency of around 6.99 MHz. In Spain, the experiments were conducted around 7.04 MHz using an amateur radio license. To enable simultaneous observation of all probes, each of them was given a small (110 Hz) frequency offset. Unmodulated probes signals were used in the measurements. With sufficient frequency stability the sensor will separate them by frequency filtering. Narrow-band filtering will also increase the signal-to-noise ratio (SNR) and allow for lower probe power. We therefore choose a sensor bandwidth of 30 Hz.