# mGEODAR--A Mobile Radar System for Detection and Monitoring of Gravitational Mass-Movements
## 2 Materials and Methods
### Reconfigurable Signal Generation  
The mGEODAR system comprises of two oscillators and a DDS as signal generation components that can be configured individually to give a variable range of output signals (no. 1-3 in Figure 1). The limiting factor for the signal variability are the hardware components such as filters, signal splitter and mixers. Furthermore, the external power amplifier and antennas also limit the usable range of frequencies, but since they can be easily exchanged, they are not taken into consideration here. The high-frequency hardware is divided into three areas with each working at a distinct frequency range (annot. A-C in Figure 1). Valid ranges for possible frequencies are derived from the corresponding components and filter responses in each area (A) to (C). The filter transmission responses are shown in Figure 2. The three areas and their frequency ranges are namely the chirp signal \(f_{ch}\) (\(1.9\,\mathrm{GHz}\) to \(2.8\,\mathrm{GHz}\)), the local oscillator frequency \(f_{lo}\) (\(7.6\,\mathrm{GHz}\) to \(8.4\,\mathrm{GHz}\)) and the transmitted signal \(f_{tx}\) (\(9.1\,\mathrm{GHz}\) to \(11\,\mathrm{GHz}\)). Note, the values are approximate and are optimised later in Section 3. The three areas are related to each other through the signal mixers, which perform an up-conversion of \(f_{ch}\) by \(f_{lo}\) on the transmitter side, i.e., \(f_{tx}=f_{ch}+f_{lo}\). So not all combinationsof \(f_{ch}\) and \(f_{lo}\) yield a usable transmit frequency \(f_{tx}\) as for example the minimal achievable frequency is \(9.5\,\mathrm{GHz}\) whereas the maximal frequency goes beyond the passband of (C) in Figure 2.  
Beside the absolute frequency of the transmitted signal, the pulse bandwidth \(B\) is of greatest interest as it defines the range resolution \(\Delta r\) (see Section 2.2). A maximal pulse bandwidth of approximately \(1400\,\mathrm{MHz}\) is permitted by the DDS, i.e., the sampling clock of the DDS is \(f_{s}=3.5\,\mathrm{GHz}\) and the first Nyquist image ranges from \(f_{s}/2\) to \(f_{s}\), thus conservatively from \(1.9\,\mathrm{GHz}\) to \(3.3\,\mathrm{GHz}\) (see Figure 5A for the usable signal). However, the signal strength generated by the DDS in super-Nyquist operation follows a sinc-response, thus its output amplitude is far from flat over such large bandwidth [13]. A desired amplitude flatness can be slightly recovered by the high-pass filter response in the chirp signal area (Figure 2A). By choosing a different local oscillator frequency \(f_{lo}\), the output of the DDS can be shifted to be compensated by the filter. Exactly such shifting of \(f_{lo}\) is performed as signal optimization measurements in Section 3. In this paper, the mGEODAR radar features two measuring modes of different linear frequency chirps which are referred to as research mode and detection mode. For the high-resolution research mode, a bandwidth of \(400\,\mathrm{MHz}\) ranging from \(10.2\,\mathrm{GHz}\) to \(10.6\,\mathrm{GHz}\) is chosen. As discussed later, this resembles the maximal useful bandwidth with the mGEODAR radar system because the external power amplifier and antennas are designed for these frequencies. The research mode consists of a triangular modulation that varies continuously between up and down chirp once it is initiated. The chirp duration is \(\tau=0.01\,\mathrm{s}\) giving a pulse repetition rate of \(100\,\mathrm{Hz}\). Clearly, the range resolution for gravitational mass-movement research purposes should be maximized, but the data rate is approximately \(5\,\mathrm{MB/s}\). This exceeds capability for storing a continuous acquisition and may even slow down real-time processing from a circular buffer for automatic movement detection. Therefore, a low-resolution detection mode is designed that complies with the national frequency regulations for radar usage of natural hazard monitoring in Austria [14]. These constraints limit a suitable chirp pulse for continuous transmission to a bandwidth of \(30\,\mathrm{MHz}\) from \(10.41\,\mathrm{GHz}\) to \(10.44\,\mathrm{GHz}\).